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Published July 1, 2015 | Published + Supplemental Material
Journal Article Open

The free energy of mechanically unstable phases

Abstract

Phase diagrams provide 'roadmaps' to the possible states of matter. Their determination traditionally rests on the assumption that all phases, even unstable ones, have well-defined free energies under all conditions. However, this assumption is commonly violated in condensed phases due to mechanical instabilities. This long-standing problem impedes thermodynamic database development, as pragmatic attempts at solving this problem involve delicate extrapolations that are highly nonunique and that lack an underlying theoretical justification. Here we propose an efficient computational solution to this problem that has a simple interpretation, both as a topological partitioning of atomic configuration space and as a minimally constrained physical system. Our natural scheme smoothly extends the free energy of stable phases, without relying on extrapolation, thus enabling a formal assessment of widely used extrapolation schemes.

Additional Information

© 2015 Macmillan Publishers Limited. This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. Received 16 Sep 2014; Accepted 19 May 2015; Published 1 Jul 2015. This work is supported by the US National Science Foundation via grant DMR-1154895, by the US Office of Naval Research via grant N00014-12-1-0557 and by Brown University through the use of the facilities of its Center for Computation and Visualization. This work uses the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1053575. Useful comments by V. Ozolins and U. Kattner are gratefully acknowledged. Authors contributions: A.v.d.W. proposed the main concepts and developed computational tests of the approach. Q.H. contributed to the proposed free energy definition. S.K. performed exploratory electronic structure calculations that lead to the proposed free energy definition. R.S. contributed to the electronic structure calculations.

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