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

Abstract

High-pressure single-crystal synchrotron X-ray diffraction was carried out on a single crystal of natural beryl compressed in a diamond anvil cell. The pressure–volume (P–V) data from room pressure to 9.51 GPa were fitted by a third-order Birch–Murnaghan equation of state (BM-EoS) and resulted in unit-cell volume V ₀ = 675.5 ± 0.1 Å³, isothermal bulk modulus K ₀ = 180 ± 2 GPa, and its pressure derivative $K_{0}^{{\prime }}$ = 4.2 ± 0.5. We also calculated V ₀ = 675.5 ± 0.1 Å³ and K ₀ = 181 ± 1GPa with fixed $K_{0}^{{\prime }}$ at 4.0 and then obtained the axial moduli for a (K _a0)-axis and c (K _c0)-axis of 209 ± 1 and 141 ± 2 GPa by “linearized” BM-EoS approach. The axial compressibilities of a-axis and c-axis are β _a = 1.59 × 10⁻³ GPa⁻¹ and β _c = 2.36 × 10⁻³ GPa⁻¹ with an anisotropic ratio of β _a :β _c = 0.67:1.00. On the other hand, the pressure–volume–temperature (P–V–T) EoS of the natural beryl has also been measured at temperatures up to 750 K and at pressures up to 16.81 GPa, using diamond anvil cell in conjunction with in situ synchrotron angle-dispersive powder X-ray diffraction. The P–V data at room temperature and at a pressure range of 0.0001–15.84 GPa were then analyzed by third-order BM-EoS and yielded V ₀ = 675.3 ± 0.1 Å³, K ₀ = 180 ± 2 GPa, $K_{0}^{{\prime }}$ = 4.2 ± 0.3. With $K_{0}^{{\prime }}$ fixed to 4.0, we also obtained V ₀ = 675.2 ± 0.1 Å³ and K ₀ = 182 ± 1 GPa. Consequently, we fitted the P–V–T data with high-temperature BM-EoS approach using the resultant $K_{0}^{{\prime }}$ (4.2) from room-temperature BM-EoS and then obtained the thermoelastic parameters of V ₀ = 675.3 ± 0.2 Å³, K ₀ = 180 ± 1 GPa, temperature derivative of the bulk modulus (∂K/∂T) _P  = −0.017 ± 0.004 GPa K⁻¹, and thermal expansion coefficient at ambient conditions α ₀ = (2.82 ± 0.74) × 10⁻⁶ K⁻¹. Present results were also compared with previous studies for beryl. From the comparison of these fittings, we propose to constrain K ₀ = 180 GPa and $K_{0}^{{\prime }}$ = 4.2 for beryl. And we also observed that beryl exhibits anisotropic thermal expansion at relatively low temperatures, which is very consistent with previous studies. Furthermore, no phase transition was observed in the entire pressure and temperature range (up to 16.84 GPa and 750 K) of this study for the natural beryl.