{"id":982,"date":"2026-07-31T19:41:56","date_gmt":"2026-08-01T00:41:56","guid":{"rendered":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/?p=982"},"modified":"2026-07-31T19:41:59","modified_gmt":"2026-08-01T00:41:59","slug":"j-lund-h-wang-rd-braatz-re-garcia-machine-learning-of-phase-diagrams-materials-advances-323-8485-8497-2022","status":"publish","type":"post","link":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/2026\/07\/31\/j-lund-h-wang-rd-braatz-re-garcia-machine-learning-of-phase-diagrams-materials-advances-323-8485-8497-2022\/","title":{"rendered":"J Lund, H Wang, RD Braatz, RE Garc\u00eda “Machine learning of phase diagrams.” Materials Advances. 3(23): 8485-8497, 2022."},"content":{"rendered":"\n

J Lund, H Wang, RD Braatz, RE Garc\u00eda “Machine learning of phase diagrams.<\/em>” Materials Advances.<\/strong> 3(23): 8485-8497, 2022. https:\/\/doi.org\/10.1039\/d2ma00524g<\/a><\/p>\n\n\n\n

Abstract<\/h2>\n\n\n\n

By starting from experimental- and\u00a0ab initio<\/em>-determined phase diagrams (PDs) of materials, a machine learning (ML) method is developed to infer the free energy function for each phase. The ML method is based on a custom two-step explore-exploit\u00a0k<\/em>-nearest neighbor strategy, which samples the multidimensional space of Gibbs free energy parameters and user-defined physical constraints into a database of millions of PDs in order to identify the target material properties. The method presented herein is 1000\u00d7 to 100 000\u00d7 faster than currently available approaches, and defines a new paradigm on the quantification of properties of materials and devices. As an example application, the developed methodology is combined with the most widely used thermodynamic models \u2013 the regular solution, Redlich\u2013Kister, and sublattice formalisms \u2013 to infer the properties of materials for lithium-ion battery applications in a matter of hours, reconstructing without human bias, well-established CALPHAD formulations while identifying previously missed stable and metastable phases and associated properties. For the EC\u2013DMC\u2013PC systems, the ML method allows to distinguish between stable and metastable phase boundaries, while simultaneously considering the relevant phases. For the high-power density LiFePO4<\/sub>\u00a0chemistry, a room-temperature metastable phase is identified. Its appearance highlights a previously unreported driving force for the transformation kinetics between lithiated and delithiated states that serves as a stepping stone to access a high-temperature eutectoid state that can be applied to engineer solid-state chemistries. For the high-energy density LiCoO2<\/sub>\u00a0chemistry, a highly lithiated electronically insulating phase is thermochemically favorable, particularly at grain corners and boundaries, greatly improving the description of the experimental voltage profile, irrespective of the used baseline free energy model to describe the relevant phases.<\/p>\n","protected":false},"excerpt":{"rendered":"

