Ab initio investigation of osmium carbide

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International Journal of Refractory Metals & Hard Materials 26 (2008) 61–67

Ab initio investigation of osmium carbide

M. Zemzemi, M. Hebbache *

Laboratoire Materiaux et Phenomenes Quantiques (UMR 7162), Universite Denis Diderot,

Paris 7, 10 rue Alice Domon et Lonie Duquet, 75205 Paris Cedex 13, France

Received 18 December 2006; accepted 11 April 2007

Abstract

Osmium carbide has been synthesized by Kempter and Nadler 46 years ago. According to the authors, OsC crystallizes in WC-typestructure and has a hardness equal to 2000 kg mm�2. Up to date, almost nothing is known about the physical properties of this carbide.We studied electronic, elastic, plastic and mechanical properties of this carbide using an approach based on the density-functional theory.We found that the work of the above mentioned authors is sound. The calculated lattice parameters are in good agreement with thatgiven by Kempter and Nadler and a rough estimate also showed that the measured hardness is reasonable. However, we found thatthe hexagonal structure of osmium carbide is unstable.� 2007 Elsevier Ltd. All rights reserved.

PACS: 62.20.Dc; 62.20.Qp; 71.15.Pd; 71.20.Be

Keywords: Ab initio calculation; Hard materials; Osmium carbide

1. Introduction

Carbon forms binary compounds with almost all thetransition metals. The most stable carbides are obtainedwith transition metals of groups IV, V and VI which havevery high melting points [1]. Transition metal carbides pos-sess various other exceptional properties which makes themvery interesting for technical applications. Important prop-erties are their great hardness, wear resistance, good ther-mal shock resistance, thermal conductivity and weakoxidation.

It is believed that the late transition metals of the secondand third row of group VIII, namely the platinum group(Os, Ir, Pt, Ru, Re, Rh), do not form solid carbide phases,nor nitride phases. Nevertheless, nitrides of three noblemetals belonging to the platinum group, namely platinum,iridium and osmium have been synthesized recently [2–4].The pressure–temperature stability range of platinum metalcarbides should also be investigated. Platinum metals are

0263-4368/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijrmhm.2007.04.003

* Corresponding author. Tel.: +33 144278255; fax: +33 144272852.E-mail address: [email protected] (M. Hebbache).

usually used as the major constituents in cemented carbidecutting tools. The alloying of cemented carbides with thesenoble metals increase significantly their hardness, compres-sive and yield strengths.

Actually, osmium carbide has been synthesized byKempter and Nadler 46 years ago [5,6]. They also mea-sured its hardness. According to them, OsC crystallizes inthe tungsten carbide structure with a microhardness equalto 2000 kg mm�2. Almost nothing is known about thiscarbide.

The aim of the present work is to investigate the struc-tural stability and the physical properties of OsC, in partic-ular its hardness. Our computation was carried out withinthe density-functional theory [7]. We used the full-potentiallinearized augmented-plane-wave (FP-LAPW) method asimplemented in WIENk2k package [8]. The generalizedgradient approximation for the exchange–correlationenergy (GGA), as parameterized by Perdew and Zunger[9], has been employed. The 5s, 6p and 4f states of osmiumwere treated as semi-core states and the 1s state of carbonas a core state. As a convergence criterion, the energydifference between two successive iterations was required

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62 M. Zemzemi, M. Hebbache / International Journal of Refractory Metals & Hard Materials 26 (2008) 61–67

to be within a value of 0.2 lRy. This was achieved by con-sidering a k-mesh of 1500 points in the Brillouin zone and alarge basis set cut-off, i.e., RmtKmax = 10 [8].

The paper is organized as follows. In the next section,the synthesis and the structure of OsC are reviewed. Elec-tronic, elastic, plastic and mechanical properties of osmiumcarbide are described in Sections 3 and 4.

