Upload
dreamgurl9011
View
222
Download
0
Embed Size (px)
Citation preview
7/28/2019 Ch-5 Compatibility Mode
1/55
Chap: 05
IMPERFECTIONS IN SOLIDS
Chapter 4-
7/28/2019 Ch-5 Compatibility Mode
2/55
ISSUES TO ADDRESS...ISSUES TO ADDRESS...ISSUES TO ADDRESS...ISSUES TO ADDRESS...
What t es of defects arise in
IMPERFECTIONS IN SOLIDS
What are crystal imperfections?
Chapter 4-
solids? Can the number and type of defects be variedand controlled?
How do defects affect material properties?
1
Are defects undesirable?
7/28/2019 Ch-5 Compatibility Mode
3/55
Why bother about imperfections?
Defects or disrupted regions may be as
small as 0.01%. Can be ignored if we are studying
structure insensitive properties.
Chapter 4-
Properties of crystalline materials dealt inengineering practice are structuresensitive.
Even ppm level imperfection can radicallychange the properties.
7/28/2019 Ch-5 Compatibility Mode
4/55
The Big Picture
Mechanical properties are often related to thedefect structure, with macroscopic failurecommonly resulting from a coalescence ofdama e around existin flaws in a material
Chapter 4-
compact
We have to better understand material structurein order to predict mechanical performance of amaterial.
7/28/2019 Ch-5 Compatibility Mode
5/55
The Bigger Picture
Presence of imperfections are not always
bad. Point imperfections in the form of controlled
impurities can improve the properties of the
Chapter 4-
ma er a s ras ca y. eg. Alloys where presence of impurities
improve the mechanical properties of thematerial.
Dopants in semiconductors drasticallyimproves the electrical properties.
7/28/2019 Ch-5 Compatibility Mode
6/55
What are imperfections?
We can define imperfections or defects in acrystal as:
Chapter 4-
Discontinuity or absence of periodicityin certain region of the space lattice.
7/28/2019 Ch-5 Compatibility Mode
7/55
Vacancy atoms
Interstitial atoms Substitutional atoms
Point defects(0-D)
TYPES OF IMPERFECTIONS
Chapter 4-
s oca ons Grain Boundaries
(1-D)
Area defects(2-D)
Foreign particle/ Volume defectsLarge Voids/pores/
Non-Cryst regions~10
3-D
7/28/2019 Ch-5 Compatibility Mode
8/55
POINT IMPERFECTIONS
Imperfections of zero dimensions
May be created at the time of formation
Chapter 4-
o crys a sMay be created at a later time due tosome thermal disorder
They are thermodynamically stable
7/28/2019 Ch-5 Compatibility Mode
9/55
Vacancies:-vacant atomic sites in a structure.
Vacancydistortionof planes
POINT DEFECTS
Chapter 4- 3
Impurity
Substitutional Interstitial
7/28/2019 Ch-5 Compatibility Mode
10/55
Self-Interstitials:
-"extra" atoms positioned between atomic sites.
self-interstitialdistortion
of lanes
Chapter 4-
Low probability
because atoms aresubstantially largerthan the void
7/28/2019 Ch-5 Compatibility Mode
11/55
Defects in Ceramics
Still have interstitials and vacancies
Chapter 4-
7/28/2019 Ch-5 Compatibility Mode
12/55
Substitutional ions
Chapter 4-
7/28/2019 Ch-5 Compatibility Mode
13/55
Frenkel Defect--a cation is out of place.
Schottky Defect--a paired set of cation and anion vacancies.
Shottky
Defect: Adapted from Fig. 13.20,
DEFECTS IN CERAMIC STRUCTURES
Schottky
Chapter 4- 7
Frenkel
Defect
Equilibrium concentration of defects /2~ D
Q kTe
Callister 5e. (Fig. 13.20 is from
W.G. Moffatt, G.W. Pearsall,and J. Wulff, The Structure andProperties of Materials, Vol. 1,Structure, John Wiley andSons, Inc., p. 78.) See Fig.12.21, Callister 6e.
