Alkali and Plagioclase Feldspars Solution Models

Handout #3 Reading Stormer (1975) Am. Mineral 60, 667-674. Whitney and Stormer (1977) Am. Mineral 62, 687-691. Andersen and Lindsley (1981) GCA 45, 847-853. Supplementary Reading Griffen, Dana T. Silicate Crystal Chemistry, Chapter 2. New York, NY: Oxford University Press, 1992. ISBN: 0195044423 Ribbe, P. H. (ed.) Feldspar Mineralogy (Reviews in Mineralogy, Vol. 2, 2nd ed.). Washington, D. C.: Mineralogical Society of America, 1983. ISBN: 0939950146 Two feldspar themometry-barometry The use of coexisting plagioclase and alkali feldspars to predict temperature and pressure of equi­ libration was first proposed by Barth (1951) who used natural phase assemblages to calibrate a thermometer. Stormer and Whitney and Stormer subsequently develop a simple thermodynamic model for treating feldspar equilibria. The important assumptions for this model were: 1. Use one of the conditions of equilibrium. PF µAF Ab = µAb where AF = alkali feldspar and PF = plagioclase feldspar. F 2. Assume that Or content in PF has no effect on aP Ab and that An content in AF has no effect AF on aAb . The equilibrium condition can be written AF oAF µAF Ab = µAb + RT lnaAb PF oP F F µP Ab = µAb + RT lnaAb 3. Assume that the standard state chemical potential for pure Ab in both phases was the same. Then 0 = RT ln aAF Ab F aP Ab = RT ln AF AF γAb XAb P F PF γAb XAb PF 4. Assume γAb = 1, so ln AF XAb AF = ln γAb PF XAb AF ln γAb = 1 AF 2 AF 3 (2WGOr − WGAb ) (XOr ) + 2 (WGAb − WGOr ) (XOr ) RT Several of the simplifications of the Whitney and Stormer thermometer have been dealt with in subsequent models of feldspar equilibria, and some have not. 1 First Assumption The µo ’s are not equal and we require two sets of W ’s! So PF µAF Ab = µAb AF µAb = µoAbdisordAF + RT ln γAb XAb where W ’s were appropriate to disordered 0. o ordered plag F µP + RT ln γAb XAb Ab = µAB potentially we also need W ’s for a different solution. at T₁ C2/m T G o disord. PF µAb C2/m C1 T₁ o ord. PF µAb Ab X Or C1 X Second Assumption A ternary solution model would be more appropriate. RT ln γ1 = WG12 X12 X2 + WG21 X22 X1 +WG13 X12 X3 + WG31 X32 X1 +WG23 X22 X3 + WG32 X32 X2 Margules formulations for ternary and quaternary solutions were developed by Wohl (1946, 1953). Lindsley and Anderson (1981) go through the exercise of deriving an expression for a ternary asym­ metric model. These models, like the ones for binary systems, assume that a polynomial of degree 2 (symmetric) or degree 3 (asymmetric) in component 2 and 3 are adequate models of the excess free energy of mixing. 2