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

Abstract

Thermal equation of state of an Al-rich phase with Na_1.13Mg_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, V ₀=182.77(6) Å³ (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 K ₀=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 K ₀=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)×10⁻⁹ T 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.