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Margules method

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Book Chapter

A two-parameter Margules method for modelling the thermodynamic mixing properties of albite-water melts

Author(s)
James G. Blencoe
Book: The Second Hutton Symposium on the Origin of Granites and Related Rocks
Series: GSA Special Papers
Publisher: Geological Society of America
Published: 01 January 1992
DOI: 10.1130/SPE272-p423
... A two-parameter Margules method has been developed for modelling the thermodynamic mixing properties and hypersolidus phase relations of albite-water (ab-w) melts. The method is based largely on phase-equilibrium and calorimetric data that are either currently available or readily obtainable...
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A two-parameter Margules method has been developed for modelling the thermodynamic mixing properties and hypersolidus phase relations of albite-water (ab-w) melts. The method is based largely on phase-equilibrium and calorimetric data that are either currently available or readily obtainable; P-V-T data are not required. The new modelling method has been applied to calculate: (1) thermodynamic mixing properties for ab-w melts at 2.5 kbar, 815°C; and (2) hypersolidus phase relations for the ab-w system at 2.5 kbar. Results are uniformly positive—activity-composition relations are similar to those predicted by equations based on P-V-T data, excess enthalpies are in good agreement with data obtained from calorimetry, and calculated phase relations are fully compatible with phase-equilibrium data for ab-w melts acquired at 2.5 kbar. It is concluded that the Margules method for thermodynamic modelling of ab-w melts is a practical alternative to the P-V-T modelling method.

Journal Article

Garnet-biotite geothermometry revised; new Margules parameters and a natural specimen data set from Maine

M. J. Holdaway, Biswajit Mukhopadhyay, M. D. Dyar, C. V. Guidotti, B. L. Dutrow
Published: 01 June 1997
American Mineralogist (1997) 82 (5-6): 582–595.
DOI: https://doi.org/10.2138/am-1997-5-618
... as the Fe oxidation state of both minerals. Fe-Mg and Δ W Al Margules parameters for biotite have been retrieved by combining experimental results on [6] Al-free and [6] Al-bearing biotite using statistical methods. Margules parameters, per mole of biotite are W MgFe Bt = 40719 − 30 T J/mole, Δ W Al Bt = W...
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Journal Article

Beyond the Margules equation: a universal thermodynamic equation for solid solutions including coupled substitution, long- and short-range order

Matthias Gottschalk
Published: 01 May 2016
European Journal of Mineralogy (2016) 28 (2): 219–244.
DOI: https://doi.org/10.1127/ejm/2015/0027-2502
.... The formalism is applicable to multicomponent systems as well as to trace elements, handles long- and short-range order and can be applied to coupled substitutions. The necessary parameters can be obtained from force-field , DFT or other calculation methods capable of determining 0 K excess enthalpies...
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Includes: Supplemental Content
Journal Article

Mixing properties of sanidine crystalline solutions: III. Calculations based on two-phase data

J. B. Thompson, Jr., D. R. Waldbaum
Published: 01 June 1969
American Mineralogist (1969) 54 (5-6): 811–838.
... temperature and to obtain Margules parameters by linear least-squares fits to the values plotted. The other method makes use of near-linear relationships in the critical region between the square of the difference in composition of the two phases, the mean composition, and reciprocal temperature. Analysis...
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Journal Article

Oxide melt solution calorimetry of Fe 2+ -bearing oxides and application to the magnetite–maghemite (Fe 3 O 4 –Fe 8/3 O 4 ) system

Kristina I. Lilova, Fen Xu, Kevin M. Rosso, Carolyn I. Pearce, Saeed Kamali, Alexandra Navrotsky
Published: 01 January 2012
American Mineralogist (2012) 97 (1): 164–175.
DOI: https://doi.org/10.2138/am.2012.3883
.... The enthalpies of wüstite (FeO) and magnetite (Fe 3 O 4 ) oxidation to hematite (Fe 2 O 3 ) were measured using oxidative drop solution calorimetry in which the final product is dissolved ferric oxide. Two methods were applied: drop solution calorimetry at 1073 K in lead borate solvent and at 973 K in sodium...
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Journal Article

A statistical model of thermodynamic mixing properties of Ca-Mg-Fe 2+ garnets

Biswajit Mukhopadhyay, M. J. Holdaway, Andrea M. Koziol
Published: 01 February 1997
American Mineralogist (1997) 82 (1-2): 165–181.
DOI: https://doi.org/10.2138/am-1997-1-219
...Biswajit Mukhopadhyay; M. J. Holdaway; Andrea M. Koziol Abstract At present the most widely used models of thermodynamic mixing properties of garnet are those that are optimized to fit the experimental phase-equilibrium data along various binary garnet joins using the method of mathematical...
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Journal Article

