Abstract

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  
x=(r+1-l)/2y=32t+36f
and  
z=63f

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.

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