Thermodynamics of pyrope–majorite, Mg₃Al₂Si₃O₁₂–Mg₄Si₄O₁₂, solid solution from atomistic model calculations

Abstract

Static lattice energy calculations, based on empirical pair potentials have been performed for a large set of different structures with compositions between pyrope and majorite, and with different states of order of octahedral cations. The energies have been cluster expanded using pair and quaternary terms. The derived ordering constants have been used to constrain Monte–Carlo simulations of temperature-dependent properties in the ranges of 1073–3673 K and 0–20 GPa. The free energies of mixing have been calculated using the method of thermodynamic integration. At zero pressure the cubic/tetragonal transition is predicted for pure majorite at 3300 K. The transition temperature decreases with the increase of the pyrope mole fraction. A miscibility gap associated with the transition starts to develop at about 2000 K and x _maj = 0.8, and widens with the decrease in temperature and the increase in pressure. Activity–composition relations in the range of 0–20 GPa and 1073–2673 K are described with the help of a high-order Redlich–Kister polynomial.

Keywords:

• Pyrope–majorite s.s.
• Monte–Carlo simulations
• Cubic/tetragonal transition
• Activity–composition relations

Acknowledgements

The majority of the results included in this publication have been developed as illustration materials for the lecture course “Introduction to Computer Simulations of Minerals” read during the Spring semester 2005 at the University of Münster by AP and VVL. Ulrik Hans, Jürgen Hansmann, Elis Hoffman, Arne Janßen and Dominik Niedermeier are thanked for asking tough questions and for the help in the computation. The support of the Deutsche Forschungsgemeinschaft (grant Wi 1232/14-2) is greatly acknowledged. JDG would like to thank the Government of Western Australia for funding under the Premier's Research Fellowship program.