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Research ArticleMolecular Dynamics Study on Lubrication Mechanism inCrystalline Structure between Copper and Sulfur
Ken-ichi Saitoh1 Tomohiro Sato1 Masanori Takuma1
Yoshimasa Takahashi1 and Ryuketsu Chin2
1Department of Mechanical Engineering Faculty of Engineering Kansai University 3-3-35 Yamate-cho Suita Osaka 564-8680 Japan2Kobe Steel Ltd 2-3-1 Shinhama Arai-cho Takasago Hyogo 676-8670 Japan
Correspondence should be addressed to Ken-ichi Saitoh saitoukansai-uacjp
Received 11 August 2015 Revised 24 September 2015 Accepted 29 September 2015
Academic Editor Te-Hua Fang
Copyright copy 2015 Ken-ichi Saitoh et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
To clarify the nanosized mechanism of good lubrication in copper disulfide (Cu2S) crystal which is used as a sliding material
atomistic modeling of Cu2S is conducted and molecular dynamics (MD) simulations are performed in this paper The interatomic
interaction between atoms and crystalline structure in the phase of hexagonal crystal of Cu2S are carefully estimated by first-
principle calculations Then approximating these interactions we originally construct a conventional interatomic potentialfunction of Cu
2S crystal in its hexagonal phase By using this potential function we performMD simulation of Cu
2S crystal which
is subjected to shear loading parallel to the basal plane We compare results obtained by different conditions of sliding directionsUnlike ordinary hexagonalmetallic crystals it is found that the easy-glide direction does not always show small shear stress for Cu
2S
crystal Besides it is found that shearing velocity affects largely the magnitude of averaged shear stress Generally speaking highervelocity results in higher resistance against shear deformation As a result it is understood that Cu
2S crystal exhibits somewhat
liquid-like (amorphous) behavior in sliding condition and shear resistance increases with increase of sliding speed
1 Introduction
In recent years using lead (Pb) in metallic material is strictlyprohibited due to risk to human health That is why lead-free alloy is now being sought for mechanical materialsIt has been recognized that bronze which is composed ofcopper (Cu) and tin (Sn) atoms forms a material withgood performance of lubrication by the addition of Pbatoms Therefore Cu-Sn alloys are widely used for slidingmechanical elements such as brake frictionmaterials (brake-pads) ormechanical bearingmaterials Broadly speaking it isunderstood that Pb solids basically have low melting pointand they easily tend to be fluidic under high temperatureand high pressure condition as in the environment insidethe sliding equipment One example of substitution of Pbis bismuth (Bi) but it is regarded as one of rare metalsand it is hard to obtain much Therefore it requires us toclear the hurdle concerning both cost and safety Recentlyit is reported that bronze with the addition of sulfur (S)
atoms shows very good performance of lubrication in slidingmaterial and it has already been patented and been actuallydeveloped as an engineering material for industrial use [1]Historically it has been well known that S atoms provide anice machinability (in cutting) of copper alloy because theywork as ldquotip-breakerrdquo in cutting process [2] Besides S atom iswell accepted as a component of solid lubricant like Pb atomFor example molybdenum disulfide MoS
2 including many
S atoms exhibits high performance as the solid lubricantTherefore alloys made of Cu and S may provide good slidingand friction performance In those alloys S atom will play arole of the long-standing Pb atom instead Nevertheless thelubricating mechanism in Cu-S system has not been clarifiedyet and we should uncover it by studying further
Hirai et al have succeeded in developing a bronze madewith microscopic dispersion of copper sulfide (Cu
2S) and
they are now proceeding to its industrial use [3] Akamatsuet al are also exploring the fabricating method of Cu
2S alloy
by the motivation of avoiding the risk to human health [4]
Hindawi Publishing CorporationJournal of MaterialsVolume 2015 Article ID 963257 13 pageshttpdxdoiorg1011552015963257
2 Journal of Materials
In the field of mineralogy Cu2S crystal is well known as a
mineral called chalcocite Recently since the Cu2S structure
has a unique electronic behavior as for ionic conductivity itis planned to be used for switching device applications suchas a solar power plant material [5] and a superconductivitymaterial [6 7] In the context of unique sliding and frictionbehavior of Cu
2S crystal already found experimentally the
present authors have studied it by atomistic modeling One ofstable stoichiometries of copper and sulfide system is foundat Cu
2S (Cu S = 2 1) Interestingly this Cu
2S compound
exhibits very complicated solid phase transition behavior[8 9] Around the standard temperature the unit structureof Cu
2S is orthorhombic but it transforms into hexagonal
symmetry above 105∘C (degrees Celsius)Moreover in highertemperature above 460∘C it is transformed into cubic crys-tal
When copper alloys are used for sliding and frictionmaterials they are generally placed in a severe condition ofhigh temperature beyond several hundred ∘C and thereforethe behavior of hexagonal crystal (HC) would be worthstudying extensively In Cu
2S crystal consequently one S
atom has two neighbor Cu atoms So they tend to organizea triangular conformation and keep their firm interatomicbonding when they are stabilized The same mechanismconcerning S atom is also suggested in MoS
2system which
is famous as good solid lubricant where the S atom makesfirm bonding with metal atoms [10]
Other than chalcocite (Cu2S) there are some well-known
natural minerals based on copper alloy [11 12] such asbornite (Cu
5FeS4) chalcopyrite (CuFeS
2) covellite (CuS)
and digenite (Cu9S5) All of these alloys are interesting as
for interrelationship in their fabrication and all of them maybe applied to new functional material in the future Amongthem however Cu
2S crystal is still a main compound so it
should be focused on particularlyThus in this paper we willstudy the atomistic structure of Cu
2S in HC and discuss its
atomistic behavior in sliding and friction processIn the present study aiming at unempirical approach
the first-principle (ab initio) calculation is utilized to identifythe crystal structure of Cu
2S So far there have been some
studies of copper sulfides by ab initio method which aremainly employing density functional theory (DFT) [5 13 14]The electronic structure has been reproduced but unfortu-nately there still remains ambiguity about atomic positionof coppers in the unit crystal and so further modelingand discussion will be required Therefore in this studyby using conventional DFT software package Wien2k [15]the optimization of the unit structure of the Cu
2S in HC
is carried out based on Kashida et alrsquos structural model[13] As a result we obtain its energetically stable structureand we determine its basic crystalline information that islattice constants as for lengths 119886 and 119888 assuming the HCconfiguration
In order to understand the dynamics of sliding or fric-tion occurring in Cu
2S crystal molecular dynamics (MD)
simulation is suitable Lattice constants 119886 and 119888 and ground-state energies which are obtained by ab initio calculations areused in the determination of interatomic potential for MDsimulation In the MD simulation an existing interatomic
potential function of MoS2[10] is referred to for its function
or functional form This seems reasonable because thosetwo crystals of metal sulfide (Cu
2S and MoS
2) have many
common features as described aboveThus we simulate atomistically the sliding of Cu
2S crystal
by using MD method with an original and nonempiricalinteratomic potential The computation model is built bystacking layers on slip plane (basal plane) of HC lattice and itis at the first place compressed and then shear deformation isapplied Here the compression is crucial since in the actualsituation the friction behavior in sliding is to take placeunder severe contact condition with large compressive stress(pressure on the contacting surface) We will focus on thedependence on crystalline direction of sliding or on slidingvelocity in such severe condition
This paper is organized as follows Following the Intro-duction we describe the basic information of crystal struc-ture of Cu
2S and show some theories needed for the
modeling and the calculation Then the essence of the abinitio calculation is shown and the procedure to implementthe interatomic potential is briefly presented Thereafterthe MD model used in sliding simulation is explainedThe summary of results in ab initio calculation and MDresults of sliding simulation are shown and their discus-sion is made Finally the conclusion of this paper will bemade
2 Theory and Method
21 Atomic Structure of Cu2S Crystal As pure compounds
of copper sulfide there are covellite (CuS) and chalcocite(Cu2S) and the latter is focused on now For Cu
2S
orthorhombic crystal is obtained in room temperature butbeyond 105∘C it transforms into hexagonal crystal (HC)Furthermore in higher temperature than 460∘C it changes tocubic crystal [8] Copper alloys are often subject to very highpressure and relatively high temperature during operationsuch as in the surface layer of mechanical bearing Thusthe present simulation should focus on the temperaturerange around several hundred kelvins Accordingly the Cu
2S
material here is assumed to be in HC HC is also taken inMoS2and carbon allotrope (graphite or nanometer-thickness
graphene) and both of them are well-known solid lubricantsAmong conventional metals however HC metal such asmagnesium (Mg) is relatively inferior in deformation dueto the lack of crystalline slip systems when compared withface-centered cubic (fcc) crystals such as aluminum (Al) andCu Only the basal slip of hexagonal crystal is always wellactivated in Mg crystal and so its slip is highly directiondependent It is guessed that sliding motion in HC structurewill prefer such direction-dependent featureThis leads to thefact that compounds with HC structure such as Cu
2S and
MoS2 will be good at lubrication
22 First-Principle Calculation Cu atoms are metal andinclude metallic bonds but on the other hand S atomsare nonmetal and show large electronegativity Accordinglybond between atoms inside Cu
2S seems very complicated
Journal of Materials 3
Possibly ionic bond and metallic bond would be nonlinearlyinterrelated In considering the structure and bonding stateof solid crystal it is helpful to reproduce and observe thedetailed electron density distribution Besides those resultscan be taken into account in the construction of accurateinteratomic potential for MD simulations First-principle(FP) calculation (in Latin words ab initio calculation)refers to all quantum-mechanical computational chemistrymethods and is sometimes called ldquoband calculationrdquo Itobtains electron density around atomic nuclei based on theperiodic crystal structure of constituent atoms Nowadaysa number of software packages of FP method are availablein many researches Among those software packages ourchoice is WIEN2k package [15] which is based on densityfunctional theory (DFT) The characteristic of WIEN2k isthat it uses full-potential formulation instead of muffin-tinapproximation and that it uses the linearized augmentedplane wave basis set with local orbitals (LAPW + lo) As forcorrelation exchange term it can apply either local densityapproximation (LDA) or generalized gradient approximation(GGA)The detailed theory and usage are not the main focusof this study and should be omitted here
While all the S atoms in Cu2S are simply located at the
lattice point of HC it is suggested that Cu atoms seem tohave large mobility inside the unit cell especially in hightemperature keeping their symmetric atomic configurationSince actual position ofCu atoms inCu
2S is quite complicated
and is in fact giving controversy the present study employsexisting crystal model used in previous computation ofKashida et al [13] It is confirmed that the model agrees withexperimental fact as well as theoretical one Initial atomicposition of Cu
2S in HC is shown in Table 1 Figure 1 shows
initial position of atoms in Cu2S crystal unit
In order to obtain the minimum (ground-state) energythe atomic configuration is adjusted via the function ofoptimization in the software Lattice constants for angle(120572 120573 120574) are fixed so that the HC lattice should bemaintainedOn the other hand lattice constants for lengths (119886 119888) arechanged as follows Keeping a certain ratio of 119888119886 the lengths(119886 119888) are varied from compressive state to tensile one Thedeviation of 119888119886 from the initial value is +4sim+10 Thevolumetric change by the change of (119886 119888) ranges withinminus2sim+6 The exchange correlation energy of PBE-GGA isemployed Judgement of the energy convergence is done at00001 Ry where 1 Ry = 2180 times 10
minus18 J = 1360 eV Table 2summarizes calculation conditions and parameters used inthe present study The number of 119896-points is varied andapproximately above 20000 we may say that the total energywill be converged and shows sufficient accuracy Thereforewe recognize that 46 times 46 times 22 = 46552 119896-points arelarge enough and this will be used through the presentstudy
23 The Potential Function of Cu2S for MD As mentioned
above copper disulfide Cu2S has a variety of crystalline
structures depending on the temperature The structure isorthorhombic in standard temperature HC above 105∘C andcubic further above 460∘C Here as HC is assumed and
Table 1 Cu2S atomic coordinates and crystal data
(a)
Element Coordinate (relative to unit cell)119909 119910 119911
S 13 23 14Cu(1) 0 0 14Cu(2) 13 23 0578
(b)
Property Unit ValueLattice constant(1) 119886 nm 0389Lattice constant(2) 119888 nm 0688Lattice constant(3) 120572 deg 900Lattice constant(4) 120573 deg 900Lattice constant(5) 120574 deg 1200Atoms per unit cell mdash 3Space group mdash P6
3
120572 120573120574
c
a
Cu
Cu
CuCu
Cu
Cu
CuCu
CuCu
S
S
Figure 1 Crystal structure of Cu2S (hexagonal crystal unit 13 of
conventional hexagonal prism)
the composition ratio is Cu S = 2 1 one S atom shouldcorrespond to two Cu atoms Therefore those three atomscompose a structural unit and the three-body bond is formedas a function of their angle By the way MoS
2has HC
structure as well The structural feature common to thoseHC lattices is that their slip plane is only limited to thebasal plane (0001) This is completely different from fcc orbcc which is accompanying many slip systems In fact theslip of HC lattice takes place only when a certain conditionhas been fulfilled Thus the potential function which wasproposed for MoS
2[10] can be utilized as the reference to
construct the function needed in the present study for Cu2S
Though MoS2and Cu
2S have the contrary ratio as to S
atom a lot of common features are likely to be found inthese two crystals For example angular-dependent three-body interaction is crucial for stabilization of both crystalsTo begin with we apply the potential forms used in theMoS2study and then our results obtained by first-principle
calculation are properly fitted to a new potential functionfor Cu
2S We insist that since the fitting data is obtained
theoretically only by DFT calculations the new potentialfunction will be an unempirical (ab initio) one
4 Journal of Materials
Table 2 Calculation condition for structural optimization of Cu2S
crystal
Exchange correlation potential mdash PBE-GGAEnergy to separate core from valence states Rylowast minus60Energy convergence criteria Rylowast 00001
Change of 119888119886 ratioRate of change +4sim+10Increment of rate (for 119888119886) +2
Volume changeRate of change minus2sim+6Increment of rate (for 119888119886) +1lowastEnergy unit 1 Ry = 2180 times 10minus18 J = 1360 eV
The detail of the new potential function for Cu2S is as fol-
lows The potential function is a summation of three distinctpotential functions as shown in (1) Ionic and metallic bondsare represented by Born-Mayer-Huggins (BMH) potential120601BMH and Morse potential 120601Morse as expressed in (2) and(3) respectively Angular-dependent potential for the bond ofCu-S interaction 120601angle is represented as (4) which is three-body potential Parameters for those potential functions aresummarized in Table 3
120601 = 120601BMH + 120601Morse + 120601angle (1)
120601BMH =
1199111198941199111198951198902
119903
+ 1198910(119887119894+ 119887119895) exp(
119886119894+ 119886119895minus 119903
119887119894+ 119887119895
) +
119888119894119888119895
1199036 (2)
120601Morse = 119863119894119895[exp minus2120573
119894119895(119903119894119895minus 1199030)
minus 2 exp minus120573119894119895(119903119894119895minus 1199030)]
(3)
120601angle = 119867120579(120579 minus 120579
0)2
(4)
In those equations 119911119894or 119911119895is electronic charge of each atom
and the values 119911S = minus20 and 119911Cu = +10 are employed for Sand Cu atoms respectively 119891
0= 1 [kcalA] = 4186 [kJA] is
the parameter which determines the stiffness of each ionicsphere and is transferred from the study of MoS
2 In the
Morse potential the equilibrium distance 1199030and bond energy
119863119894119895are fitted to those in the optimized structure which is
obtained in our ab initio calculation In the angular potentialequilibrium three-body angle 120579
0is also determined by our
ab initio calculation But it is difficult to derive the springconstant 119867
120579just from our ab initio calculation so the same
value as in MoS2is applied here Of course the value of 119867
120579
influences rigidity But its function form is basically harmonicand we found that the effect of spring constant on sliding isnot so crucial
24 Molecular Dynamics Model for Cu2S Sliding Figure 2
shows theMDmodel for sliding simulation In the first placethe optimized atomic configuration obtained by ab initiocalculation is prepared and then is thermally equilibratedat a finite temperature Then the structure is compressed
Table 3 Interatomic potential parameters for Cu2S crystal
(a) B-M-H potential
Atoms 119886119894
119887119894
119888119894
Unit [A] [A] [kJ05sdotA3mol05]Cu 0696 0085 0000S 1831 0085 70000
(b) Morse potential
Application 119863119894119895
120573119894119895
1199030
Unit [kJmol] [1A] [A]Cu-S 152076 1800 2532
(c) Angular potential
Application 119867120579
1205790
Unit [kJmol] [deg]Cu-S-Cu 196648 98943S-Cu-S 196648 98943
in 119911 direction as shown in Figure 2 After that the atomicvelocity in the 119909 direction of two special regions (shownwith yellow color in the figure) is constrained so that sheardeformation is applied to the whole region in the directionparallel to the slip plane These processes are supposedto mimic a Cu
2S crystal in sliding condition This kind
of dynamic sliding simulation has been often studied fortribology-system as found in literatures so far [16] and itsadvantage is that we can observe directly the sliding behaviorof atomic system
It is supposed that crystalline slip plane of Cu2S plays
an important role in the slip deformation As stated aboveCu2S crystal unit has the HC conformation and the pri-
mary slip plane should be (0001) in Millerrsquos indices Theprimary slip direction should be the shortest interatomicdistance existing on the (0001) plane that is ⟨21 10⟩ Wewill call it (b)-direction hereafter The second easiest slipdirection should be ⟨0110⟩ which we call (a)-direction here-after In the present study we configure these two possibleslip directions for sliding simulation and compare theseresults
Other factors affecting sliding behavior of Cu2S would be
velocity and temperature Sliding velocities are varied so thatcorresponding shear velocities are 01 10 and 50ms Thereader should feel that these velocities seem quite higher thanused in actual slidingmachine or equipment However in theMD simulation time increment has to be very short such as1 fs (femtosecond) or less so such large deformation rate isinevitable
25 Analyzing MD Results In the present study the MDresults are mainly analyzed by radial distribution function(RDF) and atomic shear stress Strict formalization of stresstensor with regard to three-body term would require furtherdiscussion at this stage [17] so we use here an approximateand practial treatment These analyzing methods for MDresults are explained below
Journal of Materials 5
A model sliding in (b)-direction
z
yAtoms
A model sliding in (a)-direction
z
x
Cu
S
Fixed
Parallel to basal plane
Basal plane(0001)
(a)-direction
(b)-direction(slip direction of hexagonal crystal)
The model for researching dependence on direction or velocity
⟨0110⟩
110⟩⟨2
Figure 2 Abstract of MD sliding model of Cu2S crystal
251 Crystal Structure Analysis by Radial Distribution Func-tion (RDF) Usually solid crystal has a three-dimensionalorderThe Cu
2S crystal used in the present study exhibits HC
structure One of themethods to identify the crystalline orderis radial distribution function (RDF) 119892(119903) [18] Briefly speak-ing the function 119892(119903) gives the number density of neighboratoms which are found in a certain distance from each atomIts distribution shows some peaks at some specific distancesinherent to the crystalline orderWhen the temperature arisesor when the crystalline order is partially lost due to outbreakof lattice defects the peak value of RDF generally reduces andthe shape at the peak becomes broadenedThus by observingthe change of the peak position and the shape of the curve ofRDF the deterioration of the crystalline order can be detectedand occurrence of lattice defects can be guessed
252 Atomic Stress Analysis (Approximate Treatment includ-ing Three-Body Terms) Since our MD model is in solidstate the behavior of sliding and friction is reflected by ashear stress averaged over the specimen Therefore atomic-scale stress is being analysed But we note that stress (orstrain) is basically the concept in continuum mechanicsand is not essential for any atomic system The facts thatatomic positions are discrete and that interatomic potentialhas nonlocal nature will conflict with the local theory of
continuum Accordingly we need to formulate atomic stresstogether with some approximation
Suppose that total potential energy inside the systemcomprises all the superposition of pairwise interactions 120601(119903)When any selected atom 119894 conducts homogeneous deforma-tion with regard to the relative position to another neighboratom 119895 strain at the interatomic space between 119894 and 119895 can bepresented by their interatomic distance 119903(119894 119895) and interatomicvector r(119894 119895) (this assumes that there is no slip no phasetransition nor long atomic diffusion over the lattice) Thenatomic stress tensor occurring at the atom 119894 is expressed as
120590 (119894) =
1
2Ω (119894)
sum
119895
120597120601 (119894 119895)
120597119903 (119894 119895)
r (119894 119895) otimes r (119894 119895)119903 (119894 119895)
(5)
where the summation is composed of the work done byatomic motion which is called ldquovirialrdquo Ω(119894) in the denom-inator is the volume supposedly occupied by the atom 119894so (5) is regarded as the energy density around that atomIn the present study Ω(119894) is assumed to be a constantwhich has been estimated in the reference structure (whichhas been estimated in the undeformed lattice) Additionallyvector product (r otimes r) means the dyadic between interatomicvectors so (5) has the form of the second-order (symmetric)tensor and its components are six Thus if an interatomicpotential of MD contains just pairwise term the virial can be
6 Journal of Materials
straightforwardly converted to atomic stress But if it includesthree-body terms depending on the angle as in the presentinteratomic potential they can never strictly be decomposedinto virials of each pair of atoms However we can apply anapproximate formulation to a triplet 119894 119895 and 119896 (119894 119895 119896) Inpractice the combination of virials of each pair (119894 119895) (119895 119896)and (119896 119894) is used as the net virial of the triplet As a result theformulation of atomic stress comes to the expression
120590120572120573
(119894) =
1
2Ω (119894)
sum
119895
120597120601pair (119894 119895)
120597119903 (119894 119895)
119903120572(119894 119895) 119903
120573(119894 119895)
119903 (119894 119895)
+
1
3Ω (119894)
sum
119895119896
(
120597120601angle (119894 119895)
120597119903 (119894 119895)
119903120572(119894 119895) 119903
120573(119894 119895)
119903 (119894 119895)
+
120597120601angle (119895 119896)
120597119903 (119895 119896)
119903120572(119895 119896) 119903
120573(119895 119896)
119903 (119895 119896)
+
120597120601angle (119896 119894)
120597119903 (119896 119894)
119903120572(119896 119894) 119903
120573(119896 119894)
119903 (119896 119894)
)
(6)
where the first term corresponds to pair interaction 120601pair(119903)and the second term is for three-body interaction Inthis expression Ω(119894) 120601pair(119894 119895) 120601angle(119894 119895) 119903(119894 119895) and119903120572(119894 119895) (120572 120573 = 1 2 3) are atomic volume pairwise potential
function three-body potential function interatomic distance(between 119894 and 119895) and its vector components In comparingall the components in (6) during actual MD simulation it isunderstood that three-body term is relatively large so that itis not negligible This expression of atomic stress includingthree-body term is also utilized in widely used MD software(eg LAMMPS) [19] Besides this estimation of atomicstress was found appropriate when we applied it to anotherMD study using the three-body-type Tersoff potential (forSi-Ge system) [20]
3 Results and Discussion
31 Optimization of Lattice Constant of Cu2S Crystal by
First-Principle Calculation The relation between volume andenergy of Cu
2S crystal unit is obtained as in Figure 3 by first-
principle (FP) calculation including structural optimizationFor the variety of the lattice constant ratio 119888119886 the lowestenergy is obtained at the deviation Δ119888119886 = 8 Moreoverunder that condition volume expansion at +3 shows thesmallest energy From this optimized structure thereforelattice constants of the HC structure are 119886 = 0383 nm and119888 = 0731 nm for which 119888119886 is 191 The length for 119888 andthe ratio 119888119886 seem relatively larger than the HC structure ofusual metals It means that layers of sulfur (S) and copper(Cu) atoms are remarkably separated from each other in theCu2S crystal In the present paper these optimized lattice
constants are used as values to configure atomic positions inthe specimen of Cu
2S crystal
32 Construction of Interatomic Potential Function for MDCalculations It is experimentally and theoretically under-stood that interaction between Cu and S atoms is generally
Minimum
Change of volume ()
Difference from initial structure
+10+8
+6+4
Ener
gy d
iffer
ence
(eV
)
6543210minus1minus2minus001
009
01
008
007
006
005
004
003
002
001
0
Figure 3 Volume-energy relation of Cu2S crystal structure
Distance r (nm)090807060504030201
minus8
minus6
minus4
minus2
0
2
4
6
8
Mo-S bondCu-S bond
FP calculation
times10minus19En
ergy
EminusE0
(J)
Figure 4 Distance-energy relation of Cu-S interaction obtained byFP calculation (Mo-S interaction is also shown for comparison)
strong So the Cu-S interaction can be expressed by Morsepotential function as shown by (3) The optimized configu-ration of Cu-S dimer is obtained by the FP calculation by us[21] From this we determine both the equilibrium distanceparameters 119903
0 120573119894119895and the energy parameter 119863
119894119895needed
in Morse potential Figure 4 shows the relation betweeninteratomic distance and its energy which is obtained by theFP calculation The obtained parameters for Morse potentialis shown in Table 4
The optimized crystalline structure of Cu2S which has
been obtained in the previous section can be used to adjust anangular-dependent three-body potential parameters shownin (4) In this process of fitting we assume that Cu atomsare located at the averaged position between tetragonal and
Journal of Materials 7
21564Aring
26712Aring
23926Aring
35219Aring
Cu
S
S
S S S S S
Cu
SS S
124125 deg
91599deg106333deg
65876deg
Figure 5 Schematic of the way to average two types of coordination for Cu atoms in Cu2S crystal
Table 4 Potential parameters fitted by FP calculations
(a) Morse potential (Cu-S)
Kind of pair 119863119894119895
120573119894119895
1199030
Unit kJmole 1nm nmCu-S 298916 1500 2029(Mo-S) (152076) (1800) (2532)
(b) Angular potential (S-Cu-S Cu-S-Cu)
Combination 1205790
Unit degS-Cu-S 98966Cu-S-Cu 98966
(c) B-M-H ionic potential (Cu-S)
Kind of pair 1199031015840
0119886Cu 119886S
Unit nm nm nm25319 070052 18314lowast
119886Slowast has been already obtained for MoS2 potential [10]
octahedral sites as shown in Figure 5 since there is possibilitythat Cu atoms may be located on both sites In practicewe just need equilibrium three-body angle 120579
0and pairwise
distance 1199031015840
0 Finally they are 120579
0= 98966
∘ and 1199031015840
0= 2532 nm
respectivelyAdditionally the BMH term requires ionic radii 119886Cu and
119886S for each element The radius of Cu atom is supposed tobe equivalent to the equilibrium length 119903
0in Morse potential
above the radius 119886S = 1834 nm for S is already available fromthe previous MD study of MoS
2[10]
Thus MD potential parameters to reproduce the HCstructure of Cu
2S are obtained by mostly FP calculation and
they are summarized in Table 4
33 Sliding and Friction Behavior of Cu2S
331 Dependency on Crystalline Orientation The depen-dence on crystalline orientation in sliding behavior of Cu
2S
is as follows Figure 6 shows the atomic configurations at119905 = 600 ps with sliding velocity V = 05ms comparingbetween models which are sliding in (a)-direction (⟨0110⟩)sliding and in (b)-direction (⟨21 10⟩) Both models oncecollapse and lose their crystalline stacking during sliding Butafter that the atomic structure recovers its original stackingduring long-time slidingThe difference between twomodelsis not found just visually from atomic configurations asseen in the broken black- and yellow-colored rectangularareas depicted in the figures Therefore the RDF analysiswill be helpful for identifying the change of crystallinestructures Besides in order to recognize transition of anatomic force during sliding the analysis of shear stress willbe helpful
The result of RDF analysis is shown in Figure 7 which isfor sliding velocity V = 05ms and compares results between(a)-direction and (b)-direction models In these RDF figurespeaks are found at some distances by which the nature ofcrystalline structure is confirmed In particular whenwe takea look at peaks found in the range of 02sim08 nm for twomodels the steepness of the distribution in (b)-direction istotally stronger than that in (a)-direction So the structureobtained by the sliding in (b)-direction tends to retain morelocal crystalline structure than that obtained in (a)-directionsliding
Just when the resulting sliding distance becomes 10 nmis the RDF obtained as shown in Figure 8 for different slidingvelocities (V = 10 and 50ms) At the same sliding distancethe crystalline stacking is the same and so the results maybe compared as for different velocity conditions One peakof RDF is just identified for the 1st neighbor distance whichmeans the crystalline structure has been lost and the atomicmovement shows somewhat of fluidity
Shear stress averaged over the whole specimen 120591totrepresents the resistance to the slidingThe time transition of120591tot reflects atomic force state in the sliding During relaxationprocess in fact a certain value of shear stress already occursThis is due to atomic rearrangement inside the crystal unitAfter the specimen is fully relaxed we reset the stress valueLet the value at the beginning of sliding be 120591tot(0) Then the
8 Journal of Materials
Disordered
Ordered layer
CuCu
CuCu
SS
S
To front
To back
To right
To left
Disordered
Ordered layer
CuCuCu
S
S
S Cu
(A) (a)-direction (⟨0110⟩) sliding (the sliding direction is normal to the figure plane)
(B) (b)-direction ( 110⟩) sliding (the sliding direction is right and left)⟨2
Figure 6 Comparison of instantaneous atomic configurations obtained at 119905 = 600 ps with V = 05ms (the picture is drawn onto 119910-119911 plane)
absolute value of deviation of current value 120591tot from initialvalue 120591tot(0) is defined to be
120591119886=
1003816100381610038161003816120591tot minus 120591tot (0)
1003816100381610038161003816 (7)
This stress deviation 120591119886reflects a sudden increase of friction