Fig. 2. WC-type structure of OsC showing atomic positions and slipplanes. Os and C atoms are shown with large and small circles,respectively. Slip planes: ABCD, CDHI and GHI are the (0001) basalplane, the (1010) prism plane and the (1012) pyramidal plane, respec-tively. EFG is the (0002) plane containing the carbon atoms. The valenceelectronic charge density in these planes are shown in Figs. 5–8.

2. Synthesis and structure of OsC

In 1906, Moissan [10] showed that molten platinum met-als dissolve appreciable amounts of carbon which precipi-tate as graphite on cooling. Kempter and Nadler [5]obtained both graphite and osmium carbide by heatingOs–C pellets at 2800 �C for 15 min. According to theseauthors, the synthesis of this carbide depends strongly onexperimental conditions (relative contents of the startingmaterials, temperature and heating time). OsC is suggestedto possess a narrow range of temperature stability [5].Fig. 1 shows the schematic phase diagram drawn by Moff-att [11]. The eutectic transformation temperature is2732 �C [5] and the eutectic point is at about 18 at.% C.The solubility of C in Os is very small, less than 4 at.%.

According to Kempter and Nadler [5], OsC crystallizesin the tungsten carbide structure. The latter can be seenas a simple hexagonal lattice with a two atoms basis.Osmium and carbon atoms are located at (000) and(2/3, 1/3,1/2), respectively. The measured lattice constantsare a = 0.29077 nm and c = 0.28218 nm [5]. Fig. 2 showsthis structure. Along the z axis, the structure is formedby two alternating layers of osmium and carbon atoms,i.e., the (0002) and (00 01) planes. The optimized lattice

Fig. 1. Schematic phase diagram of the Os–C system [10]. The dashed lines de

parameters are a = 0.2907 nm and c = 0.2771 nm. Thesevalues are slightly different from that given by Kempterand Nadler [5].

limit the solid phase of OsC. The solubility of C in Os is less than 4 at.%.

Fig. 3. Band structure of OsC. The zero of the energy scale corresponds tothe Fermi energy. The low lying C-2s band is not shown.

M. Zemzemi, M. Hebbache / International Journal of Refractory Metals & Hard Materials 26 (2008) 61–67 63

3. Electronic properties

The high stability of diamond is correlated to sp3 hybri-dation issued from the carbon atoms. Such hybridationexists at least in carbides of the group IV–VI metals. i.e.,excitation of some d-electrons of the metal to sp levelsand formation of covalent bonds with the electrons of car-bon atoms. Metallic and ionic bondings are also involvedin transition metal carbides. This is due, respectively, topartial transfer of electrons from the metal to carbon atoms

Fig. 4. Main partial densities of states: Os–d (full line), C–p

and partial delocalization of the metal electrons. Structuralstability and hardness of osmium carbide are studiedbelow. To this end, band structure and density of states(DOS) are plotted and shear modulus are calculated.

Fig. 3 shows the band structure along a path whichincludes six high symmetry points. The zero of the energyscale corresponds to the Fermi energy. The valence andconduction bands overlap each other. OsC has a metalliccharacter.

The partial density of states (DOS) are shown in Figs. 4and 5 (see also Refs. [12–14]). The p-band of the carbon isaround �7.5 eV and well separated from the s-bandaround �13 eV. Between �10 and �5 eV, there is a strongmixture of C–p and Os–d states which indicates a covalentinteraction. As expected, a low density exists below theFermi level. It originates mainly from p electrons of carbonatoms and d electrons of osmium atoms. In contrast to themost stable transition metal carbides, the s electrons of car-bon form a low lying band with a small admixture from theOs–d electrons. Though there are various exceptions, this isusually considered as a sign of instability. The principalmechanism of bonding is primarily between p electronsof carbon and d electrons of osmium. The s electrons ofcarbon are rather delocalized. The contribution of f elec-trons of osmium is negligible.

