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Margules equation

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Journal Article
Published: 01 May 2016
European Journal of Mineralogy (2016) 28 (2): 219–244.
... to the regular solution and for two neighbors to the Margules -equation. For a two-site solid solution with interaction to only the neighboring site and the possibility of interchanging atoms between the sites, this formalism reduces to the Bragg-Williams model. As an example, the formalism is applied...
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Examples for a  regular  solution and the  <span class="search-highlight">Margules</span> -<span class="search-highlight">equation</span> for binary mi...
Published: 01 May 2016
Fig. 1 Examples for a regular solution and the Margules -equation for binary mixing at a single site ( x 1 = 1 −x 2 ).
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<span class="search-highlight">Margules</span> <span class="search-highlight">equation</span> fitted to excess volume of garnet on pyrope-grossular joi...
Published: 01 January 2016
Figure 1 Margules equation fitted to excess volume of garnet on pyrope-grossular join. The binary Margules equation was used to approximately fit the asymmetric excess volume calculated from garnet synthesized in multi-anvil (MA). The error bars were calculated from uncertainties from the molar
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Excess enthalpies using a) the asymmetric <span class="search-highlight">Margules</span> <span class="search-highlight">equation</span> by  Smelik et a...
Published: 02 January 2004
Figure 18. Excess enthalpies using a) the asymmetric Margules equation by Smelik et al. (2001) with −6882.5 kJ/mol and −6461.9 kJ/mol for Δ f h° czo and Δ f h° ep b) a regular solution model with −6894.7 ± 8.2 kJ/mol and −6457.0 ± 3.5 kJ/mol Δ f h° czo and Δ f h° ep .
Journal Article
Published: 01 January 2005
American Mineralogist (2005) 90 (1): 229–239.
... ideal with pressure. The consolute temperature rises about 80 °C in 17 kbar, with little change in consolute composition. The binary Margules equation of state provides a prediction of the rise of the solvus that is impressively convergent with the new observations. This convergence is especially...
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Journal Article
Published: 01 January 2016
American Mineralogist (2016) 101 (1): 193–204.
...Figure 1 Margules equation fitted to excess volume of garnet on pyrope-grossular join. The binary Margules equation was used to approximately fit the asymmetric excess volume calculated from garnet synthesized in multi-anvil (MA). The error bars were calculated from uncertainties from the molar...
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Journal Article
Published: 01 February 1974
American Mineralogist (1974) 59 (1-2): 98–109.
... are analyzed in terms of least-squares fitting to a two-constant (W G1 , W G2 ) Margules equation (Thompson, 1967) in order to derive analytic expressions for the solvus boundary. The simplest, best representation of the data is given by the equations W G1 = 12, 189 ± 864 - 2, 419 ± 581 × T (°K)/1000 + 36.6...
Journal Article
Published: 01 February 1997
Russ. Geol. Geophys. (1997) 38 (2): 559–586.
... to determine compositional dependences of molar volumes. Excess mixing volumes of pyrope-knorringite garnets can be described by a symmetrical Margules equation with W V = 0.056 J/bar. Spinel-picrochromite solid solution is best approximated by an asymmetrical model with W V ,Al = –0.0483 and W V ,Cr = 0.0722...
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Journal Article
Published: 01 December 1973
American Mineralogist (1973) 58 (11-12): 998–1008.
.... Within the limits of experimental error, the two-phase data are symmetric with respect to composition. Nurnerical analysis of the experimental data in terms of a one-constant Margules equation (Thompson, 1967) yields the following relationship for the mixing parameter of the Gibbs Free Energy Function: W...
Journal Article
Published: 01 December 1968
American Mineralogist (1968) 53 (11-12): 1965–1999.
...J. B. Thompson, Jr.; D. R. Waldbaum Abstract A statistical analysis of the ion-exchange data of Orville (1963) for highly disordered alkali feldspars shows that the Gibbs energy of mixing of these feldspars can be represented satisfactorily by an asymmetric Margules equation containing only two...
