Density functional theory for calculation of elastic properties of orthorhombic crystals: Application to TiSi2

A theoretical formalism to calculate the single crystal elastic constants f or orthorhombic crystals from first principle calculations is described. Th is is applied for TiSi2 and we calculate the elastic constants using a full potential linear muffin-tin orbital method using the local density approxi mation (LDA) and generalized gradient approximation (GGA). The calculated v alues compare favorably with recent experimental results. An expression to calculate the bulk modulus along crystallographic axes of single crystals, using elastic constants, has been derived. From this the calculated linear bulk moduli are found to be in good agreement with the experiments. The she ar modulus, Young's modulus, and Poisson's ratio for ideal polycrystalline TiSi2 are also calculated and compared with corresponding experimental valu es. The directional bulk modulus and the Young's modulus for single crystal TiSi2 are estimated from the elastic constants obtained from LDA as well a s GGA calculations and are compared with the experimental results. The shea r anisotropic factors and anisotropy in the linear bulk modulus are obtaine d from the single crystal elastic constants. From the site and angular mome ntum decomposed density of states combined with a charge density analysis a nd the elastic anisotropies, the chemical bonding nature between the consti tuents in TiSi2 is analyzed. The Debye temperature is calculated from the a verage elastic wave velocity obtained from shear and bulk modulus as well a s the integration of elastic wave velocities in different directions of the single crystal. The calculated elastic properties are found to be in good agreement with experimental values when the generalized gradient approximat ion is used for the exchange and correlation potential. (C) 1998 American I nstitute of Physics. [S0021-8979(98)03821-3].