High-pressure thermo-elastic properties of beryl (Al4Be6Si12O36) from ab initio calculations,and observations about the source of thermal expansion

Ab initio calculations of thermo-elastic properties of beryl (Al₄Be₆Si₁₂O₃₆) have been carried out at the hybrid HF/DFT level by using the B3LYP and WC1LYP Hamiltonians. Static geometries and vibrational frequencies were calculated at different values of the unit cell volume to get static pressure and mode-γ Grüneisen’s parameters. Zero point and thermal pressures were calculated by following a standard statistical-thermodynamics approach, within the limit of the quasi-harmonic approximation, and added to the static pressure at each volume, to get the total pressure (P) as a function of both temperature (T) and cell volume (V). The resulting P(V, T) curves were fitted by appropriate EoS’, to get bulk modulus (K ₀) and its derivative (K′), at different temperatures. The calculation successfully reproduced the available experimental data concerning compressibility at room temperature (the WC1LYP Hamiltonian provided K ₀ and K′ values of 180.2 Gpa and 4.0, respectively) and the low values observed for the thermal expansion coefficient. A zone-centre soft mode ( P6/mcc to Pbar{1} ) phase transition was predicted to occur at a pressure of about 14 GPa; the reduction of the frequency of the soft vibrational mode, as the pressure is increased, and the similar behaviour of the majority of the low-frequency modes, provided an explanation of the thermal behaviour of the crystal, which is consistent with the RUM model (Rigid Unit Model; Dove et al. in Miner Mag 59:629–639, 1995), where the negative contribution to thermal expansion is ascribed to a geometric effect connected to the tilting of rigid polyhedra in framework silicates.