THE PARAGONITE-MUSCOVITE SOLVUS .2. NUMERICAL GEOTHERMOMETERS FOR NATURAL, QUASI-BINARY PARAGONITE-MUSCOVITE PAIRS

Three parametric (nonthermodynamic) equations have been developed to c alculate final equilibration temperatures for natural, quasibinary par agonite-muscovite (Pg-Ms) pairs (mole fraction margarite in Pg < 0.05, Si/formula unit less-than-or-equal-to 6.2 and/or SIGMA (Mg + Fe2+ + F e3+) less-than-or-equal-to 0.35 for coexistent Ms). The first two equa tions are paragonite-based and muscovite-based, because they yield equ ilibration temperatures that depend on the Na-K compositions of K-satu rated Pg and Na-saturated Ms, respectively. The third equation is clos ure-based, because it yields equilibration temperatures that vary with the width of the pp between the Na-K compositions of coexisting Pg an d Ms (i.e., the degree of solvus closure). Equilibration temperatures can be estimated, using just one of the geothermometers, or by averagi ng the temperatures obtained from any combination of the three equatio ns. Comparison of the three calculated temperatures yields information on the mutual consistencies of the Na-K compositions of coexisting Pg and Ms with respect to their utility in Pg-Ms solvus thermometry. Geo thermometric inconsistencies in the Na-K compositions of quasibinary P g-Ms pairs can be caused by (1) inaccuracies in determinations of the Na-K compositions of the coexisting micas, (2) H3O+ --> K+ and vacancy --> K+ substitution in muscovite and/or paragonite, and (3) crystalli zation and preservation of quasibinary Pg-Ms pairs with metastable Na- K compositions. Due to the effects of pressure on the stability relati ons of Pg-Ms pairs and the K/Na ratios of Na-saturated muscovites, pra ctical applications of Pg-Ms solvus thermometry are restricted to quas ibinary Pg-Ms pairs that equilibrated at pressures between approximate ly 2 and 8 kbar. Within this pressure range, the utility of Pg-Ms solv us thermometry is limited thermally to approximately 300 less-than-or- equal-to T less-than-or-equal-to 700-degrees-C by (1) the decompositio n of K-saturated paragonite at temperatures between approximately 580 and 700-degrees-C, and (2) steepening of the solvus limbs at temperatu res below 300-degrees-C. Graphical and calculated Pg-Ms solvi based on solvus data for synthetic, binary Pg-Ms micas are inconsistent with s olvus data for natural, quasibinary Pg-Ms micas. Consequently, these s olvi should not be used to estimate equilibration temperatures for nat ural, quasibinary Pg-Ms pairs.