In the WC-type structure, each carbon atom is sur-rounded by six osmium atoms located at 0.2177 nm andtwo osmium atoms at 0.3622 nm (see Fig. 2). Figs. 5–7show, respectively, the difference valence electronic chargedensity (d-VECD) in (0001) basal plane, in (00 02) planeand in a (1010) prism plane. The d-VECD is the valence

(dashed line), C–s (dotted line). The unit is states/eV.

Fig. 5. Two different representations of the difference valence electron charge density (d-VECD) in the (0001) basal plane, containing osmium atoms(crystal valence charge density minus superposed atomic densities). The unit of d-VECD is e/A3. Top: Red (not seen on a black and white figure), green(grey) and blue (black) colors correspond to a d-VECD equal to 0.01, 0.12 and 0.24, respectively. The valence charge is delocalized. Bottom: contour plotshows that two-center directional Os–Os bonds are absent. A small charge distributed between three osmium atoms can be seen (circle in the bottomfigure/red zone in the top figure). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of thisarticle.)


density of the crystal minus the superposed atomic densi-ties. The two-center covalent components of the C–C andOs–Os bonds are absent while the three-center Os–Osand C–C bonds are weak (Figs. 5 and 6). This is in agree-ment with the conclusions drawn from the DOS. The hard-ness is intimately connected to the strength of the chemicalbonds. It may thus be anticipated that a dislocation glidecould be easy on these planes (see below). Chemical bondsneed to be cut in a slip process. Fig. 8 shows the d-VECDin the pyramidal plane (1012) containing two Os–C bonds.As predicted, a weak covalent bond exists between the car-bon atom and its nearest neighbor (see above). Activationof dislocations slip on these planes will requires high criti-cal resolved shear stress (CRSS).

In this section, we revealed various features of OsC: (1)It has a metallic character; (2) its Fermi level is not in a

DOS minimum; (3) a covalent interaction between C–pand Os–d exists, two-center Os–Os and C–C bonds areabsent and three-center Os–Os and C–C bonds are weak.This confers a weak stability to the structure of OsC.

4. Mechanical properties

The method of calculation of the independent elasticconstants in the framework of the density-functionaltheory is described in Refs. [15,16]. The first values of theBrugger-type elastic constants CIJ of OsC are given inTable 1. The value of the bulk modulus can bededuced from that of elastic constants (see Table 1). Thelarge value of the bulk modulus means that OsC can with-stand high hydrostatic stress but not large shear stresses(see below).

Fig. 6. Difference VECD in the plane (0002) containing carbon atoms. Same scale than for Fig. 5. Delocalized three-center C–C bonds can be seen (green/grey color in the top figure, blue curve in the bottom figure). (For interpretation of the references to colour in this figure legend, the reader is referred to theweb version of this article.)


The hardness is more or less correlated to all physicalquantities which express the strength of interatomic bonds:melting point, energy of cohesion, band gap, bulk modu-lus, etc. However, the best way to estimate the hardnessof a metallic material is to calculate its resistance to dislo-cations glide. It depends on active slip systems and is rep-resented by some shear modulus. The latter can bewritten by means of elastic constants CIJ. The data givenin Table 2 show the rough correlation between the hardnessand the shear modulus.

In hexagonal crystals the dislocations glide can occur ona basal, prismatic or pyramidal planes (see Fig. 2). Forexample, it has been shown that plastic deformations ofosmium occur through a slip on basal and prismatic planes[17,18]. The Vickers hardness of osmium is about 3–7 GPa.The structure of OsC is issued from the hcp structure ofosmium. Carbon atoms took the place of osmium atomson the (0002) plane. The hcp structure of Os is much moreextended along the z axis, c = 0.43193 nm and a =

0.27348 nm, than the WC structure of OsC while thevalence electrons density increases on going from the hcpstructure of Os to the WC structure of OsC. Consequently,osmium carbide should be slightly harder than osmium.