due to roughness of slide planes The time transition of 120591119886
is obtained as shown in Figure 9 Figure 9(A) shows therelation between the time and the stress deviation 120591
119886 120591119886is
averaged over the whole specimen Those graphs show that120591119886for (a)-direction sliding is larger than that in (b)-direction
The downward arrows in the figure display each maximumvalue At low velocity atoms near contact layers feel relativelylarger resistance to slide in (a)-direction sliding while the
(b)-direction sliding seems much easier However for thecases with higher velocity such as V = 10ms or 50ms thetendency of stress 120591
119886is changed as shown in Figures 9(B)
and 9(C) As shown in Figure 9(B) for example for V =10ms the peak value in (b)-direction is sometimes largerthan that in (a)-direction especially during 50ndash100 ps or 250ndash300 ps
We summarize the dependency of sliding direction asfollows When the shear velocity is small (b)-direction(⟨0110⟩) sliding is easier than (a)-direction (⟨0110⟩) How-ever once the sliding has completed such as to 100 or200 ps from the start of sliding distinction between slidingdirections becomes negligible The cause of this behaviorwould be guessed and explained as follows When the sliding
Journal of Materials 9
(a)
(a)-direction(b)-direction
(a)
(b)16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)
(a)-direction(b)-direction
(b)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)(b)
(a)-direction(b)-direction
(b)
(b)
(a)
(a)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)-direction(b)-direction
(b)
(b)
(a)
(a)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(A) Shear length = 02nm (B) 04nm
(C) 06nm (D) 08nm
Figure 7 Time transition of RDF for V = 05ms (comparison between (a)- and (b)-direction sliding)
is carried out sufficiently the crystalline structure of Cu2S
has collapsed and the crystalline slip system (plane anddirection) no longer determines the sliding behavior Evenif there exists a certain easy-glide plane or direction thecrystal does not always show especially smaller shear stressin sliding
332 Dependency on Sliding Velocity Figure 10(A) shows therelation between shear distance and shear stress deviation 120591
119886
It compares results for a variety of velocities ranging from 05to 50ms For all velocities and for the sliding distance up to02 nm 120591
119886linearly increases with the same gradientThis fact
means that the material deforms in elastic manner for smallsliding and deformation However after that 120591
119886decreases
suddenly The larger the sliding velocity is the larger theaveraged value of 120591
119886is obtained It is reasonable that time rate
of decrease is smaller for higher speed sliding As the wholetime calculated here is seen the case of V= 50ms exhibits the
largest level of 120591119886 For (b)-direction Figure 10(B) shows that
the value of 120591119886increases with increase of sliding velocity It
is concluded that shear stress of this material depends largelyon sliding velocity
The relation between 120591119886and sliding velocity V is sum-
marized in Table 5 120591ave time average of 120591119886 is also shown
at the bottom line It indicates that 120591ave of (a)-directionis approximately 10 smaller than that of (b)-directionWhile the easiest glide directionplane of the HC struc-ture is ⟨0110⟩(0001) (ie (b)-direction) it does not showsmall resistance in the sliding Thus it is concluded thatCu2S crystal does surely show sliding motion but it is
not by usual crystalline slip (glide) mechanism of ordinarymetals
On the other hand the fact that shear stress increaseswith increase of velocity is interesting It means that thismaterial deforms by slidingwith somewhat liquid-like (amor-phous) behavior The deformation rate (ie velocity) in such
10 Journal of Materials
(a)
(a)
(b)
(b)
r (nm)04504035030250201501
14
12
1
08
06
04
02
0
g(r)
(a)-direction(b)-direction
(a) (b)
r (nm)04504035030250201501
12
1
08
06
04
0
02
g(r)
(a)-direction(b)-direction
(a) (b)
r (nm)04504035030250201501
14
12
1
08
06
04
02
0
g(r)
(a)-direction(b)-direction
(a) (b)
(a) (b)
(B) = 10ms
(C) = 50ms
(A) Velocity = 05ms
Figure 8 The comparison of RDF at the same sliding distance (10 nm) between (a)- and (b)-direction sliding
Table 5 Relation between averaged shear stress 120591ave and slidingvelocity V
Sliding velocityVms
Averaged shear stress 120591ave GPa(A) (a)-direction sliding (B) (b)-direction sliding
05 193 22810 214 25450 264 283Average 224 255
amorphous substance produces shear stress inside due toits viscosity and so the shear stress depends on sliding(shear) velocity gradient As shown in Figure 11 averagedshear stresses 120591ave summarized in Table 5 are replotted interms of sliding velocity As recognized in Figure 11 shearstress is almost proportional to the sliding velocity In the
present simulation condition system temperature is kept at10 kelvins which is quite low But the atomic mobility atcontact layers between materials should rise due to the workdone by sliding motion In observing atomic motion theyshow intermittent slip which is sometimes called ldquostick andslipmotionrdquo in nanotribological consideration Furthermorewhen in Figure 11 we extrapolate approximated straight linesdown to V = 0 shear stress 120591ave does not return to zero butit remains at a finite value 120591
0= 20sim25GPa These ideal shear
stresses at V = 0 correspond to static friction of materials Italso means that 120591
0are at least required for layered atoms to
exhibit a material flow
4 Conclusion
In this paper we perform a molecular dynamics (MD)study on copper sulfide material (Cu
2S) under the sliding
Journal of Materials 11
0
20
40
60
80
0 200 400 600 800 1000
Shea
r stre
ss (G
Pa)
Time (ps)
(b)
(a)
= 05ms (a)-dir = 05ms (b)-dir
minus20
0
20
40
60
80
0 100 200 300 400 500 600
Shea
r stre
ss (G
Pa)
Time (ps)
(a)(b)
minus20
= 10ms (a)-dir = 10ms (b)-dir
(a)
(b)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
minus20
Time (ps)
= 50ms (a)-dir = 50ms (b)-dir
200150100500
(A) = 05ms (B) = 10ms
(C) = 50ms
Figure 9 Comparison of the absolute value of shear stress deviation 120591119886between (a)- and (b)-direction
motion The MD simulation includes a new implementationof potential energy function for Cu
2S crystal where some
first-principle calculations are utilized The potential energyfunction has three-body term The following results areobtained and we will make conclusion
(1) First-principle calculations are performed for thehexagonal unit structure of Cu
2S crystal From the
optimized structure original lattice parameters 119886
and 119888 of unit cell and stable configuration of S andCu atoms are obtained Based on those results aninteratomic potential function including ionic andMorse terms as well as angular-dependent term isconstructed for Cu and S system It is confirmedthat this potential function can show enough stability
for the hexagonal crystal structure of Cu2S in MD
simulations(2) An easy-glide direction ⟨21 10⟩ on (0001) plane gen-
erally found for usual hexagonal crystals is not thedirection with small resistance to sliding
(3) Cu2S crystal shows partially liquid-like structure and
behavior in which the shear stress occurring in thematerial depends on the sliding velocity
In the further study we should clarify the tempera-ture dependence and dependency on compressive conditionduring sliding of Cu
2S It is supposed that they are made
possible by analyzing more atomic trajectories obtained byMD simulations It will lead to total understanding of slidingmechanism of Cu
2S crystal
12 Journal of Materials
0
20
40
60
80
0 01 02 03 04 05
Shea
r stre
ss (G
Pa)
Shear distance (nm)
Slow decrease
Fast decrease
minus20
= 50ms (a)-dir = 10ms (a)-dir
= 05ms (a)-dir
0 01 02 03 04 05Shear distance (nm)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
Stress increase by velocity
minus20
= 50ms (b)-dir = 10ms (b)-dir
= 05ms (b)-dir
(A) (a)-direction ( ) sliding (B) (b)-direction ( ) sliding110⟩⟨2 ⟨0110⟩
Figure 10 Relation between shear distance and the deviation of shear stress 120591119886 comparison among different sliding velocities
0
5
10
15
20
25
30
0 1 2 3 4 5
(a)-direction(b)-direction
Linear fit ((a)-dir)Linear fit ((b)-dir)
(ms)
120591 a(G
Pa)
Figure 11 Averaged shear stress replotted against sliding velocity((a)- and (b)-directions (⟨21 10⟩ and ⟨0110⟩))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This study is partly supported by NEDO Innovative Project(2012-2013) and by the ldquoStrategic Project to Support the For-mation of Research Bases at Private Universities MatchingFund Subsidy from MEXT (Ministry of Education CultureSports Science and Technology) (2012ndash2015)rdquo The authorsalso acknowledge Kurimoto Ltd for financial support
References
[1] T Sato Y Hirai T Fukui T Ejima M Takuma and K SaitohldquoAtomic-modeling and simulation of copper sulfide as microsolid lubricantrdquoMRS Proceedings vol 1513 p 20 2013
[2] H Sueyoshi Y Yamano K Inoue Y Maeda and K YamadaldquoMechanical properties of copper sulfide-dispersed lead-freebronzerdquoMaterials Transactions vol 50 no 4 pp 776ndash781 2009
[3] Y Hirai Y Ueda M Yamamoto T Kobayashi and TMaruyama Japanese Patent 132986 2009
[4] K Akamatsu T Kobayashi A Nishimoto T Maruyama andY Arachi ldquoDevelopment of new copper alloymdashinfluence ofmetallic elements on the human bodyrdquo Rikogaku to Gijyutsuvol 16 pp 31ndash36 2009 (Japanese)
[5] L-W Wang ldquoHigh chalcocite Cu2S a solid-liquid hybrid
phaserdquoPhysical Review Letters vol 108 no 8 Article ID 0857032012
[6] T Ejima K-I Saitoh N Shinke M Taruma Y Hirai and TSato ldquoAtomic-level analysis of copper sulfide (CU2S) crystalstructure and sliding characteristicsrdquo Technology Reports ofKansai University vol 54 pp 23ndash33 2012
[7] I I Mazin ldquoStructural and electronic properties of the two-dimensional superconductor CuS with 1(13)-valent copperrdquoPhysical Review B vol 85 Article ID 115133 2012
[8] M J Buerger and B J Wuensch ldquoDistribution of atoms in highchalcocite Cu
2Srdquo Science vol 141 no 3577 pp 276ndash277 1963
[9] B J Wuensch and M J Buerger ldquoThe crystal structure ofchalcocite Cu
2Srdquo Mineralogical Society of America Special
Paper vol 1 pp 163ndash170 1963 Proceedings of the 3rd GenralMeeting
[10] T Onodera Y Morlta A Suzuki et al ldquoA computationalchemistry study on friction of h-MoS2 Part I Mechanism ofsingle sheet lubricationrdquo The Journal of Physical Chemistry Bvol 113 no 52 pp 16526ndash16536 2009
[11] Y Ding D R Veblen and C T Prewitt ldquoPossible FeCu order-ing schemes in the 2a superstructure of bornite (Cu
5FeS4)rdquo
American Mineralogist vol 90 no 8-9 pp 1265ndash1269 2005
Journal of Materials 13
[12] H Zheng J B Rivest T A Miller et al ldquoObservation of tran-sient structural-transformation dynamics in a Cu
2S nanorodrdquo
Science vol 333 no 6039 pp 206ndash209 2011[13] S KashidaW ShimosakaMMori andDYoshimura ldquoValence
band photoemission study of the copper chalcogenide com-pounds Cu2S Cu2Se and Cu2Terdquo Journal of Physics andChemistry of Solids vol 64 no 12 pp 2357ndash2363 2003
[14] P Lukashev W R L Lambrecht T Kotani and M VanSchilfgaarde ldquoElectronic and crystal structure of Cu2-x S full-potential electronic structure calculationsrdquo Physical Review Bvol 76 no 19 Article ID 195202 2007
[15] P Blaha K Schwarz G Madsen D Kvasnicka and J LuitzldquoWIEN2krdquo httpwwwwien2katindexhtml
[16] P A Romero T T Jarvi N Beckmann M Mrovec andM Moseler ldquoCoarse graining and localized plasticity betweensliding nanocrystalline metalsrdquo Physical Review Letters vol 113no 3 Article ID 036101 2014
[17] S Izumi and S Sakai ldquoInternal displacement and elasticproperties of the silicon tersoff modelrdquo JSME InternationalJournal Series A Solid Mechanics and Material Engineering vol47 no 1 pp 54ndash61 2004
[18] M P Allen and D J Tildesley Computer Simulation of LiquidsOxford University Press Oxford UK 1989
[19] Sandia Nantional Laboratory ldquoLarge-scale AtomicMolecularMassively Parallel Simulatorrdquo httplammpssandiagov
[20] T Yamaguchi and K Saitoh ldquoMolecular dyanmics study onmechanical properties in the structure of self-assembled quan-tum dotrdquoWorld Journal of Nano Science and Engineering vol 2pp 189ndash195 2012
[21] T Ejima Atomic-level analysis on sliding characteristic of coppersulfide [MS thesis] Graduate School of Kansai University 2013
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
2 Journal of Materials
In the field of mineralogy Cu2S crystal is well known as a
mineral called chalcocite Recently since the Cu2S structure
has a unique electronic behavior as for ionic conductivity itis planned to be used for switching device applications suchas a solar power plant material [5] and a superconductivitymaterial [6 7] In the context of unique sliding and frictionbehavior of Cu
2S crystal already found experimentally the
present authors have studied it by atomistic modeling One ofstable stoichiometries of copper and sulfide system is foundat Cu
2S (Cu S = 2 1) Interestingly this Cu
2S compound
exhibits very complicated solid phase transition behavior[8 9] Around the standard temperature the unit structureof Cu
2S is orthorhombic but it transforms into hexagonal
symmetry above 105∘C (degrees Celsius)Moreover in highertemperature above 460∘C it is transformed into cubic crys-tal
When copper alloys are used for sliding and frictionmaterials they are generally placed in a severe condition ofhigh temperature beyond several hundred ∘C and thereforethe behavior of hexagonal crystal (HC) would be worthstudying extensively In Cu
2S crystal consequently one S
atom has two neighbor Cu atoms So they tend to organizea triangular conformation and keep their firm interatomicbonding when they are stabilized The same mechanismconcerning S atom is also suggested in MoS
2system which
is famous as good solid lubricant where the S atom makesfirm bonding with metal atoms [10]
Other than chalcocite (Cu2S) there are some well-known
natural minerals based on copper alloy [11 12] such asbornite (Cu
5FeS4) chalcopyrite (CuFeS
2) covellite (CuS)
and digenite (Cu9S5) All of these alloys are interesting as
for interrelationship in their fabrication and all of them maybe applied to new functional material in the future Amongthem however Cu
2S crystal is still a main compound so it
should be focused on particularlyThus in this paper we willstudy the atomistic structure of Cu
2S in HC and discuss its
atomistic behavior in sliding and friction processIn the present study aiming at unempirical approach
the first-principle (ab initio) calculation is utilized to identifythe crystal structure of Cu
2S So far there have been some
studies of copper sulfides by ab initio method which aremainly employing density functional theory (DFT) [5 13 14]The electronic structure has been reproduced but unfortu-nately there still remains ambiguity about atomic positionof coppers in the unit crystal and so further modelingand discussion will be required Therefore in this studyby using conventional DFT software package Wien2k [15]the optimization of the unit structure of the Cu
2S in HC
is carried out based on Kashida et alrsquos structural model[13] As a result we obtain its energetically stable structureand we determine its basic crystalline information that islattice constants as for lengths 119886 and 119888 assuming the HCconfiguration
In order to understand the dynamics of sliding or fric-tion occurring in Cu
2S crystal molecular dynamics (MD)
simulation is suitable Lattice constants 119886 and 119888 and ground-state energies which are obtained by ab initio calculations areused in the determination of interatomic potential for MDsimulation In the MD simulation an existing interatomic
potential function of MoS2[10] is referred to for its function
or functional form This seems reasonable because thosetwo crystals of metal sulfide (Cu
2S and MoS
2) have many
common features as described aboveThus we simulate atomistically the sliding of Cu
2S crystal
by using MD method with an original and nonempiricalinteratomic potential The computation model is built bystacking layers on slip plane (basal plane) of HC lattice and itis at the first place compressed and then shear deformation isapplied Here the compression is crucial since in the actualsituation the friction behavior in sliding is to take placeunder severe contact condition with large compressive stress(pressure on the contacting surface) We will focus on thedependence on crystalline direction of sliding or on slidingvelocity in such severe condition
This paper is organized as follows Following the Intro-duction we describe the basic information of crystal struc-ture of Cu
2S and show some theories needed for the
modeling and the calculation Then the essence of the abinitio calculation is shown and the procedure to implementthe interatomic potential is briefly presented Thereafterthe MD model used in sliding simulation is explainedThe summary of results in ab initio calculation and MDresults of sliding simulation are shown and their discus-sion is made Finally the conclusion of this paper will bemade
2 Theory and Method
21 Atomic Structure of Cu2S Crystal As pure compounds
of copper sulfide there are covellite (CuS) and chalcocite(Cu2S) and the latter is focused on now For Cu
2S
orthorhombic crystal is obtained in room temperature butbeyond 105∘C it transforms into hexagonal crystal (HC)Furthermore in higher temperature than 460∘C it changes tocubic crystal [8] Copper alloys are often subject to very highpressure and relatively high temperature during operationsuch as in the surface layer of mechanical bearing Thusthe present simulation should focus on the temperaturerange around several hundred kelvins Accordingly the Cu
2S
material here is assumed to be in HC HC is also taken inMoS2and carbon allotrope (graphite or nanometer-thickness
graphene) and both of them are well-known solid lubricantsAmong conventional metals however HC metal such asmagnesium (Mg) is relatively inferior in deformation dueto the lack of crystalline slip systems when compared withface-centered cubic (fcc) crystals such as aluminum (Al) andCu Only the basal slip of hexagonal crystal is always wellactivated in Mg crystal and so its slip is highly directiondependent It is guessed that sliding motion in HC structurewill prefer such direction-dependent featureThis leads to thefact that compounds with HC structure such as Cu
2S and
MoS2 will be good at lubrication
22 First-Principle Calculation Cu atoms are metal andinclude metallic bonds but on the other hand S atomsare nonmetal and show large electronegativity Accordinglybond between atoms inside Cu
2S seems very complicated
Journal of Materials 3
Possibly ionic bond and metallic bond would be nonlinearlyinterrelated In considering the structure and bonding stateof solid crystal it is helpful to reproduce and observe thedetailed electron density distribution Besides those resultscan be taken into account in the construction of accurateinteratomic potential for MD simulations First-principle(FP) calculation (in Latin words ab initio calculation)refers to all quantum-mechanical computational chemistrymethods and is sometimes called ldquoband calculationrdquo Itobtains electron density around atomic nuclei based on theperiodic crystal structure of constituent atoms Nowadaysa number of software packages of FP method are availablein many researches Among those software packages ourchoice is WIEN2k package [15] which is based on densityfunctional theory (DFT) The characteristic of WIEN2k isthat it uses full-potential formulation instead of muffin-tinapproximation and that it uses the linearized augmentedplane wave basis set with local orbitals (LAPW + lo) As forcorrelation exchange term it can apply either local densityapproximation (LDA) or generalized gradient approximation(GGA)The detailed theory and usage are not the main focusof this study and should be omitted here
While all the S atoms in Cu2S are simply located at the
lattice point of HC it is suggested that Cu atoms seem tohave large mobility inside the unit cell especially in hightemperature keeping their symmetric atomic configurationSince actual position ofCu atoms inCu
2S is quite complicated
and is in fact giving controversy the present study employsexisting crystal model used in previous computation ofKashida et al [13] It is confirmed that the model agrees withexperimental fact as well as theoretical one Initial atomicposition of Cu
2S in HC is shown in Table 1 Figure 1 shows
initial position of atoms in Cu2S crystal unit
In order to obtain the minimum (ground-state) energythe atomic configuration is adjusted via the function ofoptimization in the software Lattice constants for angle(120572 120573 120574) are fixed so that the HC lattice should bemaintainedOn the other hand lattice constants for lengths (119886 119888) arechanged as follows Keeping a certain ratio of 119888119886 the lengths(119886 119888) are varied from compressive state to tensile one Thedeviation of 119888119886 from the initial value is +4sim+10 Thevolumetric change by the change of (119886 119888) ranges withinminus2sim+6 The exchange correlation energy of PBE-GGA isemployed Judgement of the energy convergence is done at00001 Ry where 1 Ry = 2180 times 10
minus18 J = 1360 eV Table 2summarizes calculation conditions and parameters used inthe present study The number of 119896-points is varied andapproximately above 20000 we may say that the total energywill be converged and shows sufficient accuracy Thereforewe recognize that 46 times 46 times 22 = 46552 119896-points arelarge enough and this will be used through the presentstudy
23 The Potential Function of Cu2S for MD As mentioned
above copper disulfide Cu2S has a variety of crystalline
structures depending on the temperature The structure isorthorhombic in standard temperature HC above 105∘C andcubic further above 460∘C Here as HC is assumed and
Table 1 Cu2S atomic coordinates and crystal data
(a)
Element Coordinate (relative to unit cell)119909 119910 119911
S 13 23 14Cu(1) 0 0 14Cu(2) 13 23 0578
(b)
Property Unit ValueLattice constant(1) 119886 nm 0389Lattice constant(2) 119888 nm 0688Lattice constant(3) 120572 deg 900Lattice constant(4) 120573 deg 900Lattice constant(5) 120574 deg 1200Atoms per unit cell mdash 3Space group mdash P6
3
120572 120573120574
c
a
Cu
Cu
CuCu
Cu
Cu
CuCu
CuCu
S
S
Figure 1 Crystal structure of Cu2S (hexagonal crystal unit 13 of
conventional hexagonal prism)
the composition ratio is Cu S = 2 1 one S atom shouldcorrespond to two Cu atoms Therefore those three atomscompose a structural unit and the three-body bond is formedas a function of their angle By the way MoS
2has HC
structure as well The structural feature common to thoseHC lattices is that their slip plane is only limited to thebasal plane (0001) This is completely different from fcc orbcc which is accompanying many slip systems In fact theslip of HC lattice takes place only when a certain conditionhas been fulfilled Thus the potential function which wasproposed for MoS
2[10] can be utilized as the reference to
construct the function needed in the present study for Cu2S
Though MoS2and Cu
2S have the contrary ratio as to S
atom a lot of common features are likely to be found inthese two crystals For example angular-dependent three-body interaction is crucial for stabilization of both crystalsTo begin with we apply the potential forms used in theMoS2study and then our results obtained by first-principle
calculation are properly fitted to a new potential functionfor Cu
2S We insist that since the fitting data is obtained
theoretically only by DFT calculations the new potentialfunction will be an unempirical (ab initio) one
4 Journal of Materials
Table 2 Calculation condition for structural optimization of Cu2S
crystal
Exchange correlation potential mdash PBE-GGAEnergy to separate core from valence states Rylowast minus60Energy convergence criteria Rylowast 00001
Change of 119888119886 ratioRate of change +4sim+10Increment of rate (for 119888119886) +2
Volume changeRate of change minus2sim+6Increment of rate (for 119888119886) +1lowastEnergy unit 1 Ry = 2180 times 10minus18 J = 1360 eV
The detail of the new potential function for Cu2S is as fol-
lows The potential function is a summation of three distinctpotential functions as shown in (1) Ionic and metallic bondsare represented by Born-Mayer-Huggins (BMH) potential120601BMH and Morse potential 120601Morse as expressed in (2) and(3) respectively Angular-dependent potential for the bond ofCu-S interaction 120601angle is represented as (4) which is three-body potential Parameters for those potential functions aresummarized in Table 3
120601 = 120601BMH + 120601Morse + 120601angle (1)
120601BMH =
1199111198941199111198951198902
119903
+ 1198910(119887119894+ 119887119895) exp(
119886119894+ 119886119895minus 119903
119887119894+ 119887119895
) +
119888119894119888119895
1199036 (2)
120601Morse = 119863119894119895[exp minus2120573
119894119895(119903119894119895minus 1199030)
minus 2 exp minus120573119894119895(119903119894119895minus 1199030)]
(3)
120601angle = 119867120579(120579 minus 120579
0)2
(4)
In those equations 119911119894or 119911119895is electronic charge of each atom
and the values 119911S = minus20 and 119911Cu = +10 are employed for Sand Cu atoms respectively 119891
0= 1 [kcalA] = 4186 [kJA] is
the parameter which determines the stiffness of each ionicsphere and is transferred from the study of MoS
2 In the
Morse potential the equilibrium distance 1199030and bond energy
119863119894119895are fitted to those in the optimized structure which is
obtained in our ab initio calculation In the angular potentialequilibrium three-body angle 120579
0is also determined by our
ab initio calculation But it is difficult to derive the springconstant 119867
120579just from our ab initio calculation so the same
value as in MoS2is applied here Of course the value of 119867
120579
influences rigidity But its function form is basically harmonicand we found that the effect of spring constant on sliding isnot so crucial
24 Molecular Dynamics Model for Cu2S Sliding Figure 2
shows theMDmodel for sliding simulation In the first placethe optimized atomic configuration obtained by ab initiocalculation is prepared and then is thermally equilibratedat a finite temperature Then the structure is compressed
Table 3 Interatomic potential parameters for Cu2S crystal
(a) B-M-H potential
Atoms 119886119894
119887119894
119888119894
Unit [A] [A] [kJ05sdotA3mol05]Cu 0696 0085 0000S 1831 0085 70000
(b) Morse potential
Application 119863119894119895
120573119894119895
1199030
Unit [kJmol] [1A] [A]Cu-S 152076 1800 2532
(c) Angular potential
Application 119867120579
1205790
Unit [kJmol] [deg]Cu-S-Cu 196648 98943S-Cu-S 196648 98943
in 119911 direction as shown in Figure 2 After that the atomicvelocity in the 119909 direction of two special regions (shownwith yellow color in the figure) is constrained so that sheardeformation is applied to the whole region in the directionparallel to the slip plane These processes are supposedto mimic a Cu
2S crystal in sliding condition This kind
of dynamic sliding simulation has been often studied fortribology-system as found in literatures so far [16] and itsadvantage is that we can observe directly the sliding behaviorof atomic system
It is supposed that crystalline slip plane of Cu2S plays
an important role in the slip deformation As stated aboveCu2S crystal unit has the HC conformation and the pri-
mary slip plane should be (0001) in Millerrsquos indices Theprimary slip direction should be the shortest interatomicdistance existing on the (0001) plane that is ⟨21 10⟩ Wewill call it (b)-direction hereafter The second easiest slipdirection should be ⟨0110⟩ which we call (a)-direction here-after In the present study we configure these two possibleslip directions for sliding simulation and compare theseresults
Other factors affecting sliding behavior of Cu2S would be
velocity and temperature Sliding velocities are varied so thatcorresponding shear velocities are 01 10 and 50ms Thereader should feel that these velocities seem quite higher thanused in actual slidingmachine or equipment However in theMD simulation time increment has to be very short such as1 fs (femtosecond) or less so such large deformation rate isinevitable
25 Analyzing MD Results In the present study the MDresults are mainly analyzed by radial distribution function(RDF) and atomic shear stress Strict formalization of stresstensor with regard to three-body term would require furtherdiscussion at this stage [17] so we use here an approximateand practial treatment These analyzing methods for MDresults are explained below
Journal of Materials 5
A model sliding in (b)-direction
z
yAtoms
A model sliding in (a)-direction
z
x
Cu
S
Fixed
Parallel to basal plane
Basal plane(0001)
(a)-direction
(b)-direction(slip direction of hexagonal crystal)
The model for researching dependence on direction or velocity
⟨0110⟩
110⟩⟨2
Figure 2 Abstract of MD sliding model of Cu2S crystal
251 Crystal Structure Analysis by Radial Distribution Func-tion (RDF) Usually solid crystal has a three-dimensionalorderThe Cu
2S crystal used in the present study exhibits HC
structure One of themethods to identify the crystalline orderis radial distribution function (RDF) 119892(119903) [18] Briefly speak-ing the function 119892(119903) gives the number density of neighboratoms which are found in a certain distance from each atomIts distribution shows some peaks at some specific distancesinherent to the crystalline orderWhen the temperature arisesor when the crystalline order is partially lost due to outbreakof lattice defects the peak value of RDF generally reduces andthe shape at the peak becomes broadenedThus by observingthe change of the peak position and the shape of the curve ofRDF the deterioration of the crystalline order can be detectedand occurrence of lattice defects can be guessed
252 Atomic Stress Analysis (Approximate Treatment includ-ing Three-Body Terms) Since our MD model is in solidstate the behavior of sliding and friction is reflected by ashear stress averaged over the specimen Therefore atomic-scale stress is being analysed But we note that stress (orstrain) is basically the concept in continuum mechanicsand is not essential for any atomic system The facts thatatomic positions are discrete and that interatomic potentialhas nonlocal nature will conflict with the local theory of
continuum Accordingly we need to formulate atomic stresstogether with some approximation
Suppose that total potential energy inside the systemcomprises all the superposition of pairwise interactions 120601(119903)When any selected atom 119894 conducts homogeneous deforma-tion with regard to the relative position to another neighboratom 119895 strain at the interatomic space between 119894 and 119895 can bepresented by their interatomic distance 119903(119894 119895) and interatomicvector r(119894 119895) (this assumes that there is no slip no phasetransition nor long atomic diffusion over the lattice) Thenatomic stress tensor occurring at the atom 119894 is expressed as
120590 (119894) =
1
2Ω (119894)
sum
119895
120597120601 (119894 119895)
120597119903 (119894 119895)
r (119894 119895) otimes r (119894 119895)119903 (119894 119895)
(5)
where the summation is composed of the work done byatomic motion which is called ldquovirialrdquo Ω(119894) in the denom-inator is the volume supposedly occupied by the atom 119894so (5) is regarded as the energy density around that atomIn the present study Ω(119894) is assumed to be a constantwhich has been estimated in the reference structure (whichhas been estimated in the undeformed lattice) Additionallyvector product (r otimes r) means the dyadic between interatomicvectors so (5) has the form of the second-order (symmetric)tensor and its components are six Thus if an interatomicpotential of MD contains just pairwise term the virial can be
6 Journal of Materials
straightforwardly converted to atomic stress But if it includesthree-body terms depending on the angle as in the presentinteratomic potential they can never strictly be decomposedinto virials of each pair of atoms However we can apply anapproximate formulation to a triplet 119894 119895 and 119896 (119894 119895 119896) Inpractice the combination of virials of each pair (119894 119895) (119895 119896)and (119896 119894) is used as the net virial of the triplet As a result theformulation of atomic stress comes to the expression
120590120572120573
(119894) =
1
2Ω (119894)
sum
119895
120597120601pair (119894 119895)
120597119903 (119894 119895)
119903120572(119894 119895) 119903
120573(119894 119895)
119903 (119894 119895)
+
1
3Ω (119894)
sum
