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Licensed Unlicensed Requires Authentication Published by De Gruyter November 24, 2015

Tetrahedral plot diagram: A geometrical solution for quaternary systems

Toshiaki Shimura and Anthony I.S. Kemp
From the journal American Mineralogist


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

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.

Received: 2015-4-4
Accepted: 2015-4-28
Published Online: 2015-11-24
Published in Print: 2015-11-1

© 2015 by Walter de Gruyter Berlin/Boston

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