Table 1 in Ref. [16] gives some slip systems of hexago-nal structures and the corresponding shear modulus. C44 isthe shear modulus G1 associated with the basal slip, i.e.,on (0001) plane in any direction. The calculation of thisshear modulus requires a deformation which convertsthe hexagonal structure to a monoclinic structure. Wefound that the value of C44 is less than 10 GPa. The shearmodulus G2 = C66 = (C11 � C12)/2 is associated with theprismatic slip on (1010). The preferred slip directionsare h0001i, h1120i and h11 23i. The value of G2 is equalto 84 GPa. The shape change produced by a pyramidalslip is the same to that produced by simultaneous slipson a basal plane and a prismatic plane. The shear moduliG associated with pyramidal slip systems are then combi-nations of two other shear modulus, for example G1 and

Fig. 7. Difference VECD in the (1010) prism plane containing osmium atoms. Same scale than for Fig. 5. Os–Os bonds are absent.

Fig. 8. Difference VECD in the (1012) pyramidal plane containing onecarbon atom (located at G point of Fig. 2) and two osmium atoms (pointsH and I). The interaction between C–p and Os–d electrons tends to formcovalent bonds between carbon atom and its nearest neighbor.

Table 1Brugger-type elastic constants CIJ and bulk modulus B of osmium carbide,in units of GPa

Structure C11 C12 C13 C33 C44 C66 B

WC-type 514 345 288 641 <10 85 390

C66 = (C11 � C12)/2.


G2. Using the analytic expressions of G given in Ref. [16],we found that their values are in the range 150–220 GPa.

A high CRSS is required to activate a dislocations glideon pyramidal planes.

It is clear that OsC has the same slip systems thanosmium. The data reported in Table 2 suggest that thehardness of OsC should be equal to 12 GPa if the indenta-tion is made on a prismatic plane. It should be lower than12 GPa if it is the basal plane which is indented. The hard-ness proposed by Kempter and Nadler [5] corresponds toan indentation made on a pyramidal plane. The anisotropyin hardness exists even in cubic crystals, and is more pro-nounced in low symmetry crystals [20].

Table 2Vickers hardness and shear modulus of a large variety of materials (seealso Ref. [19])

Materiau VH (GPa) G (GPa)

Diamond 96 ± 5 535c-BN 63 ± 5 409 ± 6B6O 35 ± 5 204TiB2 33 ± 2 263SiO2 33 ± 2 220BP 33 ± 3 174B4C 30 ± 2 171 ± 11WC 30 ± 3 –TiC 29 ± 3 188 ± 6SiC 29 ± 3 196 ± 13ZrC 27 ± 2 166 ± 2NbC 23 ± 3 166 ± 2Al2O3 22 ± 2 162 ± 2Si3N4 21 ± 3 123 ± 2MgSiO3 18 ± 2 177TiN 18 ± 2 118HfN 15 ± 1 141VN 15 ± 1 159NbN 14 ± 1 156AlN 12 ± 1 128 ± 2GaN 12 ± 2 120ZrSiO4 12 ± 1 109� � � � � � � � �Si 12 67Ge 8 56GaAs 7 47

SiO2 is the Stishovite.


5. Conclusion

We studied electronic, elastic, plastic and mechanicalproperties of the hypothetical osmium carbide. We foundthat OsC has a metallic character. The Fermi level liesfar from a DOS minimum. In addition, the covalent com-ponent of the bonds which link osmium and carbon atomsis weak. All these features and the probable low value ofthe shear modulus C44 suggest that the structure of OsCis unstable. It can withstand large hydrostatic pressurebut not large shear stresses, i.e., it is not hard. Its hardnessvalue is lower than that of known hard carbides (see Table2 and Ref. [20]). The study of the ternary system Os–B–C isstrongly advised. On the contrary to OsC, the structure ofOsB2 is very hard [15]. It possesses holes, namely theatomic positions (b): (1/4, 3/4,z); (3/4, 1/4,�z), withz = 0.8. They could be filled by small atoms like carbon[15]. One expects an important hardening of OsB2 by theincorporation of additional carbon atoms.

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Ab initio investigation of osmium carbide