119895119896
(
120597120601angle (119894 119895)
120597119903 (119894 119895)
119903120572(119894 119895) 119903
120573(119894 119895)
119903 (119894 119895)
+
120597120601angle (119895 119896)
120597119903 (119895 119896)
119903120572(119895 119896) 119903
120573(119895 119896)
119903 (119895 119896)
+
120597120601angle (119896 119894)
120597119903 (119896 119894)
119903120572(119896 119894) 119903
120573(119896 119894)
119903 (119896 119894)
)
(6)
where the first term corresponds to pair interaction 120601pair(119903)and the second term is for three-body interaction Inthis expression Ω(119894) 120601pair(119894 119895) 120601angle(119894 119895) 119903(119894 119895) and119903120572(119894 119895) (120572 120573 = 1 2 3) are atomic volume pairwise potential
function three-body potential function interatomic distance(between 119894 and 119895) and its vector components In comparingall the components in (6) during actual MD simulation it isunderstood that three-body term is relatively large so that itis not negligible This expression of atomic stress includingthree-body term is also utilized in widely used MD software(eg LAMMPS) [19] Besides this estimation of atomicstress was found appropriate when we applied it to anotherMD study using the three-body-type Tersoff potential (forSi-Ge system) [20]
3 Results and Discussion
31 Optimization of Lattice Constant of Cu2S Crystal by
First-Principle Calculation The relation between volume andenergy of Cu
2S crystal unit is obtained as in Figure 3 by first-
principle (FP) calculation including structural optimizationFor the variety of the lattice constant ratio 119888119886 the lowestenergy is obtained at the deviation Δ119888119886 = 8 Moreoverunder that condition volume expansion at +3 shows thesmallest energy From this optimized structure thereforelattice constants of the HC structure are 119886 = 0383 nm and119888 = 0731 nm for which 119888119886 is 191 The length for 119888 andthe ratio 119888119886 seem relatively larger than the HC structure ofusual metals It means that layers of sulfur (S) and copper(Cu) atoms are remarkably separated from each other in theCu2S crystal In the present paper these optimized lattice
constants are used as values to configure atomic positions inthe specimen of Cu
2S crystal
32 Construction of Interatomic Potential Function for MDCalculations It is experimentally and theoretically under-stood that interaction between Cu and S atoms is generally
Minimum
Change of volume ()
Difference from initial structure
+10+8
+6+4
Ener
gy d
iffer
ence
(eV
)
6543210minus1minus2minus001
009
01
008
007
006
005
004
003
002
001
0
Figure 3 Volume-energy relation of Cu2S crystal structure
Distance r (nm)090807060504030201
minus8
minus6
minus4
minus2
0
2
4
6
8
Mo-S bondCu-S bond
FP calculation
times10minus19En
ergy
EminusE0
(J)
Figure 4 Distance-energy relation of Cu-S interaction obtained byFP calculation (Mo-S interaction is also shown for comparison)
strong So the Cu-S interaction can be expressed by Morsepotential function as shown by (3) The optimized configu-ration of Cu-S dimer is obtained by the FP calculation by us[21] From this we determine both the equilibrium distanceparameters 119903
0 120573119894119895and the energy parameter 119863
119894119895needed
in Morse potential Figure 4 shows the relation betweeninteratomic distance and its energy which is obtained by theFP calculation The obtained parameters for Morse potentialis shown in Table 4
The optimized crystalline structure of Cu2S which has
been obtained in the previous section can be used to adjust anangular-dependent three-body potential parameters shownin (4) In this process of fitting we assume that Cu atomsare located at the averaged position between tetragonal and
Journal of Materials 7
21564Aring
26712Aring
23926Aring
35219Aring
Cu
S
S
S S S S S
Cu
SS S
124125 deg
91599deg106333deg
65876deg
Figure 5 Schematic of the way to average two types of coordination for Cu atoms in Cu2S crystal
Table 4 Potential parameters fitted by FP calculations
(a) Morse potential (Cu-S)
Kind of pair 119863119894119895
120573119894119895
1199030
Unit kJmole 1nm nmCu-S 298916 1500 2029(Mo-S) (152076) (1800) (2532)
(b) Angular potential (S-Cu-S Cu-S-Cu)
Combination 1205790
Unit degS-Cu-S 98966Cu-S-Cu 98966
(c) B-M-H ionic potential (Cu-S)
Kind of pair 1199031015840
0119886Cu 119886S
Unit nm nm nm25319 070052 18314lowast
119886Slowast has been already obtained for MoS2 potential [10]
octahedral sites as shown in Figure 5 since there is possibilitythat Cu atoms may be located on both sites In practicewe just need equilibrium three-body angle 120579
0and pairwise
distance 1199031015840
0 Finally they are 120579
0= 98966
∘ and 1199031015840
0= 2532 nm
respectivelyAdditionally the BMH term requires ionic radii 119886Cu and
119886S for each element The radius of Cu atom is supposed tobe equivalent to the equilibrium length 119903
0in Morse potential
above the radius 119886S = 1834 nm for S is already available fromthe previous MD study of MoS
2[10]
Thus MD potential parameters to reproduce the HCstructure of Cu
2S are obtained by mostly FP calculation and
they are summarized in Table 4
33 Sliding and Friction Behavior of Cu2S
331 Dependency on Crystalline Orientation The depen-dence on crystalline orientation in sliding behavior of Cu
2S
is as follows Figure 6 shows the atomic configurations at119905 = 600 ps with sliding velocity V = 05ms comparingbetween models which are sliding in (a)-direction (⟨0110⟩)sliding and in (b)-direction (⟨21 10⟩) Both models oncecollapse and lose their crystalline stacking during sliding Butafter that the atomic structure recovers its original stackingduring long-time slidingThe difference between twomodelsis not found just visually from atomic configurations asseen in the broken black- and yellow-colored rectangularareas depicted in the figures Therefore the RDF analysiswill be helpful for identifying the change of crystallinestructures Besides in order to recognize transition of anatomic force during sliding the analysis of shear stress willbe helpful
The result of RDF analysis is shown in Figure 7 which isfor sliding velocity V = 05ms and compares results between(a)-direction and (b)-direction models In these RDF figurespeaks are found at some distances by which the nature ofcrystalline structure is confirmed In particular whenwe takea look at peaks found in the range of 02sim08 nm for twomodels the steepness of the distribution in (b)-direction istotally stronger than that in (a)-direction So the structureobtained by the sliding in (b)-direction tends to retain morelocal crystalline structure than that obtained in (a)-directionsliding
Just when the resulting sliding distance becomes 10 nmis the RDF obtained as shown in Figure 8 for different slidingvelocities (V = 10 and 50ms) At the same sliding distancethe crystalline stacking is the same and so the results maybe compared as for different velocity conditions One peakof RDF is just identified for the 1st neighbor distance whichmeans the crystalline structure has been lost and the atomicmovement shows somewhat of fluidity
Shear stress averaged over the whole specimen 120591totrepresents the resistance to the slidingThe time transition of120591tot reflects atomic force state in the sliding During relaxationprocess in fact a certain value of shear stress already occursThis is due to atomic rearrangement inside the crystal unitAfter the specimen is fully relaxed we reset the stress valueLet the value at the beginning of sliding be 120591tot(0) Then the
8 Journal of Materials
Disordered
Ordered layer
CuCu
CuCu
SS
S
To front
To back
To right
To left
Disordered
Ordered layer
CuCuCu
S
S
S Cu
(A) (a)-direction (⟨0110⟩) sliding (the sliding direction is normal to the figure plane)
(B) (b)-direction ( 110⟩) sliding (the sliding direction is right and left)⟨2
Figure 6 Comparison of instantaneous atomic configurations obtained at 119905 = 600 ps with V = 05ms (the picture is drawn onto 119910-119911 plane)
absolute value of deviation of current value 120591tot from initialvalue 120591tot(0) is defined to be
120591119886=
1003816100381610038161003816120591tot minus 120591tot (0)
1003816100381610038161003816 (7)
This stress deviation 120591119886reflects a sudden increase of friction
due to roughness of slide planes The time transition of 120591119886
is obtained as shown in Figure 9 Figure 9(A) shows therelation between the time and the stress deviation 120591
119886 120591119886is
averaged over the whole specimen Those graphs show that120591119886for (a)-direction sliding is larger than that in (b)-direction
The downward arrows in the figure display each maximumvalue At low velocity atoms near contact layers feel relativelylarger resistance to slide in (a)-direction sliding while the
(b)-direction sliding seems much easier However for thecases with higher velocity such as V = 10ms or 50ms thetendency of stress 120591
119886is changed as shown in Figures 9(B)
and 9(C) As shown in Figure 9(B) for example for V =10ms the peak value in (b)-direction is sometimes largerthan that in (a)-direction especially during 50ndash100 ps or 250ndash300 ps
We summarize the dependency of sliding direction asfollows When the shear velocity is small (b)-direction(⟨0110⟩) sliding is easier than (a)-direction (⟨0110⟩) How-ever once the sliding has completed such as to 100 or200 ps from the start of sliding distinction between slidingdirections becomes negligible The cause of this behaviorwould be guessed and explained as follows When the sliding
Journal of Materials 9
(a)
(a)-direction(b)-direction
(a)
(b)16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)
(a)-direction(b)-direction
(b)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)(b)
(a)-direction(b)-direction
(b)
(b)
(a)
(a)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)-direction(b)-direction
(b)
(b)
(a)
(a)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(A) Shear length = 02nm (B) 04nm
(C) 06nm (D) 08nm
Figure 7 Time transition of RDF for V = 05ms (comparison between (a)- and (b)-direction sliding)
is carried out sufficiently the crystalline structure of Cu2S
has collapsed and the crystalline slip system (plane anddirection) no longer determines the sliding behavior Evenif there exists a certain easy-glide plane or direction thecrystal does not always show especially smaller shear stressin sliding
332 Dependency on Sliding Velocity Figure 10(A) shows therelation between shear distance and shear stress deviation 120591
119886
It compares results for a variety of velocities ranging from 05to 50ms For all velocities and for the sliding distance up to02 nm 120591
119886linearly increases with the same gradientThis fact
means that the material deforms in elastic manner for smallsliding and deformation However after that 120591
119886decreases
suddenly The larger the sliding velocity is the larger theaveraged value of 120591
119886is obtained It is reasonable that time rate
of decrease is smaller for higher speed sliding As the wholetime calculated here is seen the case of V= 50ms exhibits the
largest level of 120591119886 For (b)-direction Figure 10(B) shows that
the value of 120591119886increases with increase of sliding velocity It
is concluded that shear stress of this material depends largelyon sliding velocity
The relation between 120591119886and sliding velocity V is sum-
marized in Table 5 120591ave time average of 120591119886 is also shown
at the bottom line It indicates that 120591ave of (a)-directionis approximately 10 smaller than that of (b)-directionWhile the easiest glide directionplane of the HC struc-ture is ⟨0110⟩(0001) (ie (b)-direction) it does not showsmall resistance in the sliding Thus it is concluded thatCu2S crystal does surely show sliding motion but it is
not by usual crystalline slip (glide) mechanism of ordinarymetals
On the other hand the fact that shear stress increaseswith increase of velocity is interesting It means that thismaterial deforms by slidingwith somewhat liquid-like (amor-phous) behavior The deformation rate (ie velocity) in such
10 Journal of Materials
(a)
(a)
(b)
(b)
r (nm)04504035030250201501
14
12
1
08
06
04
02
0
g(r)
(a)-direction(b)-direction
(a) (b)
r (nm)04504035030250201501
12
1
08
06
04
0
02
g(r)
(a)-direction(b)-direction
(a) (b)
r (nm)04504035030250201501
14
12
1
08
06
04
02
0
g(r)
(a)-direction(b)-direction
(a) (b)
(a) (b)
(B) = 10ms
(C) = 50ms
(A) Velocity = 05ms
Figure 8 The comparison of RDF at the same sliding distance (10 nm) between (a)- and (b)-direction sliding
Table 5 Relation between averaged shear stress 120591ave and slidingvelocity V
Sliding velocityVms
Averaged shear stress 120591ave GPa(A) (a)-direction sliding (B) (b)-direction sliding
05 193 22810 214 25450 264 283Average 224 255
amorphous substance produces shear stress inside due toits viscosity and so the shear stress depends on sliding(shear) velocity gradient As shown in Figure 11 averagedshear stresses 120591ave summarized in Table 5 are replotted interms of sliding velocity As recognized in Figure 11 shearstress is almost proportional to the sliding velocity In the
present simulation condition system temperature is kept at10 kelvins which is quite low But the atomic mobility atcontact layers between materials should rise due to the workdone by sliding motion In observing atomic motion theyshow intermittent slip which is sometimes called ldquostick andslipmotionrdquo in nanotribological consideration Furthermorewhen in Figure 11 we extrapolate approximated straight linesdown to V = 0 shear stress 120591ave does not return to zero butit remains at a finite value 120591
0= 20sim25GPa These ideal shear
stresses at V = 0 correspond to static friction of materials Italso means that 120591
0are at least required for layered atoms to
exhibit a material flow
4 Conclusion
In this paper we perform a molecular dynamics (MD)study on copper sulfide material (Cu
2S) under the sliding
Journal of Materials 11
0
20
40
60
80
0 200 400 600 800 1000
Shea
r stre
ss (G
Pa)
Time (ps)
(b)
(a)
= 05ms (a)-dir = 05ms (b)-dir
minus20
0
20
40
60
80
0 100 200 300 400 500 600
Shea
r stre
ss (G
Pa)
Time (ps)
(a)(b)
minus20
= 10ms (a)-dir = 10ms (b)-dir
(a)
(b)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
minus20
Time (ps)
= 50ms (a)-dir = 50ms (b)-dir
200150100500
(A) = 05ms (B) = 10ms
(C) = 50ms
Figure 9 Comparison of the absolute value of shear stress deviation 120591119886between (a)- and (b)-direction
motion The MD simulation includes a new implementationof potential energy function for Cu
2S crystal where some
first-principle calculations are utilized The potential energyfunction has three-body term The following results areobtained and we will make conclusion
(1) First-principle calculations are performed for thehexagonal unit structure of Cu
2S crystal From the
optimized structure original lattice parameters 119886
and 119888 of unit cell and stable configuration of S andCu atoms are obtained Based on those results aninteratomic potential function including ionic andMorse terms as well as angular-dependent term isconstructed for Cu and S system It is confirmedthat this potential function can show enough stability
for the hexagonal crystal structure of Cu2S in MD
simulations(2) An easy-glide direction ⟨21 10⟩ on (0001) plane gen-
erally found for usual hexagonal crystals is not thedirection with small resistance to sliding
(3) Cu2S crystal shows partially liquid-like structure and
behavior in which the shear stress occurring in thematerial depends on the sliding velocity
In the further study we should clarify the tempera-ture dependence and dependency on compressive conditionduring sliding of Cu
2S It is supposed that they are made
possible by analyzing more atomic trajectories obtained byMD simulations It will lead to total understanding of slidingmechanism of Cu
2S crystal
12 Journal of Materials
0
20
40
60
80
0 01 02 03 04 05
Shea
r stre
ss (G
Pa)
Shear distance (nm)
Slow decrease
Fast decrease
minus20
= 50ms (a)-dir = 10ms (a)-dir
= 05ms (a)-dir
0 01 02 03 04 05Shear distance (nm)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
Stress increase by velocity
minus20
= 50ms (b)-dir = 10ms (b)-dir
= 05ms (b)-dir
(A) (a)-direction ( ) sliding (B) (b)-direction ( ) sliding110⟩⟨2 ⟨0110⟩
Figure 10 Relation between shear distance and the deviation of shear stress 120591119886 comparison among different sliding velocities
0
5
10
15
20
25
30
0 1 2 3 4 5
(a)-direction(b)-direction
Linear fit ((a)-dir)Linear fit ((b)-dir)
(ms)
120591 a(G
Pa)
Figure 11 Averaged shear stress replotted against sliding velocity((a)- and (b)-directions (⟨21 10⟩ and ⟨0110⟩))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This study is partly supported by NEDO Innovative Project(2012-2013) and by the ldquoStrategic Project to Support the For-mation of Research Bases at Private Universities MatchingFund Subsidy from MEXT (Ministry of Education CultureSports Science and Technology) (2012ndash2015)rdquo The authorsalso acknowledge Kurimoto Ltd for financial support
References
[1] T Sato Y Hirai T Fukui T Ejima M Takuma and K SaitohldquoAtomic-modeling and simulation of copper sulfide as microsolid lubricantrdquoMRS Proceedings vol 1513 p 20 2013
[2] H Sueyoshi Y Yamano K Inoue Y Maeda and K YamadaldquoMechanical properties of copper sulfide-dispersed lead-freebronzerdquoMaterials Transactions vol 50 no 4 pp 776ndash781 2009
[3] Y Hirai Y Ueda M Yamamoto T Kobayashi and TMaruyama Japanese Patent 132986 2009
[4] K Akamatsu T Kobayashi A Nishimoto T Maruyama andY Arachi ldquoDevelopment of new copper alloymdashinfluence ofmetallic elements on the human bodyrdquo Rikogaku to Gijyutsuvol 16 pp 31ndash36 2009 (Japanese)
[5] L-W Wang ldquoHigh chalcocite Cu2S a solid-liquid hybrid
phaserdquoPhysical Review Letters vol 108 no 8 Article ID 0857032012
[6] T Ejima K-I Saitoh N Shinke M Taruma Y Hirai and TSato ldquoAtomic-level analysis of copper sulfide (CU2S) crystalstructure and sliding characteristicsrdquo Technology Reports ofKansai University vol 54 pp 23ndash33 2012
[7] I I Mazin ldquoStructural and electronic properties of the two-dimensional superconductor CuS with 1(13)-valent copperrdquoPhysical Review B vol 85 Article ID 115133 2012
[8] M J Buerger and B J Wuensch ldquoDistribution of atoms in highchalcocite Cu
2Srdquo Science vol 141 no 3577 pp 276ndash277 1963
[9] B J Wuensch and M J Buerger ldquoThe crystal structure ofchalcocite Cu
2Srdquo Mineralogical Society of America Special
Paper vol 1 pp 163ndash170 1963 Proceedings of the 3rd GenralMeeting
[10] T Onodera Y Morlta A Suzuki et al ldquoA computationalchemistry study on friction of h-MoS2 Part I Mechanism ofsingle sheet lubricationrdquo The Journal of Physical Chemistry Bvol 113 no 52 pp 16526ndash16536 2009
[11] Y Ding D R Veblen and C T Prewitt ldquoPossible FeCu order-ing schemes in the 2a superstructure of bornite (Cu
5FeS4)rdquo
American Mineralogist vol 90 no 8-9 pp 1265ndash1269 2005
Journal of Materials 13
[12] H Zheng J B Rivest T A Miller et al ldquoObservation of tran-sient structural-transformation dynamics in a Cu
2S nanorodrdquo
Science vol 333 no 6039 pp 206ndash209 2011[13] S KashidaW ShimosakaMMori andDYoshimura ldquoValence
band photoemission study of the copper chalcogenide com-pounds Cu2S Cu2Se and Cu2Terdquo Journal of Physics andChemistry of Solids vol 64 no 12 pp 2357ndash2363 2003
[14] P Lukashev W R L Lambrecht T Kotani and M VanSchilfgaarde ldquoElectronic and crystal structure of Cu2-x S full-potential electronic structure calculationsrdquo Physical Review Bvol 76 no 19 Article ID 195202 2007
[15] P Blaha K Schwarz G Madsen D Kvasnicka and J LuitzldquoWIEN2krdquo httpwwwwien2katindexhtml
[16] P A Romero T T Jarvi N Beckmann M Mrovec andM Moseler ldquoCoarse graining and localized plasticity betweensliding nanocrystalline metalsrdquo Physical Review Letters vol 113no 3 Article ID 036101 2014
[17] S Izumi and S Sakai ldquoInternal displacement and elasticproperties of the silicon tersoff modelrdquo JSME InternationalJournal Series A Solid Mechanics and Material Engineering vol47 no 1 pp 54ndash61 2004
[18] M P Allen and D J Tildesley Computer Simulation of LiquidsOxford University Press Oxford UK 1989
[19] Sandia Nantional Laboratory ldquoLarge-scale AtomicMolecularMassively Parallel Simulatorrdquo httplammpssandiagov
[20] T Yamaguchi and K Saitoh ldquoMolecular dyanmics study onmechanical properties in the structure of self-assembled quan-tum dotrdquoWorld Journal of Nano Science and Engineering vol 2pp 189ndash195 2012
[21] T Ejima Atomic-level analysis on sliding characteristic of coppersulfide [MS thesis] Graduate School of Kansai University 2013
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Journal ofNanomaterials
Journal of Materials 3
Possibly ionic bond and metallic bond would be nonlinearlyinterrelated In considering the structure and bonding stateof solid crystal it is helpful to reproduce and observe thedetailed electron density distribution Besides those resultscan be taken into account in the construction of accurateinteratomic potential for MD simulations First-principle(FP) calculation (in Latin words ab initio calculation)refers to all quantum-mechanical computational chemistrymethods and is sometimes called ldquoband calculationrdquo Itobtains electron density around atomic nuclei based on theperiodic crystal structure of constituent atoms Nowadaysa number of software packages of FP method are availablein many researches Among those software packages ourchoice is WIEN2k package [15] which is based on densityfunctional theory (DFT) The characteristic of WIEN2k isthat it uses full-potential formulation instead of muffin-tinapproximation and that it uses the linearized augmentedplane wave basis set with local orbitals (LAPW + lo) As forcorrelation exchange term it can apply either local densityapproximation (LDA) or generalized gradient approximation(GGA)The detailed theory and usage are not the main focusof this study and should be omitted here
While all the S atoms in Cu2S are simply located at the
lattice point of HC it is suggested that Cu atoms seem tohave large mobility inside the unit cell especially in hightemperature keeping their symmetric atomic configurationSince actual position ofCu atoms inCu
2S is quite complicated
and is in fact giving controversy the present study employsexisting crystal model used in previous computation ofKashida et al [13] It is confirmed that the model agrees withexperimental fact as well as theoretical one Initial atomicposition of Cu
2S in HC is shown in Table 1 Figure 1 shows
initial position of atoms in Cu2S crystal unit
In order to obtain the minimum (ground-state) energythe atomic configuration is adjusted via the function ofoptimization in the software Lattice constants for angle(120572 120573 120574) are fixed so that the HC lattice should bemaintainedOn the other hand lattice constants for lengths (119886 119888) arechanged as follows Keeping a certain ratio of 119888119886 the lengths(119886 119888) are varied from compressive state to tensile one Thedeviation of 119888119886 from the initial value is +4sim+10 Thevolumetric change by the change of (119886 119888) ranges withinminus2sim+6 The exchange correlation energy of PBE-GGA isemployed Judgement of the energy convergence is done at00001 Ry where 1 Ry = 2180 times 10
minus18 J = 1360 eV Table 2summarizes calculation conditions and parameters used inthe present study The number of 119896-points is varied andapproximately above 20000 we may say that the total energywill be converged and shows sufficient accuracy Thereforewe recognize that 46 times 46 times 22 = 46552 119896-points arelarge enough and this will be used through the presentstudy
23 The Potential Function of Cu2S for MD As mentioned
above copper disulfide Cu2S has a variety of crystalline
structures depending on the temperature The structure isorthorhombic in standard temperature HC above 105∘C andcubic further above 460∘C Here as HC is assumed and
Table 1 Cu2S atomic coordinates and crystal data
(a)
Element Coordinate (relative to unit cell)119909 119910 119911
S 13 23 14Cu(1) 0 0 14Cu(2) 13 23 0578
(b)
Property Unit ValueLattice constant(1) 119886 nm 0389Lattice constant(2) 119888 nm 0688Lattice constant(3) 120572 deg 900Lattice constant(4) 120573 deg 900Lattice constant(5) 120574 deg 1200Atoms per unit cell mdash 3Space group mdash P6
3
120572 120573120574
c
a
Cu
Cu
CuCu
Cu
Cu
CuCu
CuCu
S
S
Figure 1 Crystal structure of Cu2S (hexagonal crystal unit 13 of
conventional hexagonal prism)
the composition ratio is Cu S = 2 1 one S atom shouldcorrespond to two Cu atoms Therefore those three atomscompose a structural unit and the three-body bond is formedas a function of their angle By the way MoS
2has HC
structure as well The structural feature common to thoseHC lattices is that their slip plane is only limited to thebasal plane (0001) This is completely different from fcc orbcc which is accompanying many slip systems In fact theslip of HC lattice takes place only when a certain conditionhas been fulfilled Thus the potential function which wasproposed for MoS
2[10] can be utilized as the reference to
construct the function needed in the present study for Cu2S
Though MoS2and Cu
2S have the contrary ratio as to S
atom a lot of common features are likely to be found inthese two crystals For example angular-dependent three-body interaction is crucial for stabilization of both crystalsTo begin with we apply the potential forms used in theMoS2study and then our results obtained by first-principle
calculation are properly fitted to a new potential functionfor Cu
2S We insist that since the fitting data is obtained
theoretically only by DFT calculations the new potentialfunction will be an unempirical (ab initio) one
4 Journal of Materials
Table 2 Calculation condition for structural optimization of Cu2S
crystal
Exchange correlation potential mdash PBE-GGAEnergy to separate core from valence states Rylowast minus60Energy convergence criteria Rylowast 00001
Change of 119888119886 ratioRate of change +4sim+10Increment of rate (for 119888119886) +2
Volume changeRate of change minus2sim+6Increment of rate (for 119888119886) +1lowastEnergy unit 1 Ry = 2180 times 10minus18 J = 1360 eV
The detail of the new potential function for Cu2S is as fol-
lows The potential function is a summation of three distinctpotential functions as shown in (1) Ionic and metallic bondsare represented by Born-Mayer-Huggins (BMH) potential120601BMH and Morse potential 120601Morse as expressed in (2) and(3) respectively Angular-dependent potential for the bond ofCu-S interaction 120601angle is represented as (4) which is three-body potential Parameters for those potential functions aresummarized in Table 3
120601 = 120601BMH + 120601Morse + 120601angle (1)
120601BMH =
1199111198941199111198951198902
119903
+ 1198910(119887119894+ 119887119895) exp(
119886119894+ 119886119895minus 119903
119887119894+ 119887119895
) +
119888119894119888119895
1199036 (2)
120601Morse = 119863119894119895[exp minus2120573
119894119895(119903119894119895minus 1199030)
minus 2 exp minus120573119894119895(119903119894119895minus 1199030)]
(3)
120601angle = 119867120579(120579 minus 120579
0)2
(4)
In those equations 119911119894or 119911119895is electronic charge of each atom
and the values 119911S = minus20 and 119911Cu = +10 are employed for Sand Cu atoms respectively 119891
0= 1 [kcalA] = 4186 [kJA] is
the parameter which determines the stiffness of each ionicsphere and is transferred from the study of MoS
2 In the
Morse potential the equilibrium distance 1199030and bond energy
119863119894119895are fitted to those in the optimized structure which is
obtained in our ab initio calculation In the angular potentialequilibrium three-body angle 120579
0is also determined by our
ab initio calculation But it is difficult to derive the springconstant 119867
120579just from our ab initio calculation so the same
value as in MoS2is applied here Of course the value of 119867
120579
influences rigidity But its function form is basically harmonicand we found that the effect of spring constant on sliding isnot so crucial
24 Molecular Dynamics Model for Cu2S Sliding Figure 2
shows theMDmodel for sliding simulation In the first placethe optimized atomic configuration obtained by ab initiocalculation is prepared and then is thermally equilibratedat a finite temperature Then the structure is compressed
Table 3 Interatomic potential parameters for Cu2S crystal
(a) B-M-H potential
Atoms 119886119894
119887119894
119888119894
Unit [A] [A] [kJ05sdotA3mol05]Cu 0696 0085 0000S 1831 0085 70000
(b) Morse potential
Application 119863119894119895
120573119894119895
1199030
Unit [kJmol] [1A] [A]Cu-S 152076 1800 2532
(c) Angular potential
Application 119867120579
1205790
Unit [kJmol] [deg]Cu-S-Cu 196648 98943S-Cu-S 196648 98943
in 119911 direction as shown in Figure 2 After that the atomicvelocity in the 119909 direction of two special regions (shownwith yellow color in the figure) is constrained so that sheardeformation is applied to the whole region in the directionparallel to the slip plane These processes are supposedto mimic a Cu
2S crystal in sliding condition This kind
of dynamic sliding simulation has been often studied fortribology-system as found in literatures so far [16] and itsadvantage is that we can observe directly the sliding behaviorof atomic system
It is supposed that crystalline slip plane of Cu2S plays
an important role in the slip deformation As stated aboveCu2S crystal unit has the HC conformation and the pri-
mary slip plane should be (0001) in Millerrsquos indices Theprimary slip direction should be the shortest interatomicdistance existing on the (0001) plane that is ⟨21 10⟩ Wewill call it (b)-direction hereafter The second easiest slipdirection should be ⟨0110⟩ which we call (a)-direction here-after In the present study we configure these two possibleslip directions for sliding simulation and compare theseresults
Other factors affecting sliding behavior of Cu2S would be
velocity and temperature Sliding velocities are varied so thatcorresponding shear velocities are 01 10 and 50ms Thereader should feel that these velocities seem quite higher thanused in actual slidingmachine or equipment However in theMD simulation time increment has to be very short such as1 fs (femtosecond) or less so such large deformation rate isinevitable
25 Analyzing MD Results In the present study the MDresults are mainly analyzed by radial distribution function(RDF) and atomic shear stress Strict formalization of stresstensor with regard to three-body term would require furtherdiscussion at this stage [17] so we use here an approximateand practial treatment These analyzing methods for MDresults are explained below
Journal of Materials 5
A model sliding in (b)-direction
z
yAtoms
A model sliding in (a)-direction
z
x
Cu
S
Fixed
Parallel to basal plane
Basal plane(0001)
(a)-direction
(b)-direction(slip direction of hexagonal crystal)
The model for researching dependence on direction or velocity
⟨0110⟩
110⟩⟨2
Figure 2 Abstract of MD sliding model of Cu2S crystal
251 Crystal Structure Analysis by Radial Distribution Func-tion (RDF) Usually solid crystal has a three-dimensionalorderThe Cu
2S crystal used in the present study exhibits HC
structure One of themethods to identify the crystalline orderis radial distribution function (RDF) 119892(119903) [18] Briefly speak-ing the function 119892(119903) gives the number density of neighboratoms which are found in a certain distance from each atomIts distribution shows some peaks at some specific distancesinherent to the crystalline orderWhen the temperature arisesor when the crystalline order is partially lost due to outbreakof lattice defects the peak value of RDF generally reduces andthe shape at the peak becomes broadenedThus by observingthe change of the peak position and the shape of the curve ofRDF the deterioration of the crystalline order can be detectedand occurrence of lattice defects can be guessed
252 Atomic Stress Analysis (Approximate Treatment includ-ing Three-Body Terms) Since our MD model is in solidstate the behavior of sliding and friction is reflected by ashear stress averaged over the specimen Therefore atomic-scale stress is being analysed But we note that stress (orstrain) is basically the concept in continuum mechanicsand is not essential for any atomic system The facts thatatomic positions are discrete and that interatomic potentialhas nonlocal nature will conflict with the local theory of
continuum Accordingly we need to formulate atomic stresstogether with some approximation
