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A linear algebraic method for the calculation of pyroxene endmember components

Die Berechnung von Pyroxen-Endgliedern mit Methoden der Linearen Algebra

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Summary

A linear algebraic model for the sequence-independent calculation of pyroxene components of microprobe analyses is presented. Assuming ideal stoichiometry, the theoretical Fe3+ is obtained by using charge balance criteria. The calculation of 11 linearly-independent endmember parameters (Jd, Ac, Ur, TiTs, CaTs, FeTs, CrTs, Pm, Fs, En, Wo) in conjunction with a rigorous mass balance enables the appreciation of the stoichiometry and the endmember definition. The presented method offers a normalized comparison base for a wide spectrum of pyroxene analyses. On the basis of the 11 linearly-independent endmember parameters other common pyroxene components (e.g. Di, Hd, Jh, FeATs, CrATs, MgTs, Fe2+Ts) may be calculated using exchange reactions.

Zusammenfassung

Unter Verwendung von Methoden der Linearen Algebra wird eine reihenfolgenunabhängige Berechnung von Pyroxen-Endgliedern aus Mikrosondenanalysen vorgestellt. Die Annahme idealer Stöchiometrie ermöglicht die Bestimmung des theoretischen Fe3+ aus einer Ladungsbilanz. Die Berechnung von 11 linear-unabhängigen Pyroxen-Endgliedern (Jd, Ac, Ur, TiTs, CaTs, FeTs, CrTs, Pm, Fs, En, Wo) erfolgt unter einer strengen Massenbilanz und gewährleistet eine theoretische Auswertung der auferlegten Bedingungen über die Stöchiometrie und die Endgliederdefinition. Darüber hinaus stellt diese Methode eine normierte Vergleichsbasis für ein breites Spektrum von Pyroxenanalysen dar. Ausgehend von den 11 linear-unabhängigen Endgliedern können weitere in der Natur auftretende Pyroxen-Endglieder wie z.B. Di, Hd, Jh, FeATs, CrATs, MgTs, Fe2+ Ts mittels Austauschreaktionen berechnet werden.

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Authors and Affiliations

  1. Institute of Petrology, University of Vienna, Austria

    H. Dietrich &  K. Petrakakis

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  1. H. Dietrich
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  2. K. Petrakakis
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Dietrich, H., Petrakakis, K. A linear algebraic method for the calculation of pyroxene endmember components. TMPM Tschermaks Petr. Mitt. 35, 275–282 (1986). https://doi.org/10.1007/BF01191990

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  • DOI: https://doi.org/10.1007/BF01191990

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