{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,20]],"date-time":"2026-10-20T12:47:43Z","timestamp":1792500463778,"version":"4.5.0"},"reference-count":32,"publisher":"AIP Publishing","issue":"15","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,10,21]]},"abstract":"<jats:p>Curvature and topology jointly organize defects in two-dimensional crystals, but their combined role remains unresolved when competing lattice symmetries coexist with spatially varying curvature. We use simulated-annealing Langevin dynamics to study Hertzian particles forming coexisting hexagonal (Hex) and square (Sq) lattices on prolate and oblate ellipsoids. Mapping reduced density and aspect ratio reveals a broad sequence of scar- and domain-based morphologies in both Hex-dominant and Sq-dominant backgrounds. Latitude-resolved comparisons show that Gaussian curvature biases defects toward its maxima under weak deformation. Strong prolateness, however, confines high curvature to small polar caps that cannot independently accommodate all defect motifs. Defects then spread toward lower-curvature latitudes to relieve defect crowding and elastic repulsion. In the Hex-dominant regime, this competition drives vertex-contacted domains with neutralized corner contacts, and compensating positive defects locate away from the poles. The Sq-dominant regime features Hex-rich triangular domains, bridged states, and linear or open scars similarly reorganized by curvature anisotropy. On oblate ellipsoids, the extended equatorial high-curvature belt allows defects to separate azimuthally while remaining curvature-localized. This work elucidates that nonuniform curvature can engineer rich defect patterns by selecting the spatial distribution of topological charge and the connectivity of finite defect motifs.<\/jats:p>","DOI":"10.1063\/5.0357442","type":"journal-article","created":{"date-parts":[[2026,10,20]],"date-time":"2026-10-20T12:02:07Z","timestamp":1792497727000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Defect organization in coexisting hexagonal and square lattices on ellipsoids"],"prefix":"10.1063","volume":"165","author":[{"given":"Wenyu","family":"Liu","sequence":"first","affiliation":[{"name":"School of Physics and Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering 1 , Tianjin 300071,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Han","family":"Xie","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, University of Waterloo 2 , Waterloo, Ontario N2L 3G1,","place":["Canada"]},{"name":"Department of Physics, The Hong Kong University of Science and Technology 3 , Clear Water Bay, Kowloon, Hong Kong,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8403-1220","authenticated-orcid":false,"given":"Baohui","family":"Li","sequence":"additional","affiliation":[{"name":"School of Physics and Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering 1 , Tianjin 300071,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7994-6231","authenticated-orcid":false,"given":"Jeff Z. Y.","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, University of Waterloo 2 , Waterloo, Ontario N2L 3G1,","place":["Canada"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7926-7597","authenticated-orcid":false,"given":"Yao","family":"Li","sequence":"additional","affiliation":[{"name":"School of Physics and Key Laboratory of Functional Polymer Materials of Ministry of Education, Nankai University, and Collaborative Innovation Center of Chemical Science and Engineering 1 , Tianjin 300071,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,10,20]]},"reference":[{"key":"2026102008020370600_c1","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1080\/00018730903043166","article-title":"Two-dimensional matter: Order, curvature and defects","volume":"58","year":"2009","journal-title":"Adv. Phys."},{"key":"2026102008020370600_c2","doi-asserted-by":"publisher","first-page":"110901","DOI":"10.1063\/1.4962629","article-title":"Perspective: Geometrically frustrated assemblies","volume":"145","year":"2016","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026102008020370600_c3","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1038\/s42254-022-00469-9","article-title":"Topological defects in biological matter","volume":"4","year":"2022","journal-title":"Nat. Rev. Phys."},{"key":"2026102008020370600_c4","doi-asserted-by":"publisher","first-page":"8738","DOI":"10.1103\/physrevb.62.8738","article-title":"Interacting topological defects on frozen topographies","volume":"62","year":"2000","journal-title":"Phys. Rev. B"},{"key":"2026102008020370600_c5","doi-asserted-by":"publisher","first-page":"12323","DOI":"10.1073\/pnas.0602755103","article-title":"Crystallography on curved surfaces","volume":"103","year":"2006","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"2026102008020370600_c6","doi-asserted-by":"publisher","first-page":"1301","DOI":"10.1103\/revmodphys.82.1301","article-title":"Vortices on curved surfaces","volume":"82","year":"2010","journal-title":"Rev. Mod. Phys."},{"key":"2026102008020370600_c7","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1038\/nmat2982","article-title":"Memory and topological frustration in nematic liquid crystals confined in porous materials","volume":"10","year":"2011","journal-title":"Nat. Mater."