The third-order elastic moduli and pressure derivatives for AlRE (RE=Y,   Pr, Nd, Tb, Dy, Ce) intermetallics with B2-structure: A first-principles   study
  The third-order elastic moduli and pressure derivatives of the second-order elastic constants of novel B2-type AlRE (RE=Y, Pr, Nd, Tb, Dy, Ce) intermetallics are presented from first-principles calculations. The elastic moduli are obtained from the coefficients of the polynomials from the nonlinear least-squares fitting of the energy-strain functions. The calculated second-order elastic constants of AlRE intermetallics are consistent with the previous calculations. To judge that our computational accuracy is reasonable, the calculated third-order constants of Al are compared with the available experimental data and other theoretical results and found very good agreement. In comparison with the theory of the linear elasticity, the third-order effects are very important with the finite strains are lager than approximately 3.5%. Finally, the pressure derivative has been discussed. 
Rui Wang, Shaofeng Wang, and Xiaozhi Wu
cond-mat.mtrl-sci