Experimental determination of the ZnFe 2 O 4 -ZnAl 2 O 4 miscibility gap with application to franklinite-gahnite exsolution intergrowths from the Sterling Hill zinc deposit, New Jersey

Antone V. Carvalho, Charles B. Sclar
Journal: Economic Geology
Published: 01 November 1988
Economic Geology (1988) 83 (7): 1447–1452.
DOI: https://doi.org/10.2113/gsecongeo.83.7.1447
.... These data show that the original homogeneous high-temperature spinels were as aluminous as F 80 G 20 .The miscibility gap in the system ZnFe 2 O 4 -ZnAl 2 O 4 was determined experimentally by hydrothermal methods. Homogeneous synthetic spinels on the join ZnFe 2 O 4 -ZnAl 2 O 4 were prepared by dry reaction...
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Journal Article

Mixing properties of aluminosilicate garnets: constraints from natural and experimental data, and applications to geothermo-barometry

Jibamitra Ganguly, Surendra K. Saxena
Published: 01 February 1984
American Mineralogist (1984) 69 (1-2): 88–97.
... disagreement with that suggested by the Fe−Mg partitioning data. We have, therefore, adopted the most reliable set of isothermal data of Cressey et al ., namely that at 1000°C, and assumed Δ S xs (Fe−Ca) ≈ Δ S XS (Mg−Ca) to obtain the W H Margules parameters of Fe−Ca join. Symmetric approximation of these data...
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Journal Article

Calculation of coherent solvi for alkali feldspar, iron-free clinopyroxene, nepheline-kalsilite, and hematite-ilmenite

J. Tullis, R. A. Yund
Published: 01 October 1979
American Mineralogist (1979) 64 (9-10): 1063–1074.
...J. Tullis; R. A. Yund Abstract The coexisting compositions of coherently exsolved phases are given by the coherent solvus. Robin's (1974b) method for calculating the coherent solvus has been modified to allow a more accurate treatment of the compositional strains. Variations in the input parameters...
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Journal Article

Application of new experimental and garnet Margules data to the garnet-biotite geothermometer

M.J. Holdaway
Published: 01 July 2000
American Mineralogist (2000) 85 (7-8): 881–892.
DOI: https://doi.org/10.2138/am-2000-0701
... sets of papers, none of the authors had the benefit of information from any of the others. To date there have been no biotite Margules studies that can be relied upon fully, largely because of the dependent nature of the methods necessary for retrieval of biotite Margules parameters (e.g., this study...
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Journal Article

Halite-sylvite thermoconsolution

David Walker, Pramod K. Verma, Lachlan M.D. Cranswick, Simon M. Clark, Raymond L. Jones, Stephan Buhre
Published: 01 January 2005
American Mineralogist (2005) 90 (1): 229–239.
DOI: https://doi.org/10.2138/am.2005.1565
...David Walker; Pramod K. Verma; Lachlan M.D. Cranswick; Simon M. Clark; Raymond L. Jones; Stephan Buhre Abstract An asymmetric binary Margules formulation for excess Gibbs energy, enthalpy, and entropy is adequate to describe the 1 bar halite-sylvite solvus in NaCl-KCl ( Thompson and Waldbaum 1969...
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Journal Article

A thermodynamic model for polymerized sodium aluminosilicate melts

Alexander G. SIMAKIN, Vladimir O. ZAVEL'SKY, Harald BEHRENS, Jaroslav KUCHERINENKO, Tamara SALOVA
Published: 01 March 2005
European Journal of Mineralogy (2005) 17 (2): 243–250.
DOI: https://doi.org/10.1127/0935-1221/2005/0017-0243
..., Project Number: 60020, Oak Ridge National Laboratory US , 37 P. Blencoe , J.G. ( 1992 ): A two-parameter Margules method for modeling the thermodynamic mixing properties of albite-water melts . Trans. Royal Soc. Edingburgh Earth Sci ., 83 , 423 – 428 . Brown , G.E. , Farges...
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Journal Article

Optimization of some key geothermobarometers for pelitic metamorphic rocks

M. J. Holdaway
Published: 01 February 2004
Mineralogical Magazine (2004) 68 (1): 1–14.
DOI: https://doi.org/10.1180/0026461046810167
... the differences. Two studies involve the assumption that the entropic Margules are symmetrical; the Mukhopadhyay et al. (1997) model allows the entropy terms to be asymmetrical as are the enthalpy terms. In my opinion, it is not necessarily best to assume symmetry, but the robust regression methods...
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Journal Article

