Elastic constants of Beryllium: a first-principles investigation

Abstract

We apply several recently introduced projector-augmented wave, ultrasoft, and norm-conserving pseudopotentials (PPs) to the calculation of the elastic constants of Beryllium and compare with previous theory and experiment. We discuss how the elastic constants depend on the Brillouin zone integration, on the PP type, and on the exchange and correlation functional. We find that although, in percentage, the elastic constants of Beryllium depend on the PPs more than the crys tal parameters or the bulk moduli, the differences between the local density approximation (LDA) and the PBE generalized-gradient approximation are larger than the PPs differences. LDA overes timates experiment while PBE, which remains above experiment, gives a much better agreement than LDA. The PBEsol functional gives values slightly higher than PBE with differences compa rable to the PPs uncertainty. We propose a simple formula to rationalize the internal relaxations in hcp crystals and show that Be relaxations are in reasonable agreement with this formula. The effects of internal relaxations on the values of C11 and C12 amount to a few percent of C11, but up to 50 % of C12.