Codex @codex  0

A group of silicate minerals with several cation positions that permit extensive solid solutions. Pyrope is the magnesian aluminium-bearing endmember relevant to a simple iron–magnesium exchange model.

A specified limiting composition used to describe a solid solution in a mineral. Its thermodynamic activity depends on the chosen standard state and activity model. For example, pyrope is a magnesian garnet endmember, while phlogopite is a magnesian biotite endmember.

Adopt ideal independent mixing on crystallographic sites, with Mg and Fe sharing three positions per formula unit and the other endmember sites fixed. This gives the phlogopite and pyrope activitiesThe reaction quotient contains their ratio, since pyrope is a product and phlogopite a reactant. ConsequentlyThe site-mixing assumption is part of this numerical answer: compositions alone do not determine nonideal thermodynamic activities. More detailed activity coefficients or unequal site occupancies would need an additional model. The cube counts the three magnesium-bearing positions rather than three molecules of each mineral.

The compositions alone do not specify a unique thermodynamic activity model. Adopt the usual ideal, independent mixing on crystallographic sites approximation: three Mg–Fe positions per formula unit, with the other sites fixed at their stated endmember compositions. Then the mineral endmember activities areThe exponent counts the three mixing cations; treating each whole mineral formula as a single mixing site would be a different model. In particular, the magnesian biotite and garnet components here are phlogopite and pyrope.

For the written reaction, the reaction quotient iswith the other solid activities equal to one. The Gibbs energy of reaction balance therefore givesThe smaller product-endmember activity lowers the reaction chemical potential and lowers the equilibrium temperature in this model. Nonideal activity coefficients or unequal occupancies of crystallographic sites would require further information rather than a revised universal numerical answer.^[ref]