How to obtain elastic constants using first-principles calculation - 1. Displacement
1. Displacement On behalf of mechanical properties, elastic constants (or elastic modulus or elastic moduli) consisting of 6 by 6 matrix are definitely important. In addition, understanding underlying theory of elasticity is indispensable to obtain by atomic scale simulation such as first-principle calculation. There are significant papers (Classic ones) as follows: BARRON, T. H. K., and KLEIN. M. L., 1963, Proc. Phys. Soc., 82, 161. "On the Strain Dependence of the Vibrational Frequency Distributions of Simple Lattices." BIRCH, F., 1947, Phys. Rev., 71, 809. "Finite Elastic Strain of Cubic Crystal." HEARMON, R. F. S., 1946, Rev. Mod. Phys., 18, 409. "The Elastic Constants of Anisotropic Materials." HUANG, K., 1950, Proc. Roy. Soc. A, 203, 178. "On the Atomic Theory of Elasticity." Among above the reported papers, Hearmon's paper is a great review (I think), which covers isotropic materials, anisotropic materials, tempera