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

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Marco E. Ciriotti
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Proof that a dominant endmember formula can always be written for a mineral or a crystal structure

Messaggio da Marco E. Ciriotti » gio 27 mag, 2021 11:24

Prossima pubblicazione.

Referenza:
▪ Hawthorne, F.C. (2021): Proof That a Dominant Endmember Formula Can Always Be Written for a Mineral or a Crystal Structure. Canadian Mineralogist, 59, (in press).

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.

NdR: da leggere!
Marco E. Ciriotti

«Things are interesting only in so far as they relate themselves to other things»

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Marco E. Ciriotti
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Iscritto il: ven 25 giu, 2004 11:31
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Re: Proof that a dominant endmember formula can always be written for a mineral or a crystal structure

Messaggio da Marco E. Ciriotti » ven 02 lug, 2021 12:09

Pubblicazione avvenuta.

Referenza:
▪ Hawthorne, F.C. (2021): Proof That a Dominant Endmember Formula Can Always Be Written for a Mineral or a Crystal Structure. Canadian Mineralogist, 59, 159-167.

NdR: per gli interessati è disponibile il PDF. Assolutamente da leggere.
Marco E. Ciriotti

«Things are interesting only in so far as they relate themselves to other things»

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Marco E. Ciriotti
Messaggi: 31675
Iscritto il: ven 25 giu, 2004 11:31
Località: via San Pietro, 55 I-10073 Devesi/Cirié TO - Italy
Contatta:

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

Messaggio da Marco E. Ciriotti » dom 03 apr, 2022 10:40

SUMMARY
[1] 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).
[2] 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.
[3] The derivation of a dominant endmember formula
for a specific chemical formula is independent of
expressing the specific chemical formula as a set
of endmember constituents.
[4] I have presented heuristic and algebraic proofs that
a specific chemical formula can always be
represented by a corresponding dominant endmember
formula.
[5] The dominant endmember is that endmember
which is closest to the formula of the mineral
considered, expressed as the smallest RSSD
(square-root of the sum of the squared differences)
from the mineral formula.
Marco E. Ciriotti

«Things are interesting only in so far as they relate themselves to other things»

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