# Equilibrium Thermodynamics in Petrology by Roger Powell

By Roger Powell

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E. 'Y2A = 1). From the point of view of performing calculations involving chemical potentials, the assumption of ideal mixing for a phase is often used. 1 for the chemical potential. The incorrectness of this is given by the distance between a-e and a-b-e-d for a particular composition, XlA' Thus the assumption will be correct in the Raoult's law region, but it will become progressively more incorrect in moving across the intermediate region. The amount of this incorrectness in the Henry's law region depends on the size of the Henry's law constant (or RT In h I A (2 ) in l~ © Roger Powell 26 Equilibrium Thermodynamics in Petrology changes from stable to metastable across the common intersection of the three lines, the so called triple point.

Roger Powell 28 Equilibrium Thermodynamics in Petrology loop for C will just touch the A-D common tangent. At this temperature, A, C and 0 can coexist in stable equilibrium, and, in terms of changing temperature, this temperature marks the position of the reaction A + 0 = C. On the T'--x diagram a horizontal line joins A, C and 0 at this temperature. Note the shapes of the single-phase fields on the T'-x diagram, particularly that the C field terminates at a point on the A-C-D line. This is because there is only one composition of C which can be in equilibrium with A + 0, regardless of how wide a solution C can form, in • A+B B+C A + C:B___ T, T A+C A +D:C ....

This is because the densities of the two phases are very similar (32·14 for olivine, 31·94 for orthopyroxene, both in g kJ- 1 kbar). 2(c) Plot the positions of talc (TA, Mg3Si40 lO(OHh), and chrysotile (CH, Mg3ShOs(OH)4) on a triangular composition diagram representing the ternary system MgD-Si0 2-H20. The lever rule principle also operates in triangular phase diagrams. 9(b) would be the fictitious phase Mg302 ( OHh, a phase consisting of just H 20 and MgO in the proportion i to ~, or in the ratio 1: 3.