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Materials Chemistry and Physics 111 (2008) 29–33Contents lists available atScienceDirectMaterials Chemistry and Physicsjournal homepage: www.elsevier.com/locate/matchemphysThe first principles study on PtC compoundE. Deligoza,∗, Y.O. Ciftcib, P.T. Jochymc, K. ColakoglubaAksaray University, Department of Physics, 68100 Aksaray, TurkeybGazi University, Department of Physics, Teknikokullar, 06500 Ankara, TurkeycInstitute of Nuclear Physics, Polish Academy of Sciences, Cracow, Polandarticle infoArticle history:Received 19 August 2007Received in revised form 28 January 2008Accepted 13 February 2008Keywords:PtCBand structureElastic propertiesThermodynamical propertiesabstractWe have studied structural, thermodynamic, elastic, and electronic properties of platinum carbide (PtC)in zinc-blende and rock-salt structures by performingab initiocalculations within the LDA approxima-tions. Particularly, we have focused on the structural and the pressure dependence of elastic moduli andrelated quantities. The other basic key properties, such as the lattice constant, cohesive energy, the phasetransition pressure, bulk modulus and its pressure derivative are also repeated and compared with theother available experimental and theoretical works.© 2008 Elsevier B.V. All rights reserved.1. IntroductionThe transition metal carbides exhibit interesting physical prop-erties, such as high stiffness, high hardness and high melting point,which are important in many industrial applications. Although thephysical and chemical properties of the transition metal carbidesare, widely, studied in the past due to their technological impor-tance[1,2], there exist only a few theoretical works[3–6,8]on thestructural, elastic, and electronic properties for other member ofthis class, platinum carbide (PtC). Ono et al.[7]recently synthesizedthe PtC at high pressure and high temperature using the diamondanvil cell technique. Ono et al.[7]predicted that the PtC is morestable in rock-salt (RS) structure according to their synchrotron X-ray diffraction data. Fan et al.[5,6]found that the RS structure ismechanically stable and the compressibility behaviour of RS-PtCis more comparable with that of experimental values. The sameauthors concluded that the RS structure is meta-stable and maytransform to the more stable zinc-blende (ZB) structure under cer-tain conditions. Li et al.[4]and the present authors predicted thatthe ZB structure is the ground-state phase of PtC at zero pressure.A very recent paper by Peng et al.[8]which has appeared whilerevising this work also predicted that the ZB structure is more sta-ble phase for PtC. It is known that due to the large mass differencebetween Pt and C, the only X-ray diffraction analysis is not sufficientto distinguish ZB and RS structures[4,5]from each other.∗Corresponding author. Tel.: +90 312 2021233; fax: +90 312 2122279.E-mail address:edeligoz@yahoo.com(E. Deligoz).The main goal of this work is shedding light on the ground struc-ture of PtC and provides some additional information to the existingdata on the structural, elastic, and thermodynamical properties ofthis compound by using theab initiototal energy calculations. Theband-structural character, partial and total density of states, andthe elastic moduli at high pressures are also estimated for PtC.The calculated properties varying with/and or without pressure arepresented and compared with the previous works. The method ofcalculation is given in Section2. The results and overall conclusionare presented and discussed in Sections3 and 4, respectively.2. Method of calculationThe SIESTA (Spanish Initiative for Electronic Simulations withThousands of Atoms) code[9,10]was utilized in this study to calcu-late the energies and atomic forces. Siesta code solves the quantummechanical equations for the electrons with the density functionalapproach in the local density approximation (LDA) parameterizedby Ceperley and Alder[11]for the electronic exchange and cor-relation potential. The interactions between electrons and coreions are simulated with separable Troullier–Martins[12]norm-conserving pseudopotentials. The basis set is based on the finiterange pseudoatomic orbitals (PAOs) of the Sankey–Niklewsky type[13], generalized to include multiple-zeta decays. We have gener-ated atomic pseudopotentials separately for both atoms, Pt and C byusing the 6s15d9and 2s22p2atomic configurations, respectively.The cut-off radii for the present atomic pseudopotentials are takenas s: 2.13 p: 2.63 d: 2.67 f: 2.32 a.u. for Pt, and 1.25 a.u. for s, p, dand f channels for C. Relativistic effects are taken into account forPt due to its heavy mass in the pseudopotential calculations.0254-0584/$ – see front matter © 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.matchemphys.2008.02.019