Suppose that total potential energy inside the systemcomprises all the superposition of pairwise interactions 120601(119903)When any selected atom 119894 conducts homogeneous deforma-tion with regard to the relative position to another neighboratom 119895 strain at the interatomic space between 119894 and 119895 can bepresented by their interatomic distance 119903(119894 119895) and interatomicvector r(119894 119895) (this assumes that there is no slip no phasetransition nor long atomic diffusion over the lattice) Thenatomic stress tensor occurring at the atom 119894 is expressed as
120590 (119894) =
1
2Ω (119894)
sum
119895
120597120601 (119894 119895)
120597119903 (119894 119895)
r (119894 119895) otimes r (119894 119895)119903 (119894 119895)
(5)
where the summation is composed of the work done byatomic motion which is called ldquovirialrdquo Ω(119894) in the denom-inator is the volume supposedly occupied by the atom 119894so (5) is regarded as the energy density around that atomIn the present study Ω(119894) is assumed to be a constantwhich has been estimated in the reference structure (whichhas been estimated in the undeformed lattice) Additionallyvector product (r otimes r) means the dyadic between interatomicvectors so (5) has the form of the second-order (symmetric)tensor and its components are six Thus if an interatomicpotential of MD contains just pairwise term the virial can be
6 Journal of Materials
straightforwardly converted to atomic stress But if it includesthree-body terms depending on the angle as in the presentinteratomic potential they can never strictly be decomposedinto virials of each pair of atoms However we can apply anapproximate formulation to a triplet 119894 119895 and 119896 (119894 119895 119896) Inpractice the combination of virials of each pair (119894 119895) (119895 119896)and (119896 119894) is used as the net virial of the triplet As a result theformulation of atomic stress comes to the expression
120590120572120573
(119894) =
1
2Ω (119894)
sum
119895
120597120601pair (119894 119895)
120597119903 (119894 119895)
119903120572(119894 119895) 119903
120573(119894 119895)
119903 (119894 119895)
+
1
3Ω (119894)
sum
119895119896
(
120597120601angle (119894 119895)
120597119903 (119894 119895)
119903120572(119894 119895) 119903
120573(119894 119895)
119903 (119894 119895)
+
120597120601angle (119895 119896)
120597119903 (119895 119896)
119903120572(119895 119896) 119903
120573(119895 119896)
119903 (119895 119896)
+
120597120601angle (119896 119894)
120597119903 (119896 119894)
119903120572(119896 119894) 119903
120573(119896 119894)
119903 (119896 119894)
)
(6)
where the first term corresponds to pair interaction 120601pair(119903)and the second term is for three-body interaction Inthis expression Ω(119894) 120601pair(119894 119895) 120601angle(119894 119895) 119903(119894 119895) and119903120572(119894 119895) (120572 120573 = 1 2 3) are atomic volume pairwise potential
function three-body potential function interatomic distance(between 119894 and 119895) and its vector components In comparingall the components in (6) during actual MD simulation it isunderstood that three-body term is relatively large so that itis not negligible This expression of atomic stress includingthree-body term is also utilized in widely used MD software(eg LAMMPS) [19] Besides this estimation of atomicstress was found appropriate when we applied it to anotherMD study using the three-body-type Tersoff potential (forSi-Ge system) [20]
3 Results and Discussion
31 Optimization of Lattice Constant of Cu2S Crystal by
First-Principle Calculation The relation between volume andenergy of Cu
2S crystal unit is obtained as in Figure 3 by first-
principle (FP) calculation including structural optimizationFor the variety of the lattice constant ratio 119888119886 the lowestenergy is obtained at the deviation Δ119888119886 = 8 Moreoverunder that condition volume expansion at +3 shows thesmallest energy From this optimized structure thereforelattice constants of the HC structure are 119886 = 0383 nm and119888 = 0731 nm for which 119888119886 is 191 The length for 119888 andthe ratio 119888119886 seem relatively larger than the HC structure ofusual metals It means that layers of sulfur (S) and copper(Cu) atoms are remarkably separated from each other in theCu2S crystal In the present paper these optimized lattice
constants are used as values to configure atomic positions inthe specimen of Cu
2S crystal
32 Construction of Interatomic Potential Function for MDCalculations It is experimentally and theoretically under-stood that interaction between Cu and S atoms is generally
Minimum
Change of volume ()
Difference from initial structure
+10+8
+6+4
Ener
gy d
iffer
ence
(eV
)
6543210minus1minus2minus001
009
01
008
007
006
005
004
003
002
001
0
Figure 3 Volume-energy relation of Cu2S crystal structure
Distance r (nm)090807060504030201
minus8
minus6
minus4
minus2
0
2
4
6
8
Mo-S bondCu-S bond
FP calculation
times10minus19En
ergy
EminusE0
(J)
Figure 4 Distance-energy relation of Cu-S interaction obtained byFP calculation (Mo-S interaction is also shown for comparison)
strong So the Cu-S interaction can be expressed by Morsepotential function as shown by (3) The optimized configu-ration of Cu-S dimer is obtained by the FP calculation by us[21] From this we determine both the equilibrium distanceparameters 119903
0 120573119894119895and the energy parameter 119863
119894119895needed
in Morse potential Figure 4 shows the relation betweeninteratomic distance and its energy which is obtained by theFP calculation The obtained parameters for Morse potentialis shown in Table 4
The optimized crystalline structure of Cu2S which has
been obtained in the previous section can be used to adjust anangular-dependent three-body potential parameters shownin (4) In this process of fitting we assume that Cu atomsare located at the averaged position between tetragonal and
Journal of Materials 7
21564Aring
26712Aring
23926Aring
35219Aring
Cu
S
S
S S S S S
Cu
SS S
124125 deg
91599deg106333deg
65876deg
Figure 5 Schematic of the way to average two types of coordination for Cu atoms in Cu2S crystal
Table 4 Potential parameters fitted by FP calculations
(a) Morse potential (Cu-S)
Kind of pair 119863119894119895
120573119894119895
1199030
Unit kJmole 1nm nmCu-S 298916 1500 2029(Mo-S) (152076) (1800) (2532)
(b) Angular potential (S-Cu-S Cu-S-Cu)
Combination 1205790
Unit degS-Cu-S 98966Cu-S-Cu 98966
(c) B-M-H ionic potential (Cu-S)
Kind of pair 1199031015840
0119886Cu 119886S
Unit nm nm nm25319 070052 18314lowast
119886Slowast has been already obtained for MoS2 potential [10]
octahedral sites as shown in Figure 5 since there is possibilitythat Cu atoms may be located on both sites In practicewe just need equilibrium three-body angle 120579
0and pairwise
distance 1199031015840
0 Finally they are 120579
0= 98966
∘ and 1199031015840
0= 2532 nm
respectivelyAdditionally the BMH term requires ionic radii 119886Cu and
119886S for each element The radius of Cu atom is supposed tobe equivalent to the equilibrium length 119903
0in Morse potential
above the radius 119886S = 1834 nm for S is already available fromthe previous MD study of MoS
2[10]
Thus MD potential parameters to reproduce the HCstructure of Cu
2S are obtained by mostly FP calculation and
they are summarized in Table 4
33 Sliding and Friction Behavior of Cu2S
331 Dependency on Crystalline Orientation The depen-dence on crystalline orientation in sliding behavior of Cu
2S
is as follows Figure 6 shows the atomic configurations at119905 = 600 ps with sliding velocity V = 05ms comparingbetween models which are sliding in (a)-direction (⟨0110⟩)sliding and in (b)-direction (⟨21 10⟩) Both models oncecollapse and lose their crystalline stacking during sliding Butafter that the atomic structure recovers its original stackingduring long-time slidingThe difference between twomodelsis not found just visually from atomic configurations asseen in the broken black- and yellow-colored rectangularareas depicted in the figures Therefore the RDF analysiswill be helpful for identifying the change of crystallinestructures Besides in order to recognize transition of anatomic force during sliding the analysis of shear stress willbe helpful
The result of RDF analysis is shown in Figure 7 which isfor sliding velocity V = 05ms and compares results between(a)-direction and (b)-direction models In these RDF figurespeaks are found at some distances by which the nature ofcrystalline structure is confirmed In particular whenwe takea look at peaks found in the range of 02sim08 nm for twomodels the steepness of the distribution in (b)-direction istotally stronger than that in (a)-direction So the structureobtained by the sliding in (b)-direction tends to retain morelocal crystalline structure than that obtained in (a)-directionsliding
Just when the resulting sliding distance becomes 10 nmis the RDF obtained as shown in Figure 8 for different slidingvelocities (V = 10 and 50ms) At the same sliding distancethe crystalline stacking is the same and so the results maybe compared as for different velocity conditions One peakof RDF is just identified for the 1st neighbor distance whichmeans the crystalline structure has been lost and the atomicmovement shows somewhat of fluidity
Shear stress averaged over the whole specimen 120591totrepresents the resistance to the slidingThe time transition of120591tot reflects atomic force state in the sliding During relaxationprocess in fact a certain value of shear stress already occursThis is due to atomic rearrangement inside the crystal unitAfter the specimen is fully relaxed we reset the stress valueLet the value at the beginning of sliding be 120591tot(0) Then the
8 Journal of Materials
Disordered
Ordered layer
CuCu
CuCu
SS
S
To front
To back
To right
To left
Disordered
Ordered layer
CuCuCu
S
S
S Cu
(A) (a)-direction (⟨0110⟩) sliding (the sliding direction is normal to the figure plane)
(B) (b)-direction ( 110⟩) sliding (the sliding direction is right and left)⟨2
Figure 6 Comparison of instantaneous atomic configurations obtained at 119905 = 600 ps with V = 05ms (the picture is drawn onto 119910-119911 plane)
absolute value of deviation of current value 120591tot from initialvalue 120591tot(0) is defined to be
120591119886=
1003816100381610038161003816120591tot minus 120591tot (0)
1003816100381610038161003816 (7)
This stress deviation 120591119886reflects a sudden increase of friction
due to roughness of slide planes The time transition of 120591119886
is obtained as shown in Figure 9 Figure 9(A) shows therelation between the time and the stress deviation 120591
119886 120591119886is
averaged over the whole specimen Those graphs show that120591119886for (a)-direction sliding is larger than that in (b)-direction
The downward arrows in the figure display each maximumvalue At low velocity atoms near contact layers feel relativelylarger resistance to slide in (a)-direction sliding while the
(b)-direction sliding seems much easier However for thecases with higher velocity such as V = 10ms or 50ms thetendency of stress 120591
119886is changed as shown in Figures 9(B)
and 9(C) As shown in Figure 9(B) for example for V =10ms the peak value in (b)-direction is sometimes largerthan that in (a)-direction especially during 50ndash100 ps or 250ndash300 ps
We summarize the dependency of sliding direction asfollows When the shear velocity is small (b)-direction(⟨0110⟩) sliding is easier than (a)-direction (⟨0110⟩) How-ever once the sliding has completed such as to 100 or200 ps from the start of sliding distinction between slidingdirections becomes negligible The cause of this behaviorwould be guessed and explained as follows When the sliding
Journal of Materials 9
(a)
(a)-direction(b)-direction
(a)
(b)16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)
(a)-direction(b)-direction
(b)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)(b)
(a)-direction(b)-direction
(b)
(b)
(a)
(a)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)-direction(b)-direction
(b)
(b)
(a)
(a)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(A) Shear length = 02nm (B) 04nm
(C) 06nm (D) 08nm
Figure 7 Time transition of RDF for V = 05ms (comparison between (a)- and (b)-direction sliding)
is carried out sufficiently the crystalline structure of Cu2S
has collapsed and the crystalline slip system (plane anddirection) no longer determines the sliding behavior Evenif there exists a certain easy-glide plane or direction thecrystal does not always show especially smaller shear stressin sliding
332 Dependency on Sliding Velocity Figure 10(A) shows therelation between shear distance and shear stress deviation 120591
119886
It compares results for a variety of velocities ranging from 05to 50ms For all velocities and for the sliding distance up to02 nm 120591
119886linearly increases with the same gradientThis fact
means that the material deforms in elastic manner for smallsliding and deformation However after that 120591
119886decreases
suddenly The larger the sliding velocity is the larger theaveraged value of 120591
119886is obtained It is reasonable that time rate
of decrease is smaller for higher speed sliding As the wholetime calculated here is seen the case of V= 50ms exhibits the
largest level of 120591119886 For (b)-direction Figure 10(B) shows that
the value of 120591119886increases with increase of sliding velocity It
is concluded that shear stress of this material depends largelyon sliding velocity
The relation between 120591119886and sliding velocity V is sum-
marized in Table 5 120591ave time average of 120591119886 is also shown
at the bottom line It indicates that 120591ave of (a)-directionis approximately 10 smaller than that of (b)-directionWhile the easiest glide directionplane of the HC struc-ture is ⟨0110⟩(0001) (ie (b)-direction) it does not showsmall resistance in the sliding Thus it is concluded thatCu2S crystal does surely show sliding motion but it is
not by usual crystalline slip (glide) mechanism of ordinarymetals
On the other hand the fact that shear stress increaseswith increase of velocity is interesting It means that thismaterial deforms by slidingwith somewhat liquid-like (amor-phous) behavior The deformation rate (ie velocity) in such
10 Journal of Materials
(a)
(a)
(b)
(b)
r (nm)04504035030250201501
14
12
1
08
06
04
02
0
g(r)
(a)-direction(b)-direction
(a) (b)
r (nm)04504035030250201501
12
1
08
06
04
0
02
g(r)
(a)-direction(b)-direction
(a) (b)
r (nm)04504035030250201501
14
12
1
08
06
04
02
0
g(r)
(a)-direction(b)-direction
(a) (b)
(a) (b)
(B) = 10ms
(C) = 50ms
(A) Velocity = 05ms
Figure 8 The comparison of RDF at the same sliding distance (10 nm) between (a)- and (b)-direction sliding
Table 5 Relation between averaged shear stress 120591ave and slidingvelocity V
Sliding velocityVms
Averaged shear stress 120591ave GPa(A) (a)-direction sliding (B) (b)-direction sliding
05 193 22810 214 25450 264 283Average 224 255
amorphous substance produces shear stress inside due toits viscosity and so the shear stress depends on sliding(shear) velocity gradient As shown in Figure 11 averagedshear stresses 120591ave summarized in Table 5 are replotted interms of sliding velocity As recognized in Figure 11 shearstress is almost proportional to the sliding velocity In the
present simulation condition system temperature is kept at10 kelvins which is quite low But the atomic mobility atcontact layers between materials should rise due to the workdone by sliding motion In observing atomic motion theyshow intermittent slip which is sometimes called ldquostick andslipmotionrdquo in nanotribological consideration Furthermorewhen in Figure 11 we extrapolate approximated straight linesdown to V = 0 shear stress 120591ave does not return to zero butit remains at a finite value 120591
0= 20sim25GPa These ideal shear
stresses at V = 0 correspond to static friction of materials Italso means that 120591
0are at least required for layered atoms to
exhibit a material flow
4 Conclusion
In this paper we perform a molecular dynamics (MD)study on copper sulfide material (Cu
2S) under the sliding
Journal of Materials 11
0
20
40
60
80
0 200 400 600 800 1000
Shea
r stre
ss (G
Pa)
Time (ps)
(b)
(a)
= 05ms (a)-dir = 05ms (b)-dir
minus20
0
20
40
60
80
0 100 200 300 400 500 600
Shea
r stre
ss (G
Pa)
Time (ps)
(a)(b)
minus20
= 10ms (a)-dir = 10ms (b)-dir
(a)
(b)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
minus20
Time (ps)
= 50ms (a)-dir = 50ms (b)-dir
200150100500
(A) = 05ms (B) = 10ms
(C) = 50ms
Figure 9 Comparison of the absolute value of shear stress deviation 120591119886between (a)- and (b)-direction
motion The MD simulation includes a new implementationof potential energy function for Cu
2S crystal where some
first-principle calculations are utilized The potential energyfunction has three-body term The following results areobtained and we will make conclusion
(1) First-principle calculations are performed for thehexagonal unit structure of Cu
2S crystal From the
optimized structure original lattice parameters 119886
and 119888 of unit cell and stable configuration of S andCu atoms are obtained Based on those results aninteratomic potential function including ionic andMorse terms as well as angular-dependent term isconstructed for Cu and S system It is confirmedthat this potential function can show enough stability
for the hexagonal crystal structure of Cu2S in MD
simulations(2) An easy-glide direction ⟨21 10⟩ on (0001) plane gen-
erally found for usual hexagonal crystals is not thedirection with small resistance to sliding
(3) Cu2S crystal shows partially liquid-like structure and
behavior in which the shear stress occurring in thematerial depends on the sliding velocity
In the further study we should clarify the tempera-ture dependence and dependency on compressive conditionduring sliding of Cu
2S It is supposed that they are made
possible by analyzing more atomic trajectories obtained byMD simulations It will lead to total understanding of slidingmechanism of Cu
2S crystal
12 Journal of Materials
0
20
40
60
80
0 01 02 03 04 05
Shea
r stre
ss (G
Pa)
Shear distance (nm)
Slow decrease
Fast decrease
minus20
= 50ms (a)-dir = 10ms (a)-dir
= 05ms (a)-dir
0 01 02 03 04 05Shear distance (nm)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
Stress increase by velocity
minus20
= 50ms (b)-dir = 10ms (b)-dir
= 05ms (b)-dir
(A) (a)-direction ( ) sliding (B) (b)-direction ( ) sliding110⟩⟨2 ⟨0110⟩
Figure 10 Relation between shear distance and the deviation of shear stress 120591119886 comparison among different sliding velocities
0
5
10
15
20
25
30
0 1 2 3 4 5
(a)-direction(b)-direction
Linear fit ((a)-dir)Linear fit ((b)-dir)
(ms)
120591 a(G
Pa)
Figure 11 Averaged shear stress replotted against sliding velocity((a)- and (b)-directions (⟨21 10⟩ and ⟨0110⟩))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This study is partly supported by NEDO Innovative Project(2012-2013) and by the ldquoStrategic Project to Support the For-mation of Research Bases at Private Universities MatchingFund Subsidy from MEXT (Ministry of Education CultureSports Science and Technology) (2012ndash2015)rdquo The authorsalso acknowledge Kurimoto Ltd for financial support
References
[1] T Sato Y Hirai T Fukui T Ejima M Takuma and K SaitohldquoAtomic-modeling and simulation of copper sulfide as microsolid lubricantrdquoMRS Proceedings vol 1513 p 20 2013
[2] H Sueyoshi Y Yamano K Inoue Y Maeda and K YamadaldquoMechanical properties of copper sulfide-dispersed lead-freebronzerdquoMaterials Transactions vol 50 no 4 pp 776ndash781 2009
[3] Y Hirai Y Ueda M Yamamoto T Kobayashi and TMaruyama Japanese Patent 132986 2009
[4] K Akamatsu T Kobayashi A Nishimoto T Maruyama andY Arachi ldquoDevelopment of new copper alloymdashinfluence ofmetallic elements on the human bodyrdquo Rikogaku to Gijyutsuvol 16 pp 31ndash36 2009 (Japanese)
[5] L-W Wang ldquoHigh chalcocite Cu2S a solid-liquid hybrid
phaserdquoPhysical Review Letters vol 108 no 8 Article ID 0857032012
[6] T Ejima K-I Saitoh N Shinke M Taruma Y Hirai and TSato ldquoAtomic-level analysis of copper sulfide (CU2S) crystalstructure and sliding characteristicsrdquo Technology Reports ofKansai University vol 54 pp 23ndash33 2012
[7] I I Mazin ldquoStructural and electronic properties of the two-dimensional superconductor CuS with 1(13)-valent copperrdquoPhysical Review B vol 85 Article ID 115133 2012
[8] M J Buerger and B J Wuensch ldquoDistribution of atoms in highchalcocite Cu
2Srdquo Science vol 141 no 3577 pp 276ndash277 1963
[9] B J Wuensch and M J Buerger ldquoThe crystal structure ofchalcocite Cu
2Srdquo Mineralogical Society of America Special
Paper vol 1 pp 163ndash170 1963 Proceedings of the 3rd GenralMeeting
[10] T Onodera Y Morlta A Suzuki et al ldquoA computationalchemistry study on friction of h-MoS2 Part I Mechanism ofsingle sheet lubricationrdquo The Journal of Physical Chemistry Bvol 113 no 52 pp 16526ndash16536 2009
[11] Y Ding D R Veblen and C T Prewitt ldquoPossible FeCu order-ing schemes in the 2a superstructure of bornite (Cu
5FeS4)rdquo
American Mineralogist vol 90 no 8-9 pp 1265ndash1269 2005
Journal of Materials 13
[12] H Zheng J B Rivest T A Miller et al ldquoObservation of tran-sient structural-transformation dynamics in a Cu
2S nanorodrdquo
Science vol 333 no 6039 pp 206ndash209 2011[13] S KashidaW ShimosakaMMori andDYoshimura ldquoValence
band photoemission study of the copper chalcogenide com-pounds Cu2S Cu2Se and Cu2Terdquo Journal of Physics andChemistry of Solids vol 64 no 12 pp 2357ndash2363 2003
[14] P Lukashev W R L Lambrecht T Kotani and M VanSchilfgaarde ldquoElectronic and crystal structure of Cu2-x S full-potential electronic structure calculationsrdquo Physical Review Bvol 76 no 19 Article ID 195202 2007
[15] P Blaha K Schwarz G Madsen D Kvasnicka and J LuitzldquoWIEN2krdquo httpwwwwien2katindexhtml
[16] P A Romero T T Jarvi N Beckmann M Mrovec andM Moseler ldquoCoarse graining and localized plasticity betweensliding nanocrystalline metalsrdquo Physical Review Letters vol 113no 3 Article ID 036101 2014
[17] S Izumi and S Sakai ldquoInternal displacement and elasticproperties of the silicon tersoff modelrdquo JSME InternationalJournal Series A Solid Mechanics and Material Engineering vol47 no 1 pp 54ndash61 2004
[18] M P Allen and D J Tildesley Computer Simulation of LiquidsOxford University Press Oxford UK 1989
[19] Sandia Nantional Laboratory ldquoLarge-scale AtomicMolecularMassively Parallel Simulatorrdquo httplammpssandiagov
[20] T Yamaguchi and K Saitoh ldquoMolecular dyanmics study onmechanical properties in the structure of self-assembled quan-tum dotrdquoWorld Journal of Nano Science and Engineering vol 2pp 189ndash195 2012
[21] T Ejima Atomic-level analysis on sliding characteristic of coppersulfide [MS thesis] Graduate School of Kansai University 2013
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
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CeramicsJournal of
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CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
4 Journal of Materials
Table 2 Calculation condition for structural optimization of Cu2S
crystal
Exchange correlation potential mdash PBE-GGAEnergy to separate core from valence states Rylowast minus60Energy convergence criteria Rylowast 00001
Change of 119888119886 ratioRate of change +4sim+10Increment of rate (for 119888119886) +2
Volume changeRate of change minus2sim+6Increment of rate (for 119888119886) +1lowastEnergy unit 1 Ry = 2180 times 10minus18 J = 1360 eV
The detail of the new potential function for Cu2S is as fol-
lows The potential function is a summation of three distinctpotential functions as shown in (1) Ionic and metallic bondsare represented by Born-Mayer-Huggins (BMH) potential120601BMH and Morse potential 120601Morse as expressed in (2) and(3) respectively Angular-dependent potential for the bond ofCu-S interaction 120601angle is represented as (4) which is three-body potential Parameters for those potential functions aresummarized in Table 3
120601 = 120601BMH + 120601Morse + 120601angle (1)
120601BMH =
1199111198941199111198951198902
119903
+ 1198910(119887119894+ 119887119895) exp(
119886119894+ 119886119895minus 119903
119887119894+ 119887119895
) +
119888119894119888119895
1199036 (2)
120601Morse = 119863119894119895[exp minus2120573
119894119895(119903119894119895minus 1199030)
minus 2 exp minus120573119894119895(119903119894119895minus 1199030)]
(3)
120601angle = 119867120579(120579 minus 120579
0)2
(4)
In those equations 119911119894or 119911119895is electronic charge of each atom
and the values 119911S = minus20 and 119911Cu = +10 are employed for Sand Cu atoms respectively 119891
0= 1 [kcalA] = 4186 [kJA] is
the parameter which determines the stiffness of each ionicsphere and is transferred from the study of MoS
2 In the
Morse potential the equilibrium distance 1199030and bond energy
119863119894119895are fitted to those in the optimized structure which is
obtained in our ab initio calculation In the angular potentialequilibrium three-body angle 120579
0is also determined by our
ab initio calculation But it is difficult to derive the springconstant 119867
120579just from our ab initio calculation so the same
value as in MoS2is applied here Of course the value of 119867
120579
influences rigidity But its function form is basically harmonicand we found that the effect of spring constant on sliding isnot so crucial
24 Molecular Dynamics Model for Cu2S Sliding Figure 2
shows theMDmodel for sliding simulation In the first placethe optimized atomic configuration obtained by ab initiocalculation is prepared and then is thermally equilibratedat a finite temperature Then the structure is compressed
Table 3 Interatomic potential parameters for Cu2S crystal
(a) B-M-H potential
Atoms 119886119894
119887119894
119888119894
Unit [A] [A] [kJ05sdotA3mol05]Cu 0696 0085 0000S 1831 0085 70000
(b) Morse potential
Application 119863119894119895
120573119894119895
1199030
Unit [kJmol] [1A] [A]Cu-S 152076 1800 2532
(c) Angular potential
Application 119867120579
1205790
Unit [kJmol] [deg]Cu-S-Cu 196648 98943S-Cu-S 196648 98943
in 119911 direction as shown in Figure 2 After that the atomicvelocity in the 119909 direction of two special regions (shownwith yellow color in the figure) is constrained so that sheardeformation is applied to the whole region in the directionparallel to the slip plane These processes are supposedto mimic a Cu
2S crystal in sliding condition This kind
of dynamic sliding simulation has been often studied fortribology-system as found in literatures so far [16] and itsadvantage is that we can observe directly the sliding behaviorof atomic system
It is supposed that crystalline slip plane of Cu2S plays
an important role in the slip deformation As stated aboveCu2S crystal unit has the HC conformation and the pri-
mary slip plane should be (0001) in Millerrsquos indices Theprimary slip direction should be the shortest interatomicdistance existing on the (0001) plane that is ⟨21 10⟩ Wewill call it (b)-direction hereafter The second easiest slipdirection should be ⟨0110⟩ which we call (a)-direction here-after In the present study we configure these two possibleslip directions for sliding simulation and compare theseresults
Other factors affecting sliding behavior of Cu2S would be
velocity and temperature Sliding velocities are varied so thatcorresponding shear velocities are 01 10 and 50ms Thereader should feel that these velocities seem quite higher thanused in actual slidingmachine or equipment However in theMD simulation time increment has to be very short such as1 fs (femtosecond) or less so such large deformation rate isinevitable
25 Analyzing MD Results In the present study the MDresults are mainly analyzed by radial distribution function(RDF) and atomic shear stress Strict formalization of stresstensor with regard to three-body term would require furtherdiscussion at this stage [17] so we use here an approximateand practial treatment These analyzing methods for MDresults are explained below
Journal of Materials 5
A model sliding in (b)-direction
z
yAtoms
A model sliding in (a)-direction
z
x
Cu
S
Fixed
Parallel to basal plane
Basal plane(0001)
(a)-direction
(b)-direction(slip direction of hexagonal crystal)
The model for researching dependence on direction or velocity
⟨0110⟩
110⟩⟨2
Figure 2 Abstract of MD sliding model of Cu2S crystal
251 Crystal Structure Analysis by Radial Distribution Func-tion (RDF) Usually solid crystal has a three-dimensionalorderThe Cu
2S crystal used in the present study exhibits HC
structure One of themethods to identify the crystalline orderis radial distribution function (RDF) 119892(119903) [18] Briefly speak-ing the function 119892(119903) gives the number density of neighboratoms which are found in a certain distance from each atomIts distribution shows some peaks at some specific distancesinherent to the crystalline orderWhen the temperature arisesor when the crystalline order is partially lost due to outbreakof lattice defects the peak value of RDF generally reduces andthe shape at the peak becomes broadenedThus by observingthe change of the peak position and the shape of the curve ofRDF the deterioration of the crystalline order can be detectedand occurrence of lattice defects can be guessed
252 Atomic Stress Analysis (Approximate Treatment includ-ing Three-Body Terms) Since our MD model is in solidstate the behavior of sliding and friction is reflected by ashear stress averaged over the specimen Therefore atomic-scale stress is being analysed But we note that stress (orstrain) is basically the concept in continuum mechanicsand is not essential for any atomic system The facts thatatomic positions are discrete and that interatomic potentialhas nonlocal nature will conflict with the local theory of
continuum Accordingly we need to formulate atomic stresstogether with some approximation
Suppose that total potential energy inside the systemcomprises all the superposition of pairwise interactions 120601(119903)When any selected atom 119894 conducts homogeneous deforma-tion with regard to the relative position to another neighboratom 119895 strain at the interatomic space between 119894 and 119895 can bepresented by their interatomic distance 119903(119894 119895) and interatomicvector r(119894 119895) (this assumes that there is no slip no phasetransition nor long atomic diffusion over the lattice) Thenatomic stress tensor occurring at the atom 119894 is expressed as
120590 (119894) =
1
2Ω (119894)
sum
119895
120597120601 (119894 119895)
120597119903 (119894 119895)
r (119894 119895) otimes r (119894 119895)119903 (119894 119895)
(5)
where the summation is composed of the work done byatomic motion which is called ldquovirialrdquo Ω(119894) in the denom-inator is the volume supposedly occupied by the atom 119894so (5) is regarded as the energy density around that atomIn the present study Ω(119894) is assumed to be a constantwhich has been estimated in the reference structure (whichhas been estimated in the undeformed lattice) Additionallyvector product (r otimes r) means the dyadic between interatomicvectors so (5) has the form of the second-order (symmetric)tensor and its components are six Thus if an interatomicpotential of MD contains just pairwise term the virial can be
6 Journal of Materials
straightforwardly converted to atomic stress But if it includesthree-body terms depending on the angle as in the presentinteratomic potential they can never strictly be decomposedinto virials of each pair of atoms However we can apply anapproximate formulation to a triplet 119894 119895 and 119896 (119894 119895 119896) Inpractice the combination of virials of each pair (119894 119895) (119895 119896)and (119896 119894) is used as the net virial of the triplet As a result theformulation of atomic stress comes to the expression
120590120572120573
(119894) =
1
2Ω (119894)
sum
119895
120597120601pair (119894 119895)
120597119903 (119894 119895)
119903120572(119894 119895) 119903
120573(119894 119895)
119903 (119894 119895)
+
1
3Ω (119894)
sum
119895119896
(
120597120601angle (119894 119895)
120597119903 (119894 119895)
119903120572(119894 119895) 119903
120573(119894 119895)
119903 (119894 119895)
+
120597120601angle (119895 119896)
120597119903 (119895 119896)
119903120572(119895 119896) 119903
120573(119895 119896)
119903 (119895 119896)
+
120597120601angle (119896 119894)
120597119903 (119896 119894)
119903120572(119896 119894) 119903
120573(119896 119894)
119903 (119896 119894)
)
(6)
where the first term corresponds to pair interaction 120601pair(119903)and the second term is for three-body interaction Inthis expression Ω(119894) 120601pair(119894 119895) 120601angle(119894 119895) 119903(119894 119895) and119903120572(119894 119895) (120572 120573 = 1 2 3) are atomic volume pairwise potential