7/28/2019 Ch-5 Compatibility Mode
14/55
Impurities must also satisfy charge balance
Ex: NaCl Na+ Cl-
Substitutional cation impurityCa2+
Na+
cationvacancy
Imperfections in ionic crystals
Chapter 4- 8
Substitutional anion impurity
initial geometry Ca2+ impurity resulting geometry
Na+ Ca2+
initial geometry O2-
impurity
O2-
Cl-
anion vacancy
Cl-
resulting geometry
7/28/2019 Ch-5 Compatibility Mode
15/55
Nonstoichiometry
Fe 2+ O 2- Fe 2+ O 2- O 2- Fe 2+
- - - -
Chapter 4-
Fe 3+ O 2- O 2- Fe 2+ O 2- Fe 2+
O 2- Fe 3+ O 2- Fe 2+ O 2- Fe 2+ O2-
7/28/2019 Ch-5 Compatibility Mode
16/55
Consequences of presence of pointimperfections
Introduces distortion in crystals
Elastic strains created in the neighborhood of
Chapter 4-
the defect. large atom creates compressive stress-strain
smaller atom introduces tensile stress-strain
all these increases the energy of the system
to reach a stable state G/F has to be minimum
7/28/2019 Ch-5 Compatibility Mode
17/55
Chapter 4-
The variation of Gibbs free energy with thenumber of point imperfections.
7/28/2019 Ch-5 Compatibility Mode
18/55
We can get Q froman experiment.
ND
N
= expQD
kT
Measure this... Replot it...
MEASURING ACTIVATION ENERGY
Chapter 4- 5
1/T
NDln 1
-QD/kN
T
exponentialdependence!
defect concentration
7/28/2019 Ch-5 Compatibility Mode
19/55
Find the equil. # of vacancies in 1m of Cu at 1000C. Given:
3
ACu = 63.5g/mol = 8.4 g/cm3
QV = 0.9eV/atom NA = 6.02 x 1023 atoms/mole
0.9eV/atom
ESTIMATING VACANCY CONC.
Chapter 4- 6
8.62 x 10-5 eV/atom-K
1273K
N = exp kT
For 1m
3
, N =
NA
ACu x x 1m3 = 8.0 x 1028 sites
= 2.7 10-4
Answer:
ND = 2.7 10-4 8.0 x 1028 sites = 2.2x 1025 vacancies
7/28/2019 Ch-5 Compatibility Mode
20/55
Impurities in Solids
Completely pure metal (or othersubstance) Impossible!!
for 99.9999% - purity still 10still 10still 10still 1022222222 to 10to 10to 10to 1023232323 impurities per mimpurities per mimpurities per mimpurities per m3333
Chapter 4-
AlloyAlloyAlloyAlloy deliberately add impurity todeliberately add impurity todeliberately add impurity todeliberately add impurity toengineer properties.engineer properties.engineer properties.engineer properties. Copper (7.5%) inCopper (7.5%) inCopper (7.5%) inCopper (7.5%) in
silversilversilversilver
7/28/2019 Ch-5 Compatibility Mode
21/55
Terminology - Alloys
Solvent component in highestconcentration also called host
Chapter 4-
Solute component present in minor
concentration
7/28/2019 Ch-5 Compatibility Mode
22/55
Two outcomes if impurity (B) added to host (A): Solid solution ofB in A (i.e., random dist. of point defects)
OR
POINT DEFECTS IN ALLOYS
Chapter 4- 8
Solid solution ofB in A plus particles of a newphase (usually for a larger amount of B)
Substitutional alloy(e.g., Cu in Ni)
Interstitial alloy(e.g., C in Fe)
Second phase particle--differentcomposition--often different structure.
