  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.