Heat capacities and entropies of mixing of pyrope-grossular (Mg 3 Al 2 Si 3 O 12 -Ca 3 Al 2 Si 3 O 12 ) garnet solid solutions: A low-temperature calorimetric and a thermodynamic investigation

Edgar Dachs, Charles A. Geiger
Published: 01 May 2006
American Mineralogist (2006) 91 (5-6): 894–906.
DOI: https://doi.org/10.2138/am.2006.2005
... members, are asymmetric in nature with the largest positive deviations in pyrope-rich compositions. An asymmetric Margules mixing model was found to be inappropriate for modeling the Δ S xs -X data and, thus, a two-parameter Redlich-Kister model was used to describe the excess entropy-composition...
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Journal Article

Excess mixing volume, microstrain, and stability of pyrope-grossular garnets

Wei Du, Simon Martin Clark, David Walker
Published: 01 January 2016
American Mineralogist (2016) 101 (1): 193–204.
DOI: https://doi.org/10.2138/am-2016-5128
...) apparatus at 6 GPa show irregular asymmetric positive quenchable excess volumes, with binary Margules parameters W V grossular = 2.04 ± 0.14 cm 3 /mol, and W V pyrope = 4.47 ± 0.15 cm 3 /mol. The two-parameter Margules equation is only an approximate description of the excess volumes in the pyrope-grossular...
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Journal Article

Thermodynamics of mixing and ordering in pyrope–grossular solid solution

V. L. Vinograd, M. H. F. Sluiter, B. Winkler, A. Putnis, U. Hålenius, J. D. Gale, U. Becker
Published: 01 February 2004
Mineralogical Magazine (2004) 68 (1): 101–121.
DOI: https://doi.org/10.1180/0026461046810174
... ; Becker and Pollok, 2002 ). The same problem can be solved with the help of the cluster variation method (e.g. Vinograd and Putnis, 1999 ). The CVM involves the formulation of the configurational free energy of the system as a function of the Margules coefficients, the Js and of a set of variational...
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Journal Article

Cation-Exchange Properties of Natural Zeolites

Roberto T. Pabalan, F. Paul Bertetti
Published: 01 January 2001
Reviews in Mineralogy and Geochemistry (2001) 45 (1): 453–518.
DOI: https://doi.org/10.2138/rmg.2001.45.14
..., based on Sr 2+ and Na + analytical uncertainties, are shown. The solid curve was fit to the 0.05 N isotherm data using a Margules solid-solution model. The dashed curves represent predicted values. Data from Pabalan and Bertetti (1999) . The thermodynamic equilibrium constant, K (A,B...
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Journal Article

In situ analysis of garnet inclusion in diamond using single-crystal X-ray diffraction and X-ray micro-tomography

Fabrizio Nestola, Marcello Merli, Paolo Nimis, Matteo Parisatto, Maya Kopylova, Andrea De Stefano, Micaela Longo, Luca Ziberna, Murli Manghnani
Published: 01 August 2012
European Journal of Mineralogy (2012) 24 (4): 599–606.
DOI: https://doi.org/10.1127/0935-1221/2012/0024-2212
... and X-ray micro-tomography. The novel experimental approach allowed us to determine the crystal structure of the garnet. The unit-cell edge a and fractional atomic coordinates of oxygen were used to determine the composition via an updated Margules model for garnets. The composition is Pyr 0.41(5) Alm...
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Journal Article

Microscopic strain in a grossular-pyrope solution anti-correlates with excess volume through local Mg-Ca cation arrangement, more strongly at high Ca/Mg ratio

Wei Du, David Walker, Simon Martin Clark, Xuefei Li, Baosheng Li
Published: 01 November 2017
American Mineralogist (2017) 102 (11): 2307–2316.
DOI: https://doi.org/10.2138/am-2017-6117
... °C under room pressure or cold hydrostatic compression to 10 GPa does not reset microstrain. Margules' formulations for microstrain and volume as a function of Ca/Mg ratio captures these features, especially the two-peaked distribution of microstrain with composition discovered by Du et al. (2016...
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Atomistic investigation of the pyrophyllitic substitution and implications on clay stability

Benoît Dubacq, Olivier Vidal, Éric Lewin
Published: 01 February 2011
American Mineralogist (2011) 96 (2-3): 241–249.
DOI: https://doi.org/10.2138/am.2011.3564
... studies of phase relations of phyllosilicates because of very slow reaction rates. Simple methods of estimations of thermodynamic properties of minerals such as oxide summation techniques are insufficient to constrain activity models for minerals. In this study, we use a recent atomistic technique...
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