Low-Cost Vibrational Free Energies in Solid Solutions with Machine Learning Force Fields

Kasper Tolborg, Aron Walsh

Research output: Contribution to journalArticlepeer-review


The rational design of alloys and solid solutions relies on accurate computational predictions of phase diagrams. The cluster expansion method has proven to be a valuable tool for studying disordered crystals. However, the effects of vibrational entropy are commonly neglected due to the computational cost. Here, we devise a method for including the vibrational free energy in cluster expansions with a low computational cost by fitting a machine learning force field (MLFF) to the relaxation trajectories available from cluster expansion construction. We demonstrate our method for two (pseudo)binary systems, Na1-xKxCl and Ag1-xPdx, for which accurate phonon dispersions and vibrational free energies are derived from the MLFF. For both systems, the inclusion of vibrational effects results in significantly better agreement with miscibility gaps in experimental phase diagrams. This methodology can allow routine inclusion of vibrational effects in calculated phase diagrams and thus more accurate predictions of properties and stability for mixtures of materials.

Original languageEnglish
Pages (from-to)11618-11624
Number of pages7
JournalJournal of Physical Chemistry Letters
Issue number51
StatePublished - 28 Dec 2023

Bibliographical note

Publisher Copyright:
© 2023 The Authors. Published by American Chemical Society


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