Читать книгу Geochemistry - William M. White - Страница 122

Sometimes it is desirable to calculate the activities of pure end-member components in solid solutions. Garnet has the general formula X₃Y₂Si₃O₁₂. Calculate the activity of pyrope, Mg₃Al₂Si₃O₁₂, in a garnet solid solution of composition:

Answer: The chemical potential of pyrope in garnet contains mixing contributions from both Mg in the cubic site and Al in the octahedral site:

The activity of pyrope is thus given by:

In the example composition above, the activity of Mg is:

and that of Al is:

The activity of pyrope in the garnet composition above is 0.002 × 0.956 = 0.00191. There is, of course, no mixing contribution from the tetrahedral site because it is occupied only by Si in both the solution and the pure pyrope phase.