Temperature dependent elastic constants for crystals with arbitrary symmetry: Combined first principles and continuum elasticity theory

Abstract

To study temperature dependent elastic constants, a new computational method is proposed by combining continuum elasticity theory and first principles calculations. A Gibbs free energy function with one variable with respect to strain at given temperature and pressure was derived, hence the full minimization of the Gibbs free energy with respect to temperature and lattice parameters can be put into effective operation by using first principles. Therefore, with this new theory, anisotropic thermal expansion and temperature dependent elastic constants can be obtained for crystals with arbitrary symmetry. In addition, we apply our method to hexagonal beryllium, hexagonal diamond and cubic diamond to illustrate its general applicability.

Temperature dependent elastic constants and ultimate strength of graphene and graphyne

“…Very recently, a new methodology has been developed by our group for implementing lattice geometry optimization and calculating temperature dependent elastic constants (TDEC) within a given temperature range [21]. This work extends this methodology to address the problem of temperature dependent lattice geometry optimization and to determine mechanical properties of two dimensional lattices.…”

“…Two dimensional lattice geometry optimization at given temperature 4 / 30 In our previous work, we have developed a new methodology for determining lattice geometries and temperature dependent elastic constants at high temperature for arbitrary symmetry three dimensional crystals [21]. The computation can be implemented by employing the first principles combined with the QHA.…”

“…One big challenge in this full minimization lies exactly with the fact that the Gibbs function is a multi-variable function, including a, b and . In our previous work [21], we have proposed a scheme to address this issue by deriving the Gibbs energy in one variable , allowing us to determine the anisotropy thermal expansion of this crystal and to obtain the linear directional thermal expansion coefficient.…”

First-Principles Calculation for the Influence of C and O on the Mechanical Properties of γ-TiAl Alloy at High Temperature

“…When the temperature is higher than 100 K, the two lines are separated and the thermal expansion coefficient of TiAlO is gradually larger than that of TiAlC. At 850 K, the thermal expansion coefficient for TiAlC is about The elastic constant can be thought of as the strain derivative of the Helmholtz free energy [40,41]. We derived the elastic constants from the second order coefficients by polynomial fitting the Helmholtz free energy densities to strain.…”

Unraveling Thermal and Dynamical Properties of the Cubic $$\mathrm{BaVO}_3$$ BaVO 3 Perovskite from First-Principles Calculation

“…In the second step, the equilibrium volume V (T, P) at the given T and P is calculated using the first-principles quasiharmonic approach [21,22]. Then, the calculated elastic stiffness coefficients from the first step at volume V (T, P) are approximated as those at finite temperatures using the procedure given in ref [23]. In order to prove the efficiency of our method, we have chosen to reproduce the calculation of an experimental data of elastic constants at fixed temperature.…”