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On the calculation of the relative amounts of endmember constituents for garnet

Frank C. Hawthorne
On the calculation of the relative amounts of endmember constituents for garnet
The Canadian Mineralogist (March 2021) 59 (1): 169-176

Abstract

It is commonly accepted that the calculation of the proportions of endmember constituents in garnet is dependent on the particular sequence of calculating the amounts of the endmembers, and this belief has been used to justify avoiding the use of endmembers in the definition of a mineral species. Calculating the amounts of endmember constituents to represent a specific mineral formula involves the solution of a set of simultaneous equations, and hence the idea that the solution is dependent on the order in which the amounts of endmember constituent are determined conflicts with the meaning of the term "simultaneous equations". Here I examine the data on which these conclusions are based and show that these sequence-dependent results arise because of the use of non-stoichiometric formulae that are not electroneutral. If a garnet formula is adjusted slightly such that it exactly fits the general formula of a garnet, (super [8]) X (sub 3) (super [6]) Y (sub 2) (super [4]) Z (sub 3) O (sub 12) , and is electroneutral, the simultaneous equations relating its chemical formula to a set of endmember constituents have a single unique solution. Thus, the argument that has been used to justify avoiding the use of endmembers in the definition of a mineral species is specious.


ISSN: 0008-4476
EISSN: 1499-1276
Coden: CAMIA6
Serial Title: The Canadian Mineralogist
Serial Volume: 59
Serial Issue: 1
Title: On the calculation of the relative amounts of endmember constituents for garnet
Author(s): Hawthorne, Frank C.
Affiliation: University of Manitoba, Geological Sciences, Winnipeg, MB, Canada
Pages: 169-176
Published: 20210304
Text Language: English
Publisher: Mineralogical Association of Canada, Ottawa, ON, Canada
References: 9
Accession Number: 2021-043773
Categories: Mineralogy of silicates
Document Type: Serial
Bibliographic Level: Analytic
Illustration Description: illus. incl. 8 tables
Country of Publication: Canada
Secondary Affiliation: GeoRef, Copyright 2021, American Geosciences Institute. Abstract, copyright, Mineralogical Association of Canada. Reference includes data from GeoScienceWorld, Alexandria, VA, United States
Update Code: 202130
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