First Principle Calculation and Data Analysis of Anisotropy in Elastic Properties of Cubic Carbides TiC, VC and NbC

Abstract

In this work first principle calculation is applied to establish systematic ground state elastic property data of three typical cubic binary monocarbides (TiC, VC and NbC). The bulk modulus, Young's modulus, shear modulus, and Poisson ' s ratio are determined from the Voigt-Reuss-Hill approximation method and compared with other published data. The micro Vickers hardness is also predicted, the hardness data is compared to published data. The anisotropy in elastic properties of the carbides is studied through calculating the universal elastic anisotropic index; percent anisotropy in compressibility and shear as well as the shear anisotropic factors on the specific crystal planes. A python program is developed to integrate first principle calculation in Materials Studio data and establish the directional anisotropy in elastic properties in 3D space and projection on key crystal planes. 3D constructions and plane projection of the elastic properties based on the maximum, minimum and averaged values approaches is used to present and compare the anisotropy feature of the carbides. The data for E, G and Poisson ' s ratio is comparatively analysed and discussed, and future direction in developing systematic data through physical modelling is discussed.