30E. Deligoz et al. / Materials Chemistry and Physics 111 (2008) 29–33Fig. 1.Energy versus volume curves of PtC.SIESTA calculates the self-consistent potential on a grid in realspace. The fineness of this grid is determined in terms of an energycut-offEcin analogy to the energy cut-off when the basis setinvolves plane waves. Here by using a double-zeta (DZ) basis andthe cut-off energies between 100 and 300 Ry with various basis sets,we found its optimal values around 250 Ry. Atoms were allowed torelax until atomic forces were less than 0.04 eV ̊A−1. For final con-verging, 256k-points were enough to obtain the converged totalenergiesEto about 1 meV atom−1for present compound.3. Results and discussion3.1. Structural and electronic propertiesFirst, the equilibrium lattice parameter was computed by mini-mizing the crystal total energy calculated for different values of thelattice constant by means of Murnaghan’s equation of state (eos)[14]as inFig. 1. From the graphs connecting the total energy andrelative volume one can clearly see that the ZB phase is more sta-ble. The bulk modulus, and its pressure derivative have also beenestimated, based on the same Murnaghan equation of state, andthe results are given inTable 1along with the other theoretical val-ues. The estimated lattice constant is very close to the other works[4–6,8]for the ZB and RS structure. The present value of bulk modu-lus inTable 1is consistent with the other theoretical (LDA) work[5]for ZB structure, but for RS structure our result is about 14% higherthan the experimental finding by Ono[7], and this discrepancy isexpected in LDA. However, the other LDA result given in Ref.[5]forthe bulk modulus (314 GPa) is based on the elastic constants (B= 1/3(C11+2C12) calculations, and our elastic constant values using thesame relation gives 332.6 GPa for RS structure which is closer tothe experimental value of 339 GPa. Obviously, the results obtainedfrom two methods are significantly different, probably, due to thehigher numerical uncertainties in the elastic constant calculations.The cohesive energy is known as a measure of the strength ofthe forces, which bind atoms together in the solid state. In this con-nection, the cohesive energy of PtC in the ZB and RS structures iscalculated. The cohesive energy (Ecoh) of a given phase is defined asthe difference in the total energy of the constituent atoms at infiniteseparation and the total energy of that particular phase:EABcoh=[EAatom+EBatom−EABtotal]whereEABtotalis the total energy of the compound PtC at equilibriumlattice constant andEAatomandEBatomare the atomic energies ofthe pure constituents. The computed cohesive energies (Ecoh)forZB and RS structures are found to be 14.85 and 14.39 eV atom−1,respectively, and they are also listed inTable 1.The transition pressure is a pressure at whichH(p) curves forboth phases crosses. The phase transition pressure, for PtC, fromZB to RS structure is found to be about 42 GPa from the Gibbs freeenergy at 0 K, and the related enthalpy versus pressure graphs forthe both phases are shown inFig. 2. The same result is also con-firmed in terms of the “common tangent technique” inFig. 1. Thetransition pressure for the same compound is found to be 52 GPaby Li et al.[4]and 51.7 GPa by Peng et al.[8]by using GGA. The dis-crepancy between the present result and the results given in Refs.[4,8]can be attributed to the nature of LDA and GGA.Although it is not our main intention here to make detailedband-structure calculations, the band structures for PtC along thehigh symmetry directions are obtained from the calculated equi-librium lattice constants, and indicated inFigs. 3 and 4for ZB andRS structure, respectively. In this figures, the Fermi level is set tobe 0 eV. It can be seen from the figures that this structures showa metallic character (no band gap) like conventional group IV andgroup V transitional metal carbides.The total and partial density of states (DOS and PDOS) corre-sponding to the band structures shown inFigs. 3 and 4are alsocalculated and the obtained result are indicated inFigs. 5 and 6with Fermi energy for ZB and RS structure, respectively. InFig. 5,Table 1Calculated equilibrium lattice constant (a0), bulk modulus (B), and the pressure derivative of bulk modulus (B′), cohesive energy (Ecoh), together with the theoretical andexperimental values for PtC in ZB and RS structuresMaterialReferencea0( ̊A)B(GPa)B′Ecoh(eV atom−1)PtC (ZB)Present (LDA)4.6872703.9214.85Theorya(LDA)4.678260.6Theorya,(GGA)4.764218.8Theoryb(GGA)4.73230Theoryc(GGA)4.731234.79, 265.774.97, 4.90PtC (RS)Present (LDA)4.427389.53.3114.39Theorya(LDA)4.425313.9Theorya,(GGA)4.506263.5Theoryb(GGA)4.49257Theoryc(GGA)4.49267.39, 282.355.25, 5.17Experimentald4.8143394.00aRef.[5][5][5].bRef.[4][4].cRef.[8][8][8].dRef.[7].
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