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Thermodynamics of mixing in an isostructural solid solution: Simulation methodologies and application to the rutile-cassiterite system

  • Xin Liu , Victor L. Vinograd EMAIL logo , Xiancai Lu EMAIL logo , Egor V. Leonenko , Nikolay N. Eremin , Rucheng Wang and Björn Winkler
Published/Copyright: April 30, 2016
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American Mineralogist
From the journal American Mineralogist Volume 101 Issue 5

Abstract

The accuracies of two different approaches to model thermodynamic mixing properties of solid solutions are explored using the rutile-cassiterite solid solution as an example. Both methods employ an expansion of the configurational enthalpy in terms of pairwise interactions energies. In the first method the partition function is directly computed from the excess energies of all Ti/Sn configurations within a 2 × 2 × 4 supercell. In the second method the free energy of mixing is calculated by a thermodynamic integration of the thermally averaged enthalpies computed with the Monte Carlo method using an 8 × 12 × 16 supercell. The phase relations derived from Monte Carlo simulations agree well with the available experimental data, under the condition that the free energy is corrected for the effect of the excess vibrational entropy. The direct calculation of the partition function provides reasonable phase relations only when the configurational entropy is corrected to be consistent with the ideal mixing in the high-temperature limit. Advantages and drawbacks of the both approaches are discussed. The findings are generally applicable to models of isostructural solid solutions.

Key words: Rutile-cassiterite; solid solution; first-principles based calculations; pairwise interactions; Monte Carlo simulations; configurational statistics

Acknowledgments

We acknowledge National Science Foundation of China (Nos. 41425009 and 41230315) and the financial support from the State Key Laboratory for Mineral Deposits Research of China. We acknowledge the computational support from the Juelich Supercomputing Centre, from the Centre for Scientific Computing at the University of Frankfurt, and from the High Performance Computing Center of Nanjing University. X.L. is grateful to the China Scholarship Council for financial support. The authors also thank J.D. Gale (Curtin University) for the help in developing the force-field model.

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Received: 2015-7-3
Accepted: 2015-12-24
Published Online: 2016-4-30
Published in Print: 2016-5-1

© 2016 by Walter de Gruyter Berlin/Boston

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https://doi.org/10.2138/am-2016-5490
Keywords for this article
Rutile-cassiterite; solid solution; first-principles based calculations; pairwise interactions; Monte Carlo simulations; configurational statistics

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  46. Joegoldsteinite: A new sulfide mineral (MnCr2S4) from the Social Circle IVA iron meteorite
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