Anisotropic elasticity ofIVBtransition-metal mononitrides determined byab initiocalculations

Abstract

Elastic parameters of IVB transition-metal mononitrides, TiN, ZrN, and HfN in the cubic NaCl crystal structure have been calculated by means of density-functional theory with the generalized gradient approximation. The elastic constants c 11 , c 12 , and c 44 were shown to be sufficiently converged with the density of the k-point mesh in the deformed Brillouin zone to discuss the elastic anisotropy of the systems. It was found that the anisotropy coefficient ϵ͑c 11 − c 12 ͒ /2c 44 increases with the atomic number of the metal element, i.e., HfN exhibits as strong anisotropy as = 2.02. The Young's modulus of HfN along ͗100͘ is approximately two times higher than that along ͗111͘. Moreover, analysis of the deformation energy by the applied strain modes shows that this elastic anisotropy originates from the strong covalent bonding between metal and nitrogen atoms along ͗100͘.

Behaviour of Di-Transition-Metal Nitride Ti1-xZrxN Alloy at High Pressure

“…Our calculated value for lattice parameter a 0 of TiN is in good agreement with the experimental data calculated by Helmersson et al [18] and it is little higher than theoretical values [5,7] ones. We have obtained the same value for a 0 of ZrN as experimental [20] one, but it is higher than the calculated values [5,7]. Our calculated lattice parameters of Ti 1−x Zr x N (x = 0.25, 0.50, and 0.75) are well with the experimental data calculated by Uglov et al [29].…”

“…Elemental ionic pseudopotentials of TiN and ZrN are combined to construct the virtual pseudopotential of Ti 1−x Zr x N: The results for lattice parameter a 0 are reported for different composition rates x in Table I and compared with experiment [18][19][20][21][22][23][24][25][26][27][28][29]17] and previous theoretical calculations [5][6][7]. Our calculated value for lattice parameter a 0 of TiN is in good agreement with the experimental data calculated by Helmersson et al [18] and it is little higher than theoretical values [5,7] ones. We have obtained the same value for a 0 of ZrN as experimental [20] one, but it is higher than the calculated values [5,7].…”

“…The anisotropy factor shows a gradual decrease with increasing pressure. As a result, we observe that G {110} > G {100} , indicating that it is easier to shear on the {100} plane along the [010] direction rather than on the {110} plane along the [1][2][3][4][5][6][7][8][9][10] direction. The calculated Poisson ratio (ν) and Young modulus (Y ) for cubic Ti 0.5 Zr 0.5 N compound are given in Table II.…”

“…Dayong Cheng et al [6] studied the elastic properties of ZrC and ZrN. Nagao et al [7] studied group IVB transition-metal * corresponding author; e-mail: boucetta_said02@yahoo.fr mononitrides, focusing on anisotropic elasticity. Hoerling et al [8] investigated thermal stability, microstructure, and mechanical properties of Ti 1−x Zr x N thin films.…”

Electronic mechanism for toughness enhancement inTixM1−xN(M=M

“…[29][30][31][32] With few exceptions, our results also compare extremely well to those obtained in similar DFT investigations. 14,27,[33][34][35] The obvious differences between the sets of DFT values shown in Table II are typically expected and they are most probably due to variations in the LDA-GGA, or k point sampling, schemes used in each calculation. With respect to Ti 0.5 Al 0.5 N, we note that for bulk modulus, shear modulus, and the elastic constants, the reported values in the literature are primarily theoretical, 4,27,36,37 closely matching the results reported herein.…”