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The transformation from a tetrahedral four-component system to an XYZ-orthogonal coordinate axis system has been solved using the geometry of a tetrahedron. If a four component mixing ratio is described as t , l , r , and f (here, t + l + r + f = 1), the transforming equations can be written as ![Formula][1] and ![Formula][2] A tetrahedral plot diagram can be easily constructed using the algorithms described in this paper. We present an implementation of these algorithms in a custom-designed Microsoft Excel spreadsheet, including adjustable viewing angles for the tetrahedral plot. This will be of general utility for petrological or mineralogical studies of quaternary systems. [1]: /embed/mml-math-1.gif [2]: /embed/mml-math-2.gif |
