Equation of state for lambda transition in quartz

Abstract

An equation of state has been developed for quartz, a substance with a lambda‐type phase transition. It has the properties of the Murnaghan equation of state in the normal region and reflects the fundamental behavior of thermodynamic functions in the anomalous region. The term jT/(i‐T)1/2 has been introduced in the temperature dependent equations of isobaric heat capacity and the volume coefficient of thermal expansion, where i and j are fitting coefficients. The i coefficient is numerically close to the temperature of the phase transition Tc and is usually in the 0.1<|i‐Tc|<20 K interval. The range of applicability of the Murnaghan equation is delineated in the PT stability field of quartz. In the lambda range, the derivative of thermal expansion with respect to temperature is pressure dependent according to rules that allow integration of the thermal expansion and molar volume for calculation of the change in thermodynamic functions from room pressure to any given pressure. Available phase equilibria and thermochemical data have been used with the proposed equation of state to calculate the standard thermodynamic properties for coesite and the SiO2 phase diagram including alpha quartz, beta quartz, and coesite.