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

Abstract

Ab initio calculations of thermo-elastic properties of beryl (Al 4 Be 6 Si 12 O 36 ) 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-thermodynamic approach, within the limit of the quasiharmonic 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 180.2Gpa and 4.0, respectively), and the low values observed for the thermal expansion coefficient. A zone-centre soft mode 𝑃6 𝑚𝑐𝑐 ⁄ → 𝑃1 ̅ 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., 1995), where the negative contribution to thermal expansion is ascribed to a geometric effect connected to the tilting of rigid polyhedra in framework silicates.

Compressibility and equation of state of beryl (Be3Al2Si6O18) by using a diamond anvil cell and in situ synchrotron X-ray diffraction

“…Their resultant bulk modulus is in reasonable agreement with those in the studies of Hazen et al (1986) (170 GPa) and Prencipe and Nestola (2005) (179 GPa) under uncertainties, but is far different from the results of Qin et al (2008) (226 GPa). Additionally, Prencipe et al (2011) predicted a phase transition of zone-center soft mode from P6/mcc to P1 at a pressure about 14 GPa by theoretical calculation. However, Qin et al (2008) stated that no evidence for the phase transition of beryl was observed in the range of experimental pressure up to 19.2 GPa.…”

“…However, there are few reports in the literature about the elasticity of beryl at high pressure (Yoon and Newnham 1973;Hazen et al 1986;Prencipe and Nestola 2005;Qin et al 2008), especially for the thermoelasticity of beryl at simultaneously high pressure and high temperature (Prencipe et al 2011). Hazen et al (1986) investigated the compressibility and high-pressure behavior of beryl at high pressure up to 6 GPa using a diamond anvil cell and obtained the value of 170 (5) GPa for bulk modulus K 0 under the assumption of its pressure derivative (K ′ 0 ) to be 4.…”

“…Even though recent theoretical studies, based on ab initio calculations (Prencipe et al 2011), give new insights into the thermoelastic properties of beryl at simultaneously high pressure and high temperature, no experimental data of unit-cell parameters and structures at high pressure and high temperature are yet obtained to define the thermoelastic properties of beryl. With the improvement in synchrotron facilities and other state-of-arts techniques, we are now able to obtain more accurate and precise data to reinvestigate the thermoelasticity of beryl at simultaneously high pressure and high temperature.…”

“…Recently, Prencipe et al (2011) examined the thermoelastic properties of beryl by means of ab initio calculations (B3LYP and WC1LYP Hamiltonians) and provided the K 0 as a value of 180 GPa. Their resultant bulk modulus is in reasonable agreement with those in the studies of Hazen et al (1986) (170 GPa) and Prencipe and Nestola (2005) (179 GPa) under uncertainties, but is far different from the results of Qin et al (2008) (226 GPa).…”

Ab initio study of the dolomite to dolomite-II high-pressure phase transition

“…The Vibrational Density Of State (VDOS) diagrams for DOL1 are shown in Figure 2, 176 following the procedure described in Prencipe et al (2011). In Table 1 and Mg polyhedra behave differently with P ( Figure S1 in the "Supplementary Material" section ).…”