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Proof that a dominant endmember formula can always be written for a mineral or a crystal structure

Frank C. Hawthorne
Proof that a dominant endmember formula can always be written for a mineral or a crystal structure
The Canadian Mineralogist (May 2021) 59 (1): 159-167

Abstract

An endmember formula must be: (1) conformable with the crystal structure of the mineral, (2) electroneutral (i.e., not carry a net electric charge), and (3) irreducible [i.e., not capable of being factored into components that have the same bond topology (atomic arrangement) as that of the original formula]. The stoichiometry of an endmember formula must match the "stoichiometry" of the sites in the structure; for ease of expression, I denote such a formula here as a chemical endmember. In order for a chemical endmember to be a true endmember, the corresponding structure must obey the valence-sum rule of bond-valence theory. For most minerals, the chemical endmember and the (true) endmember are the same. However, where local order would lead to strong deviation from the valence-sum rule for some local arrangements, such arrangements cannot occur and the (true) endmember differs from the chemical endmember. I present heuristic and algebraic proofs that a specific chemical formula can always be represented by a corresponding dominant endmember formula. That dominant endmember may be derived by calculating the difference between the mineral formula considered and all of the possible endmember compositions; the endmember formula which is closest to the mineral formula considered is the dominant endmember.


ISSN: 0008-4476
EISSN: 1499-1276
Coden: CAMIA6
Serial Title: The Canadian Mineralogist
Serial Volume: 59
Serial Issue: 1
Title: Proof that a dominant endmember formula can always be written for a mineral or a crystal structure
Author(s): Hawthorne, Frank C.
Affiliation: University of Manitoba, Department of Geological Sciences, Winnipeg, MB, Canada
Pages: 159-167
Published: 20210526
Text Language: English
Publisher: Mineralogical Association of Canada, Ottawa, ON, Canada
References: 22
Accession Number: 2021-043884
Categories: General mineralogy
Document Type: Serial
Bibliographic Level: Analytic
Illustration Description: 6 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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