This review examines the elastic response of solids under load. The definition of isothermal and adiabatic elastic constants of nth order (n ⩾ 2) for the loaded crystal is given. For the case of hydrostatic pressure, two techniques are proposed for calculating the second-, third- and fourth-order elastic constants from the energy—strain and stress—strain relations. As an example, using the proposed approach within the framework of the density functional theory, the second- to fourth-order elastic constants of bcc tungsten are calculated for the pressure range of 0—600 GPa.
Keywords: high pressures, metals, second- and higher-order elastic constants, equation of state, elastic phase transitions PACS:61.50.Ks, 62.20.de, 62.50.−p, 64.30.Ef (all) DOI:10.3367/UFNe.0185.201511f.1215 URL: https://ufn.ru/en/articles/2015/11/e/ Citation: Vekilov Yu Kh, Krasil’nikov O M, Lugovskoy A V "Elastic properties of solids at high pressure" Phys. Usp.58 1106–1114 (2015)