function three-body potential function interatomic distance(between 119894 and 119895) and its vector components In comparingall the components in (6) during actual MD simulation it isunderstood that three-body term is relatively large so that itis not negligible This expression of atomic stress includingthree-body term is also utilized in widely used MD software(eg LAMMPS) [19] Besides this estimation of atomicstress was found appropriate when we applied it to anotherMD study using the three-body-type Tersoff potential (forSi-Ge system) [20]
3 Results and Discussion
31 Optimization of Lattice Constant of Cu2S Crystal by
First-Principle Calculation The relation between volume andenergy of Cu
2S crystal unit is obtained as in Figure 3 by first-
principle (FP) calculation including structural optimizationFor the variety of the lattice constant ratio 119888119886 the lowestenergy is obtained at the deviation Δ119888119886 = 8 Moreoverunder that condition volume expansion at +3 shows thesmallest energy From this optimized structure thereforelattice constants of the HC structure are 119886 = 0383 nm and119888 = 0731 nm for which 119888119886 is 191 The length for 119888 andthe ratio 119888119886 seem relatively larger than the HC structure ofusual metals It means that layers of sulfur (S) and copper(Cu) atoms are remarkably separated from each other in theCu2S crystal In the present paper these optimized lattice
constants are used as values to configure atomic positions inthe specimen of Cu
2S crystal
32 Construction of Interatomic Potential Function for MDCalculations It is experimentally and theoretically under-stood that interaction between Cu and S atoms is generally
Minimum
Change of volume ()
Difference from initial structure
+10+8
+6+4
Ener
gy d
iffer
ence
(eV
)
6543210minus1minus2minus001
009
01
008
007
006
005
004
003
002
001
0
Figure 3 Volume-energy relation of Cu2S crystal structure
Distance r (nm)090807060504030201
minus8
minus6
minus4
minus2
0
2
4
6
8
Mo-S bondCu-S bond
FP calculation
times10minus19En
ergy
EminusE0
(J)
Figure 4 Distance-energy relation of Cu-S interaction obtained byFP calculation (Mo-S interaction is also shown for comparison)
strong So the Cu-S interaction can be expressed by Morsepotential function as shown by (3) The optimized configu-ration of Cu-S dimer is obtained by the FP calculation by us[21] From this we determine both the equilibrium distanceparameters 119903
0 120573119894119895and the energy parameter 119863
119894119895needed
in Morse potential Figure 4 shows the relation betweeninteratomic distance and its energy which is obtained by theFP calculation The obtained parameters for Morse potentialis shown in Table 4
The optimized crystalline structure of Cu2S which has
been obtained in the previous section can be used to adjust anangular-dependent three-body potential parameters shownin (4) In this process of fitting we assume that Cu atomsare located at the averaged position between tetragonal and
Journal of Materials 7
21564Aring
26712Aring
23926Aring
35219Aring
Cu
S
S
S S S S S
Cu
SS S
124125 deg
91599deg106333deg
65876deg
Figure 5 Schematic of the way to average two types of coordination for Cu atoms in Cu2S crystal
Table 4 Potential parameters fitted by FP calculations
(a) Morse potential (Cu-S)
Kind of pair 119863119894119895
120573119894119895
1199030
Unit kJmole 1nm nmCu-S 298916 1500 2029(Mo-S) (152076) (1800) (2532)
(b) Angular potential (S-Cu-S Cu-S-Cu)
Combination 1205790
Unit degS-Cu-S 98966Cu-S-Cu 98966
(c) B-M-H ionic potential (Cu-S)
Kind of pair 1199031015840
0119886Cu 119886S
Unit nm nm nm25319 070052 18314lowast
119886Slowast has been already obtained for MoS2 potential [10]
octahedral sites as shown in Figure 5 since there is possibilitythat Cu atoms may be located on both sites In practicewe just need equilibrium three-body angle 120579
0and pairwise
distance 1199031015840
0 Finally they are 120579
0= 98966
∘ and 1199031015840
0= 2532 nm
respectivelyAdditionally the BMH term requires ionic radii 119886Cu and
119886S for each element The radius of Cu atom is supposed tobe equivalent to the equilibrium length 119903
0in Morse potential
above the radius 119886S = 1834 nm for S is already available fromthe previous MD study of MoS
2[10]
Thus MD potential parameters to reproduce the HCstructure of Cu
2S are obtained by mostly FP calculation and
they are summarized in Table 4
33 Sliding and Friction Behavior of Cu2S
331 Dependency on Crystalline Orientation The depen-dence on crystalline orientation in sliding behavior of Cu
2S
is as follows Figure 6 shows the atomic configurations at119905 = 600 ps with sliding velocity V = 05ms comparingbetween models which are sliding in (a)-direction (⟨0110⟩)sliding and in (b)-direction (⟨21 10⟩) Both models oncecollapse and lose their crystalline stacking during sliding Butafter that the atomic structure recovers its original stackingduring long-time slidingThe difference between twomodelsis not found just visually from atomic configurations asseen in the broken black- and yellow-colored rectangularareas depicted in the figures Therefore the RDF analysiswill be helpful for identifying the change of crystallinestructures Besides in order to recognize transition of anatomic force during sliding the analysis of shear stress willbe helpful
The result of RDF analysis is shown in Figure 7 which isfor sliding velocity V = 05ms and compares results between(a)-direction and (b)-direction models In these RDF figurespeaks are found at some distances by which the nature ofcrystalline structure is confirmed In particular whenwe takea look at peaks found in the range of 02sim08 nm for twomodels the steepness of the distribution in (b)-direction istotally stronger than that in (a)-direction So the structureobtained by the sliding in (b)-direction tends to retain morelocal crystalline structure than that obtained in (a)-directionsliding
Just when the resulting sliding distance becomes 10 nmis the RDF obtained as shown in Figure 8 for different slidingvelocities (V = 10 and 50ms) At the same sliding distancethe crystalline stacking is the same and so the results maybe compared as for different velocity conditions One peakof RDF is just identified for the 1st neighbor distance whichmeans the crystalline structure has been lost and the atomicmovement shows somewhat of fluidity
Shear stress averaged over the whole specimen 120591totrepresents the resistance to the slidingThe time transition of120591tot reflects atomic force state in the sliding During relaxationprocess in fact a certain value of shear stress already occursThis is due to atomic rearrangement inside the crystal unitAfter the specimen is fully relaxed we reset the stress valueLet the value at the beginning of sliding be 120591tot(0) Then the
8 Journal of Materials
Disordered
Ordered layer
CuCu
CuCu
SS
S
To front
To back
To right
To left
Disordered
Ordered layer
CuCuCu
S
S
S Cu
(A) (a)-direction (⟨0110⟩) sliding (the sliding direction is normal to the figure plane)
(B) (b)-direction ( 110⟩) sliding (the sliding direction is right and left)⟨2
Figure 6 Comparison of instantaneous atomic configurations obtained at 119905 = 600 ps with V = 05ms (the picture is drawn onto 119910-119911 plane)
absolute value of deviation of current value 120591tot from initialvalue 120591tot(0) is defined to be
120591119886=
1003816100381610038161003816120591tot minus 120591tot (0)
1003816100381610038161003816 (7)
This stress deviation 120591119886reflects a sudden increase of friction
due to roughness of slide planes The time transition of 120591119886
is obtained as shown in Figure 9 Figure 9(A) shows therelation between the time and the stress deviation 120591
119886 120591119886is
averaged over the whole specimen Those graphs show that120591119886for (a)-direction sliding is larger than that in (b)-direction
The downward arrows in the figure display each maximumvalue At low velocity atoms near contact layers feel relativelylarger resistance to slide in (a)-direction sliding while the
(b)-direction sliding seems much easier However for thecases with higher velocity such as V = 10ms or 50ms thetendency of stress 120591
119886is changed as shown in Figures 9(B)
and 9(C) As shown in Figure 9(B) for example for V =10ms the peak value in (b)-direction is sometimes largerthan that in (a)-direction especially during 50ndash100 ps or 250ndash300 ps
We summarize the dependency of sliding direction asfollows When the shear velocity is small (b)-direction(⟨0110⟩) sliding is easier than (a)-direction (⟨0110⟩) How-ever once the sliding has completed such as to 100 or200 ps from the start of sliding distinction between slidingdirections becomes negligible The cause of this behaviorwould be guessed and explained as follows When the sliding
Journal of Materials 9
(a)
(a)-direction(b)-direction
(a)
(b)16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)
(a)-direction(b)-direction
(b)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)(b)
(a)-direction(b)-direction
(b)
(b)
(a)
(a)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)-direction(b)-direction
(b)
(b)
(a)
(a)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(A) Shear length = 02nm (B) 04nm
(C) 06nm (D) 08nm
Figure 7 Time transition of RDF for V = 05ms (comparison between (a)- and (b)-direction sliding)
is carried out sufficiently the crystalline structure of Cu2S
has collapsed and the crystalline slip system (plane anddirection) no longer determines the sliding behavior Evenif there exists a certain easy-glide plane or direction thecrystal does not always show especially smaller shear stressin sliding
332 Dependency on Sliding Velocity Figure 10(A) shows therelation between shear distance and shear stress deviation 120591
119886
It compares results for a variety of velocities ranging from 05to 50ms For all velocities and for the sliding distance up to02 nm 120591
119886linearly increases with the same gradientThis fact
means that the material deforms in elastic manner for smallsliding and deformation However after that 120591
119886decreases
suddenly The larger the sliding velocity is the larger theaveraged value of 120591
119886is obtained It is reasonable that time rate
of decrease is smaller for higher speed sliding As the wholetime calculated here is seen the case of V= 50ms exhibits the
largest level of 120591119886 For (b)-direction Figure 10(B) shows that
the value of 120591119886increases with increase of sliding velocity It
is concluded that shear stress of this material depends largelyon sliding velocity
The relation between 120591119886and sliding velocity V is sum-
marized in Table 5 120591ave time average of 120591119886 is also shown
at the bottom line It indicates that 120591ave of (a)-directionis approximately 10 smaller than that of (b)-directionWhile the easiest glide directionplane of the HC struc-ture is ⟨0110⟩(0001) (ie (b)-direction) it does not showsmall resistance in the sliding Thus it is concluded thatCu2S crystal does surely show sliding motion but it is
not by usual crystalline slip (glide) mechanism of ordinarymetals
On the other hand the fact that shear stress increaseswith increase of velocity is interesting It means that thismaterial deforms by slidingwith somewhat liquid-like (amor-phous) behavior The deformation rate (ie velocity) in such
10 Journal of Materials
(a)
(a)
(b)
(b)
r (nm)04504035030250201501
14
12
1
08
06
04
02
0
g(r)
(a)-direction(b)-direction
(a) (b)
r (nm)04504035030250201501
12
1
08
06
04
0
02
g(r)
(a)-direction(b)-direction
(a) (b)
r (nm)04504035030250201501
14
12
1
08
06
04
02
0
g(r)
(a)-direction(b)-direction
(a) (b)
(a) (b)
(B) = 10ms
(C) = 50ms
(A) Velocity = 05ms
Figure 8 The comparison of RDF at the same sliding distance (10 nm) between (a)- and (b)-direction sliding
Table 5 Relation between averaged shear stress 120591ave and slidingvelocity V
Sliding velocityVms
Averaged shear stress 120591ave GPa(A) (a)-direction sliding (B) (b)-direction sliding
05 193 22810 214 25450 264 283Average 224 255
amorphous substance produces shear stress inside due toits viscosity and so the shear stress depends on sliding(shear) velocity gradient As shown in Figure 11 averagedshear stresses 120591ave summarized in Table 5 are replotted interms of sliding velocity As recognized in Figure 11 shearstress is almost proportional to the sliding velocity In the
present simulation condition system temperature is kept at10 kelvins which is quite low But the atomic mobility atcontact layers between materials should rise due to the workdone by sliding motion In observing atomic motion theyshow intermittent slip which is sometimes called ldquostick andslipmotionrdquo in nanotribological consideration Furthermorewhen in Figure 11 we extrapolate approximated straight linesdown to V = 0 shear stress 120591ave does not return to zero butit remains at a finite value 120591
0= 20sim25GPa These ideal shear
stresses at V = 0 correspond to static friction of materials Italso means that 120591
0are at least required for layered atoms to
exhibit a material flow
4 Conclusion
In this paper we perform a molecular dynamics (MD)study on copper sulfide material (Cu
2S) under the sliding
Journal of Materials 11
0
20
40
60
80
0 200 400 600 800 1000
Shea
r stre
ss (G
Pa)
Time (ps)
(b)
(a)
= 05ms (a)-dir = 05ms (b)-dir
minus20
0
20
40
60
80
0 100 200 300 400 500 600
Shea
r stre
ss (G
Pa)
Time (ps)
(a)(b)
minus20
= 10ms (a)-dir = 10ms (b)-dir
(a)
(b)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
minus20
Time (ps)
= 50ms (a)-dir = 50ms (b)-dir
200150100500
(A) = 05ms (B) = 10ms
(C) = 50ms
Figure 9 Comparison of the absolute value of shear stress deviation 120591119886between (a)- and (b)-direction
motion The MD simulation includes a new implementationof potential energy function for Cu
2S crystal where some
first-principle calculations are utilized The potential energyfunction has three-body term The following results areobtained and we will make conclusion
(1) First-principle calculations are performed for thehexagonal unit structure of Cu
2S crystal From the
optimized structure original lattice parameters 119886
and 119888 of unit cell and stable configuration of S andCu atoms are obtained Based on those results aninteratomic potential function including ionic andMorse terms as well as angular-dependent term isconstructed for Cu and S system It is confirmedthat this potential function can show enough stability
for the hexagonal crystal structure of Cu2S in MD
simulations(2) An easy-glide direction ⟨21 10⟩ on (0001) plane gen-
erally found for usual hexagonal crystals is not thedirection with small resistance to sliding
(3) Cu2S crystal shows partially liquid-like structure and
behavior in which the shear stress occurring in thematerial depends on the sliding velocity
In the further study we should clarify the tempera-ture dependence and dependency on compressive conditionduring sliding of Cu
2S It is supposed that they are made
possible by analyzing more atomic trajectories obtained byMD simulations It will lead to total understanding of slidingmechanism of Cu
2S crystal
12 Journal of Materials
0
20
40
60
80
0 01 02 03 04 05
Shea
r stre
ss (G
Pa)
Shear distance (nm)
Slow decrease
Fast decrease
minus20
= 50ms (a)-dir = 10ms (a)-dir
= 05ms (a)-dir
0 01 02 03 04 05Shear distance (nm)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
Stress increase by velocity
minus20
= 50ms (b)-dir = 10ms (b)-dir
= 05ms (b)-dir
(A) (a)-direction ( ) sliding (B) (b)-direction ( ) sliding110⟩⟨2 ⟨0110⟩
Figure 10 Relation between shear distance and the deviation of shear stress 120591119886 comparison among different sliding velocities
0
5
10
15
20
25
30
0 1 2 3 4 5
(a)-direction(b)-direction
Linear fit ((a)-dir)Linear fit ((b)-dir)
(ms)
120591 a(G
Pa)
Figure 11 Averaged shear stress replotted against sliding velocity((a)- and (b)-directions (⟨21 10⟩ and ⟨0110⟩))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This study is partly supported by NEDO Innovative Project(2012-2013) and by the ldquoStrategic Project to Support the For-mation of Research Bases at Private Universities MatchingFund Subsidy from MEXT (Ministry of Education CultureSports Science and Technology) (2012ndash2015)rdquo The authorsalso acknowledge Kurimoto Ltd for financial support
References
[1] T Sato Y Hirai T Fukui T Ejima M Takuma and K SaitohldquoAtomic-modeling and simulation of copper sulfide as microsolid lubricantrdquoMRS Proceedings vol 1513 p 20 2013
[2] H Sueyoshi Y Yamano K Inoue Y Maeda and K YamadaldquoMechanical properties of copper sulfide-dispersed lead-freebronzerdquoMaterials Transactions vol 50 no 4 pp 776ndash781 2009
[3] Y Hirai Y Ueda M Yamamoto T Kobayashi and TMaruyama Japanese Patent 132986 2009
[4] K Akamatsu T Kobayashi A Nishimoto T Maruyama andY Arachi ldquoDevelopment of new copper alloymdashinfluence ofmetallic elements on the human bodyrdquo Rikogaku to Gijyutsuvol 16 pp 31ndash36 2009 (Japanese)
[5] L-W Wang ldquoHigh chalcocite Cu2S a solid-liquid hybrid
phaserdquoPhysical Review Letters vol 108 no 8 Article ID 0857032012
[6] T Ejima K-I Saitoh N Shinke M Taruma Y Hirai and TSato ldquoAtomic-level analysis of copper sulfide (CU2S) crystalstructure and sliding characteristicsrdquo Technology Reports ofKansai University vol 54 pp 23ndash33 2012
[7] I I Mazin ldquoStructural and electronic properties of the two-dimensional superconductor CuS with 1(13)-valent copperrdquoPhysical Review B vol 85 Article ID 115133 2012
[8] M J Buerger and B J Wuensch ldquoDistribution of atoms in highchalcocite Cu
2Srdquo Science vol 141 no 3577 pp 276ndash277 1963
[9] B J Wuensch and M J Buerger ldquoThe crystal structure ofchalcocite Cu
2Srdquo Mineralogical Society of America Special
Paper vol 1 pp 163ndash170 1963 Proceedings of the 3rd GenralMeeting
[10] T Onodera Y Morlta A Suzuki et al ldquoA computationalchemistry study on friction of h-MoS2 Part I Mechanism ofsingle sheet lubricationrdquo The Journal of Physical Chemistry Bvol 113 no 52 pp 16526ndash16536 2009
[11] Y Ding D R Veblen and C T Prewitt ldquoPossible FeCu order-ing schemes in the 2a superstructure of bornite (Cu
5FeS4)rdquo
American Mineralogist vol 90 no 8-9 pp 1265ndash1269 2005
Journal of Materials 13
[12] H Zheng J B Rivest T A Miller et al ldquoObservation of tran-sient structural-transformation dynamics in a Cu
2S nanorodrdquo
Science vol 333 no 6039 pp 206ndash209 2011[13] S KashidaW ShimosakaMMori andDYoshimura ldquoValence
band photoemission study of the copper chalcogenide com-pounds Cu2S Cu2Se and Cu2Terdquo Journal of Physics andChemistry of Solids vol 64 no 12 pp 2357ndash2363 2003
[14] P Lukashev W R L Lambrecht T Kotani and M VanSchilfgaarde ldquoElectronic and crystal structure of Cu2-x S full-potential electronic structure calculationsrdquo Physical Review Bvol 76 no 19 Article ID 195202 2007
[15] P Blaha K Schwarz G Madsen D Kvasnicka and J LuitzldquoWIEN2krdquo httpwwwwien2katindexhtml
[16] P A Romero T T Jarvi N Beckmann M Mrovec andM Moseler ldquoCoarse graining and localized plasticity betweensliding nanocrystalline metalsrdquo Physical Review Letters vol 113no 3 Article ID 036101 2014
[17] S Izumi and S Sakai ldquoInternal displacement and elasticproperties of the silicon tersoff modelrdquo JSME InternationalJournal Series A Solid Mechanics and Material Engineering vol47 no 1 pp 54ndash61 2004
[18] M P Allen and D J Tildesley Computer Simulation of LiquidsOxford University Press Oxford UK 1989
[19] Sandia Nantional Laboratory ldquoLarge-scale AtomicMolecularMassively Parallel Simulatorrdquo httplammpssandiagov
[20] T Yamaguchi and K Saitoh ldquoMolecular dyanmics study onmechanical properties in the structure of self-assembled quan-tum dotrdquoWorld Journal of Nano Science and Engineering vol 2pp 189ndash195 2012
[21] T Ejima Atomic-level analysis on sliding characteristic of coppersulfide [MS thesis] Graduate School of Kansai University 2013
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
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BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
Journal of Materials 5
A model sliding in (b)-direction
z
yAtoms
A model sliding in (a)-direction
z
x
Cu
S
Fixed
Parallel to basal plane
Basal plane(0001)
(a)-direction
(b)-direction(slip direction of hexagonal crystal)
The model for researching dependence on direction or velocity
⟨0110⟩
110⟩⟨2
Figure 2 Abstract of MD sliding model of Cu2S crystal
251 Crystal Structure Analysis by Radial Distribution Func-tion (RDF) Usually solid crystal has a three-dimensionalorderThe Cu
2S crystal used in the present study exhibits HC
structure One of themethods to identify the crystalline orderis radial distribution function (RDF) 119892(119903) [18] Briefly speak-ing the function 119892(119903) gives the number density of neighboratoms which are found in a certain distance from each atomIts distribution shows some peaks at some specific distancesinherent to the crystalline orderWhen the temperature arisesor when the crystalline order is partially lost due to outbreakof lattice defects the peak value of RDF generally reduces andthe shape at the peak becomes broadenedThus by observingthe change of the peak position and the shape of the curve ofRDF the deterioration of the crystalline order can be detectedand occurrence of lattice defects can be guessed
252 Atomic Stress Analysis (Approximate Treatment includ-ing Three-Body Terms) Since our MD model is in solidstate the behavior of sliding and friction is reflected by ashear stress averaged over the specimen Therefore atomic-scale stress is being analysed But we note that stress (orstrain) is basically the concept in continuum mechanicsand is not essential for any atomic system The facts thatatomic positions are discrete and that interatomic potentialhas nonlocal nature will conflict with the local theory of
continuum Accordingly we need to formulate atomic stresstogether with some approximation
Suppose that total potential energy inside the systemcomprises all the superposition of pairwise interactions 120601(119903)When any selected atom 119894 conducts homogeneous deforma-tion with regard to the relative position to another neighboratom 119895 strain at the interatomic space between 119894 and 119895 can bepresented by their interatomic distance 119903(119894 119895) and interatomicvector r(119894 119895) (this assumes that there is no slip no phasetransition nor long atomic diffusion over the lattice) Thenatomic stress tensor occurring at the atom 119894 is expressed as
120590 (119894) =
1
2Ω (119894)
sum
119895
120597120601 (119894 119895)
120597119903 (119894 119895)
r (119894 119895) otimes r (119894 119895)119903 (119894 119895)
(5)
where the summation is composed of the work done byatomic motion which is called ldquovirialrdquo Ω(119894) in the denom-inator is the volume supposedly occupied by the atom 119894so (5) is regarded as the energy density around that atomIn the present study Ω(119894) is assumed to be a constantwhich has been estimated in the reference structure (whichhas been estimated in the undeformed lattice) Additionallyvector product (r otimes r) means the dyadic between interatomicvectors so (5) has the form of the second-order (symmetric)tensor and its components are six Thus if an interatomicpotential of MD contains just pairwise term the virial can be
6 Journal of Materials
straightforwardly converted to atomic stress But if it includesthree-body terms depending on the angle as in the presentinteratomic potential they can never strictly be decomposedinto virials of each pair of atoms However we can apply anapproximate formulation to a triplet 119894 119895 and 119896 (119894 119895 119896) Inpractice the combination of virials of each pair (119894 119895) (119895 119896)and (119896 119894) is used as the net virial of the triplet As a result theformulation of atomic stress comes to the expression
120590120572120573
(119894) =
1
2Ω (119894)
sum
119895
120597120601pair (119894 119895)
120597119903 (119894 119895)
119903120572(119894 119895) 119903
120573(119894 119895)
119903 (119894 119895)
+
1
3Ω (119894)
sum
119895119896
(
120597120601angle (119894 119895)
120597119903 (119894 119895)
119903120572(119894 119895) 119903
120573(119894 119895)
119903 (119894 119895)
+
120597120601angle (119895 119896)
120597119903 (119895 119896)
119903120572(119895 119896) 119903
120573(119895 119896)
119903 (119895 119896)
+
120597120601angle (119896 119894)
120597119903 (119896 119894)
119903120572(119896 119894) 119903
120573(119896 119894)
119903 (119896 119894)
)
(6)
where the first term corresponds to pair interaction 120601pair(119903)and the second term is for three-body interaction Inthis expression Ω(119894) 120601pair(119894 119895) 120601angle(119894 119895) 119903(119894 119895) and119903120572(119894 119895) (120572 120573 = 1 2 3) are atomic volume pairwise potential
function three-body potential function interatomic distance(between 119894 and 119895) and its vector components In comparingall the components in (6) during actual MD simulation it isunderstood that three-body term is relatively large so that itis not negligible This expression of atomic stress includingthree-body term is also utilized in widely used MD software(eg LAMMPS) [19] Besides this estimation of atomicstress was found appropriate when we applied it to anotherMD study using the three-body-type Tersoff potential (forSi-Ge system) [20]
3 Results and Discussion
31 Optimization of Lattice Constant of Cu2S Crystal by
First-Principle Calculation The relation between volume andenergy of Cu
2S crystal unit is obtained as in Figure 3 by first-
principle (FP) calculation including structural optimizationFor the variety of the lattice constant ratio 119888119886 the lowestenergy is obtained at the deviation Δ119888119886 = 8 Moreoverunder that condition volume expansion at +3 shows thesmallest energy From this optimized structure thereforelattice constants of the HC structure are 119886 = 0383 nm and119888 = 0731 nm for which 119888119886 is 191 The length for 119888 andthe ratio 119888119886 seem relatively larger than the HC structure ofusual metals It means that layers of sulfur (S) and copper(Cu) atoms are remarkably separated from each other in theCu2S crystal In the present paper these optimized lattice
constants are used as values to configure atomic positions inthe specimen of Cu
2S crystal
32 Construction of Interatomic Potential Function for MDCalculations It is experimentally and theoretically under-stood that interaction between Cu and S atoms is generally
Minimum
Change of volume ()
Difference from initial structure
+10+8
+6+4
Ener
gy d
iffer
ence
(eV
)
6543210minus1minus2minus001
009
01
008
007
006
005
004
003
002
001
0
Figure 3 Volume-energy relation of Cu2S crystal structure
Distance r (nm)090807060504030201
minus8
minus6
minus4
minus2
0
2
4
6
8
Mo-S bondCu-S bond
FP calculation
times10minus19En
ergy
EminusE0
(J)
Figure 4 Distance-energy relation of Cu-S interaction obtained byFP calculation (Mo-S interaction is also shown for comparison)
strong So the Cu-S interaction can be expressed by Morsepotential function as shown by (3) The optimized configu-ration of Cu-S dimer is obtained by the FP calculation by us[21] From this we determine both the equilibrium distanceparameters 119903
0 120573119894119895and the energy parameter 119863
119894119895needed
in Morse potential Figure 4 shows the relation betweeninteratomic distance and its energy which is obtained by theFP calculation The obtained parameters for Morse potentialis shown in Table 4
The optimized crystalline structure of Cu2S which has
been obtained in the previous section can be used to adjust anangular-dependent three-body potential parameters shownin (4) In this process of fitting we assume that Cu atomsare located at the averaged position between tetragonal and
Journal of Materials 7
21564Aring
26712Aring
23926Aring
35219Aring
Cu
S
S
S S S S S
Cu
SS S
124125 deg
91599deg106333deg
65876deg
Figure 5 Schematic of the way to average two types of coordination for Cu atoms in Cu2S crystal
Table 4 Potential parameters fitted by FP calculations
(a) Morse potential (Cu-S)
Kind of pair 119863119894119895
120573119894119895
1199030
Unit kJmole 1nm nmCu-S 298916 1500 2029(Mo-S) (152076) (1800) (2532)
(b) Angular potential (S-Cu-S Cu-S-Cu)
Combination 1205790
Unit degS-Cu-S 98966Cu-S-Cu 98966
(c) B-M-H ionic potential (Cu-S)
Kind of pair 1199031015840
0119886Cu 119886S
Unit nm nm nm25319 070052 18314lowast
119886Slowast has been already obtained for MoS2 potential [10]
octahedral sites as shown in Figure 5 since there is possibilitythat Cu atoms may be located on both sites In practicewe just need equilibrium three-body angle 120579
0and pairwise
distance 1199031015840
0 Finally they are 120579
0= 98966
∘ and 1199031015840
0= 2532 nm
respectivelyAdditionally the BMH term requires ionic radii 119886Cu and
119886S for each element The radius of Cu atom is supposed tobe equivalent to the equilibrium length 119903
0in Morse potential
above the radius 119886S = 1834 nm for S is already available fromthe previous MD study of MoS
2[10]
Thus MD potential parameters to reproduce the HCstructure of Cu
2S are obtained by mostly FP calculation and
they are summarized in Table 4
33 Sliding and Friction Behavior of Cu2S
331 Dependency on Crystalline Orientation The depen-dence on crystalline orientation in sliding behavior of Cu
2S
is as follows Figure 6 shows the atomic configurations at119905 = 600 ps with sliding velocity V = 05ms comparingbetween models which are sliding in (a)-direction (⟨0110⟩)sliding and in (b)-direction (⟨21 10⟩) Both models oncecollapse and lose their crystalline stacking during sliding Butafter that the atomic structure recovers its original stackingduring long-time slidingThe difference between twomodelsis not found just visually from atomic configurations asseen in the broken black- and yellow-colored rectangularareas depicted in the figures Therefore the RDF analysiswill be helpful for identifying the change of crystallinestructures Besides in order to recognize transition of anatomic force during sliding the analysis of shear stress willbe helpful
The result of RDF analysis is shown in Figure 7 which isfor sliding velocity V = 05ms and compares results between(a)-direction and (b)-direction models In these RDF figurespeaks are found at some distances by which the nature ofcrystalline structure is confirmed In particular whenwe takea look at peaks found in the range of 02sim08 nm for twomodels the steepness of the distribution in (b)-direction istotally stronger than that in (a)-direction So the structureobtained by the sliding in (b)-direction tends to retain morelocal crystalline structure than that obtained in (a)-directionsliding
Just when the resulting sliding distance becomes 10 nmis the RDF obtained as shown in Figure 8 for different slidingvelocities (V = 10 and 50ms) At the same sliding distancethe crystalline stacking is the same and so the results maybe compared as for different velocity conditions One peakof RDF is just identified for the 1st neighbor distance whichmeans the crystalline structure has been lost and the atomicmovement shows somewhat of fluidity
Shear stress averaged over the whole specimen 120591totrepresents the resistance to the slidingThe time transition of120591tot reflects atomic force state in the sliding During relaxationprocess in fact a certain value of shear stress already occursThis is due to atomic rearrangement inside the crystal unitAfter the specimen is fully relaxed we reset the stress valueLet the value at the beginning of sliding be 120591tot(0) Then the
8 Journal of Materials
Disordered
Ordered layer
CuCu
CuCu
SS
S
To front
To back
To right
To left
Disordered
Ordered layer
CuCuCu
S
S
S Cu
(A) (a)-direction (⟨0110⟩) sliding (the sliding direction is normal to the figure plane)
(B) (b)-direction ( 110⟩) sliding (the sliding direction is right and left)⟨2
Figure 6 Comparison of instantaneous atomic configurations obtained at 119905 = 600 ps with V = 05ms (the picture is drawn onto 119910-119911 plane)
absolute value of deviation of current value 120591tot from initialvalue 120591tot(0) is defined to be
120591119886=
1003816100381610038161003816120591tot minus 120591tot (0)
1003816100381610038161003816 (7)
This stress deviation 120591119886reflects a sudden increase of friction
due to roughness of slide planes The time transition of 120591119886
is obtained as shown in Figure 9 Figure 9(A) shows therelation between the time and the stress deviation 120591
119886 120591119886is
averaged over the whole specimen Those graphs show that120591119886for (a)-direction sliding is larger than that in (b)-direction
The downward arrows in the figure display each maximumvalue At low velocity atoms near contact layers feel relativelylarger resistance to slide in (a)-direction sliding while the