7/28/2019 Ch-5 Compatibility Mode
23/55
Factors that Govern Solid Solution
Atomic size - < 15% difference
Hume-Rothary empirical rules
Chapter 4-
Crystal structure same Electro-negativity - ??
Valences more likely to dissolve another
metal of higher valence
Ag-Au, Cu-Ni, Ge-Si are ideal examples
7/28/2019 Ch-5 Compatibility Mode
24/55
Copper and Nickel
Element Cu Ni
Radii 0.128 nm 0.125
Unit cell FCC FCC
Chapter 4-
. .
Oxidation
(Valence)
+1 (+2) +2
Expect to form solid solution?
Ni 3d8 4s2 (28)
Cu - 3d
10
4s
1
(29)
Substitutional solid solution
7/28/2019 Ch-5 Compatibility Mode
25/55
Copper-ZincUnit cell Zn (HCP) Cu (FCC)
35% of Zn dissolves in Cu where as1% of Cu dissolves in Zn.
Chapter 4-
e ex ra on ng e ec ron o n s moreeasily accommodated than a deficiency ofbonding electron.
In brass 50 Cu-50 Zn the crystal structure isBCC
7/28/2019 Ch-5 Compatibility Mode
26/55
Carbon in Iron
Element C Fe
Radii 0.071 nm 0.124nm
Unit cell Hex BCC/FCC
Electro negativity 2.5 1.6
Chapter 4-
Valence +4 +2 (+3)
Solid solution ?
Interstitial or substitional?
C - 2s2 2p2
Fe 3d6 4s2
Octahedral void in fcc Fe
has radius 0.53Tetrahedral void in bcc Fehas radius 0.365
7/28/2019 Ch-5 Compatibility Mode
27/55
Specification of Composition
of Alloy of 1 and 2
Weight % C1 = [m1/m1 + m2] x 100
Atom % nm1 = m1/
/A1C1/= [nm1/nm1 + nm2] x 100
C2/= [nm2/nm1 + nm2] x 100
Chapter 4-
C1/= [C1A2/C1A2 + C2A1] x 100
C2/= [C2A1/C1A2 + C2A1] x 100
C1 = [C1/A1/C1/A1 + C2/A2] x 100 C1 + C2 = 100C2 = [C2
/A2/C1/A1 + C2
/A2] x 100 C1/+ C2
/= 100
7/28/2019 Ch-5 Compatibility Mode
28/55
Wt. % to mass of 1 component / unit volume of
materialC1
//= [C1/(C1/1) + (C2/2)] x 1000
C2//= [C2/(C1/1) + (C2/2)] x 1000
ave = [100 / (C1/1) + (C2/2)]
Chapter 4-
ave =
(C1/A1 + C2
/A2) / [(C1/A1/1) + (C2
/A2)/2]
A ave = [100 / (C1/ A1) + (C2/ A2)]
A ave = (C1/A1 + C2
/A2) / 100
7/28/2019 Ch-5 Compatibility Mode
29/55
Derivation of composition conversion equationDerivation of composition conversion equationDerivation of composition conversion equationDerivation of composition conversion equation
C1/= [C1A2/(C1A2 + C2A1)] x 100
Total alloy mass :M/= m1/+ m2
/(in units of grams)
C1
/= (nm1/nm
1+ nm
2) x 100
= [(m1//A1) (m1
//A1) + (m2//A2)] x 100
m1/= C1M
//100A1 ( since C1 = (m1//m1
/+ m2/) x 100)
Chapter 4-
C1/
= [(C1M/
/100A1)(C1M/
/100A1+ C2M/
/100A2)] x 100
C1/= (C1A2/C1A2 + C2A1) x 100
Problem: Determine the composition in atom percent of analloy that consists of 97 wt% Al and 3 wt% Cu
7/28/2019 Ch-5 Compatibility Mode
30/55
AlAlAlAl----Cu alloy compositionCu alloy compositionCu alloy compositionCu alloy composition
CAl/= {(CAlACu)/(CAlACu + CCuAAl} x 100
= {(97 x 63.55 g/mol)/
(97x63.55 g/mol + 3x26.98 g/mol)} x 100= 98.7 at%
Chapter 4-
CCu/= {(CCuAAl)/(CAlACu + CCuAAl} x 100
= {(3)(26.98 g/mol)/(3)(26.98 g/mol) +
(97)(63.55 g/mol)} x 100= 1.30 at%
7/28/2019 Ch-5 Compatibility Mode
31/55
are linear defects,
