Based on ab initio calculations, we provide a consistent modeling in pressure and temperature of the solid phases of beryllium, including theoretical phase diagram, multiphase equation of state (EOS), and elastic moduli. The quasiharmonic approximation (QHA) allows us to determine the whole theoretical phase diagram: at room temperature, QHA predicts the hexagonal compact $\left(\alpha \text{-hcp}\right)$ phase as the most stable structure up to 400 GPa, where a transition toward the body-centered-cubic $\left(\beta \text{-bcc}\right)$ phase occurs. However, the QHA does not account for the low-pressure-high-temperature bcc phase found experimentally. Combining frozen phonon and density-functional perturbation theory methods, we show that soft phonon modes as reservoirs of entropy may stabilize the low-pressure bcc phase. However the thermodynamic stability of this phase has still to be established. We provide the QHA multiphase EOS in analytic form and an evaluation of the uncertainties on the QHA solid-solid and solid-liquid phase boundaries. Then, we calculate the density and temperature dependence of elastic constants by determining the free energies of strained structures. Consistency between the polycrystalline (i.e., averaged over the elastic constants) and the EOS isothermal bulk moduli is achieved for both phases. Our results are in fair agreement with the most recent experimental data and permit us to raise questions on some experimental moduli.

• Received 22 December 2009

DOI:https://doi.org/10.1103/PhysRevB.82.104118