Journal of Petrology | Volume 27 | Number 4 | Pages 843-852 | 1986
© Oxford University Press 1986
research-article |
Phase Equilibria in the Pyroxene Quadrilateral
1Department of Earth and Environmental Sciences, CUNY, Graduate Center and Department of Geology, Brooklyn College Brooklyn, New York 11210
2Department of Inorganic Chemistry, University of Umea S-95187 Sweden
Received April 23, 1985; Revised typescript accepted November 19, 1985
ABSTRACT
Experimental phase equilibrium data on compositions of coexisting pyroxenes in the quadrilateral enstatite-diopside-ferrosilite-hedenbergite have been used to model pyroxene solid solutions and to formulate pyroxene geothermometers. Each pyroxene is treated as a solid solution of four quad-components using the Kohler formulation
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where 
Gij* is the excess free energy of mixing in a binary solution calculated with binary mole fractions (e.g. Xio = Xi/(Xi+Xj)) and Xi is the mole fraction in a multicomponent solution. The fit to the experimental data is achieved by minimizing the total Gibbs free energy of the assemblage. The following set of thermochemical data and simple mixture parameters (Wij) are found to be best suited. Standard (T = 298·15 K) enthalpy and entropy of formation from elements for fictive orthohedenbergite are –1416·8 kJ and 84·88 J K–1 mol –1 respectively. The heat capacity is given by 114·67+17·09E-3T–31·40E5T–2. The Wij data are: Opx: W12 = W21 = 25 W13 = (13·1–0-015T), W31 = (3·37–0·005T), W23 = 20, W32 = 16, W24 = 5, W42 = 7, W34 = 15, W43 = 15; Cpx: W12 = (25·484+0·0812P), W21 =(31·216–0·0061P), W31 = W13 = 0W14 = (93·3–0·045T), W41 = (–20·0+0·028T), W23 = 24, W32 = 15, W24 = 12, W42 = 12, W34 = (16·941+0·00592P), W43 = (20·697–0·00235P). Coexisting pyroxene compositions have been computed in the temperature range of 700 to 1400°C.
Two geothermometers have been constructed, one based on atomic fraction of iron (Fe/(Fe + Mg)) in orthopyroxene and the Fe-Mg distribution coefficient and the other, based on wollastonite content of clinopyroxene. The two scales yield different temperatures when applied to the same rock. In igneous pyroxenes, the Ca transfer ceased at 150 to 200°C above the closure temperature of the Fe-Mg ion-exchange. In metamorphic rocks an opposite effect seems to have prevailed.
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