(b)-direction sliding seems much easier However for thecases with higher velocity such as V = 10ms or 50ms thetendency of stress 120591
119886is changed as shown in Figures 9(B)
and 9(C) As shown in Figure 9(B) for example for V =10ms the peak value in (b)-direction is sometimes largerthan that in (a)-direction especially during 50ndash100 ps or 250ndash300 ps
We summarize the dependency of sliding direction asfollows When the shear velocity is small (b)-direction(⟨0110⟩) sliding is easier than (a)-direction (⟨0110⟩) How-ever once the sliding has completed such as to 100 or200 ps from the start of sliding distinction between slidingdirections becomes negligible The cause of this behaviorwould be guessed and explained as follows When the sliding
Journal of Materials 9
(a)
(a)-direction(b)-direction
(a)
(b)16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)
(a)-direction(b)-direction
(b)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)(b)
(a)-direction(b)-direction
(b)
(b)
(a)
(a)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)-direction(b)-direction
(b)
(b)
(a)
(a)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(A) Shear length = 02nm (B) 04nm
(C) 06nm (D) 08nm
Figure 7 Time transition of RDF for V = 05ms (comparison between (a)- and (b)-direction sliding)
is carried out sufficiently the crystalline structure of Cu2S
has collapsed and the crystalline slip system (plane anddirection) no longer determines the sliding behavior Evenif there exists a certain easy-glide plane or direction thecrystal does not always show especially smaller shear stressin sliding
332 Dependency on Sliding Velocity Figure 10(A) shows therelation between shear distance and shear stress deviation 120591
119886
It compares results for a variety of velocities ranging from 05to 50ms For all velocities and for the sliding distance up to02 nm 120591
119886linearly increases with the same gradientThis fact
means that the material deforms in elastic manner for smallsliding and deformation However after that 120591
119886decreases
suddenly The larger the sliding velocity is the larger theaveraged value of 120591
119886is obtained It is reasonable that time rate
of decrease is smaller for higher speed sliding As the wholetime calculated here is seen the case of V= 50ms exhibits the
largest level of 120591119886 For (b)-direction Figure 10(B) shows that
the value of 120591119886increases with increase of sliding velocity It
is concluded that shear stress of this material depends largelyon sliding velocity
The relation between 120591119886and sliding velocity V is sum-
marized in Table 5 120591ave time average of 120591119886 is also shown
at the bottom line It indicates that 120591ave of (a)-directionis approximately 10 smaller than that of (b)-directionWhile the easiest glide directionplane of the HC struc-ture is ⟨0110⟩(0001) (ie (b)-direction) it does not showsmall resistance in the sliding Thus it is concluded thatCu2S crystal does surely show sliding motion but it is
not by usual crystalline slip (glide) mechanism of ordinarymetals
On the other hand the fact that shear stress increaseswith increase of velocity is interesting It means that thismaterial deforms by slidingwith somewhat liquid-like (amor-phous) behavior The deformation rate (ie velocity) in such
10 Journal of Materials
(a)
(a)
(b)
(b)
r (nm)04504035030250201501
14
12
1
08
06
04
02
0
g(r)
(a)-direction(b)-direction
(a) (b)
r (nm)04504035030250201501
12
1
08
06
04
0
02
g(r)
(a)-direction(b)-direction
(a) (b)
r (nm)04504035030250201501
14
12
1
08
06
04
02
0
g(r)
(a)-direction(b)-direction
(a) (b)
(a) (b)
(B) = 10ms
(C) = 50ms
(A) Velocity = 05ms
Figure 8 The comparison of RDF at the same sliding distance (10 nm) between (a)- and (b)-direction sliding
Table 5 Relation between averaged shear stress 120591ave and slidingvelocity V
Sliding velocityVms
Averaged shear stress 120591ave GPa(A) (a)-direction sliding (B) (b)-direction sliding
05 193 22810 214 25450 264 283Average 224 255
amorphous substance produces shear stress inside due toits viscosity and so the shear stress depends on sliding(shear) velocity gradient As shown in Figure 11 averagedshear stresses 120591ave summarized in Table 5 are replotted interms of sliding velocity As recognized in Figure 11 shearstress is almost proportional to the sliding velocity In the
present simulation condition system temperature is kept at10 kelvins which is quite low But the atomic mobility atcontact layers between materials should rise due to the workdone by sliding motion In observing atomic motion theyshow intermittent slip which is sometimes called ldquostick andslipmotionrdquo in nanotribological consideration Furthermorewhen in Figure 11 we extrapolate approximated straight linesdown to V = 0 shear stress 120591ave does not return to zero butit remains at a finite value 120591
0= 20sim25GPa These ideal shear
stresses at V = 0 correspond to static friction of materials Italso means that 120591
0are at least required for layered atoms to
exhibit a material flow
4 Conclusion
In this paper we perform a molecular dynamics (MD)study on copper sulfide material (Cu
2S) under the sliding
Journal of Materials 11
0
20
40
60
80
0 200 400 600 800 1000
Shea
r stre
ss (G
Pa)
Time (ps)
(b)
(a)
= 05ms (a)-dir = 05ms (b)-dir
minus20
0
20
40
60
80
0 100 200 300 400 500 600
Shea
r stre
ss (G
Pa)
Time (ps)
(a)(b)
minus20
= 10ms (a)-dir = 10ms (b)-dir
(a)
(b)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
minus20
Time (ps)
= 50ms (a)-dir = 50ms (b)-dir
200150100500
(A) = 05ms (B) = 10ms
(C) = 50ms
Figure 9 Comparison of the absolute value of shear stress deviation 120591119886between (a)- and (b)-direction
motion The MD simulation includes a new implementationof potential energy function for Cu
2S crystal where some
first-principle calculations are utilized The potential energyfunction has three-body term The following results areobtained and we will make conclusion
(1) First-principle calculations are performed for thehexagonal unit structure of Cu
2S crystal From the
optimized structure original lattice parameters 119886
and 119888 of unit cell and stable configuration of S andCu atoms are obtained Based on those results aninteratomic potential function including ionic andMorse terms as well as angular-dependent term isconstructed for Cu and S system It is confirmedthat this potential function can show enough stability
for the hexagonal crystal structure of Cu2S in MD
simulations(2) An easy-glide direction ⟨21 10⟩ on (0001) plane gen-
erally found for usual hexagonal crystals is not thedirection with small resistance to sliding
(3) Cu2S crystal shows partially liquid-like structure and
behavior in which the shear stress occurring in thematerial depends on the sliding velocity
In the further study we should clarify the tempera-ture dependence and dependency on compressive conditionduring sliding of Cu
2S It is supposed that they are made
possible by analyzing more atomic trajectories obtained byMD simulations It will lead to total understanding of slidingmechanism of Cu
2S crystal
12 Journal of Materials
0
20
40
60
80
0 01 02 03 04 05
Shea
r stre
ss (G
Pa)
Shear distance (nm)
Slow decrease
Fast decrease
minus20
= 50ms (a)-dir = 10ms (a)-dir
= 05ms (a)-dir
0 01 02 03 04 05Shear distance (nm)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
Stress increase by velocity
minus20
= 50ms (b)-dir = 10ms (b)-dir
= 05ms (b)-dir
(A) (a)-direction ( ) sliding (B) (b)-direction ( ) sliding110⟩⟨2 ⟨0110⟩
Figure 10 Relation between shear distance and the deviation of shear stress 120591119886 comparison among different sliding velocities
0
5
10
15
20
25
30
0 1 2 3 4 5
(a)-direction(b)-direction
Linear fit ((a)-dir)Linear fit ((b)-dir)
(ms)
120591 a(G
Pa)
Figure 11 Averaged shear stress replotted against sliding velocity((a)- and (b)-directions (⟨21 10⟩ and ⟨0110⟩))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This study is partly supported by NEDO Innovative Project(2012-2013) and by the ldquoStrategic Project to Support the For-mation of Research Bases at Private Universities MatchingFund Subsidy from MEXT (Ministry of Education CultureSports Science and Technology) (2012ndash2015)rdquo The authorsalso acknowledge Kurimoto Ltd for financial support
References
[1] T Sato Y Hirai T Fukui T Ejima M Takuma and K SaitohldquoAtomic-modeling and simulation of copper sulfide as microsolid lubricantrdquoMRS Proceedings vol 1513 p 20 2013
[2] H Sueyoshi Y Yamano K Inoue Y Maeda and K YamadaldquoMechanical properties of copper sulfide-dispersed lead-freebronzerdquoMaterials Transactions vol 50 no 4 pp 776ndash781 2009
[3] Y Hirai Y Ueda M Yamamoto T Kobayashi and TMaruyama Japanese Patent 132986 2009
[4] K Akamatsu T Kobayashi A Nishimoto T Maruyama andY Arachi ldquoDevelopment of new copper alloymdashinfluence ofmetallic elements on the human bodyrdquo Rikogaku to Gijyutsuvol 16 pp 31ndash36 2009 (Japanese)
[5] L-W Wang ldquoHigh chalcocite Cu2S a solid-liquid hybrid
phaserdquoPhysical Review Letters vol 108 no 8 Article ID 0857032012
[6] T Ejima K-I Saitoh N Shinke M Taruma Y Hirai and TSato ldquoAtomic-level analysis of copper sulfide (CU2S) crystalstructure and sliding characteristicsrdquo Technology Reports ofKansai University vol 54 pp 23ndash33 2012
[7] I I Mazin ldquoStructural and electronic properties of the two-dimensional superconductor CuS with 1(13)-valent copperrdquoPhysical Review B vol 85 Article ID 115133 2012
[8] M J Buerger and B J Wuensch ldquoDistribution of atoms in highchalcocite Cu
2Srdquo Science vol 141 no 3577 pp 276ndash277 1963
[9] B J Wuensch and M J Buerger ldquoThe crystal structure ofchalcocite Cu
2Srdquo Mineralogical Society of America Special
Paper vol 1 pp 163ndash170 1963 Proceedings of the 3rd GenralMeeting
[10] T Onodera Y Morlta A Suzuki et al ldquoA computationalchemistry study on friction of h-MoS2 Part I Mechanism ofsingle sheet lubricationrdquo The Journal of Physical Chemistry Bvol 113 no 52 pp 16526ndash16536 2009
[11] Y Ding D R Veblen and C T Prewitt ldquoPossible FeCu order-ing schemes in the 2a superstructure of bornite (Cu
5FeS4)rdquo
American Mineralogist vol 90 no 8-9 pp 1265ndash1269 2005
Journal of Materials 13
[12] H Zheng J B Rivest T A Miller et al ldquoObservation of tran-sient structural-transformation dynamics in a Cu
2S nanorodrdquo
Science vol 333 no 6039 pp 206ndash209 2011[13] S KashidaW ShimosakaMMori andDYoshimura ldquoValence
band photoemission study of the copper chalcogenide com-pounds Cu2S Cu2Se and Cu2Terdquo Journal of Physics andChemistry of Solids vol 64 no 12 pp 2357ndash2363 2003
[14] P Lukashev W R L Lambrecht T Kotani and M VanSchilfgaarde ldquoElectronic and crystal structure of Cu2-x S full-potential electronic structure calculationsrdquo Physical Review Bvol 76 no 19 Article ID 195202 2007
[15] P Blaha K Schwarz G Madsen D Kvasnicka and J LuitzldquoWIEN2krdquo httpwwwwien2katindexhtml
[16] P A Romero T T Jarvi N Beckmann M Mrovec andM Moseler ldquoCoarse graining and localized plasticity betweensliding nanocrystalline metalsrdquo Physical Review Letters vol 113no 3 Article ID 036101 2014
[17] S Izumi and S Sakai ldquoInternal displacement and elasticproperties of the silicon tersoff modelrdquo JSME InternationalJournal Series A Solid Mechanics and Material Engineering vol47 no 1 pp 54ndash61 2004
[18] M P Allen and D J Tildesley Computer Simulation of LiquidsOxford University Press Oxford UK 1989
[19] Sandia Nantional Laboratory ldquoLarge-scale AtomicMolecularMassively Parallel Simulatorrdquo httplammpssandiagov
[20] T Yamaguchi and K Saitoh ldquoMolecular dyanmics study onmechanical properties in the structure of self-assembled quan-tum dotrdquoWorld Journal of Nano Science and Engineering vol 2pp 189ndash195 2012
[21] T Ejima Atomic-level analysis on sliding characteristic of coppersulfide [MS thesis] Graduate School of Kansai University 2013
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
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CeramicsJournal of
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CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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Biomaterials
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TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
6 Journal of Materials
straightforwardly converted to atomic stress But if it includesthree-body terms depending on the angle as in the presentinteratomic potential they can never strictly be decomposedinto virials of each pair of atoms However we can apply anapproximate formulation to a triplet 119894 119895 and 119896 (119894 119895 119896) Inpractice the combination of virials of each pair (119894 119895) (119895 119896)and (119896 119894) is used as the net virial of the triplet As a result theformulation of atomic stress comes to the expression
120590120572120573
(119894) =
1
2Ω (119894)
sum
119895
120597120601pair (119894 119895)
120597119903 (119894 119895)
119903120572(119894 119895) 119903
120573(119894 119895)
119903 (119894 119895)
+
1
3Ω (119894)
sum
119895119896
(
120597120601angle (119894 119895)
120597119903 (119894 119895)
119903120572(119894 119895) 119903
120573(119894 119895)
119903 (119894 119895)
+
120597120601angle (119895 119896)
120597119903 (119895 119896)
119903120572(119895 119896) 119903
120573(119895 119896)
119903 (119895 119896)
+
120597120601angle (119896 119894)
120597119903 (119896 119894)
119903120572(119896 119894) 119903
120573(119896 119894)
119903 (119896 119894)
)
(6)
where the first term corresponds to pair interaction 120601pair(119903)and the second term is for three-body interaction Inthis expression Ω(119894) 120601pair(119894 119895) 120601angle(119894 119895) 119903(119894 119895) and119903120572(119894 119895) (120572 120573 = 1 2 3) are atomic volume pairwise potential
function three-body potential function interatomic distance(between 119894 and 119895) and its vector components In comparingall the components in (6) during actual MD simulation it isunderstood that three-body term is relatively large so that itis not negligible This expression of atomic stress includingthree-body term is also utilized in widely used MD software(eg LAMMPS) [19] Besides this estimation of atomicstress was found appropriate when we applied it to anotherMD study using the three-body-type Tersoff potential (forSi-Ge system) [20]
3 Results and Discussion
31 Optimization of Lattice Constant of Cu2S Crystal by
First-Principle Calculation The relation between volume andenergy of Cu
2S crystal unit is obtained as in Figure 3 by first-
principle (FP) calculation including structural optimizationFor the variety of the lattice constant ratio 119888119886 the lowestenergy is obtained at the deviation Δ119888119886 = 8 Moreoverunder that condition volume expansion at +3 shows thesmallest energy From this optimized structure thereforelattice constants of the HC structure are 119886 = 0383 nm and119888 = 0731 nm for which 119888119886 is 191 The length for 119888 andthe ratio 119888119886 seem relatively larger than the HC structure ofusual metals It means that layers of sulfur (S) and copper(Cu) atoms are remarkably separated from each other in theCu2S crystal In the present paper these optimized lattice
constants are used as values to configure atomic positions inthe specimen of Cu
2S crystal
32 Construction of Interatomic Potential Function for MDCalculations It is experimentally and theoretically under-stood that interaction between Cu and S atoms is generally
Minimum
Change of volume ()
Difference from initial structure
+10+8
+6+4
Ener
gy d
iffer
ence
(eV
)
6543210minus1minus2minus001
009
01
008
007
006
005
004
003
002
001
0
Figure 3 Volume-energy relation of Cu2S crystal structure
Distance r (nm)090807060504030201
minus8
minus6
minus4
minus2
0
2
4
6
8
Mo-S bondCu-S bond
FP calculation
times10minus19En
ergy
EminusE0
(J)
Figure 4 Distance-energy relation of Cu-S interaction obtained byFP calculation (Mo-S interaction is also shown for comparison)
strong So the Cu-S interaction can be expressed by Morsepotential function as shown by (3) The optimized configu-ration of Cu-S dimer is obtained by the FP calculation by us[21] From this we determine both the equilibrium distanceparameters 119903
0 120573119894119895and the energy parameter 119863
119894119895needed
in Morse potential Figure 4 shows the relation betweeninteratomic distance and its energy which is obtained by theFP calculation The obtained parameters for Morse potentialis shown in Table 4
The optimized crystalline structure of Cu2S which has
been obtained in the previous section can be used to adjust anangular-dependent three-body potential parameters shownin (4) In this process of fitting we assume that Cu atomsare located at the averaged position between tetragonal and
Journal of Materials 7
21564Aring
26712Aring
23926Aring
35219Aring
Cu
S
S
S S S S S
Cu
SS S
124125 deg
91599deg106333deg
65876deg
Figure 5 Schematic of the way to average two types of coordination for Cu atoms in Cu2S crystal
Table 4 Potential parameters fitted by FP calculations
(a) Morse potential (Cu-S)
Kind of pair 119863119894119895
120573119894119895
1199030
Unit kJmole 1nm nmCu-S 298916 1500 2029(Mo-S) (152076) (1800) (2532)
(b) Angular potential (S-Cu-S Cu-S-Cu)
Combination 1205790
Unit degS-Cu-S 98966Cu-S-Cu 98966
(c) B-M-H ionic potential (Cu-S)
Kind of pair 1199031015840
0119886Cu 119886S
Unit nm nm nm25319 070052 18314lowast
119886Slowast has been already obtained for MoS2 potential [10]
octahedral sites as shown in Figure 5 since there is possibilitythat Cu atoms may be located on both sites In practicewe just need equilibrium three-body angle 120579
0and pairwise
distance 1199031015840
0 Finally they are 120579
0= 98966
∘ and 1199031015840
0= 2532 nm
respectivelyAdditionally the BMH term requires ionic radii 119886Cu and
119886S for each element The radius of Cu atom is supposed tobe equivalent to the equilibrium length 119903
0in Morse potential
above the radius 119886S = 1834 nm for S is already available fromthe previous MD study of MoS
2[10]
Thus MD potential parameters to reproduce the HCstructure of Cu
2S are obtained by mostly FP calculation and
they are summarized in Table 4
33 Sliding and Friction Behavior of Cu2S
331 Dependency on Crystalline Orientation The depen-dence on crystalline orientation in sliding behavior of Cu
2S
is as follows Figure 6 shows the atomic configurations at119905 = 600 ps with sliding velocity V = 05ms comparingbetween models which are sliding in (a)-direction (⟨0110⟩)sliding and in (b)-direction (⟨21 10⟩) Both models oncecollapse and lose their crystalline stacking during sliding Butafter that the atomic structure recovers its original stackingduring long-time slidingThe difference between twomodelsis not found just visually from atomic configurations asseen in the broken black- and yellow-colored rectangularareas depicted in the figures Therefore the RDF analysiswill be helpful for identifying the change of crystallinestructures Besides in order to recognize transition of anatomic force during sliding the analysis of shear stress willbe helpful
The result of RDF analysis is shown in Figure 7 which isfor sliding velocity V = 05ms and compares results between(a)-direction and (b)-direction models In these RDF figurespeaks are found at some distances by which the nature ofcrystalline structure is confirmed In particular whenwe takea look at peaks found in the range of 02sim08 nm for twomodels the steepness of the distribution in (b)-direction istotally stronger than that in (a)-direction So the structureobtained by the sliding in (b)-direction tends to retain morelocal crystalline structure than that obtained in (a)-directionsliding
Just when the resulting sliding distance becomes 10 nmis the RDF obtained as shown in Figure 8 for different slidingvelocities (V = 10 and 50ms) At the same sliding distancethe crystalline stacking is the same and so the results maybe compared as for different velocity conditions One peakof RDF is just identified for the 1st neighbor distance whichmeans the crystalline structure has been lost and the atomicmovement shows somewhat of fluidity
Shear stress averaged over the whole specimen 120591totrepresents the resistance to the slidingThe time transition of120591tot reflects atomic force state in the sliding During relaxationprocess in fact a certain value of shear stress already occursThis is due to atomic rearrangement inside the crystal unitAfter the specimen is fully relaxed we reset the stress valueLet the value at the beginning of sliding be 120591tot(0) Then the
8 Journal of Materials
Disordered
Ordered layer
CuCu
CuCu
SS
S
To front
To back
To right
To left
Disordered
Ordered layer
CuCuCu
S
S
S Cu
(A) (a)-direction (⟨0110⟩) sliding (the sliding direction is normal to the figure plane)
(B) (b)-direction ( 110⟩) sliding (the sliding direction is right and left)⟨2
Figure 6 Comparison of instantaneous atomic configurations obtained at 119905 = 600 ps with V = 05ms (the picture is drawn onto 119910-119911 plane)
absolute value of deviation of current value 120591tot from initialvalue 120591tot(0) is defined to be
120591119886=
1003816100381610038161003816120591tot minus 120591tot (0)
1003816100381610038161003816 (7)
This stress deviation 120591119886reflects a sudden increase of friction
due to roughness of slide planes The time transition of 120591119886
is obtained as shown in Figure 9 Figure 9(A) shows therelation between the time and the stress deviation 120591
119886 120591119886is
averaged over the whole specimen Those graphs show that120591119886for (a)-direction sliding is larger than that in (b)-direction
The downward arrows in the figure display each maximumvalue At low velocity atoms near contact layers feel relativelylarger resistance to slide in (a)-direction sliding while the
(b)-direction sliding seems much easier However for thecases with higher velocity such as V = 10ms or 50ms thetendency of stress 120591
119886is changed as shown in Figures 9(B)
and 9(C) As shown in Figure 9(B) for example for V =10ms the peak value in (b)-direction is sometimes largerthan that in (a)-direction especially during 50ndash100 ps or 250ndash300 ps
We summarize the dependency of sliding direction asfollows When the shear velocity is small (b)-direction(⟨0110⟩) sliding is easier than (a)-direction (⟨0110⟩) How-ever once the sliding has completed such as to 100 or200 ps from the start of sliding distinction between slidingdirections becomes negligible The cause of this behaviorwould be guessed and explained as follows When the sliding
Journal of Materials 9
(a)
(a)-direction(b)-direction
(a)
(b)16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)
(a)-direction(b)-direction
(b)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)(b)
(a)-direction(b)-direction
(b)
(b)
(a)
(a)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)-direction(b)-direction
(b)
(b)
(a)
(a)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(A) Shear length = 02nm (B) 04nm
(C) 06nm (D) 08nm
Figure 7 Time transition of RDF for V = 05ms (comparison between (a)- and (b)-direction sliding)
is carried out sufficiently the crystalline structure of Cu2S
has collapsed and the crystalline slip system (plane anddirection) no longer determines the sliding behavior Evenif there exists a certain easy-glide plane or direction thecrystal does not always show especially smaller shear stressin sliding
332 Dependency on Sliding Velocity Figure 10(A) shows therelation between shear distance and shear stress deviation 120591
119886
It compares results for a variety of velocities ranging from 05to 50ms For all velocities and for the sliding distance up to02 nm 120591
119886linearly increases with the same gradientThis fact
means that the material deforms in elastic manner for smallsliding and deformation However after that 120591
119886decreases
suddenly The larger the sliding velocity is the larger theaveraged value of 120591
119886is obtained It is reasonable that time rate
of decrease is smaller for higher speed sliding As the wholetime calculated here is seen the case of V= 50ms exhibits the
largest level of 120591119886 For (b)-direction Figure 10(B) shows that
the value of 120591119886increases with increase of sliding velocity It
is concluded that shear stress of this material depends largelyon sliding velocity
The relation between 120591119886and sliding velocity V is sum-
marized in Table 5 120591ave time average of 120591119886 is also shown
at the bottom line It indicates that 120591ave of (a)-directionis approximately 10 smaller than that of (b)-directionWhile the easiest glide directionplane of the HC struc-ture is ⟨0110⟩(0001) (ie (b)-direction) it does not showsmall resistance in the sliding Thus it is concluded thatCu2S crystal does surely show sliding motion but it is
not by usual crystalline slip (glide) mechanism of ordinarymetals
On the other hand the fact that shear stress increaseswith increase of velocity is interesting It means that thismaterial deforms by slidingwith somewhat liquid-like (amor-phous) behavior The deformation rate (ie velocity) in such
10 Journal of Materials
(a)
(a)
(b)
(b)
r (nm)04504035030250201501
14
12
1
08
06
04
02
0
g(r)
(a)-direction(b)-direction
(a) (b)
r (nm)04504035030250201501
12
1
08
06
04
0
02
g(r)
(a)-direction(b)-direction
(a) (b)
r (nm)04504035030250201501
14
12
1
08
06
04
02
0
g(r)
(a)-direction(b)-direction
(a) (b)
(a) (b)
(B) = 10ms
(C) = 50ms
(A) Velocity = 05ms
Figure 8 The comparison of RDF at the same sliding distance (10 nm) between (a)- and (b)-direction sliding
Table 5 Relation between averaged shear stress 120591ave and slidingvelocity V
Sliding velocityVms
Averaged shear stress 120591ave GPa(A) (a)-direction sliding (B) (b)-direction sliding
05 193 22810 214 25450 264 283Average 224 255
amorphous substance produces shear stress inside due toits viscosity and so the shear stress depends on sliding(shear) velocity gradient As shown in Figure 11 averagedshear stresses 120591ave summarized in Table 5 are replotted interms of sliding velocity As recognized in Figure 11 shearstress is almost proportional to the sliding velocity In the
present simulation condition system temperature is kept at10 kelvins which is quite low But the atomic mobility atcontact layers between materials should rise due to the workdone by sliding motion In observing atomic motion theyshow intermittent slip which is sometimes called ldquostick andslipmotionrdquo in nanotribological consideration Furthermorewhen in Figure 11 we extrapolate approximated straight linesdown to V = 0 shear stress 120591ave does not return to zero butit remains at a finite value 120591
0= 20sim25GPa These ideal shear
stresses at V = 0 correspond to static friction of materials Italso means that 120591
0are at least required for layered atoms to
exhibit a material flow
4 Conclusion
In this paper we perform a molecular dynamics (MD)study on copper sulfide material (Cu
2S) under the sliding
Journal of Materials 11
0
20
40
60
80
0 200 400 600 800 1000
Shea
r stre
ss (G
Pa)
Time (ps)
(b)
(a)
= 05ms (a)-dir = 05ms (b)-dir
minus20
0
20
40
60
80
0 100 200 300 400 500 600
Shea
r stre
ss (G
Pa)
Time (ps)
(a)(b)
minus20
= 10ms (a)-dir = 10ms (b)-dir
(a)
(b)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
minus20
Time (ps)
= 50ms (a)-dir = 50ms (b)-dir
200150100500
(A) = 05ms (B) = 10ms
(C) = 50ms
Figure 9 Comparison of the absolute value of shear stress deviation 120591119886between (a)- and (b)-direction
motion The MD simulation includes a new implementationof potential energy function for Cu
2S crystal where some
first-principle calculations are utilized The potential energyfunction has three-body term The following results areobtained and we will make conclusion
(1) First-principle calculations are performed for thehexagonal unit structure of Cu
2S crystal From the
optimized structure original lattice parameters 119886
and 119888 of unit cell and stable configuration of S andCu atoms are obtained Based on those results aninteratomic potential function including ionic andMorse terms as well as angular-dependent term isconstructed for Cu and S system It is confirmedthat this potential function can show enough stability
for the hexagonal crystal structure of Cu2S in MD
simulations(2) An easy-glide direction ⟨21 10⟩ on (0001) plane gen-
erally found for usual hexagonal crystals is not thedirection with small resistance to sliding
(3) Cu2S crystal shows partially liquid-like structure and
behavior in which the shear stress occurring in thematerial depends on the sliding velocity
In the further study we should clarify the tempera-ture dependence and dependency on compressive conditionduring sliding of Cu
2S It is supposed that they are made
possible by analyzing more atomic trajectories obtained byMD simulations It will lead to total understanding of slidingmechanism of Cu
2S crystal
12 Journal of Materials
0
20
40
60
80
0 01 02 03 04 05
Shea
r stre
ss (G
Pa)
Shear distance (nm)
Slow decrease
Fast decrease
minus20
= 50ms (a)-dir = 10ms (a)-dir
= 05ms (a)-dir
0 01 02 03 04 05Shear distance (nm)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
Stress increase by velocity
minus20
= 50ms (b)-dir = 10ms (b)-dir
= 05ms (b)-dir
(A) (a)-direction ( ) sliding (B) (b)-direction ( ) sliding110⟩⟨2 ⟨0110⟩
Figure 10 Relation between shear distance and the deviation of shear stress 120591119886 comparison among different sliding velocities
0
5
10
15
20
25
30
0 1 2 3 4 5
(a)-direction(b)-direction
Linear fit ((a)-dir)Linear fit ((b)-dir)
(ms)
120591 a(G
Pa)
Figure 11 Averaged shear stress replotted against sliding velocity((a)- and (b)-directions (⟨21 10⟩ and ⟨0110⟩))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This study is partly supported by NEDO Innovative Project(2012-2013) and by the ldquoStrategic Project to Support the For-mation of Research Bases at Private Universities MatchingFund Subsidy from MEXT (Ministry of Education CultureSports Science and Technology) (2012ndash2015)rdquo The authorsalso acknowledge Kurimoto Ltd for financial support
References
[1] T Sato Y Hirai T Fukui T Ejima M Takuma and K SaitohldquoAtomic-modeling and simulation of copper sulfide as microsolid lubricantrdquoMRS Proceedings vol 1513 p 20 2013
[2] H Sueyoshi Y Yamano K Inoue Y Maeda and K YamadaldquoMechanical properties of copper sulfide-dispersed lead-freebronzerdquoMaterials Transactions vol 50 no 4 pp 776ndash781 2009
[3] Y Hirai Y Ueda M Yamamoto T Kobayashi and TMaruyama Japanese Patent 132986 2009
[4] K Akamatsu T Kobayashi A Nishimoto T Maruyama andY Arachi ldquoDevelopment of new copper alloymdashinfluence ofmetallic elements on the human bodyrdquo Rikogaku to Gijyutsuvol 16 pp 31ndash36 2009 (Japanese)
[5] L-W Wang ldquoHigh chalcocite Cu2S a solid-liquid hybrid
phaserdquoPhysical Review Letters vol 108 no 8 Article ID 0857032012
[6] T Ejima K-I Saitoh N Shinke M Taruma Y Hirai and TSato ldquoAtomic-level analysis of copper sulfide (CU2S) crystalstructure and sliding characteristicsrdquo Technology Reports ofKansai University vol 54 pp 23ndash33 2012
[7] I I Mazin ldquoStructural and electronic properties of the two-dimensional superconductor CuS with 1(13)-valent copperrdquoPhysical Review B vol 85 Article ID 115133 2012
[8] M J Buerger and B J Wuensch ldquoDistribution of atoms in highchalcocite Cu
2Srdquo Science vol 141 no 3577 pp 276ndash277 1963
[9] B J Wuensch and M J Buerger ldquoThe crystal structure ofchalcocite Cu
2Srdquo Mineralogical Society of America Special
Paper vol 1 pp 163ndash170 1963 Proceedings of the 3rd GenralMeeting
[10] T Onodera Y Morlta A Suzuki et al ldquoA computationalchemistry study on friction of h-MoS2 Part I Mechanism ofsingle sheet lubricationrdquo The Journal of Physical Chemistry Bvol 113 no 52 pp 16526ndash16536 2009
[11] Y Ding D R Veblen and C T Prewitt ldquoPossible FeCu order-ing schemes in the 2a superstructure of bornite (Cu
5FeS4)rdquo
American Mineralogist vol 90 no 8-9 pp 1265ndash1269 2005
Journal of Materials 13
[12] H Zheng J B Rivest T A Miller et al ldquoObservation of tran-sient structural-transformation dynamics in a Cu
2S nanorodrdquo
Science vol 333 no 6039 pp 206ndash209 2011[13] S KashidaW ShimosakaMMori andDYoshimura ldquoValence
band photoemission study of the copper chalcogenide com-pounds Cu2S Cu2Se and Cu2Terdquo Journal of Physics andChemistry of Solids vol 64 no 12 pp 2357ndash2363 2003
[14] P Lukashev W R L Lambrecht T Kotani and M VanSchilfgaarde ldquoElectronic and crystal structure of Cu2-x S full-potential electronic structure calculationsrdquo Physical Review Bvol 76 no 19 Article ID 195202 2007
[15] P Blaha K Schwarz G Madsen D Kvasnicka and J LuitzldquoWIEN2krdquo httpwwwwien2katindexhtml
