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

Abstract

A theoretical formalism to calculate the single crystal elastic constants for orthorhombic crystals from first principle calculations is described. This is applied for TiSi2 and we calculate the elastic constants using a full potential linear muffin-tin orbital method using the local density approximation (LDA) and generalized gradient approximation (GGA). The calculated values 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 shear modulus, Young’s modulus, and Poisson’s ratio for ideal polycrystalline TiSi2 are also calculated and compared with corresponding experimental values. The directional bulk modulus and the Young’s modulus for single crystal TiSi2 are estimated from the elastic constants obtained from LDA as well as GGA calculations and are compared with the experimental results. The shear anisotropic factors and anisotropy in the linear bulk modulus are obtained from the single crystal elastic constants. From the site and angular momentum decomposed density of states combined with a charge density analysis and the elastic anisotropies, the chemical bonding nature between the constituents in TiSi2 is analyzed. The Debye temperature is calculated from the average elastic wave velocity obtained from shear and bulk modulus as well as 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 approximation is used for the exchange and correlation potential.

First-principles calculation of the structure and elastic properties of a 3D-polymerized fullerite

“…18. Hill's average bulk and shear moduli, 18,25 calculated from the ab initio, single-crystal elastic constants reported in this work, are B H ϭ304 GPa and G H ϭ301 GPa, respectively. The values found for both elastic moduli are far below the reported experimental results for the polymerized fullerites ͑which range from 540 to 1700 GPa for the bulk moduli͒.…”

“…The distortion matrices used to generate the strained lattices were conveniently chosen as to permit one to express the strain energy as a function of as few independent elastic constants as possible. 18 For the calculation of the elastic tensor components, the deformation parameter ␦ was limited to Ϯ1.5% of the lattice parameters, in order to avoid having any significant contribution to the strain energy from terms of order O(␦ 3 ) and higher. The nine independent elastic constants calculated for the ͑32-28͒ structure are given in Table III.…”

Mechanical, electronic, and optical properties of the A4B6 layered ferroelectrics: ab initio calculation

“…respectively [25,26]. The Hill average [24] was used to calculate the polycrystalline modulus in a manner similar to our recent works [17,18].Using the relations given above, the calculated bulk modulus, shear modulus, Young's modulus, and Poisson's ratio for SnS and GeS are given in Table 3.…”

Elastic properties of Fe–Mn random alloys studied by ab initio calculations

“…[2][3][4] At the same time, the experimental data 1 indicate that a change of elastic constants upon the magnetic phase transition, i.e., between 400 and 600 K, is small ͑Ͻ11% ͒, which is within the general accuracy of calculating elastic constants by first-principles methods. 18,19 It is well known that the energetics of a magnetic alloy above the magnetic transition temperature is well described by the DLM model. 13,20 We, therefore, adopt this model for the calculations of elastic constants.…”