Temperature dependent elastic constants for crystals with arbitrary   symmetry: combined first principles and continuum elasticity theory
  To study temperature dependent elastic constants, a new computational method is proposed by combining continuum elasticity theory and first principles calculations. A Gibbs free energy function with one variable with respect to strain at given temperature and pressure was derived, hence the full minimization of the Gibbs free energy with respect to temperature and lattice parameters can be put into effective operation by using first principles. Therefore, with this new theory, anisotropic thermal expansion and temperature dependent elastic constants can be obtained for crystals with arbitrary symmetry. In addition, we apply our method to hexagonal beryllium, hexagonal diamond and cubic diamond to illustrate its general applicability. 
Tianjiao Shao, Bin Wen, Roderick Melnik, Shan Yao, Yoshiyuki Kawazoe,   Yongjun Tian
cond-mat.mtrl-sci