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Calculation of phase diagrams from internally consistent thermodynamic data; real-time AFM diagrams on your Macintosh

Spear Frank, S.; Cheney, J.T.

Abstracts with Programs - Geological Society of America 30(7): 379

1998

An algorithm is presented for the calculation of quantitative phase diagrams depicting stable mineral assemblages and compositions based on internally consistent thermodynamic data and the petrogenetic grid derived from these data. The algorithm is applied to the calculation of AFM diagrams in the KFMASH system appropriate to the metamorphism of pelitic schists.The P-T stability of every divariant assemblage within the KFMASH system is bounded by univariant reactions in the KFMASH, KMASH, KFASH or KASH system. The software creates graphics regions for the P-T stability of each of the 46 distinct, divariant assemblages from sequences of line segments calculated along the appropriate bounding reactions and Macintosh toolbox routines for creating regions. Once every region is created, the Macintosh toolbox routine "PtInRgn" (point-in-region) is used to determine whether a user-specified P-T point falls within the stability field of each assemblage. The stable divariant assemblages are determined by checking all regions, and the compositions of minerals in the stable assemblages calculated and plotted. The advantages of this algorithm over routines that find the lowest free energy assemblage for a specified bulk composition are speed of execution, a direct and obvious relationship to the petrogenetic grid, and assemblages with very small compositional limits are not missed. Implementation of the algorithm is coded as a module for program Gibbs. Individual AFM diagrams may be calculated at any P-T condition, and sequences of AFM diagrams along any P-T path can be saved as PICT images for creating animations. The stability region of an assemblage can also be viewed on the petrogenetic grid and pseudosections showing the sequence of stable mineral assemblages in a specific bulk composition can be calculated and plotted. Minor changes to the thermodynamic data base can be readily incorporated and the entire petrogenetic grid and AFM diagram region database updated in minutes. The algorithm and its implementation are a useful tool for researchers to explore the implications of a petrogenetic grid. Results are also useful to students learning to understand petrogenetic grids and the progressive metamorphism of pelitic mineral assemblages.

Related references

**Real-time AFM diagrams on your Macintosh**. American Mineralogist 88(2-3): 473, 2003