Abstract
An effective algorithm for the quasi-harmonic calculation of thermo-elastic stiffness constants of materials is discussed and implemented into the Crystal program for quantum-mechanical simulations of extended systems. Two different approaches of increasing complexity and accuracy are presented. The first one is a quasi-static approximation where the thermal dependence of elastic constants is assumed to be due only to the thermal expansion of the system. The second one is fully quasi-harmonic, takes into account thermal expansion, and explicitly computes Helmholtz free energy derivatives with respect to strain. The conversion of isothermal into adiabatic thermo-elastic constants is also addressed. The algorithm is formally presented and applied to the description of the thermo-elastic response of the forsterite mineral.
Highlights
In the last several decades, computational modeling has rapidly gained in popularity as a powerful complementary tool to the experimental characterization of materials
The first two steps of the algorithm, which we have just briefly described, have been performed by using four different functionals of the density functional theory (DFT), which belong to three different classes: the local-density approximation (LDA), two generalized-gradient approximation (GGA) functionals (PBE and PBEsol) and one hybrid functional (PBE0)
Given that the fully quasi-harmonic description of the thermo-elasticity of forsterite is a rather computationally expensive task, and given that different functionals provide consistent trends for the thermal dependence of structural and mechanical properties of solids, we have decided to use the PBEsol functional for this task. This is because, from the analysis of the results shown in Figure 2, it provides a good description of the absolute value of the bulk modulus of the system, and, being a GGA functional, it has a lower cost than the hybrid PBE0 one
Summary
In the last several decades, computational modeling has rapidly gained in popularity as a powerful complementary tool to the experimental characterization of materials. Taking a step forward, computational materials design is an emerging field of research where simulations guide the process of discovering new materials or engineering specific materials’ properties [1] In this respect, the density functional theory (DFT) arguably represents the method-of-choice because of an ideal balance between its high accuracy (due to its rigorous quantum-mechanical derivation) and modest computational cost, so if compared to other quantum-mechanical methodologies of comparable accuracy [2]. The effective inclusion of thermal effects (fully neglected by static DFT calculations) is much needed in order to widen the application domain and enhance the predictiveness of the computational approach In this context, let us briefly review some of the progresses made in the last few years in the development of the C RYSTAL program for quantum-mechanical simulations of the condensed matter [17,18]. The single-crystal thermo-elasticity of forsterite has been accurately determined experimentally at several temperatures from 300 K to 1700 K so that it represents an ideal system to validate and discuss our methodology [32]
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