{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T23:53:48Z","timestamp":1782345228525,"version":"3.54.5"},"reference-count":23,"publisher":"AIP Publishing","issue":"20","funder":[{"DOI":"10.13039\/100000183","name":"Army Research Office","doi-asserted-by":"publisher","award":["W911NF-22-2-0103"],"award-info":[{"award-number":["W911NF-22-2-0103"]}],"id":[{"id":"10.13039\/100000183","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CBET-2133179"],"award-info":[{"award-number":["CBET-2133179"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2025,11,28]]},"abstract":"<jats:p>Layered \u201cmosaic\u201d metal-halide perovskite materials display a wide-variety of microstructures that span the order\u2013disorder spectrum and can be tuned via the composition of their constituent B-site octahedral species. Such materials are typically modeled using computationally expensive ab\u00a0initio methods, but these approaches are greatly limited to small sample sizes. Here, we develop a highly efficient hard-particle packing algorithm to model large samples of these layered complex alloys that enables an accurate determination of the geometrical and topological properties of the B-site arrangements within the plane of the inorganic layers across length scales. Our results are in good agreement with various experiments and, therefore, our algorithm bypasses the need for full-blown ab\u00a0initio calculations. The accurate predictive power of our algorithm demonstrates how our minimalist hard-particle model effectively captures complex interactions and dynamics like incoherent thermal motion, out-of-plane octahedral tilting, and bond compression\/stretching. We specifically show that the composition-dependent miscibility predicted by our algorithm for certain silver\u2013iron and copper\u2013indium layered alloys is consistent with previous experimental observations. We further quantify the degree of mixing in the simulated structures across length scales using our recently developed sensitive \u201cmixing\u201d metric. The large structural snapshots provided by our algorithm also shed light on previous experimentally measured magnetic properties of a copper\u2013indium system. The generalization of our algorithm to model 3D perovskite alloys is also discussed. In summary, our packing model and mixing metric enable one to accurately explore the enormous space of hypothetical layered mosaic alloy compositions and identify materials with potentially desirable optoelectronic and magnetic properties.<\/jats:p>","DOI":"10.1063\/5.0303040","type":"journal-article","created":{"date-parts":[[2025,11,24]],"date-time":"2025-11-24T13:23:50Z","timestamp":1763990630000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":3,"title":["Communication: Modeling layered mosaic perovskite alloy microstructures across length scales via a packing algorithm"],"prefix":"10.1063","volume":"163","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3743-4294","authenticated-orcid":false,"given":"Murray","family":"Skolnick","sequence":"first","affiliation":[{"name":"Department of Chemistry, Princeton University 1 , Princeton, New Jersey 08544,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4614-335X","authenticated-orcid":false,"given":"Salvatore","family":"Torquato","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Department of Physics, Princeton Institute for the Science and Technology of Materials, and Program in Applied and Computational Mathematics, Princeton University 2 , Princeton, New Jersey 08544,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2025,11,24]]},"reference":[{"key":"2025112408234692700_c1","doi-asserted-by":"publisher","first-page":"216719","DOI":"10.1016\/j.ccr.2025.216719","volume":"539","year":"2025","journal-title":"Coord. Chem. Rev."},{"key":"2025112408234692700_c2","doi-asserted-by":"publisher","first-page":"8689","DOI":"10.1039\/d1sc01159f","volume":"12","year":"2021","journal-title":"Chem. Sci."},{"key":"2025112408234692700_c3","doi-asserted-by":"publisher","first-page":"e202300957","DOI":"10.1002\/anie.202300957","volume":"62","year":"2023","journal-title":"Angew. Chem., Int. Ed."