Computers & Geosciences Vol. 12. No. 3. pp. 247-266. 1986 0098-3004: 86 $3.00 + 0.00 Printed in Great Britain Pergamon Journals Ltd PTPATH: A FORTRAN PROGRAM TO CALCULATE PRESSURE-TEMPERATURE PATHS FROM ZONED METAMORPHIC GARNETS FRANK S. SPEAR Department of Geology. Rensselaer Polytechnic Institute, Troy, NY 12181, U.S.A. (Received 6 Afay 1985; accepted 29 November 1985) Abstract--Program PTPATH generates and solves systems of simultaneous linear differential equations that relate intensive thermodynamic variables in a heterogeneous chemical system. The program can be u~d to infer changes in pressure and temperature from changes in the chemical composition of zoned minerals such as garnet where the zoning profiles are generated by reaction mechanisms. The only required input data are the "equilibrium" (i.e. peak metamorphic) compositions of the minerals in the matrix of the rock and the changes in mineral composition along the zoning profile. Key Wordv: P-T paths, Gibbs Method. Garnet zoning, Phase equilibria, Thermodynamics. INTRODUCTION Spear and Sclverstone (1983) described a technique whereby the chemical zoning profile in a metamorphic garnet could be used to compute the pressure- temperature path followed by the garnet. The calcula- tions rcquircd by this procedure arc Icngthy and in- volved, and cannot be performed without computer assistance. This report describes a FORTRAN pro- gram that has been written to perform these calcula- tions. METIIOD The theoretical basis of the technique described by Spear and Selverstone is as follows. In a hetero- geneous system (i.e. mineral assemblage) with a vari- ance ofn, it is necessary (and sufficient) to specify only n intensive parameters of the system at which point all other intensive parameters of the system are known (at least in principle). In a similar manner, it is necess- ary to specify the change in only n parameters in order to compute the change in all other intensive par- ameters. The choice of independent parameters is arbitrary. Because the composition of a mineral can be measured, it is a logical choice. Specifically, n com- position parameters are selected as independent inten- sive parameters and all other variables such as tem- perature, pressure, chemical potentials, and all other composition parameters are selected as dependent. For example, T and P can be written as functions of n independent compositional terms: T = f(X,, X 2, Xj ..... X,) e = f(x,, x,, x, ..... x,) The total differentials of T and P are: xj,,, x/, 2 +... dX., Xs.. . and x,.i xj..2 + " I ' dX.. xj,,, Calculation of AP is done by numerical integration of the given equations: xj.j and Ap = where the AX~ might be the change in almadine com- ponent from the core to the rim of a zoned garnet. Calculation of the slopes (dT/dX,) and (dP/dX~) is achieved by employing the thermodynamic technique known as the Gibbs Method (Spear, Ferry, and Rumble, 1982). In the Gibbs Method, a system of linear differential equations is set up that formulates analytically the phase equilibria of the heterogeneous system. The equations consist of (I) a Gibbs-Duhem 247