Abstract:

First-principles methods based on density functional theory (DFT) are nowadays routinely applied to calculate the elastic constants of materials at temperature of 0 K. Nevertheless, the first-principles calculations of elastic constants at finite temperature are not straightforward. In the present work, the feasibility of the ab initio molecular dynamic (AIMD) method in calculations of the temperature dependent elastic constants of relatively “soft” metals, taking face centered cubic (FCC) aluminum (Al) as example, is explored. The AIMD calculations are performed with carefully selected strain tensors and strain magnitude. In parallel with the AIMD calculations, first-principles calculations with the quasiharmonic approximation (QHA) are performed as well. We show that all three independent elastic constant components (C₁₁, C₁₂ and C₄₄) of Al from both the AIMD and QHA calculations decrease with increasing temperature T, in good agreement with those from experimental measurements. Our work allows us to quantify the individual contributions of the volume expansion, lattice vibration (excluding those contributed to the volume expansion), and electronic temperature effects to the temperature induced variation of the elastic constants. For Al with stable FCC crystal structure, the volume expansion effect contributes the major part (about 75%~80%) in the temperature induced variation of the elastic constants. The contribution of the lattice vibration is minor (about 20%~25%) while the electronic temperature effect is negligible. Although the elastic constants soften with increasing temperature, FCC Al satisfies the Born elastic stability criteria with temperature up to the experimental melting point.

Key words: Elastic constant, First-principle, Molecular dynamics, Vibration, Aluminum