geometrically one dimensional defect may arise due to incomplete crystal plane or due to
plastic deformation
Dislocations:
LINEAR DEFECTS
Chapter 4- 11
crystal undergoes shear part of the crystal is displaced in the direction of
the shear due to the shear stress cause slip between crystal plane when they move,
produce permanent (plastic) deformation. Boundary between slipped and unslipped region isthe line of dislocation
7/28/2019 Ch-5 Compatibility Mode
32/55
Schematic of a Zinc (HCP):
before deformation after tensile elongation
Chapter 4-
7/28/2019 Ch-5 Compatibility Mode
33/55
a
Slipvector
T
Edge dislocations
Chapter 4-
a. Elastic strain
around the
dislocation.b. A possible
arrangement of
Atoms
b
7/28/2019 Ch-5 Compatibility Mode
34/55
Edge Dislocation: MovementEdge Dislocation: MovementEdge Dislocation: MovementEdge Dislocation: Movement
b
Chapter 4-
7/28/2019 Ch-5 Compatibility Mode
35/55
Chapter 4-
Slip plane
Dislocationline
7/28/2019 Ch-5 Compatibility Mode
36/55
To determine the Burgers vector of a dislocation in a two-
dimensional primitive square lattice, proceed as follows:Trace around the end of the dislocation plane to form a
closed loop. Record the number of lattice vectors traveled
along each side of the loop (shown here by the numbers
in the boxes):
Chapter 4-
7/28/2019 Ch-5 Compatibility Mode
37/55
Chapter 4-
Screw dislocation: The dislocation line is parallel to thethe slip vector.
b
7/28/2019 Ch-5 Compatibility Mode
38/55
Screw DislocationScrew DislocationScrew DislocationScrew Dislocation
Chapter 4-
7/28/2019 Ch-5 Compatibility Mode
39/55
Motion of Screw Dislocation
Chapter 4-
Apply shear
7/28/2019 Ch-5 Compatibility Mode
40/55
Chapter 4-
Mi d Di l ti
7/28/2019 Ch-5 Compatibility Mode
41/55
Mixed Dislocation
Chapter 4-
7/28/2019 Ch-5 Compatibility Mode
42/55
Dislocations of the same sign repel andthose of opposite sign cancel each other
Dislocations can interact with point
imperfections Dislocations usually appear during growth
Chapter 4-
o crys a s or as a resu o pr or mec an cadeformation of the crystal.
Unlike point imperfections they are not
thermodynamically stable They can be removed by proper posttreatment
7/28/2019 Ch-5 Compatibility Mode
43/55
Dislocation motion requires the successive bumpingof a half plane of atoms (from left to right here).
Bonds across the slipping planes are broken and
remade in succession.
BOND BREAKING AND REMAKING
Chapter 4- 13
Atomic view of edgedislocation motion from
left to right as a crystalis sheared.
For metallic materials, b will point in
A close-packed crystallograhic
direction and will be of magnitudeE ual to interatomic s acin .
7/28/2019 Ch-5 Compatibility Mode
44/55
Motion of edge dislocation
Chapter 4-
7/28/2019 Ch-5 Compatibility Mode
45/55
AREA DEFECTS
2 D imperfections
Regions of distortions that lie on the surfaceor grain boundaries having a layer ofthickness of a few
Chapter 4-
ur ace a oms are on e o ess neares
neighbours as compared to coordinationnumbers.
