Computational petrology: Subsolidus equilibria in the upper mantle
Abstract
Processes that take place in the Earth’s mantle are not accessible to direct
observation. Natural samples of mantle material that have been transported to the surface as xenoliths provide useful information on phase relations and compositions of phases at the
pressure and temperature conditions of each rock fragment. In the past, considerable effort has been devoted by petrologists to investigate upper mantle processes experimentally.
Results of high temperatures, high pressure experiments have provided insight into lower
crust-upper mantle phase relations as a function of temperature, pressure and composition.
However, the attainment of equilibrium in these experiments, especially in complex
systems, may be very difficult to test rigorously. Furthermore, experimental results may
also require extrapolation to different pressures, temperatures or bulk compositions. More
recently, thermodynamic modeling has proved to be a very powerful approach to this
problem, allowing the deciphering the physicochemical conditions at which mantle
processes occur. On the other hand, a comprehensive thermodynamic model to investigate
lower crust-upper mantle phase assemblages in complex systems does not exist. ¶ In this study, a new thermodynamic model to describe phase equilibria between silicate and/or oxide crystalline phases has been derived. For every solution phase the molar Gibbs free energy is given by the sum of contributions from the energy of the end-members, ideal mixing on sites, and excess site mixing terms. It is here argued that the end-member term of the Gibbs free energy for complex solid solution phases (e.g. pyroxene, spinel) has not previously been treated in the most appropriate manner. As an example, the correct expression of this term for a pyroxene solution in a general (Na-Ca-Mg-Fe2+-Al-Cr-Fe3+-Si-Ti) system is presented and the principle underlying its formulation for any complex solution phase is elucidated. ¶ ...