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Among them, BaZrS3 has attracted particular attention due to its thermal and chemical stability, favorable optoelectronic properties, and low thermal conductivity. Here, we combine molecular dynamics and Monte Carlo simulations based on a machine-learned interatomic potential with scanning transmission electron microscopy to investigate mixing thermodynamics and phase stability in the BaZrS3xSe3\u20133x system. We identify an unusual ordered structure, with signatures of anion ordering persisting at room temperature, most prominently at 33% S, where S and Se atoms form alternating layers within the crystal. Free-energy calculations yield the temperature\u2013composition phase diagram, including a nonperovskite \u03b4 phase in the Se-rich limit and a perovskite phase in the S-rich limit, separated by a broad two-phase region. Analysis of the dielectric function and the absorption coefficient demonstrates that composition, crystal structure, and anion ordering jointly control the optical band gap. Selenium alloying enables tuning between approximately 1.5 and 1.9 eV, while anion ordering within a given composition reduces the gap by about 0.2 eV. Lastly, variations between structural polymorphs give rise to band gap differences of up to 0.5 eV.<\/jats:p>","DOI":"10.1021\/acs.chemmater.6c01949","type":"journal-article","created":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T15:04:22Z","timestamp":1790089462000},"page":"10251-10258","source":"Crossref","is-referenced-by-count":0,"title":["Anion Ordering\nand Phase Stability Govern Optical\nBand Gaps in BaZrS3\n                    <i>x<\/i>\n                    Se3\u20133\n                    <i>x<\/i>"],"prefix":"10.1021","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5262-3339","authenticated-orcid":true,"given":"Erik","family":"Fransson","sequence":"first","affiliation":[{"name":"Chalmers University of Technology , , ,","place":["Gothenburg, Sweden, SE-41296"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Xu","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology , , , ,","place":["Cambridge, Massachusetts, United States, 02139"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Prakriti","family":"Kayastha","sequence":"additional","affiliation":[{"name":"Northumbria University , , ,","place":["Newcastle upon Tyne, United Kingdom, NE1 8QH"]},{"name":"University College London , , ,","place":["London, United Kingdom, WC1E 6BT"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kevin","family":"Ye","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology , , , ,","place":["Cambridge, Massachusetts, United States, 02139"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ida","family":"Sadeghi","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology , , , ,","place":["Cambridge, Massachusetts, United States, 02139"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3116-6719","authenticated-orcid":true,"given":"Rafael","family":"Jaramillo","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology , , , ,","place":["Cambridge, Massachusetts, United States, 02139"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7726-3533","authenticated-orcid":true,"given":"James M.","family":"LeBeau","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology , , , ,","place":["Cambridge, Massachusetts, United States, 02139"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2992-9871","authenticated-orcid":true,"given":"Lucy","family":"Whalley","sequence":"additional","affiliation":[{"name":"Northumbria University , , ,","place":["Newcastle upon Tyne, United Kingdom, NE1 8QH"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2516-6061","authenticated-orcid":true,"given":"Paul","family":"Erhart","sequence":"additional","affiliation":[{"name":"Chalmers University of Technology , , ,","place":["Gothenburg, Sweden, SE-41296"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,9,22]]},"reference":[{"key":"2026101406315612000_cit1","unstructured":"Best Research-Cell Efficiencies (NREL).\n          . 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Mater."},{"key":"2026101406315612000_cit5","doi-asserted-by":"publisher","DOI":"10.1002\/solr.202201078","article-title":"High-Temperature Equilibrium of 3D\nand 2D Chalcogenide Perovskites","volume":"7","author":"Kayastha","year":"2023","journal-title":"Solar RRL"},{"key":"2026101406315612000_cit6","doi-asserted-by":"publisher","first-page":"3892","DOI":"10.1039\/D1TC00374G","article-title":"Examining\nthe electron transport\nin chalcogenide perovskite BaZrS3","volume":"9","author":"Osei-Agyemang","year":"2021","journal-title":"Journal of Materials Chemistry C"},{"key":"2026101406315612000_cit7","doi-asserted-by":"publisher","first-page":"11465","DOI":"10.1021\/acs.jpclett.3c02940","article-title":"Ultralow lattice thermal\ntransport and considerable wave-like phonon tunneling in chalcogenide\nperovskite BaZrS3","volume":"14","author":"Wu","year":"2023","journal-title":"J. Phys. Chem.