},{"key":"2025112408234692700_c4","article-title":"Mosaic layered halide-perovskite spin glasses: Mechanochemical alloying of a ferromagnet and a paramagnet"},{"key":"2025112408234692700_c5","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/0022-3697(59)90061-7","volume":"10","year":"1959","journal-title":"J.\u00a0Phys. Chem. Solids"},{"key":"2025112408234692700_c6","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1016\/j.ccr.2014.10.005","volume":"289\u2013290","year":"2015","journal-title":"Coord. Chem. Rev."},{"key":"2025112408234692700_c7","doi-asserted-by":"publisher","first-page":"236","DOI":"10.1021\/ar50139a003","volume":"12","year":"1979","journal-title":"Acc. Chem. Res."},{"key":"2025112408234692700_c8","volume-title":"Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods","year":"2009"},{"key":"2025112408234692700_c9","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1039\/c8ee02820f","volume":"12","year":"2019","journal-title":"Energy Environ. Sci."},{"key":"2025112408234692700_c10","doi-asserted-by":"publisher","first-page":"7708","DOI":"10.1039\/d0sc01580f","volume":"11","year":"2020","journal-title":"Chem. Sci."},{"key":"2025112408234692700_c11","doi-asserted-by":"publisher","first-page":"19099","DOI":"10.1021\/jacs.9b09945","volume":"141","year":"2019","journal-title":"J.\u00a0Am. Chem. Soc."},{"key":"2025112408234692700_c12","doi-asserted-by":"publisher","first-page":"19662","DOI":"10.1039\/c9ta04325j","volume":"7","year":"2019","journal-title":"J.\u00a0Mater. Chem. A"},{"key":"2025112408234692700_c13","doi-asserted-by":"publisher","first-page":"041104","DOI":"10.1103\/physreve.80.041104","volume":"80","year":"2009","journal-title":"Phys. Rev. E"},{"key":"2025112408234692700_c14","doi-asserted-by":"publisher","first-page":"876","DOI":"10.1038\/nature08239","volume":"460","year":"2009","journal-title":"Nature"},{"key":"2025112408234692700_c15","doi-asserted-by":"publisher","first-page":"031302","DOI":"10.1103\/physreve.86.031302","volume":"86","year":"2012","journal-title":"Phys. Rev. E"},{"key":"2025112408234692700_c16","doi-asserted-by":"publisher","first-page":"2450","DOI":"10.1021\/acs.jpcb.1c00497","volume":"125","year":"2021","journal-title":"J.\u00a0Phys. Chem. B"},{"key":"2025112408234692700_c17","doi-asserted-by":"publisher","first-page":"119774","DOI":"10.1016\/j.actamat.2024.119774","volume":"268","year":"2024","journal-title":"Acta Mater."},{"key":"2025112408234692700_c18","year":"2023"},{"key":"2025112408234692700_c21","doi-asserted-by":"publisher","first-page":"274003","DOI":"10.1088\/1751-8121\/ac72d7","volume":"55","year":"2022","journal-title":"J.\u00a0Phys. A: Math. Theor."},{"key":"2025112408234692700_c22","doi-asserted-by":"publisher","first-page":"033262","DOI":"10.1103\/physrevresearch.6.033262","volume":"6","year":"2024","journal-title":"Phys. Rev. Res."},{"key":"2025112408234692700_c26","volume-title":"Introduction to Percolation Theory","year":"1992"},{"key":"2025112408234692700_c27","doi-asserted-by":"publisher","first-page":"020901","DOI":"10.1063\/1.5036657","volume":"149","year":"2018","journal-title":"J.\u00a0Chem. Phys."},{"key":"2025112408234692700_c28","doi-asserted-by":"publisher","first-page":"1780","DOI":"10.1038\/s41557-023-01305-y","volume":"15","year":"2023","journal-title":"Nat. Chem."}],"container-title":["The Journal of Chemical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0303040\/20812403\/201101_1_5.0303040.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0303040\/20812403\/201101_1_5.0303040.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,24]],"date-time":"2025-11-24T13:23:51Z","timestamp":1763990631000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/163\/20\/201101\/3373188\/Communication-Modeling-layered-mosaic-perovskite"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,24]]},"references-count":23,"journal-issue":{"issue":"20","published-print":{"date-parts":[[2025,11,28]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0303040","relation":{},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2025,11,28]]},"published":{"date-parts":[[2025,11,24]]},"article-number":"201101"}}