[16] P A Romero T T Jarvi N Beckmann M Mrovec andM Moseler ldquoCoarse graining and localized plasticity betweensliding nanocrystalline metalsrdquo Physical Review Letters vol 113no 3 Article ID 036101 2014
[17] S Izumi and S Sakai ldquoInternal displacement and elasticproperties of the silicon tersoff modelrdquo JSME InternationalJournal Series A Solid Mechanics and Material Engineering vol47 no 1 pp 54ndash61 2004
[18] M P Allen and D J Tildesley Computer Simulation of LiquidsOxford University Press Oxford UK 1989
[19] Sandia Nantional Laboratory ldquoLarge-scale AtomicMolecularMassively Parallel Simulatorrdquo httplammpssandiagov
[20] T Yamaguchi and K Saitoh ldquoMolecular dyanmics study onmechanical properties in the structure of self-assembled quan-tum dotrdquoWorld Journal of Nano Science and Engineering vol 2pp 189ndash195 2012
[21] T Ejima Atomic-level analysis on sliding characteristic of coppersulfide [MS thesis] Graduate School of Kansai University 2013
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
Journal of Materials 7
21564Aring
26712Aring
23926Aring
35219Aring
Cu
S
S
S S S S S
Cu
SS S
124125 deg
91599deg106333deg
65876deg
Figure 5 Schematic of the way to average two types of coordination for Cu atoms in Cu2S crystal
Table 4 Potential parameters fitted by FP calculations
(a) Morse potential (Cu-S)
Kind of pair 119863119894119895
120573119894119895
1199030
Unit kJmole 1nm nmCu-S 298916 1500 2029(Mo-S) (152076) (1800) (2532)
(b) Angular potential (S-Cu-S Cu-S-Cu)
Combination 1205790
Unit degS-Cu-S 98966Cu-S-Cu 98966
(c) B-M-H ionic potential (Cu-S)
Kind of pair 1199031015840
0119886Cu 119886S
Unit nm nm nm25319 070052 18314lowast
119886Slowast has been already obtained for MoS2 potential [10]
octahedral sites as shown in Figure 5 since there is possibilitythat Cu atoms may be located on both sites In practicewe just need equilibrium three-body angle 120579
0and pairwise
distance 1199031015840
0 Finally they are 120579
0= 98966
∘ and 1199031015840
0= 2532 nm
respectivelyAdditionally the BMH term requires ionic radii 119886Cu and
119886S for each element The radius of Cu atom is supposed tobe equivalent to the equilibrium length 119903
0in Morse potential
above the radius 119886S = 1834 nm for S is already available fromthe previous MD study of MoS
2[10]
Thus MD potential parameters to reproduce the HCstructure of Cu
2S are obtained by mostly FP calculation and
they are summarized in Table 4
33 Sliding and Friction Behavior of Cu2S
331 Dependency on Crystalline Orientation The depen-dence on crystalline orientation in sliding behavior of Cu
2S
is as follows Figure 6 shows the atomic configurations at119905 = 600 ps with sliding velocity V = 05ms comparingbetween models which are sliding in (a)-direction (⟨0110⟩)sliding and in (b)-direction (⟨21 10⟩) Both models oncecollapse and lose their crystalline stacking during sliding Butafter that the atomic structure recovers its original stackingduring long-time slidingThe difference between twomodelsis not found just visually from atomic configurations asseen in the broken black- and yellow-colored rectangularareas depicted in the figures Therefore the RDF analysiswill be helpful for identifying the change of crystallinestructures Besides in order to recognize transition of anatomic force during sliding the analysis of shear stress willbe helpful
The result of RDF analysis is shown in Figure 7 which isfor sliding velocity V = 05ms and compares results between(a)-direction and (b)-direction models In these RDF figurespeaks are found at some distances by which the nature ofcrystalline structure is confirmed In particular whenwe takea look at peaks found in the range of 02sim08 nm for twomodels the steepness of the distribution in (b)-direction istotally stronger than that in (a)-direction So the structureobtained by the sliding in (b)-direction tends to retain morelocal crystalline structure than that obtained in (a)-directionsliding
Just when the resulting sliding distance becomes 10 nmis the RDF obtained as shown in Figure 8 for different slidingvelocities (V = 10 and 50ms) At the same sliding distancethe crystalline stacking is the same and so the results maybe compared as for different velocity conditions One peakof RDF is just identified for the 1st neighbor distance whichmeans the crystalline structure has been lost and the atomicmovement shows somewhat of fluidity
Shear stress averaged over the whole specimen 120591totrepresents the resistance to the slidingThe time transition of120591tot reflects atomic force state in the sliding During relaxationprocess in fact a certain value of shear stress already occursThis is due to atomic rearrangement inside the crystal unitAfter the specimen is fully relaxed we reset the stress valueLet the value at the beginning of sliding be 120591tot(0) Then the
8 Journal of Materials
Disordered
Ordered layer
CuCu
CuCu
SS
S
To front
To back
To right
To left
Disordered
Ordered layer
CuCuCu
S
S
S Cu
(A) (a)-direction (⟨0110⟩) sliding (the sliding direction is normal to the figure plane)
(B) (b)-direction ( 110⟩) sliding (the sliding direction is right and left)⟨2
Figure 6 Comparison of instantaneous atomic configurations obtained at 119905 = 600 ps with V = 05ms (the picture is drawn onto 119910-119911 plane)
absolute value of deviation of current value 120591tot from initialvalue 120591tot(0) is defined to be
120591119886=
1003816100381610038161003816120591tot minus 120591tot (0)
1003816100381610038161003816 (7)
This stress deviation 120591119886reflects a sudden increase of friction
due to roughness of slide planes The time transition of 120591119886
is obtained as shown in Figure 9 Figure 9(A) shows therelation between the time and the stress deviation 120591
119886 120591119886is
averaged over the whole specimen Those graphs show that120591119886for (a)-direction sliding is larger than that in (b)-direction
The downward arrows in the figure display each maximumvalue At low velocity atoms near contact layers feel relativelylarger resistance to slide in (a)-direction sliding while the
(b)-direction sliding seems much easier However for thecases with higher velocity such as V = 10ms or 50ms thetendency of stress 120591
119886is changed as shown in Figures 9(B)
and 9(C) As shown in Figure 9(B) for example for V =10ms the peak value in (b)-direction is sometimes largerthan that in (a)-direction especially during 50ndash100 ps or 250ndash300 ps
We summarize the dependency of sliding direction asfollows When the shear velocity is small (b)-direction(⟨0110⟩) sliding is easier than (a)-direction (⟨0110⟩) How-ever once the sliding has completed such as to 100 or200 ps from the start of sliding distinction between slidingdirections becomes negligible The cause of this behaviorwould be guessed and explained as follows When the sliding
Journal of Materials 9
(a)
(a)-direction(b)-direction
(a)
(b)16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)
(a)-direction(b)-direction
(b)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)(b)
(a)-direction(b)-direction
(b)
(b)
(a)
(a)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)-direction(b)-direction
(b)
(b)
(a)
(a)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(A) Shear length = 02nm (B) 04nm
(C) 06nm (D) 08nm
Figure 7 Time transition of RDF for V = 05ms (comparison between (a)- and (b)-direction sliding)
is carried out sufficiently the crystalline structure of Cu2S
has collapsed and the crystalline slip system (plane anddirection) no longer determines the sliding behavior Evenif there exists a certain easy-glide plane or direction thecrystal does not always show especially smaller shear stressin sliding
332 Dependency on Sliding Velocity Figure 10(A) shows therelation between shear distance and shear stress deviation 120591
119886
It compares results for a variety of velocities ranging from 05to 50ms For all velocities and for the sliding distance up to02 nm 120591
119886linearly increases with the same gradientThis fact
means that the material deforms in elastic manner for smallsliding and deformation However after that 120591
119886decreases
suddenly The larger the sliding velocity is the larger theaveraged value of 120591
119886is obtained It is reasonable that time rate
of decrease is smaller for higher speed sliding As the wholetime calculated here is seen the case of V= 50ms exhibits the
largest level of 120591119886 For (b)-direction Figure 10(B) shows that
the value of 120591119886increases with increase of sliding velocity It
is concluded that shear stress of this material depends largelyon sliding velocity
The relation between 120591119886and sliding velocity V is sum-
marized in Table 5 120591ave time average of 120591119886 is also shown
at the bottom line It indicates that 120591ave of (a)-directionis approximately 10 smaller than that of (b)-directionWhile the easiest glide directionplane of the HC struc-ture is ⟨0110⟩(0001) (ie (b)-direction) it does not showsmall resistance in the sliding Thus it is concluded thatCu2S crystal does surely show sliding motion but it is
not by usual crystalline slip (glide) mechanism of ordinarymetals
On the other hand the fact that shear stress increaseswith increase of velocity is interesting It means that thismaterial deforms by slidingwith somewhat liquid-like (amor-phous) behavior The deformation rate (ie velocity) in such
10 Journal of Materials
(a)
(a)
(b)
(b)
r (nm)04504035030250201501
14
12
1
08
06
04
02
0
g(r)
(a)-direction(b)-direction
(a) (b)
r (nm)04504035030250201501
12
1
08
06
04
0
02
g(r)
(a)-direction(b)-direction
(a) (b)
r (nm)04504035030250201501
14
12
1
08
06
04
02
0
g(r)
(a)-direction(b)-direction
(a) (b)
(a) (b)
(B) = 10ms
(C) = 50ms
(A) Velocity = 05ms
Figure 8 The comparison of RDF at the same sliding distance (10 nm) between (a)- and (b)-direction sliding
Table 5 Relation between averaged shear stress 120591ave and slidingvelocity V
Sliding velocityVms
Averaged shear stress 120591ave GPa(A) (a)-direction sliding (B) (b)-direction sliding
05 193 22810 214 25450 264 283Average 224 255
amorphous substance produces shear stress inside due toits viscosity and so the shear stress depends on sliding(shear) velocity gradient As shown in Figure 11 averagedshear stresses 120591ave summarized in Table 5 are replotted interms of sliding velocity As recognized in Figure 11 shearstress is almost proportional to the sliding velocity In the
present simulation condition system temperature is kept at10 kelvins which is quite low But the atomic mobility atcontact layers between materials should rise due to the workdone by sliding motion In observing atomic motion theyshow intermittent slip which is sometimes called ldquostick andslipmotionrdquo in nanotribological consideration Furthermorewhen in Figure 11 we extrapolate approximated straight linesdown to V = 0 shear stress 120591ave does not return to zero butit remains at a finite value 120591
0= 20sim25GPa These ideal shear
stresses at V = 0 correspond to static friction of materials Italso means that 120591
0are at least required for layered atoms to
exhibit a material flow
4 Conclusion
In this paper we perform a molecular dynamics (MD)study on copper sulfide material (Cu
2S) under the sliding
Journal of Materials 11
0
20
40
60
80
0 200 400 600 800 1000
Shea
r stre
ss (G
Pa)
Time (ps)
(b)
(a)
= 05ms (a)-dir = 05ms (b)-dir
minus20
0
20
40
60
80
0 100 200 300 400 500 600
Shea
r stre
ss (G
Pa)
Time (ps)
(a)(b)
minus20
= 10ms (a)-dir = 10ms (b)-dir
(a)
(b)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
minus20
Time (ps)
= 50ms (a)-dir = 50ms (b)-dir
200150100500
(A) = 05ms (B) = 10ms
(C) = 50ms
Figure 9 Comparison of the absolute value of shear stress deviation 120591119886between (a)- and (b)-direction
motion The MD simulation includes a new implementationof potential energy function for Cu
2S crystal where some
first-principle calculations are utilized The potential energyfunction has three-body term The following results areobtained and we will make conclusion
(1) First-principle calculations are performed for thehexagonal unit structure of Cu
2S crystal From the
optimized structure original lattice parameters 119886
and 119888 of unit cell and stable configuration of S andCu atoms are obtained Based on those results aninteratomic potential function including ionic andMorse terms as well as angular-dependent term isconstructed for Cu and S system It is confirmedthat this potential function can show enough stability
for the hexagonal crystal structure of Cu2S in MD
simulations(2) An easy-glide direction ⟨21 10⟩ on (0001) plane gen-
erally found for usual hexagonal crystals is not thedirection with small resistance to sliding
(3) Cu2S crystal shows partially liquid-like structure and
behavior in which the shear stress occurring in thematerial depends on the sliding velocity
In the further study we should clarify the tempera-ture dependence and dependency on compressive conditionduring sliding of Cu
2S It is supposed that they are made
possible by analyzing more atomic trajectories obtained byMD simulations It will lead to total understanding of slidingmechanism of Cu
2S crystal
12 Journal of Materials
0
20
40
60
80
0 01 02 03 04 05
Shea
r stre
ss (G
Pa)
Shear distance (nm)
Slow decrease
Fast decrease
minus20
= 50ms (a)-dir = 10ms (a)-dir
= 05ms (a)-dir
0 01 02 03 04 05Shear distance (nm)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
Stress increase by velocity
minus20
= 50ms (b)-dir = 10ms (b)-dir
= 05ms (b)-dir
(A) (a)-direction ( ) sliding (B) (b)-direction ( ) sliding110⟩⟨2 ⟨0110⟩
Figure 10 Relation between shear distance and the deviation of shear stress 120591119886 comparison among different sliding velocities
0
5
10
15
20
25
30
0 1 2 3 4 5
(a)-direction(b)-direction
Linear fit ((a)-dir)Linear fit ((b)-dir)
(ms)
120591 a(G
Pa)
Figure 11 Averaged shear stress replotted against sliding velocity((a)- and (b)-directions (⟨21 10⟩ and ⟨0110⟩))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This study is partly supported by NEDO Innovative Project(2012-2013) and by the ldquoStrategic Project to Support the For-mation of Research Bases at Private Universities MatchingFund Subsidy from MEXT (Ministry of Education CultureSports Science and Technology) (2012ndash2015)rdquo The authorsalso acknowledge Kurimoto Ltd for financial support
References
[1] T Sato Y Hirai T Fukui T Ejima M Takuma and K SaitohldquoAtomic-modeling and simulation of copper sulfide as microsolid lubricantrdquoMRS Proceedings vol 1513 p 20 2013
[2] H Sueyoshi Y Yamano K Inoue Y Maeda and K YamadaldquoMechanical properties of copper sulfide-dispersed lead-freebronzerdquoMaterials Transactions vol 50 no 4 pp 776ndash781 2009
[3] Y Hirai Y Ueda M Yamamoto T Kobayashi and TMaruyama Japanese Patent 132986 2009
[4] K Akamatsu T Kobayashi A Nishimoto T Maruyama andY Arachi ldquoDevelopment of new copper alloymdashinfluence ofmetallic elements on the human bodyrdquo Rikogaku to Gijyutsuvol 16 pp 31ndash36 2009 (Japanese)
[5] L-W Wang ldquoHigh chalcocite Cu2S a solid-liquid hybrid
phaserdquoPhysical Review Letters vol 108 no 8 Article ID 0857032012
[6] T Ejima K-I Saitoh N Shinke M Taruma Y Hirai and TSato ldquoAtomic-level analysis of copper sulfide (CU2S) crystalstructure and sliding characteristicsrdquo Technology Reports ofKansai University vol 54 pp 23ndash33 2012
[7] I I Mazin ldquoStructural and electronic properties of the two-dimensional superconductor CuS with 1(13)-valent copperrdquoPhysical Review B vol 85 Article ID 115133 2012
[8] M J Buerger and B J Wuensch ldquoDistribution of atoms in highchalcocite Cu
2Srdquo Science vol 141 no 3577 pp 276ndash277 1963
[9] B J Wuensch and M J Buerger ldquoThe crystal structure ofchalcocite Cu
2Srdquo Mineralogical Society of America Special
Paper vol 1 pp 163ndash170 1963 Proceedings of the 3rd GenralMeeting
[10] T Onodera Y Morlta A Suzuki et al ldquoA computationalchemistry study on friction of h-MoS2 Part I Mechanism ofsingle sheet lubricationrdquo The Journal of Physical Chemistry Bvol 113 no 52 pp 16526ndash16536 2009
[11] Y Ding D R Veblen and C T Prewitt ldquoPossible FeCu order-ing schemes in the 2a superstructure of bornite (Cu
5FeS4)rdquo
American Mineralogist vol 90 no 8-9 pp 1265ndash1269 2005
Journal of Materials 13
[12] H Zheng J B Rivest T A Miller et al ldquoObservation of tran-sient structural-transformation dynamics in a Cu
2S nanorodrdquo
Science vol 333 no 6039 pp 206ndash209 2011[13] S KashidaW ShimosakaMMori andDYoshimura ldquoValence
band photoemission study of the copper chalcogenide com-pounds Cu2S Cu2Se and Cu2Terdquo Journal of Physics andChemistry of Solids vol 64 no 12 pp 2357ndash2363 2003
[14] P Lukashev W R L Lambrecht T Kotani and M VanSchilfgaarde ldquoElectronic and crystal structure of Cu2-x S full-potential electronic structure calculationsrdquo Physical Review Bvol 76 no 19 Article ID 195202 2007
[15] P Blaha K Schwarz G Madsen D Kvasnicka and J LuitzldquoWIEN2krdquo httpwwwwien2katindexhtml
[16] P A Romero T T Jarvi N Beckmann M Mrovec andM Moseler ldquoCoarse graining and localized plasticity betweensliding nanocrystalline metalsrdquo Physical Review Letters vol 113no 3 Article ID 036101 2014
[17] S Izumi and S Sakai ldquoInternal displacement and elasticproperties of the silicon tersoff modelrdquo JSME InternationalJournal Series A Solid Mechanics and Material Engineering vol47 no 1 pp 54ndash61 2004
[18] M P Allen and D J Tildesley Computer Simulation of LiquidsOxford University Press Oxford UK 1989
[19] Sandia Nantional Laboratory ldquoLarge-scale AtomicMolecularMassively Parallel Simulatorrdquo httplammpssandiagov
[20] T Yamaguchi and K Saitoh ldquoMolecular dyanmics study onmechanical properties in the structure of self-assembled quan-tum dotrdquoWorld Journal of Nano Science and Engineering vol 2pp 189ndash195 2012
[21] T Ejima Atomic-level analysis on sliding characteristic of coppersulfide [MS thesis] Graduate School of Kansai University 2013
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
8 Journal of Materials
Disordered
Ordered layer
CuCu
CuCu
SS
S
To front
To back
To right
To left
Disordered
Ordered layer
CuCuCu
S
S
S Cu
(A) (a)-direction (⟨0110⟩) sliding (the sliding direction is normal to the figure plane)
(B) (b)-direction ( 110⟩) sliding (the sliding direction is right and left)⟨2
Figure 6 Comparison of instantaneous atomic configurations obtained at 119905 = 600 ps with V = 05ms (the picture is drawn onto 119910-119911 plane)
absolute value of deviation of current value 120591tot from initialvalue 120591tot(0) is defined to be
120591119886=
1003816100381610038161003816120591tot minus 120591tot (0)
1003816100381610038161003816 (7)
This stress deviation 120591119886reflects a sudden increase of friction
due to roughness of slide planes The time transition of 120591119886
is obtained as shown in Figure 9 Figure 9(A) shows therelation between the time and the stress deviation 120591
119886 120591119886is
averaged over the whole specimen Those graphs show that120591119886for (a)-direction sliding is larger than that in (b)-direction
The downward arrows in the figure display each maximumvalue At low velocity atoms near contact layers feel relativelylarger resistance to slide in (a)-direction sliding while the
(b)-direction sliding seems much easier However for thecases with higher velocity such as V = 10ms or 50ms thetendency of stress 120591
119886is changed as shown in Figures 9(B)
and 9(C) As shown in Figure 9(B) for example for V =10ms the peak value in (b)-direction is sometimes largerthan that in (a)-direction especially during 50ndash100 ps or 250ndash300 ps
We summarize the dependency of sliding direction asfollows When the shear velocity is small (b)-direction(⟨0110⟩) sliding is easier than (a)-direction (⟨0110⟩) How-ever once the sliding has completed such as to 100 or200 ps from the start of sliding distinction between slidingdirections becomes negligible The cause of this behaviorwould be guessed and explained as follows When the sliding
Journal of Materials 9
(a)
(a)-direction(b)-direction
(a)
(b)16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)
(a)-direction(b)-direction
(b)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)(b)
(a)-direction(b)-direction
(b)
(b)
(a)
(a)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)-direction(b)-direction
(b)
(b)
(a)
(a)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(A) Shear length = 02nm (B) 04nm
(C) 06nm (D) 08nm
Figure 7 Time transition of RDF for V = 05ms (comparison between (a)- and (b)-direction sliding)
is carried out sufficiently the crystalline structure of Cu2S
has collapsed and the crystalline slip system (plane anddirection) no longer determines the sliding behavior Evenif there exists a certain easy-glide plane or direction thecrystal does not always show especially smaller shear stressin sliding
332 Dependency on Sliding Velocity Figure 10(A) shows therelation between shear distance and shear stress deviation 120591
119886
It compares results for a variety of velocities ranging from 05to 50ms For all velocities and for the sliding distance up to02 nm 120591
119886linearly increases with the same gradientThis fact
means that the material deforms in elastic manner for smallsliding and deformation However after that 120591
119886decreases
suddenly The larger the sliding velocity is the larger theaveraged value of 120591
119886is obtained It is reasonable that time rate
of decrease is smaller for higher speed sliding As the wholetime calculated here is seen the case of V= 50ms exhibits the
largest level of 120591119886 For (b)-direction Figure 10(B) shows that
the value of 120591119886increases with increase of sliding velocity It
is concluded that shear stress of this material depends largelyon sliding velocity
The relation between 120591119886and sliding velocity V is sum-
marized in Table 5 120591ave time average of 120591119886 is also shown
at the bottom line It indicates that 120591ave of (a)-directionis approximately 10 smaller than that of (b)-directionWhile the easiest glide directionplane of the HC struc-ture is ⟨0110⟩(0001) (ie (b)-direction) it does not showsmall resistance in the sliding Thus it is concluded thatCu2S crystal does surely show sliding motion but it is
not by usual crystalline slip (glide) mechanism of ordinarymetals
On the other hand the fact that shear stress increaseswith increase of velocity is interesting It means that thismaterial deforms by slidingwith somewhat liquid-like (amor-phous) behavior The deformation rate (ie velocity) in such
10 Journal of Materials
(a)
(a)
(b)
(b)
r (nm)04504035030250201501
14
12
1
08
06
04
02
0
g(r)
(a)-direction(b)-direction
(a) (b)
r (nm)04504035030250201501
12
1
08
06
04
0
02
g(r)
(a)-direction(b)-direction
(a) (b)
r (nm)04504035030250201501
14
12
1
08
06
04
02
0
g(r)
(a)-direction(b)-direction
(a) (b)
(a) (b)
(B) = 10ms
(C) = 50ms
(A) Velocity = 05ms
Figure 8 The comparison of RDF at the same sliding distance (10 nm) between (a)- and (b)-direction sliding
Table 5 Relation between averaged shear stress 120591ave and slidingvelocity V
Sliding velocityVms
Averaged shear stress 120591ave GPa(A) (a)-direction sliding (B) (b)-direction sliding
05 193 22810 214 25450 264 283Average 224 255
amorphous substance produces shear stress inside due toits viscosity and so the shear stress depends on sliding(shear) velocity gradient As shown in Figure 11 averagedshear stresses 120591ave summarized in Table 5 are replotted interms of sliding velocity As recognized in Figure 11 shearstress is almost proportional to the sliding velocity In the
present simulation condition system temperature is kept at10 kelvins which is quite low But the atomic mobility atcontact layers between materials should rise due to the workdone by sliding motion In observing atomic motion theyshow intermittent slip which is sometimes called ldquostick andslipmotionrdquo in nanotribological consideration Furthermorewhen in Figure 11 we extrapolate approximated straight linesdown to V = 0 shear stress 120591ave does not return to zero butit remains at a finite value 120591
0= 20sim25GPa These ideal shear
stresses at V = 0 correspond to static friction of materials Italso means that 120591
0are at least required for layered atoms to
exhibit a material flow
4 Conclusion
In this paper we perform a molecular dynamics (MD)study on copper sulfide material (Cu
2S) under the sliding
Journal of Materials 11
0
20
40
60
80
0 200 400 600 800 1000
Shea
r stre
ss (G
Pa)
Time (ps)
(b)
(a)
= 05ms (a)-dir = 05ms (b)-dir
minus20
0
20
40
60
80
0 100 200 300 400 500 600
Shea
r stre
ss (G
Pa)
Time (ps)
(a)(b)
minus20
= 10ms (a)-dir = 10ms (b)-dir
(a)
(b)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
minus20
Time (ps)
= 50ms (a)-dir = 50ms (b)-dir
200150100500
(A) = 05ms (B) = 10ms
(C) = 50ms
Figure 9 Comparison of the absolute value of shear stress deviation 120591119886between (a)- and (b)-direction
motion The MD simulation includes a new implementationof potential energy function for Cu
2S crystal where some
first-principle calculations are utilized The potential energyfunction has three-body term The following results areobtained and we will make conclusion
(1) First-principle calculations are performed for thehexagonal unit structure of Cu
2S crystal From the
optimized structure original lattice parameters 119886
and 119888 of unit cell and stable configuration of S andCu atoms are obtained Based on those results aninteratomic potential function including ionic andMorse terms as well as angular-dependent term isconstructed for Cu and S system It is confirmedthat this potential function can show enough stability
for the hexagonal crystal structure of Cu2S in MD
simulations(2) An easy-glide direction ⟨21 10⟩ on (0001) plane gen-
erally found for usual hexagonal crystals is not thedirection with small resistance to sliding
(3) Cu2S crystal shows partially liquid-like structure and
behavior in which the shear stress occurring in thematerial depends on the sliding velocity
In the further study we should clarify the tempera-ture dependence and dependency on compressive conditionduring sliding of Cu
2S It is supposed that they are made
possible by analyzing more atomic trajectories obtained byMD simulations It will lead to total understanding of slidingmechanism of Cu
2S crystal
12 Journal of Materials
0
20
40
60
80
0 01 02 03 04 05
Shea
r stre
ss (G
Pa)
Shear distance (nm)
Slow decrease
Fast decrease
minus20
= 50ms (a)-dir = 10ms (a)-dir
= 05ms (a)-dir
0 01 02 03 04 05Shear distance (nm)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
Stress increase by velocity
minus20
= 50ms (b)-dir = 10ms (b)-dir
= 05ms (b)-dir
(A) (a)-direction ( ) sliding (B) (b)-direction ( ) sliding110⟩⟨2 ⟨0110⟩
Figure 10 Relation between shear distance and the deviation of shear stress 120591119886 comparison among different sliding velocities
0
5
10
15
20
25
30
0 1 2 3 4 5
(a)-direction(b)-direction
Linear fit ((a)-dir)Linear fit ((b)-dir)
(ms)
120591 a(G
Pa)
Figure 11 Averaged shear stress replotted against sliding velocity((a)- and (b)-directions (⟨21 10⟩ and ⟨0110⟩))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This study is partly supported by NEDO Innovative Project(2012-2013) and by the ldquoStrategic Project to Support the For-mation of Research Bases at Private Universities MatchingFund Subsidy from MEXT (Ministry of Education CultureSports Science and Technology) (2012ndash2015)rdquo The authorsalso acknowledge Kurimoto Ltd for financial support
References
[1] T Sato Y Hirai T Fukui T Ejima M Takuma and K SaitohldquoAtomic-modeling and simulation of copper sulfide as microsolid lubricantrdquoMRS Proceedings vol 1513 p 20 2013
[2] H Sueyoshi Y Yamano K Inoue Y Maeda and K YamadaldquoMechanical properties of copper sulfide-dispersed lead-freebronzerdquoMaterials Transactions vol 50 no 4 pp 776ndash781 2009
[3] Y Hirai Y Ueda M Yamamoto T Kobayashi and TMaruyama Japanese Patent 132986 2009
[4] K Akamatsu T Kobayashi A Nishimoto T Maruyama andY Arachi ldquoDevelopment of new copper alloymdashinfluence ofmetallic elements on the human bodyrdquo Rikogaku to Gijyutsuvol 16 pp 31ndash36 2009 (Japanese)
[5] L-W Wang ldquoHigh chalcocite Cu2S a solid-liquid hybrid
phaserdquoPhysical Review Letters vol 108 no 8 Article ID 0857032012
[6] T Ejima K-I Saitoh N Shinke M Taruma Y Hirai and TSato ldquoAtomic-level analysis of copper sulfide (CU2S) crystalstructure and sliding characteristicsrdquo Technology Reports ofKansai University vol 54 pp 23ndash33 2012
[7] I I Mazin ldquoStructural and electronic properties of the two-dimensional superconductor CuS with 1(13)-valent copperrdquoPhysical Review B vol 85 Article ID 115133 2012
[8] M J Buerger and B J Wuensch ldquoDistribution of atoms in highchalcocite Cu
2Srdquo Science vol 141 no 3577 pp 276ndash277 1963
[9] B J Wuensch and M J Buerger ldquoThe crystal structure ofchalcocite Cu
2Srdquo Mineralogical Society of America Special
Paper vol 1 pp 163ndash170 1963 Proceedings of the 3rd GenralMeeting
[10] T Onodera Y Morlta A Suzuki et al ldquoA computationalchemistry study on friction of h-MoS2 Part I Mechanism ofsingle sheet lubricationrdquo The Journal of Physical Chemistry Bvol 113 no 52 pp 16526ndash16536 2009
[11] Y Ding D R Veblen and C T Prewitt ldquoPossible FeCu order-ing schemes in the 2a superstructure of bornite (Cu
5FeS4)rdquo
American Mineralogist vol 90 no 8-9 pp 1265ndash1269 2005
Journal of Materials 13
[12] H Zheng J B Rivest T A Miller et al ldquoObservation of tran-sient structural-transformation dynamics in a Cu
2S nanorodrdquo
Science vol 333 no 6039 pp 206ndash209 2011[13] S KashidaW ShimosakaMMori andDYoshimura ldquoValence
band photoemission study of the copper chalcogenide com-pounds Cu2S Cu2Se and Cu2Terdquo Journal of Physics andChemistry of Solids vol 64 no 12 pp 2357ndash2363 2003
[14] P Lukashev W R L Lambrecht T Kotani and M VanSchilfgaarde ldquoElectronic and crystal structure of Cu2-x S full-potential electronic structure calculationsrdquo Physical Review Bvol 76 no 19 Article ID 195202 2007
[15] P Blaha K Schwarz G Madsen D Kvasnicka and J LuitzldquoWIEN2krdquo httpwwwwien2katindexhtml
[16] P A Romero T T Jarvi N Beckmann M Mrovec andM Moseler ldquoCoarse graining and localized plasticity betweensliding nanocrystalline metalsrdquo Physical Review Letters vol 113no 3 Article ID 036101 2014
[17] S Izumi and S Sakai ldquoInternal displacement and elasticproperties of the silicon tersoff modelrdquo JSME InternationalJournal Series A Solid Mechanics and Material Engineering vol47 no 1 pp 54ndash61 2004
[18] M P Allen and D J Tildesley Computer Simulation of LiquidsOxford University Press Oxford UK 1989
[19] Sandia Nantional Laboratory ldquoLarge-scale AtomicMolecularMassively Parallel Simulatorrdquo httplammpssandiagov
[20] T Yamaguchi and K Saitoh ldquoMolecular dyanmics study onmechanical properties in the structure of self-assembled quan-tum dotrdquoWorld Journal of Nano Science and Engineering vol 2pp 189ndash195 2012
[21] T Ejima Atomic-level analysis on sliding characteristic of coppersulfide [MS thesis] Graduate School of Kansai University 2013
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
Journal of Materials 9
(a)
(a)-direction(b)-direction
(a)
(b)16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)
(a)-direction(b)-direction
(b)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)(b)
(a)-direction(b)-direction
(b)
(b)
(a)
(a)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(a)-direction(b)-direction
(b)
(b)
(a)
(a)
16
14
12
1
08
06
04
02
0
g(r)
r (nm)04504035030250201501
(A) Shear length = 02nm (B) 04nm
(C) 06nm (D) 08nm
Figure 7 Time transition of RDF for V = 05ms (comparison between (a)- and (b)-direction sliding)
is carried out sufficiently the crystalline structure of Cu2S
has collapsed and the crystalline slip system (plane anddirection) no longer determines the sliding behavior Evenif there exists a certain easy-glide plane or direction thecrystal does not always show especially smaller shear stressin sliding
332 Dependency on Sliding Velocity Figure 10(A) shows therelation between shear distance and shear stress deviation 120591
119886
It compares results for a variety of velocities ranging from 05to 50ms For all velocities and for the sliding distance up to02 nm 120591
119886linearly increases with the same gradientThis fact
means that the material deforms in elastic manner for smallsliding and deformation However after that 120591
119886decreases
suddenly The larger the sliding velocity is the larger theaveraged value of 120591
119886is obtained It is reasonable that time rate
of decrease is smaller for higher speed sliding As the wholetime calculated here is seen the case of V= 50ms exhibits the
largest level of 120591119886 For (b)-direction Figure 10(B) shows that