\nLett."},{"key":"2026101406315612000_cit8","doi-asserted-by":"publisher","DOI":"10.1002\/adom.202500915","article-title":"BaZrS3 Lights Up: The Interplay of Electrons,\nPhotons, and Phonons in Strongly Luminescent Single Crystals","volume":"13","author":"Nielsen","year":"2025","journal-title":"Adv. Opt. Mater."},{"key":"2026101406315612000_cit9","doi-asserted-by":"publisher","DOI":"10.1002\/solr.201900555","article-title":"Extraordinary strong\nband-edge absorption\nin distorted chalcogenide perovskites","volume":"4","author":"Nishigaki","year":"2020","journal-title":"Solar\nRRL"},{"key":"2026101406315612000_cit10","doi-asserted-by":"publisher","DOI":"10.1103\/PRXEnergy.3.033008","article-title":"Assessing Carrier Mobility,\nDopability,\nand Defect Tolerance in the Chalcogenide Perovskite BaZrS3","volume":"3","author":"Yuan","year":"2024","journal-title":"PRX Energy"},{"key":"2026101406315612000_cit11","doi-asserted-by":"crossref","unstructured":"Mualem, Y.; Cahen, D.; Rakita, Y.; Barad, H. N.\n          Using bond characteristics\nto predict self-healing properties in materials for sustainable energy\nconversion\n          ChemRxiv\n          2025.","DOI":"10.26434\/chemrxiv-2025-8r4l2-v2"},{"key":"2026101406315612000_cit12","doi-asserted-by":"publisher","DOI":"10.1002\/adfm.202105563","article-title":"Making BaZrS3 Chalcogenide\nPerovskite Thin Films by Molecular Beam Epitaxy","volume":"31","author":"Sadeghi","year":"2021","journal-title":"Adv. Funct. 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Funct. Mater."},{"key":"2026101406315612000_cit17","doi-asserted-by":"publisher","first-page":"821","DOI":"10.1021\/acs.chemmater.5b04213","article-title":"Alloying and Defect\nControl within Chalcogenide Perovskites for Optimized\nPhotovoltaic Application","volume":"28","author":"Meng","year":"2016","journal-title":"Chem. Mater."},{"key":"2026101406315612000_cit18","doi-asserted-by":"publisher","first-page":"4955","DOI":"10.1021\/acs.jpclett.2c00880","article-title":"Control of\nPolaronic Behavior and\nCarrier Lifetimes via Metal and Anion Alloying in Chalcogenide Perovskites","volume":"13","author":"Li","year":"2022","journal-title":"J. Phys. Chem. Lett."},{"key":"2026101406315612000_cit19","doi-asserted-by":"publisher","DOI":"10.1002\/adfm.202405135","article-title":"A Processing\nRoute to Chalcogenide Perovskites Alloys with Tunable Band Gap via\nAnion Exchange","volume":"34","author":"Ye","year":"2024","journal-title":"Adv. Funct. Mater."},{"key":"2026101406315612000_cit20","doi-asserted-by":"publisher","DOI":"10.1142\/S0217979225500596","article-title":"Effect of anion (S\u20132 & Se\u20132) replacement on photovoltaic properties in transition\nmetal (Ba-Barium) chalcogenide perovskites","volume":"39","author":"Pandit","year":"2025","journal-title":"Int. J. Modern Phys. B"},{"key":"2026101406315612000_cit21","doi-asserted-by":"publisher","DOI":"10.1142\/S0217984924503457","article-title":"Physical properties\nand power conversion efficiency of SrZrX3 (X = S and Se)\nchalcogenide perovskite solar cell","volume":"38","author":"Pandit","year":"2024","journal-title":"Mod. Phys.\nLett. B"},{"key":"2026101406315612000_cit22","doi-asserted-by":"publisher","first-page":"6894","DOI":"10.1021\/acs.chemmater.2c01289","article-title":"On the\nPhase Stability of Chalcogenide\nPerovskites","volume":"34","author":"Jess","year":"2022","journal-title":"Chem. Mater."},{"key":"2026101406315612000_cit23","doi-asserted-by":"publisher","first-page":"12480","DOI":"10.1021\/acs.inorgchem.3c01696","article-title":"How the temperature\nand composition govern the structure and band gap of Zr-based chalcogenide\nperovskites: Insights from ML accelerated AIMD","volume":"62","author":"Jaykhedkar","year":"2023","journal-title":"Inorg. Chem."},{"key":"2026101406315612000_cit24","doi-asserted-by":"publisher","first-page":"12826","DOI":"10.1021\/acs.inorgchem.4c01308","article-title":"Thermal Stability\nof Chalcogenide Perovskites","volume":"63","author":"Bystricky\u0301","year":"2024","journal-title":"Inorg. Chem."},{"key":"2026101406315612000_cit25","doi-asserted-by":"publisher","first-page":"24157","DOI":"10.1021\/acs.inorgchem.4c03895","article-title":"High-Temperature\nPolymorphism and Band-Gap Evolution in BaZrS3","volume":"63","author":"Jaiswal","year":"2024","journal-title":"Inorg. Chem."},{"key":"2026101406315612000_cit26","doi-asserted-by":"publisher","first-page":"2064","DOI":"10.1021\/acs.jpclett.4c03517","article-title":"Octahedral\nTilt-Driven\nPhase Transitions in BaZrS3 Chalcogenide Perovskite","volume":"16","author":"Kayastha","year":"2025","journal-title":"J. Phys. Chem. Lett."