Bonding and classification of nanolayered ternary carbides

Abstract

We have investigated the elastic properties of nanolayered M 2 AC, with M = Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W and A = Al, Ga, Ge, Sn, by ab initio calculations. We suggest that M 2 AC can be classified into two groups: One where the bulk modulus of the binary MC is conserved and another group where the bulk modulus is decreased. This classification can be understood in terms of coupling between MC and A layers, which is defined by the valence electron population. These results may have implications for the understanding of properties and the performance of this class of solids.Transition-metal carbides are suitable for many technological applications due to their high hardness, high melting point, and excellent electrical conductivity. However, the intrinsic brittleness of these carbides hinders their broader applications as structural materials. Owing to a combination of both metallic and ceramic properties, nanolayered ternary metal carbides of M n+1 AC n type (space group P6 3 / mmc) represent an exception, where n =1-2, M is an early transition metal, and A is mostly a IIIA or a IVA group element. 1 For example, Ti 3 SiC 2 , the most studied M n+1 AC n phase, exhibits an elastic modulus of more than 330 GPa, 1 fully reversible plasticity, 2 and negligible thermopower. 3 Also, M 2 AC phases have been investigated both experimentally 1,4-16 and theoretically. [17][18][19][20][21][22] It is reported that these ternary carbides exhibit improved ductility, 1,15 oxidation resistance, 1,7,9,10 and electrical conductivity. 1,11 They also demonstrate good damage tolerance and thermal shock resistance. 1 However, a systematic correlation between the electronic structure and properties of M n+1 AC n has not been explored in the literature. Here, we discuss the correlation between the chemical bonding and the elastic properties of M 2 AC by ab initio calculations.The VASP code 23,24 is used for the present calculations, wherein the generalized-gradient projector-augmented wave potentials are employed. 25 The following parameters were applied: 1 ϫ 10 −4 eV relaxation convergence for ions, 1 ϫ 10 −5 eV electronic relaxation convergence, conjugate gradient optimization of the wave functions, reciprocal-space integration with a Monkhorst-Pack scheme, 26 energy cutoff of 500 eV, k-points grid of 9 ϫ 9 ϫ 9, and the tetrahedron method with Blöchl corrections 27 for the energy. Spinpolarized configurations were not considered since no significant changes in structures and elastic properties were previously identified for Cr 2 AlC (Ref. 28). The equilibrium volume and the bulk modulus were calculated by a leastsquare fit of the volume-energy curves using the third-order Birch-Murnaghan's equations of states. 29 These volumeenergy curves stem from the relaxation of both the lattice parameter a and the hexagonal c / a ratio. The partial density of states and charge-density distributions are obtained using the relaxed structures at the equilibrium volumes. The input lattice parameters of the M 2 AC studied are taken from Ref. 1 and t...

Structure and Bonding of Nanolayered Ternary Phosphides

“…The pseudogap, common to all M 2 SbP phases studied (see Figure 2), is likely to split the bonding and antibonding orbitals. This behavior is consistent with previous reports on MAX phases [37][38][39].…”

“…It is known that MAX phases are usually stacks of 'hard' M-X bond and "soft" M-A bond along c direction. For example, the Ti-C bond strength is much stronger than Ti-Al bond in Ti 2 AlC [38]. However, for Ti 2 SbP (shown in Figure 4(a)), in addition to the Ti-P hybridization (covalent bonding), there is also a strong interaction between Ti and Sb atoms (metallic bonding).…”

“…However, there is also a difference with respect to the role of the A element. In the MAX phases [37,38] the A-M hybridization is weaker than the Sb-M hybridization in the M 2 SbP phases. At the same time, the chemical bonding between M and X elements in the MAX phases and between M and P in the here studied phosphides is rather similar (see Figures 3(a), (b), (c)).…”

First-principles study of structural, electronic and elastic properties of Nb4AlC3

“…Hence, at low temperatures the Debye temperature calculated from elastic constants is the same as that determined from specific heat measurements. One of the standard methods to calculate the Debye temperature (θ D ) is from elastic constants data, since θ D may be estimated from the average sound velocity, ν m by the following equation [38,39]:…”

“…where ν l and ν t are the longitudinal and transverse sound velocity obtained using the shear modulus G and the bulk modulus B from Navier's equation [38,40]:…”