Calculation of elastic constants at high pressure from first-principles

Abstract

Elastic constants can be defined by either energy-strain or stress-strain relationships. Although the formal theory is well established, their actual computation via the energy-strain relationship can lead to erroneous results at non-zero pressure. This work explicitly illustrates the problem by computing the elastic constants of fcc-Al via both routes using density functional theory. Following an overview of proposals to address the difficulties, a solution based on adding a correction to the energy derivative which represents the work done by the strain is put forward. In some respects the method is equivalent to other solutions that have been introduced but has the advantages of physical transparency and reduced mathematical complexity.