},{"key":"2026101406315612000_cit27","doi-asserted-by":"publisher","first-page":"7639","DOI":"10.1021\/ja972442p","article-title":"Commensurate Columnar Composite Compounds: Synthesis\nand Structure of Ba15Zr14Se42 and\nSr21Ti19Se57","volume":"120","author":"Tranchitella","year":"1998","journal-title":"J. Am. Chem. Soc."},{"key":"2026101406315612000_cit28","doi-asserted-by":"publisher","first-page":"6864","DOI":"10.1039\/D5NA00628G","article-title":"Hexagonal ABX3 nanocrystals: rod-shaped\nBaNbS3 and BaTaS3; BaTiSe3, BaZrSe3, and other selenide derivatives for optoelectronic applications","volume":"7","author":"Agarwal","year":"2025","journal-title":"Nanoscale Adv."},{"key":"2026101406315612000_cit29","doi-asserted-by":"publisher","DOI":"10.1063\/1.5097940","article-title":"BaZrSe3: Ab initio study of anion substitution for bandgap tuning\nin a chalcogenide material","volume":"125","author":"Ong","year":"2019","journal-title":"J. Appl. Phys."},{"key":"2026101406315612000_cit30","doi-asserted-by":"publisher","first-page":"13755","DOI":"10.1039\/D3CP01522J","article-title":"Computational study\nof the fundamental properties of Zr-based chalcogenide perovskites\nfor optoelectronics","volume":"25","author":"Liu","year":"2023","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026101406315612000_cit31","doi-asserted-by":"publisher","DOI":"10.1088\/0965-0393\/18\/1\/015012","article-title":"Visualization\nand analysis of atomistic simulation data with OVITO\u2013the Open\nVisualization Tool","volume":"18","author":"Stukowski","year":"2010","journal-title":"Modell. Simul. Mater. Sci.\nEng."},{"key":"2026101406315612000_cit32","doi-asserted-by":"publisher","DOI":"10.1063\/5.0106617","article-title":"GPUMD: A package for\nconstructing accurate machine-learned potentials and performing highly\nefficient atomistic simulations","volume":"157","author":"Fan","year":"2022","journal-title":"J. Chem. Phys."},{"key":"2026101406315612000_cit33","doi-asserted-by":"publisher","DOI":"10.1002\/mgea.70028","article-title":"GPUMD 4.0: A high-performance molecular dynamics\npackage for versatile materials simulations with machine-learned potentials","volume":"3","author":"Xu","year":"2025","journal-title":"Mater. Genome Eng. 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Theory Simul."},{"key":"2026101406315612000_cit43","doi-asserted-by":"publisher","DOI":"10.1002\/adts.201900015","article-title":"ICET \u2013 A Python\nLibrary for Constructing and Sampling Alloy Cluster Expansions","volume":"2","author":"\u00c5ngqvist","year":"2019","journal-title":"Adv. Theory Simul."},{"key":"2026101406315612000_cit44","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.77.224115","article-title":"Algorithm for generating\nderivative structures","volume":"77","author":"Hart","year":"2008","journal-title":"Phys. Rev. B"},{"key":"2026101406315612000_cit45","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevMaterials.2.045401","article-title":"First-principles\nthermodynamics study of phase stability\nin inorganic halide perovskite solid solutions","volume":"2","author":"Bechtel","year":"2018","journal-title":"Phys. Rev. Mater."},{"key":"2026101406315612000_cit46","doi-asserted-by":"publisher","DOI":"10.1038\/s41524-020-0338-1","article-title":"Anion order in oxysulfide\nperovskites: origins and\nimplications","volume":"6","author":"Pilania","year":"2020","journal-title":"npj Comput. Mater."},{"key":"2026101406315612000_cit47","doi-asserted-by":"publisher","DOI":"10.1063\/5.0263017","article-title":"Spontaneous\nordering in ultra-large anion size-mismatched BaZr(S1\u2013xOx)3","volume":"126","author":"Shang","year":"2025","journal-title":"Appl. Phys. Lett."},{"key":"2026101406315612000_cit48","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1021\/cg401230a","article-title":"Study of\nAnion Order\/Disorder in\nRTaN2O (R = La, Ce, Pr) Perovskite Nitride Oxides","volume":"14","author":"Porter","year":"2014","journal-title":"Cryst. Growth Des."},{"key":"2026101406315612000_cit49","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1038\/nchem.908","article-title":"Anion order in perovskite oxynitrides","volume":"3","author":"Yang","year":"2011","journal-title":"Nat. Chem."},{"key":"2026101406315612000_cit50","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1063\/1.1749657","article-title":"Statistical\nMechanics of Fluid Mixtures","volume":"3","author":"Kirkwood","year":"1935","journal-title":"J. Chem. Phys."},{"key":"2026101406315612000_cit51","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.85.184203","article-title":"Scalable parallel\nMonte Carlo algorithm for atomistic\nsimulations of precipitation in alloys","volume":"85","author":"Sadigh","year":"2012","journal-title":"Phys.\nRev. 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