J Lund, H Wang, RD Braatz, RE Garc\u00eda “Machine learning of phase…<\/p>\n

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Continue reading \"J Lund, H Wang, RD Braatz, RE Garc\u00eda “Machine learning of phase diagrams.” Materials Advances. 3(23): 8485-8497, 2022.\"<\/span>…<\/a><\/div>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"jetpack_seo_schema_type":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[45],"tags":[9,81,22,7],"class_list":["post-982","post","type-post","status-publish","format-standard","hentry","category-papers","tag-batteries","tag-machine-learning","tag-phase-diagrams","tag-thermodynamics","entry"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/peeeSR-fQ","jetpack_likes_enabled":true,"jetpack-related-posts":[{"id":879,"url":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/2021\/01\/21\/k-s-n-vikrant-x-l-phuah-j-lund-han-wang-c-s-hellberg-n-bernstein-w-rheinheimer-c-m-bishop-h-wang-and-r-e-garcia-modeling-of-flash-sintering-of-ionic-ceramics-mrs-bulletin-janua\/","url_meta":{"origin":982,"position":0},"title":"K.S.N. Vikrant, X.L. Phuah, J. Lund, Han Wang, C.S. Hellberg, N. Bernstein, W. Rheinheimer, C.M. Bishop, H. Wang, and R.E. Garc\u00eda “Modeling of flash sintering of ionic ceramics.” MRS Bulletin, 46(1):67-75, 2021.","author":"redwing","date":"01\/21\/2021","format":false,"excerpt":"K.S.N. Vikrant, X.L. Phuah, J. Lund, Han Wang, C.S. Hellberg, N. Bernstein, W. Rheinheimer, C.M. Bishop, H. Wang, and R.E. Garc\u00eda \"Modeling of flash sintering of ionic ceramics.\" MRS Bulletin, 46(1):67-75, 2021.\u00a0doi:10.1557\/s43577-020-00012-0 abstract A fundamental understanding of the influence of defects in ionic ceramics at the atomic, microstructural, and macroscopic\u2026","rel":"","context":"In "Papers"","block_context":{"text":"Papers","link":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/category\/papers\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":315,"url":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/2017\/10\/29\/effect-of-charge-separation-on-the-stability-of-large-wavelength-fluctuations-during-spinodal-decomposition\/","url_meta":{"origin":982,"position":1},"title":"CM Bishop, RE Garc\u00eda, WC Carter “Effect of charge separation on the stability of large wavelength fluctuations during spinodal decomposition” \u00a0Acta materialia, 51(6): 1517-1524, 2003.","author":"redwing","date":"10\/29\/2017","format":false,"excerpt":"CM Bishop, RE Garc\u00eda, WC Carter \"Effect of charge separation on the stability of large wavelength fluctuations during spinodal decomposition\" \u00a0Acta materialia, 51(6): 1517-1524, 2003. Abstract A stability analysis of phase separation of charged species by spinodal decomposition is presented. The charge effects introduce a short wave number cutoff for\u2026","rel":"","context":"In "Papers"","block_context":{"text":"Papers","link":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/category\/papers\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":396,"url":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/2017\/10\/31\/gibbs-phase-equilibria-and-symbolic-computation-of-thermodynamic-properties\/","url_meta":{"origin":982,"position":2},"title":"T Cool, A Bartol, M Kasenga, K Modi, RE Garc\u00eda “Gibbs: Phase equilibria and symbolic computation of thermodynamic properties.”\u00a0Calphad. 34(4):393-404, 2010","author":"redwing","date":"10\/31\/2017","format":false,"excerpt":"T Cool, A Bartol, M Kasenga, K Modi, RE Garc\u00eda \"Gibbs: Phase equilibria and symbolic computation of thermodynamic properties.\"\u00a0Calphad. 34(4):393-404, 2010. Abstract A general purpose open source, Python-based framework, Gibbs, is presented to perform multiphysical equilibrium calculations of material properties. The developed architecture allows to prototype symbolic and numerical representations\u2026","rel":"","context":"In "Papers"","block_context":{"text":"Papers","link":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/category\/papers\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":781,"url":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/2018\/10\/26\/oat-matheus-re-garcia-cm-bishop-phase-field-theory-and-coexistence-of-ferroelectric-phases-near-the-morphotropic-phase-boundary-acta-materialia-in-press-oct-2018\/","url_meta":{"origin":982,"position":3},"title":"OA Torres-Matheus, RE Garc\u00eda, CM Bishop. \u201cPhase Coexistence Near the Morphotropic Phase Boundary.\u201d Acta Materialia. 164:577-585, 2019.","author":"redwing","date":"10\/26\/2018","format":false,"excerpt":"OA Torres-Matheus, RE Garc\u00eda, CM Bishop. \u201cPhase \u00a0Coexistence Near the Morphotropic Phase Boundary.\u201d Acta Materialia. 164:577-585, 2019.\u00a0https:\/\/doi.org\/10.1016\/j.actamat.2018.10.041 Abstract A novel multiphase field theory for ferroelectric systems in the vicinity of a polymorphic phase boundary (PPB) is developed by coupling the Landau-Devonshire thermodynamic potentials of the individual phases. The model naturally\u2026","rel":"","context":"In "Papers"","block_context":{"text":"Papers","link":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/category\/papers\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":901,"url":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/2021\/08\/07\/o-a-torres-matheus-r-e-garcia-and-c-m-bishop-physics-based-optimization-of-landau-parameters-for-ferroelectrics-application-to-bzt-50bct-modelling-and-simulation-in-materials-science-and\/","url_meta":{"origin":982,"position":4},"title":"O. A. Torres-Matheus, R.E. Garc\u00eda, and C. M. Bishop “Physics-based optimization of Landau parameters for ferroelectrics: application to BZT-50BCT.” Modelling and Simulation in Materials Science and Engineering. 29 075001, 2021.","author":"redwing","date":"08\/07\/2021","format":false,"excerpt":"O. A. Torres-Matheus, R.E. Garc\u00eda and C. M. Bishop \"Physics-based optimization of Landau parameters for ferroelectrics: application to BZT-50BCT.\" Modelling and Simulation in Materials Science and Engineering. 29, 075001,. 2021. https:\/\/doi.org\/10.1088\/1361-651X\/ac1a60 Abstract In analogy to thermochemical parameter optimization in the CALculation of PHAse Diagrams (CALPHAD) approach that relies on a\u2026","rel":"","context":"In "Papers"","block_context":{"text":"Papers","link":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/category\/papers\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":318,"url":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/2017\/10\/29\/thermodynamically-consistent-variational-principles-with-applications-to-electrically-and-magnetically-active-systems\/","url_meta":{"origin":982,"position":5},"title":"RE Garc\u00eda, CM Bishop, WC Carter “Thermodynamically consistent variational principles with applications to electrically and magnetically active systems” Acta Materialia, 52(1):11-21, 2004.","author":"redwing","date":"10\/29\/2017","format":false,"excerpt":"RE Garc\u00eda, CM Bishop, WC Carter \"Thermodynamically consistent variational principles with applications to electrically and magnetically active systems\" Acta Materialia, 52(1):11-21, 2004. Abstract We propose a theoretical framework to derive thermodynamically consistent equilibrium equations and kinetic driving forces to describe the time evolution for electrically and magnetically active materials. This\u2026","rel":"","context":"In "Papers"","block_context":{"text":"Papers","link":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/category\/papers\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/wp-json\/wp\/v2\/posts\/982","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/wp-json\/wp\/v2\/comments?post=982"}],"version-history":[{"count":1,"href":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/wp-json\/wp\/v2\/posts\/982\/revisions"}],"predecessor-version":[{"id":983,"href":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/wp-json\/wp\/v2\/posts\/982\/revisions\/983"}],"wp:attachment":[{"href":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/wp-json\/wp\/v2\/media?parent=982"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/wp-json\/wp\/v2\/categories?post=982"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/engineering.purdue.edu\/ComputationalMaterials\/index.php\/wp-json\/wp\/v2\/tags?post=982"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}