Hence they are at higher energy state
compared to atoms in the interior. The broken bonds of these atoms give riseto surface energy.
7/28/2019 Ch-5 Compatibility Mode
46/55
Grain boundaries: are boundaries between crystals. are produced by the solidification process, for example. have a change in crystal orientation across them. impede dislocation motion.
AREA DEFECTS: GRAIN BOUNDARIES
Chapter 4-
grain
boundaries
heatflow
Angle of misalignment
7/28/2019 Ch-5 Compatibility Mode
47/55
Area Defects
Tilt Boundary array of edge defectsTwin Boundary
Chapter 4-
Twist Boundary array of screw defects(atleast 2 sets of parallel screwdislocation)
7/28/2019 Ch-5 Compatibility Mode
48/55
Twin BoundariesTwin BoundariesTwin BoundariesTwin Boundaries
Chapter 4-
A twin boundary is a special type of grain boundary acrosswhich there is a specific mirror lattice symmetry. Atoms on
one side of the boundary are located in mirror-imagepositions of the atoms on the other side. The region ofmaterial between these boundaries is termed a twin.
7/28/2019 Ch-5 Compatibility Mode
49/55
Twin BoundaryTwin BoundaryTwin BoundaryTwin Boundary
Twinned
Chapter 4-
Twin boundaries
region
Oth I t f i l d f t
7/28/2019 Ch-5 Compatibility Mode
50/55
Other Interfacial defects
Stacking faultsABCABCABABCABC
Stacking fault is a thin region of hcp in fcclattice.
Chapter 4-
Twin stacking fault
Bulk defects like pores, cracks etc occur
during process Atomic vibrations Not all atoms vibratewith same energy, distribution of energies
present.
7/28/2019 Ch-5 Compatibility Mode
51/55
Useful up to 2000X magnification. Polishing removes surface features (e.g., scratches) Etching changes reflectance, depending on crystal
orientation. microscope
OPTICAL MICROSCOPY (1)
Chapter 4- 16
micrograph ofBrass (Cu and Zn)
Adapted from Fig. 4.11(b) and (c),Callister 6e. (Fig. 4.11(c) is courtesyof J.E. Burke, General Electric Co.
0.75mm
O ICAL IC OSCO Y ( )
7/28/2019 Ch-5 Compatibility Mode
52/55
microscope
surface roove
polished surface
Grain boundaries... are imperfections, are more susceptible
to etching, may be revealed as
dark lines,
OPTICAL MICROSCOPY (2)
Chapter 4-
Fe-Cr alloy
grain boundary
17
c ange rec on n a
polycrystal.Adapted from Fig. 4.12(a)and (b), Callister 6e.(Fig. 4.12(b) is courtesyof L.C. Smith and C.Brady, the NationalBureau of Standards,Washington, DC [now theNational Institute ofStandards andTechnology, Gaithersburg,MD].)
ASTM grainsize number
N = 2n-1
no. grains/in2at 100xmagnification
SUMMARY
7/28/2019 Ch-5 Compatibility Mode
53/55
Point, Line, and Area defects arise in solids.
The number and type of defects can be varied
and controlled (e.g., T controls vacancy conc.)
Defects affect material properties (e.g., grain
SUMMARY
Chapter 4- 18
oun ar es con ro crys a s p .
Defects may be desirable or undesirable(e.g., dislocations may be good or bad, dependingon whether plastic deformation is desirable or not.)
7/28/2019 Ch-5 Compatibility Mode
54/55
Top view of screw dislocationTop view of screw dislocationTop view of screw dislocationTop view of screw dislocation
Atoms above theslip plane
Chapter 4-
A B
CD
b
Mi d di l tii d di l ii d di l iMi d di l ti
7/28/2019 Ch-5 Compatibility Mode
55/55
Mixed dislocationMixed dislocationMixed dislocationMixed dislocation
Edge dislocation
Chapter 4-
Screw dislocation