High-temperature and high-pressure equation of state for the hexagonal phase in the system NaAlSiO₄ - MgAl₂O₄

Thermal equation of state of an Al-rich phase with Na_1.13 Mg_1.51Al_4.47Si_1.62O₁₂ composition has been derived from in situ X-ray diffraction experiments using synchrotron radiation and a multianvil apparatus at pressures up to 24 GPa and temperatures up to 1,900 K. The Al-rich phase exhibited a hexagonal symmetry throughout the present pressure-temperature conditions and the refined unit-cell parameters at ambient condition were: a = 8.729(1) Å, c = 2.7695(5) Å, V₀ =182.77(6) ų (Z = 1; formula weight = 420.78 g/mol), yielding the zero-pressure density ρ₀ = 3.823(1) g/cm³. A least-square fitting of the pressure-volume-temperature data based on Anderson's pressure scale of gold (Anderson et al. in J Appl Phys 65:1534-543, 1989) to high-temperature Birch-Murnaghan equation of state yielded the isothermal bulk modulus K₀ = 176(2) GPa, its pressure derivative K′₀ = 4.9(3), temperature derivative (∂K_T/∂ T)_P = -0.030(3) GPa K^-1 and thermal expansivity α(T) = 3.36(6)×10^-5 + 7.2(1.9)×10^-9 T, while those values of K₀ = 181.7(4) GPa, (∂K_T/∂T)_P = -0.020(2) GPa K^-1 and α(T) = 3.28(7)×10^-5 + 3.0(9)×10^-9T were obtained when K′₀ was assumed to be 4.0. The estimated bulk density of subducting MORB becomes denser with increasing depth as compared with earlier estimates (Ono et al. in Phys Chem Miner 29:527-531 2002; Vanpeteghem et al. in Phys Earth Planet Inter 138:223-230 2003; Guignot and Andrault in Phys Earth Planet Inter 143-44:107-128 2004), although the difference is insignificant (<0.6%) when the proportions of the hexagonal phase in the MORB compositions (∼20%) are taken into account.