the value of 120591119886increases with increase of sliding velocity It
is concluded that shear stress of this material depends largelyon sliding velocity
The relation between 120591119886and sliding velocity V is sum-
marized in Table 5 120591ave time average of 120591119886 is also shown
at the bottom line It indicates that 120591ave of (a)-directionis approximately 10 smaller than that of (b)-directionWhile the easiest glide directionplane of the HC struc-ture is ⟨0110⟩(0001) (ie (b)-direction) it does not showsmall resistance in the sliding Thus it is concluded thatCu2S crystal does surely show sliding motion but it is
not by usual crystalline slip (glide) mechanism of ordinarymetals
On the other hand the fact that shear stress increaseswith increase of velocity is interesting It means that thismaterial deforms by slidingwith somewhat liquid-like (amor-phous) behavior The deformation rate (ie velocity) in such
10 Journal of Materials
(a)
(a)
(b)
(b)
r (nm)04504035030250201501
14
12
1
08
06
04
02
0
g(r)
(a)-direction(b)-direction
(a) (b)
r (nm)04504035030250201501
12
1
08
06
04
0
02
g(r)
(a)-direction(b)-direction
(a) (b)
r (nm)04504035030250201501
14
12
1
08
06
04
02
0
g(r)
(a)-direction(b)-direction
(a) (b)
(a) (b)
(B) = 10ms
(C) = 50ms
(A) Velocity = 05ms
Figure 8 The comparison of RDF at the same sliding distance (10 nm) between (a)- and (b)-direction sliding
Table 5 Relation between averaged shear stress 120591ave and slidingvelocity V
Sliding velocityVms
Averaged shear stress 120591ave GPa(A) (a)-direction sliding (B) (b)-direction sliding
05 193 22810 214 25450 264 283Average 224 255
amorphous substance produces shear stress inside due toits viscosity and so the shear stress depends on sliding(shear) velocity gradient As shown in Figure 11 averagedshear stresses 120591ave summarized in Table 5 are replotted interms of sliding velocity As recognized in Figure 11 shearstress is almost proportional to the sliding velocity In the
present simulation condition system temperature is kept at10 kelvins which is quite low But the atomic mobility atcontact layers between materials should rise due to the workdone by sliding motion In observing atomic motion theyshow intermittent slip which is sometimes called ldquostick andslipmotionrdquo in nanotribological consideration Furthermorewhen in Figure 11 we extrapolate approximated straight linesdown to V = 0 shear stress 120591ave does not return to zero butit remains at a finite value 120591
0= 20sim25GPa These ideal shear
stresses at V = 0 correspond to static friction of materials Italso means that 120591
0are at least required for layered atoms to
exhibit a material flow
4 Conclusion
In this paper we perform a molecular dynamics (MD)study on copper sulfide material (Cu
2S) under the sliding
Journal of Materials 11
0
20
40
60
80
0 200 400 600 800 1000
Shea
r stre
ss (G
Pa)
Time (ps)
(b)
(a)
= 05ms (a)-dir = 05ms (b)-dir
minus20
0
20
40
60
80
0 100 200 300 400 500 600
Shea
r stre
ss (G
Pa)
Time (ps)
(a)(b)
minus20
= 10ms (a)-dir = 10ms (b)-dir
(a)
(b)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
minus20
Time (ps)
= 50ms (a)-dir = 50ms (b)-dir
200150100500
(A) = 05ms (B) = 10ms
(C) = 50ms
Figure 9 Comparison of the absolute value of shear stress deviation 120591119886between (a)- and (b)-direction
motion The MD simulation includes a new implementationof potential energy function for Cu
2S crystal where some
first-principle calculations are utilized The potential energyfunction has three-body term The following results areobtained and we will make conclusion
(1) First-principle calculations are performed for thehexagonal unit structure of Cu
2S crystal From the
optimized structure original lattice parameters 119886
and 119888 of unit cell and stable configuration of S andCu atoms are obtained Based on those results aninteratomic potential function including ionic andMorse terms as well as angular-dependent term isconstructed for Cu and S system It is confirmedthat this potential function can show enough stability
for the hexagonal crystal structure of Cu2S in MD
simulations(2) An easy-glide direction ⟨21 10⟩ on (0001) plane gen-
erally found for usual hexagonal crystals is not thedirection with small resistance to sliding
(3) Cu2S crystal shows partially liquid-like structure and
behavior in which the shear stress occurring in thematerial depends on the sliding velocity
In the further study we should clarify the tempera-ture dependence and dependency on compressive conditionduring sliding of Cu
2S It is supposed that they are made
possible by analyzing more atomic trajectories obtained byMD simulations It will lead to total understanding of slidingmechanism of Cu
2S crystal
12 Journal of Materials
0
20
40
60
80
0 01 02 03 04 05
Shea
r stre
ss (G
Pa)
Shear distance (nm)
Slow decrease
Fast decrease
minus20
= 50ms (a)-dir = 10ms (a)-dir
= 05ms (a)-dir
0 01 02 03 04 05Shear distance (nm)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
Stress increase by velocity
minus20
= 50ms (b)-dir = 10ms (b)-dir
= 05ms (b)-dir
(A) (a)-direction ( ) sliding (B) (b)-direction ( ) sliding110⟩⟨2 ⟨0110⟩
Figure 10 Relation between shear distance and the deviation of shear stress 120591119886 comparison among different sliding velocities
0
5
10
15
20
25
30
0 1 2 3 4 5
(a)-direction(b)-direction
Linear fit ((a)-dir)Linear fit ((b)-dir)
(ms)
120591 a(G
Pa)
Figure 11 Averaged shear stress replotted against sliding velocity((a)- and (b)-directions (⟨21 10⟩ and ⟨0110⟩))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This study is partly supported by NEDO Innovative Project(2012-2013) and by the ldquoStrategic Project to Support the For-mation of Research Bases at Private Universities MatchingFund Subsidy from MEXT (Ministry of Education CultureSports Science and Technology) (2012ndash2015)rdquo The authorsalso acknowledge Kurimoto Ltd for financial support
References
[1] T Sato Y Hirai T Fukui T Ejima M Takuma and K SaitohldquoAtomic-modeling and simulation of copper sulfide as microsolid lubricantrdquoMRS Proceedings vol 1513 p 20 2013
[2] H Sueyoshi Y Yamano K Inoue Y Maeda and K YamadaldquoMechanical properties of copper sulfide-dispersed lead-freebronzerdquoMaterials Transactions vol 50 no 4 pp 776ndash781 2009
[3] Y Hirai Y Ueda M Yamamoto T Kobayashi and TMaruyama Japanese Patent 132986 2009
[4] K Akamatsu T Kobayashi A Nishimoto T Maruyama andY Arachi ldquoDevelopment of new copper alloymdashinfluence ofmetallic elements on the human bodyrdquo Rikogaku to Gijyutsuvol 16 pp 31ndash36 2009 (Japanese)
[5] L-W Wang ldquoHigh chalcocite Cu2S a solid-liquid hybrid
phaserdquoPhysical Review Letters vol 108 no 8 Article ID 0857032012
[6] T Ejima K-I Saitoh N Shinke M Taruma Y Hirai and TSato ldquoAtomic-level analysis of copper sulfide (CU2S) crystalstructure and sliding characteristicsrdquo Technology Reports ofKansai University vol 54 pp 23ndash33 2012
[7] I I Mazin ldquoStructural and electronic properties of the two-dimensional superconductor CuS with 1(13)-valent copperrdquoPhysical Review B vol 85 Article ID 115133 2012
[8] M J Buerger and B J Wuensch ldquoDistribution of atoms in highchalcocite Cu
2Srdquo Science vol 141 no 3577 pp 276ndash277 1963
[9] B J Wuensch and M J Buerger ldquoThe crystal structure ofchalcocite Cu
2Srdquo Mineralogical Society of America Special
Paper vol 1 pp 163ndash170 1963 Proceedings of the 3rd GenralMeeting
[10] T Onodera Y Morlta A Suzuki et al ldquoA computationalchemistry study on friction of h-MoS2 Part I Mechanism ofsingle sheet lubricationrdquo The Journal of Physical Chemistry Bvol 113 no 52 pp 16526ndash16536 2009
[11] Y Ding D R Veblen and C T Prewitt ldquoPossible FeCu order-ing schemes in the 2a superstructure of bornite (Cu
5FeS4)rdquo
American Mineralogist vol 90 no 8-9 pp 1265ndash1269 2005
Journal of Materials 13
[12] H Zheng J B Rivest T A Miller et al ldquoObservation of tran-sient structural-transformation dynamics in a Cu
2S nanorodrdquo
Science vol 333 no 6039 pp 206ndash209 2011[13] S KashidaW ShimosakaMMori andDYoshimura ldquoValence
band photoemission study of the copper chalcogenide com-pounds Cu2S Cu2Se and Cu2Terdquo Journal of Physics andChemistry of Solids vol 64 no 12 pp 2357ndash2363 2003
[14] P Lukashev W R L Lambrecht T Kotani and M VanSchilfgaarde ldquoElectronic and crystal structure of Cu2-x S full-potential electronic structure calculationsrdquo Physical Review Bvol 76 no 19 Article ID 195202 2007
[15] P Blaha K Schwarz G Madsen D Kvasnicka and J LuitzldquoWIEN2krdquo httpwwwwien2katindexhtml
[16] P A Romero T T Jarvi N Beckmann M Mrovec andM Moseler ldquoCoarse graining and localized plasticity betweensliding nanocrystalline metalsrdquo Physical Review Letters vol 113no 3 Article ID 036101 2014
[17] S Izumi and S Sakai ldquoInternal displacement and elasticproperties of the silicon tersoff modelrdquo JSME InternationalJournal Series A Solid Mechanics and Material Engineering vol47 no 1 pp 54ndash61 2004
[18] M P Allen and D J Tildesley Computer Simulation of LiquidsOxford University Press Oxford UK 1989
[19] Sandia Nantional Laboratory ldquoLarge-scale AtomicMolecularMassively Parallel Simulatorrdquo httplammpssandiagov
[20] T Yamaguchi and K Saitoh ldquoMolecular dyanmics study onmechanical properties in the structure of self-assembled quan-tum dotrdquoWorld Journal of Nano Science and Engineering vol 2pp 189ndash195 2012
[21] T Ejima Atomic-level analysis on sliding characteristic of coppersulfide [MS thesis] Graduate School of Kansai University 2013
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
10 Journal of Materials
(a)
(a)
(b)
(b)
r (nm)04504035030250201501
14
12
1
08
06
04
02
0
g(r)
(a)-direction(b)-direction
(a) (b)
r (nm)04504035030250201501
12
1
08
06
04
0
02
g(r)
(a)-direction(b)-direction
(a) (b)
r (nm)04504035030250201501
14
12
1
08
06
04
02
0
g(r)
(a)-direction(b)-direction
(a) (b)
(a) (b)
(B) = 10ms
(C) = 50ms
(A) Velocity = 05ms
Figure 8 The comparison of RDF at the same sliding distance (10 nm) between (a)- and (b)-direction sliding
Table 5 Relation between averaged shear stress 120591ave and slidingvelocity V
Sliding velocityVms
Averaged shear stress 120591ave GPa(A) (a)-direction sliding (B) (b)-direction sliding
05 193 22810 214 25450 264 283Average 224 255
amorphous substance produces shear stress inside due toits viscosity and so the shear stress depends on sliding(shear) velocity gradient As shown in Figure 11 averagedshear stresses 120591ave summarized in Table 5 are replotted interms of sliding velocity As recognized in Figure 11 shearstress is almost proportional to the sliding velocity In the
present simulation condition system temperature is kept at10 kelvins which is quite low But the atomic mobility atcontact layers between materials should rise due to the workdone by sliding motion In observing atomic motion theyshow intermittent slip which is sometimes called ldquostick andslipmotionrdquo in nanotribological consideration Furthermorewhen in Figure 11 we extrapolate approximated straight linesdown to V = 0 shear stress 120591ave does not return to zero butit remains at a finite value 120591
0= 20sim25GPa These ideal shear
stresses at V = 0 correspond to static friction of materials Italso means that 120591
0are at least required for layered atoms to
exhibit a material flow
4 Conclusion
In this paper we perform a molecular dynamics (MD)study on copper sulfide material (Cu
2S) under the sliding
Journal of Materials 11
0
20
40
60
80
0 200 400 600 800 1000
Shea
r stre
ss (G
Pa)
Time (ps)
(b)
(a)
= 05ms (a)-dir = 05ms (b)-dir
minus20
0
20
40
60
80
0 100 200 300 400 500 600
Shea
r stre
ss (G
Pa)
Time (ps)
(a)(b)
minus20
= 10ms (a)-dir = 10ms (b)-dir
(a)
(b)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
minus20
Time (ps)
= 50ms (a)-dir = 50ms (b)-dir
200150100500
(A) = 05ms (B) = 10ms
(C) = 50ms
Figure 9 Comparison of the absolute value of shear stress deviation 120591119886between (a)- and (b)-direction
motion The MD simulation includes a new implementationof potential energy function for Cu
2S crystal where some
first-principle calculations are utilized The potential energyfunction has three-body term The following results areobtained and we will make conclusion
(1) First-principle calculations are performed for thehexagonal unit structure of Cu
2S crystal From the
optimized structure original lattice parameters 119886
and 119888 of unit cell and stable configuration of S andCu atoms are obtained Based on those results aninteratomic potential function including ionic andMorse terms as well as angular-dependent term isconstructed for Cu and S system It is confirmedthat this potential function can show enough stability
for the hexagonal crystal structure of Cu2S in MD
simulations(2) An easy-glide direction ⟨21 10⟩ on (0001) plane gen-
erally found for usual hexagonal crystals is not thedirection with small resistance to sliding
(3) Cu2S crystal shows partially liquid-like structure and
behavior in which the shear stress occurring in thematerial depends on the sliding velocity
In the further study we should clarify the tempera-ture dependence and dependency on compressive conditionduring sliding of Cu
2S It is supposed that they are made
possible by analyzing more atomic trajectories obtained byMD simulations It will lead to total understanding of slidingmechanism of Cu
2S crystal
12 Journal of Materials
0
20
40
60
80
0 01 02 03 04 05
Shea
r stre
ss (G
Pa)
Shear distance (nm)
Slow decrease
Fast decrease
minus20
= 50ms (a)-dir = 10ms (a)-dir
= 05ms (a)-dir
0 01 02 03 04 05Shear distance (nm)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
Stress increase by velocity
minus20
= 50ms (b)-dir = 10ms (b)-dir
= 05ms (b)-dir
(A) (a)-direction ( ) sliding (B) (b)-direction ( ) sliding110⟩⟨2 ⟨0110⟩
Figure 10 Relation between shear distance and the deviation of shear stress 120591119886 comparison among different sliding velocities
0
5
10
15
20
25
30
0 1 2 3 4 5
(a)-direction(b)-direction
Linear fit ((a)-dir)Linear fit ((b)-dir)
(ms)
120591 a(G
Pa)
Figure 11 Averaged shear stress replotted against sliding velocity((a)- and (b)-directions (⟨21 10⟩ and ⟨0110⟩))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This study is partly supported by NEDO Innovative Project(2012-2013) and by the ldquoStrategic Project to Support the For-mation of Research Bases at Private Universities MatchingFund Subsidy from MEXT (Ministry of Education CultureSports Science and Technology) (2012ndash2015)rdquo The authorsalso acknowledge Kurimoto Ltd for financial support
References
[1] T Sato Y Hirai T Fukui T Ejima M Takuma and K SaitohldquoAtomic-modeling and simulation of copper sulfide as microsolid lubricantrdquoMRS Proceedings vol 1513 p 20 2013
[2] H Sueyoshi Y Yamano K Inoue Y Maeda and K YamadaldquoMechanical properties of copper sulfide-dispersed lead-freebronzerdquoMaterials Transactions vol 50 no 4 pp 776ndash781 2009
[3] Y Hirai Y Ueda M Yamamoto T Kobayashi and TMaruyama Japanese Patent 132986 2009
[4] K Akamatsu T Kobayashi A Nishimoto T Maruyama andY Arachi ldquoDevelopment of new copper alloymdashinfluence ofmetallic elements on the human bodyrdquo Rikogaku to Gijyutsuvol 16 pp 31ndash36 2009 (Japanese)
[5] L-W Wang ldquoHigh chalcocite Cu2S a solid-liquid hybrid
phaserdquoPhysical Review Letters vol 108 no 8 Article ID 0857032012
[6] T Ejima K-I Saitoh N Shinke M Taruma Y Hirai and TSato ldquoAtomic-level analysis of copper sulfide (CU2S) crystalstructure and sliding characteristicsrdquo Technology Reports ofKansai University vol 54 pp 23ndash33 2012
[7] I I Mazin ldquoStructural and electronic properties of the two-dimensional superconductor CuS with 1(13)-valent copperrdquoPhysical Review B vol 85 Article ID 115133 2012
[8] M J Buerger and B J Wuensch ldquoDistribution of atoms in highchalcocite Cu
2Srdquo Science vol 141 no 3577 pp 276ndash277 1963
[9] B J Wuensch and M J Buerger ldquoThe crystal structure ofchalcocite Cu
2Srdquo Mineralogical Society of America Special
Paper vol 1 pp 163ndash170 1963 Proceedings of the 3rd GenralMeeting
[10] T Onodera Y Morlta A Suzuki et al ldquoA computationalchemistry study on friction of h-MoS2 Part I Mechanism ofsingle sheet lubricationrdquo The Journal of Physical Chemistry Bvol 113 no 52 pp 16526ndash16536 2009
[11] Y Ding D R Veblen and C T Prewitt ldquoPossible FeCu order-ing schemes in the 2a superstructure of bornite (Cu
5FeS4)rdquo
American Mineralogist vol 90 no 8-9 pp 1265ndash1269 2005
Journal of Materials 13
[12] H Zheng J B Rivest T A Miller et al ldquoObservation of tran-sient structural-transformation dynamics in a Cu
2S nanorodrdquo
Science vol 333 no 6039 pp 206ndash209 2011[13] S KashidaW ShimosakaMMori andDYoshimura ldquoValence
band photoemission study of the copper chalcogenide com-pounds Cu2S Cu2Se and Cu2Terdquo Journal of Physics andChemistry of Solids vol 64 no 12 pp 2357ndash2363 2003
[14] P Lukashev W R L Lambrecht T Kotani and M VanSchilfgaarde ldquoElectronic and crystal structure of Cu2-x S full-potential electronic structure calculationsrdquo Physical Review Bvol 76 no 19 Article ID 195202 2007
[15] P Blaha K Schwarz G Madsen D Kvasnicka and J LuitzldquoWIEN2krdquo httpwwwwien2katindexhtml
[16] P A Romero T T Jarvi N Beckmann M Mrovec andM Moseler ldquoCoarse graining and localized plasticity betweensliding nanocrystalline metalsrdquo Physical Review Letters vol 113no 3 Article ID 036101 2014
[17] S Izumi and S Sakai ldquoInternal displacement and elasticproperties of the silicon tersoff modelrdquo JSME InternationalJournal Series A Solid Mechanics and Material Engineering vol47 no 1 pp 54ndash61 2004
[18] M P Allen and D J Tildesley Computer Simulation of LiquidsOxford University Press Oxford UK 1989
[19] Sandia Nantional Laboratory ldquoLarge-scale AtomicMolecularMassively Parallel Simulatorrdquo httplammpssandiagov
[20] T Yamaguchi and K Saitoh ldquoMolecular dyanmics study onmechanical properties in the structure of self-assembled quan-tum dotrdquoWorld Journal of Nano Science and Engineering vol 2pp 189ndash195 2012
[21] T Ejima Atomic-level analysis on sliding characteristic of coppersulfide [MS thesis] Graduate School of Kansai University 2013
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
Journal of Materials 11
0
20
40
60
80
0 200 400 600 800 1000
Shea
r stre
ss (G
Pa)
Time (ps)
(b)
(a)
= 05ms (a)-dir = 05ms (b)-dir
minus20
0
20
40
60
80
0 100 200 300 400 500 600
Shea
r stre
ss (G
Pa)
Time (ps)
(a)(b)
minus20
= 10ms (a)-dir = 10ms (b)-dir
(a)
(b)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
minus20
Time (ps)
= 50ms (a)-dir = 50ms (b)-dir
200150100500
(A) = 05ms (B) = 10ms
(C) = 50ms
Figure 9 Comparison of the absolute value of shear stress deviation 120591119886between (a)- and (b)-direction
motion The MD simulation includes a new implementationof potential energy function for Cu
2S crystal where some
first-principle calculations are utilized The potential energyfunction has three-body term The following results areobtained and we will make conclusion
(1) First-principle calculations are performed for thehexagonal unit structure of Cu
2S crystal From the
optimized structure original lattice parameters 119886
and 119888 of unit cell and stable configuration of S andCu atoms are obtained Based on those results aninteratomic potential function including ionic andMorse terms as well as angular-dependent term isconstructed for Cu and S system It is confirmedthat this potential function can show enough stability
for the hexagonal crystal structure of Cu2S in MD
simulations(2) An easy-glide direction ⟨21 10⟩ on (0001) plane gen-
erally found for usual hexagonal crystals is not thedirection with small resistance to sliding
(3) Cu2S crystal shows partially liquid-like structure and
behavior in which the shear stress occurring in thematerial depends on the sliding velocity
In the further study we should clarify the tempera-ture dependence and dependency on compressive conditionduring sliding of Cu
2S It is supposed that they are made
possible by analyzing more atomic trajectories obtained byMD simulations It will lead to total understanding of slidingmechanism of Cu
2S crystal
12 Journal of Materials
0
20
40
60
80
0 01 02 03 04 05
Shea
r stre
ss (G
Pa)
Shear distance (nm)
Slow decrease
Fast decrease
minus20
= 50ms (a)-dir = 10ms (a)-dir
= 05ms (a)-dir
0 01 02 03 04 05Shear distance (nm)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
Stress increase by velocity
minus20
= 50ms (b)-dir = 10ms (b)-dir
= 05ms (b)-dir
(A) (a)-direction ( ) sliding (B) (b)-direction ( ) sliding110⟩⟨2 ⟨0110⟩
Figure 10 Relation between shear distance and the deviation of shear stress 120591119886 comparison among different sliding velocities
0
5
10
15
20
25
30
0 1 2 3 4 5
(a)-direction(b)-direction
Linear fit ((a)-dir)Linear fit ((b)-dir)
(ms)
120591 a(G
Pa)
Figure 11 Averaged shear stress replotted against sliding velocity((a)- and (b)-directions (⟨21 10⟩ and ⟨0110⟩))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This study is partly supported by NEDO Innovative Project(2012-2013) and by the ldquoStrategic Project to Support the For-mation of Research Bases at Private Universities MatchingFund Subsidy from MEXT (Ministry of Education CultureSports Science and Technology) (2012ndash2015)rdquo The authorsalso acknowledge Kurimoto Ltd for financial support
References
[1] T Sato Y Hirai T Fukui T Ejima M Takuma and K SaitohldquoAtomic-modeling and simulation of copper sulfide as microsolid lubricantrdquoMRS Proceedings vol 1513 p 20 2013
[2] H Sueyoshi Y Yamano K Inoue Y Maeda and K YamadaldquoMechanical properties of copper sulfide-dispersed lead-freebronzerdquoMaterials Transactions vol 50 no 4 pp 776ndash781 2009
[3] Y Hirai Y Ueda M Yamamoto T Kobayashi and TMaruyama Japanese Patent 132986 2009
[4] K Akamatsu T Kobayashi A Nishimoto T Maruyama andY Arachi ldquoDevelopment of new copper alloymdashinfluence ofmetallic elements on the human bodyrdquo Rikogaku to Gijyutsuvol 16 pp 31ndash36 2009 (Japanese)
[5] L-W Wang ldquoHigh chalcocite Cu2S a solid-liquid hybrid
phaserdquoPhysical Review Letters vol 108 no 8 Article ID 0857032012
[6] T Ejima K-I Saitoh N Shinke M Taruma Y Hirai and TSato ldquoAtomic-level analysis of copper sulfide (CU2S) crystalstructure and sliding characteristicsrdquo Technology Reports ofKansai University vol 54 pp 23ndash33 2012
[7] I I Mazin ldquoStructural and electronic properties of the two-dimensional superconductor CuS with 1(13)-valent copperrdquoPhysical Review B vol 85 Article ID 115133 2012
[8] M J Buerger and B J Wuensch ldquoDistribution of atoms in highchalcocite Cu
2Srdquo Science vol 141 no 3577 pp 276ndash277 1963
[9] B J Wuensch and M J Buerger ldquoThe crystal structure ofchalcocite Cu
2Srdquo Mineralogical Society of America Special
Paper vol 1 pp 163ndash170 1963 Proceedings of the 3rd GenralMeeting
[10] T Onodera Y Morlta A Suzuki et al ldquoA computationalchemistry study on friction of h-MoS2 Part I Mechanism ofsingle sheet lubricationrdquo The Journal of Physical Chemistry Bvol 113 no 52 pp 16526ndash16536 2009
[11] Y Ding D R Veblen and C T Prewitt ldquoPossible FeCu order-ing schemes in the 2a superstructure of bornite (Cu
5FeS4)rdquo
American Mineralogist vol 90 no 8-9 pp 1265ndash1269 2005
Journal of Materials 13
[12] H Zheng J B Rivest T A Miller et al ldquoObservation of tran-sient structural-transformation dynamics in a Cu
2S nanorodrdquo
Science vol 333 no 6039 pp 206ndash209 2011[13] S KashidaW ShimosakaMMori andDYoshimura ldquoValence
band photoemission study of the copper chalcogenide com-pounds Cu2S Cu2Se and Cu2Terdquo Journal of Physics andChemistry of Solids vol 64 no 12 pp 2357ndash2363 2003
[14] P Lukashev W R L Lambrecht T Kotani and M VanSchilfgaarde ldquoElectronic and crystal structure of Cu2-x S full-potential electronic structure calculationsrdquo Physical Review Bvol 76 no 19 Article ID 195202 2007
[15] P Blaha K Schwarz G Madsen D Kvasnicka and J LuitzldquoWIEN2krdquo httpwwwwien2katindexhtml
[16] P A Romero T T Jarvi N Beckmann M Mrovec andM Moseler ldquoCoarse graining and localized plasticity betweensliding nanocrystalline metalsrdquo Physical Review Letters vol 113no 3 Article ID 036101 2014
[17] S Izumi and S Sakai ldquoInternal displacement and elasticproperties of the silicon tersoff modelrdquo JSME InternationalJournal Series A Solid Mechanics and Material Engineering vol47 no 1 pp 54ndash61 2004
[18] M P Allen and D J Tildesley Computer Simulation of LiquidsOxford University Press Oxford UK 1989
[19] Sandia Nantional Laboratory ldquoLarge-scale AtomicMolecularMassively Parallel Simulatorrdquo httplammpssandiagov
[20] T Yamaguchi and K Saitoh ldquoMolecular dyanmics study onmechanical properties in the structure of self-assembled quan-tum dotrdquoWorld Journal of Nano Science and Engineering vol 2pp 189ndash195 2012
[21] T Ejima Atomic-level analysis on sliding characteristic of coppersulfide [MS thesis] Graduate School of Kansai University 2013
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
12 Journal of Materials
0
20
40
60
80
0 01 02 03 04 05
Shea
r stre
ss (G
Pa)
Shear distance (nm)
Slow decrease
Fast decrease
minus20
= 50ms (a)-dir = 10ms (a)-dir
= 05ms (a)-dir
0 01 02 03 04 05Shear distance (nm)
0
20
40
60
80
Shea
r stre
ss (G
Pa)
Stress increase by velocity
minus20
= 50ms (b)-dir = 10ms (b)-dir
= 05ms (b)-dir
(A) (a)-direction ( ) sliding (B) (b)-direction ( ) sliding110⟩⟨2 ⟨0110⟩
Figure 10 Relation between shear distance and the deviation of shear stress 120591119886 comparison among different sliding velocities
0
5
10
15
20
25
30
0 1 2 3 4 5
(a)-direction(b)-direction
Linear fit ((a)-dir)Linear fit ((b)-dir)
(ms)
120591 a(G
Pa)
Figure 11 Averaged shear stress replotted against sliding velocity((a)- and (b)-directions (⟨21 10⟩ and ⟨0110⟩))
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This study is partly supported by NEDO Innovative Project(2012-2013) and by the ldquoStrategic Project to Support the For-mation of Research Bases at Private Universities MatchingFund Subsidy from MEXT (Ministry of Education CultureSports Science and Technology) (2012ndash2015)rdquo The authorsalso acknowledge Kurimoto Ltd for financial support
References
[1] T Sato Y Hirai T Fukui T Ejima M Takuma and K SaitohldquoAtomic-modeling and simulation of copper sulfide as microsolid lubricantrdquoMRS Proceedings vol 1513 p 20 2013
[2] H Sueyoshi Y Yamano K Inoue Y Maeda and K YamadaldquoMechanical properties of copper sulfide-dispersed lead-freebronzerdquoMaterials Transactions vol 50 no 4 pp 776ndash781 2009
[3] Y Hirai Y Ueda M Yamamoto T Kobayashi and TMaruyama Japanese Patent 132986 2009
[4] K Akamatsu T Kobayashi A Nishimoto T Maruyama andY Arachi ldquoDevelopment of new copper alloymdashinfluence ofmetallic elements on the human bodyrdquo Rikogaku to Gijyutsuvol 16 pp 31ndash36 2009 (Japanese)
[5] L-W Wang ldquoHigh chalcocite Cu2S a solid-liquid hybrid
phaserdquoPhysical Review Letters vol 108 no 8 Article ID 0857032012
[6] T Ejima K-I Saitoh N Shinke M Taruma Y Hirai and TSato ldquoAtomic-level analysis of copper sulfide (CU2S) crystalstructure and sliding characteristicsrdquo Technology Reports ofKansai University vol 54 pp 23ndash33 2012
[7] I I Mazin ldquoStructural and electronic properties of the two-dimensional superconductor CuS with 1(13)-valent copperrdquoPhysical Review B vol 85 Article ID 115133 2012
[8] M J Buerger and B J Wuensch ldquoDistribution of atoms in highchalcocite Cu
2Srdquo Science vol 141 no 3577 pp 276ndash277 1963
[9] B J Wuensch and M J Buerger ldquoThe crystal structure ofchalcocite Cu
2Srdquo Mineralogical Society of America Special
Paper vol 1 pp 163ndash170 1963 Proceedings of the 3rd GenralMeeting
[10] T Onodera Y Morlta A Suzuki et al ldquoA computationalchemistry study on friction of h-MoS2 Part I Mechanism ofsingle sheet lubricationrdquo The Journal of Physical Chemistry Bvol 113 no 52 pp 16526ndash16536 2009
[11] Y Ding D R Veblen and C T Prewitt ldquoPossible FeCu order-ing schemes in the 2a superstructure of bornite (Cu
5FeS4)rdquo
American Mineralogist vol 90 no 8-9 pp 1265ndash1269 2005
Journal of Materials 13
[12] H Zheng J B Rivest T A Miller et al ldquoObservation of tran-sient structural-transformation dynamics in a Cu
2S nanorodrdquo
Science vol 333 no 6039 pp 206ndash209 2011[13] S KashidaW ShimosakaMMori andDYoshimura ldquoValence
band photoemission study of the copper chalcogenide com-pounds Cu2S Cu2Se and Cu2Terdquo Journal of Physics andChemistry of Solids vol 64 no 12 pp 2357ndash2363 2003
[14] P Lukashev W R L Lambrecht T Kotani and M VanSchilfgaarde ldquoElectronic and crystal structure of Cu2-x S full-potential electronic structure calculationsrdquo Physical Review Bvol 76 no 19 Article ID 195202 2007
[15] P Blaha K Schwarz G Madsen D Kvasnicka and J LuitzldquoWIEN2krdquo httpwwwwien2katindexhtml
[16] P A Romero T T Jarvi N Beckmann M Mrovec andM Moseler ldquoCoarse graining and localized plasticity betweensliding nanocrystalline metalsrdquo Physical Review Letters vol 113no 3 Article ID 036101 2014
[17] S Izumi and S Sakai ldquoInternal displacement and elasticproperties of the silicon tersoff modelrdquo JSME InternationalJournal Series A Solid Mechanics and Material Engineering vol47 no 1 pp 54ndash61 2004
[18] M P Allen and D J Tildesley Computer Simulation of LiquidsOxford University Press Oxford UK 1989
[19] Sandia Nantional Laboratory ldquoLarge-scale AtomicMolecularMassively Parallel Simulatorrdquo httplammpssandiagov
[20] T Yamaguchi and K Saitoh ldquoMolecular dyanmics study onmechanical properties in the structure of self-assembled quan-tum dotrdquoWorld Journal of Nano Science and Engineering vol 2pp 189ndash195 2012
[21] T Ejima Atomic-level analysis on sliding characteristic of coppersulfide [MS thesis] Graduate School of Kansai University 2013
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
Journal of Materials 13
[12] H Zheng J B Rivest T A Miller et al ldquoObservation of tran-sient structural-transformation dynamics in a Cu
2S nanorodrdquo
Science vol 333 no 6039 pp 206ndash209 2011[13] S KashidaW ShimosakaMMori andDYoshimura ldquoValence
band photoemission study of the copper chalcogenide com-pounds Cu2S Cu2Se and Cu2Terdquo Journal of Physics andChemistry of Solids vol 64 no 12 pp 2357ndash2363 2003
[14] P Lukashev W R L Lambrecht T Kotani and M VanSchilfgaarde ldquoElectronic and crystal structure of Cu2-x S full-potential electronic structure calculationsrdquo Physical Review Bvol 76 no 19 Article ID 195202 2007
[15] P Blaha K Schwarz G Madsen D Kvasnicka and J LuitzldquoWIEN2krdquo httpwwwwien2katindexhtml
[16] P A Romero T T Jarvi N Beckmann M Mrovec andM Moseler ldquoCoarse graining and localized plasticity betweensliding nanocrystalline metalsrdquo Physical Review Letters vol 113no 3 Article ID 036101 2014
[17] S Izumi and S Sakai ldquoInternal displacement and elasticproperties of the silicon tersoff modelrdquo JSME InternationalJournal Series A Solid Mechanics and Material Engineering vol47 no 1 pp 54ndash61 2004
[18] M P Allen and D J Tildesley Computer Simulation of LiquidsOxford University Press Oxford UK 1989
[19] Sandia Nantional Laboratory ldquoLarge-scale AtomicMolecularMassively Parallel Simulatorrdquo httplammpssandiagov
[20] T Yamaguchi and K Saitoh ldquoMolecular dyanmics study onmechanical properties in the structure of self-assembled quan-tum dotrdquoWorld Journal of Nano Science and Engineering vol 2pp 189ndash195 2012
[21] T Ejima Atomic-level analysis on sliding characteristic of coppersulfide [MS thesis] Graduate School of Kansai University 2013
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Smart Materials Research
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MetallurgyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
BioMed Research International
MaterialsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Nano
materials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal ofNanomaterials
Submit your manuscripts athttpwwwhindawicom
ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CorrosionInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Polymer ScienceInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CeramicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CompositesJournal of
NanoparticlesJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Biomaterials
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
NanoscienceJournal of
TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Journal of
NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
CrystallographyJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CoatingsJournal of
Advances in
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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
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