Elastic properties of solid-solution refractory metal carbides with vacancy from virtual crystal approximation and supercell method

The virtual crystal approximation (VCA), as an efficient approach, has been used to study the alloys composed of refractory metals. In this work, we estimate the VCA in the application of solid-solution refractory metal carbides with point defects within the framework of ab initio calculations. Results indicate the VCA predicted Cij are different from those from supercell method with the same stress-stain approach. The elastic constants C44 from VCA are close to the average values derived from the refractory metal carbides. For the solid-solution refractory metal carbides with the severe lattice distortion, Cij are very sensitive to the atomic displacement and their moduli are softened. The carbon vacancies have a large effect on the elastic constants, whereas product a small effect on the anisotropy and hardness of solid-solution refractory metal carbides.