Linear and Non-Linear Elastic Constants of Crystalline Materials from First-Principles Calculations

Novel methods based on the use of density functional theory (DFT) calculations are developed and applied to calculate linear and non-linear elastic constants of materials at zero and finite temperature. These methods rely on finite difference techniques and are designed to be general, numerically accurate, and suitable to investigate the thermoelastic properties of anharmonic materials. A first method was developed to compute the third-order elastic constants of crystalline materials at zero temperature, a task that is numerically challenging and is currently undertaken by using approaches typically applicable to cubic and hexagonal crystalline systems. This method relies on numerical differentiation of the second Piola-Kirchhoff stress tensor, and with respect to existing methods, it is numerically accurate and computationally efficient, and it allows for the calculation of the full set of elastic constants of any crystalline system, regardless of their symmetry. This method has been applied to aluminum, diamond, silicon, magnesium, and graphene. We further develop our methodology by extending it to finite temperature. We base our method on the quasi-harmonic approximation along with conventional and novel techniques to compute Grüneisen parameters to include temperature effects and calculate elastic constants at finite temperature