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Plot of Δ H  mix  vs. composition for the clinozoisite series (error bars a...
Published: 01 January 2001
and the measured value for the given composition in the solid solution. The distribution is highly asymmetric with maximum value of the Δ H mix being about 20 kJ/mol near X Al 2 Fe = 0.65.. The curve fit to the data represents the two-parameter Margules expression shown in Equation 4. The results derived from
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Excess Gibbs energy,  E , for (Cs + ,K + )-, (Na + ,K + )-, (NH 4  + ,K + )...
Published: 01 January 2001
Figure 17. Excess Gibbs energy, E , for (Cs + ,K + )-, (Na + ,K + )-, (NH 4 + ,K + )-, (Ca 2+ ,K + )- and (Sr 2+ ,K + )-clinoptilolite solid solutions calculated using Equation (23) and the Margules parameters listed in Table 10 .
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Excess Gibbs energy,  E , for (NH 4  + ,Na + )-, (Li + ,Na + )-, (K + ,Na +...
Published: 01 January 2001
Figure 16. Excess Gibbs energy, E , for (NH 4 + ,Na + )-, (Li + ,Na + )-, (K + ,Na + )-, (Cs + ,Na + )-, (Ca 2+ ,Na + )-, and (Sr 2+ ,Na + )-clinoptilolite solid solutions calculated using Equation (23) and the Margules parameters listed in Table 10 .
Published: 01 January 1992
DOI: 10.1130/SPE272-p423
... 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...
Journal Article
Published: 01 February 1990
American Mineralogist (1990) 75 (1-2): 209–220.
... mole percent natroalunite at each temperature studied. We have fit these results by using a subregular Margules model for alunite-natroalunite mixing. Individual-ion activity coefficients for aqueous Na + and K + at 250 °C and 500 bars were estimated using Pitzer’s equations. At this temperature, γ Na...
Journal Article
Published: 01 December 1978
American Mineralogist (1978) 63 (11-12): 1225–1240.
... system from 400 to 1000°C at 0.5, 2.0, and 5.0 kbar; (3) thermodynamic mixing-parameter equations for (Na,K) 3 K(AlSiO 4 ) 4 crystalline solutions; and (4) calculated nepheline-kalsilite solvi and subsolidus activity-composition relations for the Na 3 K(AlSiO 4 ) 4 −K 4 (AlSiO 4 ) 4 system at pressures...
Journal Article
Published: 01 December 1977
American Mineralogist (1977) 62 (11-12): 1200–1215.
... there is significant scatter in the molal volume data, least-squares fit polynomial equations calculated from these data suggest small, positive excess volumes for synthetic (Na,K)Al 2 (AlSi 3 O 10 )(OH) 2 micas over the entire compositional range. Cubic least-squares fit polynomial equations calculated from the 2, 4...
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Microstrain data from ALS and BNL for dry garnets compared to a <span class="search-highlight">Margules</span>-in...
Published: 01 November 2017
Figure 10. Microstrain data from ALS and BNL for dry garnets compared to a Margules-inspired fitting equation. The equation gives a two-peaked distribution of microstrains such as we observe across two independent data collection exercises at two different synchrotrons (ALS and BNL
Journal Article
Journal: Lithosphere
Publisher: GSW
Published: 13 July 2021
Lithosphere (2021) 2021 (Special 1): 3474828.
... equation and binary interaction parameter correlation. The activity coefficient in the aqueous phase relies on a unified model of a gas equilibrium constant, the Margules expression, and a Pizter interaction model. An extensive experimental databank is developed to calibrate the proposed model...
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( a ) Tetrahedral rotation (α, in degrees) in the Na +  and K +  cavities a...
Published: 01 May 2016
thickness modulus (Å/GPa). ( e ) Volume/bulk modulus (Å 3 /GPa) as a function of Na + content in the series. Insets: Least-square fitting equations, correlation coefficients (R or R 2 ), standard deviations (SD), and Margules’ coefficients (W i ). (Color online.)