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

Aug 5, 2026

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The rational design of alloys and solid solutions depends on accurate computational phase-diagram predictions, yet vibrational entropy is often omitted because of high computational cost. A method is presented to incorporate vibrational free energy into cluster expansions using low-cost machine-learning force fields fitted to relaxation trajectories from cluster-expansion construction. The approach is demonstrated for Na1−xKxCl and Ag1−xPdx, yielding phonon dispersions and vibrational free energies. Adding vibrational effects gives only marginal improvement in miscibility-gap agreement, enabling routine vibrational contributions and improved property and stability predictions for material mixtures.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages8

Reading Time20 min

AccessFree to download

Abstract

Method overview

Demonstration on (pseudo)binary systems

Impact on phase-diagram predictions

Aalborg Universitet Low-Cost Vibrational Free Energies in Solid Solutions with Machine Learning Force Fields Tolborg, Kasper; Walsh, Aron Published in: The Journal of Physical Chemistry Letters DOI (link to publication from Publisher): 10.1021/acs.jpclett.3c03083 Creative Commons License CC BY 4.0 Publication date: 2023 Document Version Publisher's PDF, also known as Version of record Link to publication from Aalborg University Citation for published version (APA): Tolborg, K. , & Walsh, A. (2023) . Low-Cost Vibrational Free Energies in Solid Solutions with Machine Learning Force Fields. The Journal of Physical Chemistry Letters, 14(51), 11618-11624. [https://doi.org/10.1021/acs.jpclett.3c03083](https://doi.org/10.1021/acs.jpclett.3c03083) General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. -Users may download and print one copy of any publication from the public portal for the purpose of private study or research. -You may not further distribute the material or use it for any profit-making activity or commercial gain -You may freely distribute the URL identifying the publication in the public portal Take down policy If you believe that this document breaches copyright please contact [us at vbn@aub.aau.dk](us at vbn@aub.aau.dk) providing details, and we will remove access to the work immediately and investigate your claim. This article is licensed under CC-BY 4.0 [pubs.acs.org/JPCL](pubs.acs.org/JPCL) Letter Low-Cost Vibrational Free Energies in Solid Solutions with Machine Learning Force Fields Kasper Tolborg* and Aron Walsh Cite This: J. Phys. Chem. Lett. 2023, 14, 11618−11624 Read Online ACCESS Metrics & More Article Recommendations *sı Supporting Information Downloaded via 130.225.247.9 1 on April 1 1, 2024 at 09:08:37 (UTC) . See [https://pubs.acs.org/sharingguidelines](https://pubs.acs.org/sharingguidelines) for options on how to legitimately share published articles. ABSTRACT: The rational design of alloys and solid solutions relies on accurate computational predictions of phase diagrams. The cluster expansion method has proven tobe 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 includingthe 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 insignificantly 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. A lloytechsnaonldogsyolidransolutgingiofnsrofomrmstruanctntralegrmalatparterialsoftmodero semconductors and catalysts. Recent years have seen renewed interest in compositionally complex materials with the advent of high-entropy alloys and compounds. 1−3 First-principles calculations of compositional phase diagrams and derived properties can significantly aid the design and understanding of alloys and solid solutions.2,4 The most common tool for firstprinciples calculations of compositional phase diagrams is the cluster expansion (CE). In this method, the energy of anatomic configuration is expanded in a set of basis functions, and interaction parameters of pairs, triplets, etc., are fitte

FAQs

Why are vibrational entropy effects often neglected in cluster expansion studies?

Because computing vibrational contributions is typically too costly, making it difficult to include vibrational entropy in practical phase-diagram calculations.

How does the proposed method include vibrational free energy with low computational cost?

It fits a machine-learning force field to relaxation trajectories available during cluster expansion construction, enabling vibrational free energies to be incorporated into the cluster-expansion framework.

Which systems are used to demonstrate the approach, and what is the observed impact?

The method is demonstrated for Na1−xKxCl and Ag1−xPdx. Including vibrational effects leads to insignificantly better agreement with miscibility gaps in experimental phase diagrams.

Aug 5, 2026

Upload by Eliana