Electronic origin of elastic properties of titanium carbonitride alloys

Abstract

We have carried out numerical ab initio calculations of the elastic constants for several cubic ordered structures modeling titanium carbonitride (TiC x N 1Àx ) alloys. The calculations were performed using the full-potential linear augmented plane-wave method (FPLAPW) to calculate the total energy as functions of volume and strain, after which the data were fit to the traditional Murnaghan equation of state and to a polynomial function of strain to determine the formation energy; the bulk modulus; and the elastic constants C 11 , C 12 , and C 44 . The predicted equilibrium lattice parameters are slightly higher than those found experimentally (on average by 0.2 pct). The computed formation energy indicates that the alloys are stable in the entire range of the carbon concentration x and the maximum stability is obtained for 0.5 # x # 0.75. The computed bulk modulus, the shear modulus G, and the Young's modulus E are within approximately 2, 1, and 2 pct of the experimentally measured characteristics, respectively. The maximum deviation is observed for TiC and TiN. The moduli G, E, and Poisson's ratio reach a maximum value at approximately the middle of the concentration range, which is due to the fact that the shear modulus C 44 shows a maximum value for a valence electron concentration (VEC) in the range of 8.25 to 8.5. The other shear modulus (C 11 -C 12 )/2 does not exhibit any maximum overall concentration range and instead has a flat dependence in the range mentioned previously. Such a concentration behavior of the elastic constants is related to specific changes in the band structure of TiC x N 1Àx alloys caused by the orthorhombic and monoclinic strains that determine the shear moduli (C 11 -C 12 )/2 and C 44 , respectively.

Ab initio study of low-temperature phase transformations in ternary solid solution TiCcN1−c

“…The results of our calculations are in reasonable agreement with those from Ref. [8,9]. For the c st ¼ 1/2, and 1/4 our calculations predict the energy preference of the same structures as in [9], while at c st ¼ 3/4 our results show that DO 22 structure is more stable as compared with L1 2 .…”

“…This may be due to the higher accuracy of our total energy calculations that approximately one order of magnitude higher than in [9]. It worth mentioning that we present also the formation energies of the phases with c st ¼ 1/8 and c st ¼ 7/8 not considered in [8,9]. The formation energies (per atom on the C/N sublattice) for energetically preferable phases are presented in Fig.…”

“…The electronic origin of the non-monotonic behavior of hardness and elastic constants in TiC c N 1Àc was the subject of the discussion in [7,8]. The behavior of these mechanical properties was associated with the valence electron concentration per cell.…”

“…Prior cold work is shown to result in significant hardening after heat treatment, whereas prior quenching results in a smaller increase in hardness. As mentioned in [8] the hardness is not a simple physical property. During an indentation test, a variety of material properties, such as dislocation motion and viscous material flow, can significantly influence the results.…”

“…In these calculations, alloy configurations are simulated in two different ways: a) the virtual crystal method in which the ionic pseudopotential is approximated by the weighted average of C and N and then the usual ab initio selfconsistent pseudopotential calculation is done, and b) the supercell method, with a set of particular atomic arrangements chosen to mimic random alloys. In [8] the numerical ab initio calculations of the elastic constants for several cubic ordered structures modeling titanium carbonitride alloys are reported. The calculations were performed using the full-potential linear augmented plane wave method (FPLAPW) to calculate the total energy as functions of volume and strain, after which the data were fit to the traditional Murnaghan equation of state and to a polynomial function of strain to determine the formation energy; the bulk modulus; and the elastic constants C 11 , C 12 , and C 44 .…”