Effect of Valence Electron Concentration on Elastic Properties of 4d Transition Metal Carbides MC (M = Y, Zr, Nb, and Rh)

Abstract

The electronic structure and elastic properties of the 4d transition metal carbides MC (M = Y, Zr, Nb, Rh) were studied by means of extended Huckel tight-binding band electronic structure calculations. As the valence electron population of M increases, the bulk modulus of the MC compounds in the rocksalt structure does not increase monotonically. The dominant covalent bonding in these compounds is found to be M-C bonding, which mainly arises from the interaction between M 4d and C 2p orbitals. The bonding characteristics between M and C atoms affecting the variation of the bulk modulus can be understood on the basis of their electronic structure. The increasing bulk modulus from YC to NbC is associated with stronger interactions between M 4d and C 2p orbitals and the successive filling of M 4d-C 2p bonding states. The decreased bulk modulus for RhC is related to the partial occupation of Rh-C antibonding states. clarified in these studies are useful in interpreting their physical properties. The common viewpoint is that covalent bonds can be formed between both metal-carbon and metal-metal pairs of atoms. At the same time, a transfer of electrons from M to C takes place, implying a certain degree of ionic bonding. We stress the importance of covalent metal-carbon bonds in explaining the stability and observed mechanical properties of these compounds. These pro- perties are understood to arise in large part from strong covalent bonding between transition metal d and carbon p orbitals. In this paper, we present the results of the electronic structures calculated for the carbides of 4d transition metals Y, Zr, Nb, and Rh. The presence of covalent M-C bonds and metallic M-M bonds is confirmed and analyzed in detail. In addition, the number of valence d electrons in the metals induces changes in bonding and elasticity in these compounds. It is, therefore, our goal to understand the relationship between the M-C bond strength and elastic properties of 4d transition metal carbides (MC) in the rocksalt structure as a function of the valence electron concentration (VEC) per atom, which is the total number of valence electrons in the structure divided by the number of atoms in a unit cell. As the VEC increases, the bulk modulus (B) increases from YC to NbC, and then decreases for RhC. This variation of B with the number of metal d electrons can be explained as arising from the orbital mixing between metal and carbon and the successive filling of the consequent bonding and antibonding M 4d-C 2p states. The focus is on the trends in the electronic structure and the nature of bonding, which are essential for the understanding of the elastic properties of the transition metal carbides. Our approach is based on a thorough complementary analysis of the density of states (DOS) and crystal orbital overlap population (COOP) to gain more profound insight into the bonding of this class of materials and get more detailed information on the bonding character than previous- ly achieved. The COOP curves are indicative of the nature and strength of the bonding between a given pair of atoms, with positive and negative regions indicating bonding and antibonding states, respectively. The chemical bonding of M-C and M-M is quantitatively discussed by use of the bond overlap population based on supercell band structure calcu- lations.