},{"key":"2026102008020370600_c8","doi-asserted-by":"publisher","first-page":"8107","DOI":"10.1039\/c3sm50468a","article-title":"Defect science and engineering of liquid crystals under geometrical frustration","volume":"9","year":"2013","journal-title":"Soft Matter"},{"key":"2026102008020370600_c9","doi-asserted-by":"publisher","first-page":"185502","DOI":"10.1103\/physrevlett.89.185502","article-title":"Crystalline order on a sphere and the generalized Thomson problem","volume":"89","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"2026102008020370600_c10","doi-asserted-by":"publisher","first-page":"1716","DOI":"10.1126\/science.1081160","article-title":"Grain boundary scars and spherical crystallography","volume":"299","year":"2003","journal-title":"Science"},{"key":"2026102008020370600_c11","doi-asserted-by":"publisher","first-page":"947","DOI":"10.1038\/nature09620","article-title":"Pleats in crystals on curved surfaces","volume":"468","year":"2010","journal-title":"Nature"},{"key":"2026102008020370600_c12","doi-asserted-by":"publisher","first-page":"948","DOI":"10.1038\/nmat3429","article-title":"Fractionalization of interstitials in curved colloidal crystals","volume":"11","year":"2012","journal-title":"Nat. Mater."},{"key":"2026102008020370600_c13","doi-asserted-by":"publisher","first-page":"11461","DOI":"10.1039\/c3sm52394b","article-title":"Topological defects of tetratic liquid-crystal order on a soft spherical surface","volume":"9","year":"2013","journal-title":"Soft Matter"},{"key":"2026102008020370600_c14","doi-asserted-by":"publisher","first-page":"117801","DOI":"10.1103\/physrevlett.114.117801","article-title":"Forming a cube from a sphere with tetratic order","volume":"114","year":"2015","journal-title":"Phys. Rev. Lett."},{"key":"2026102008020370600_c15","doi-asserted-by":"publisher","first-page":"2558","DOI":"10.1039\/d5sm01271f","article-title":"Using particle shape to control defects in colloidal crystals on spherical interfaces","volume":"22","year":"2026","journal-title":"Soft Matter"},{"key":"2026102008020370600_c16","doi-asserted-by":"publisher","first-page":"1193","DOI":"10.1021\/acs.nanolett.4c05865","article-title":"Competing hexagonal and square lattices on a spherical surface","volume":"25","year":"2025","journal-title":"Nano Lett."},{"key":"2026102008020370600_c17","doi-asserted-by":"publisher","first-page":"134501","DOI":"10.1063\/1.4822101","article-title":"Tetratic phase of Hertzian spheres: Monte Carlo simulation","volume":"139","year":"2013","journal-title":"J.\u00a0Chem. Phys."},{"key":"2026102008020370600_c18","doi-asserted-by":"publisher","first-page":"3258","DOI":"10.1080\/00268976.2018.1464676","article-title":"The phase diagram and melting scenarios of two-dimensional Hertzian spheres","volume":"116","year":"2018","journal-title":"Mol. Phys."},{"key":"2026102008020370600_c19","doi-asserted-by":"publisher","first-page":"045408","DOI":"10.1103\/physreve.111.045408","article-title":"Filling spherical surfaces by mixed triangle and square tiles","volume":"111","year":"2025","journal-title":"Phys. Rev. E"},{"key":"2026102008020370600_c20","doi-asserted-by":"publisher","first-page":"7631","DOI":"10.1039\/d5sm00697j","article-title":"Transitional patterns on a spherical surface: From scars to domain defects of mixed lattices","volume":"21","year":"2025","journal-title":"Soft Matter"},{"key":"2026102008020370600_c21","doi-asserted-by":"publisher","first-page":"054106","DOI":"10.1103\/physrevb.76.054106","article-title":"Crystalline order on Riemannian manifolds with variable Gaussian curvature and boundary","volume":"76","year":"2007","journal-title":"Phys. Rev. B"},{"key":"2026102008020370600_c22","doi-asserted-by":"publisher","first-page":"104301","DOI":"10.1103\/physrevlett.116.104301","article-title":"Curvature-controlled defect localization in elastic surface crystals","volume":"116","year":"2016","journal-title":"Phys. Rev. Lett."},{"key":"2026102008020370600_c23","doi-asserted-by":"publisher","first-page":"5872","DOI":"10.1039\/c5sm01118c","article-title":"The role of curvature anisotropy in the ordering of spheres on an ellipsoid","volume":"11","year":"2015","journal-title":"Soft Matter"},{"key":"2026102008020370600_c24","doi-asserted-by":"publisher","first-page":"9220","DOI":"10.1073\/pnas.1222196110","article-title":"Capillarity-induced ordering of spherical colloids on an interface with anisotropic curvature","volume":"110","year":"2013","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"2026102008020370600_c25","doi-asserted-by":"publisher","first-page":"078003","DOI":"10.1103\/physrevlett.125.078003","article-title":"Simple, general criterion for onset of disclination disorder on curved surfaces","volume":"125","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"2026102008020370600_c26","doi-asserted-by":"publisher","first-page":"048201","DOI":"10.1103\/physrevlett.132.048201","article-title":"Programmable potentials choreograph defects in a colloidal crystal shell","volume":"132","year":"2024","journal-title":"Phys. Rev. Lett."},{"key":"2026102008020370600_c27","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1126\/science.220.4598.671","article-title":"Optimization by simulated annealing","volume":"220","year":"1983","journal-title":"Science"},{"key":"2026102008020370600_c28","doi-asserted-by":"publisher","first-page":"108171","DOI":"10.1016\/j.cpc.2021.108171","article-title":"LAMMPS\u2014A flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales","volume":"271","year":"2022","journal-title":"Comput. Phys. Commun."},{"key":"2026102008020370600_c29","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1016\/0021-9991(83)90014-1","article-title":"Rattle: A \u2018velocity\u2019 version of the shake algorithm for molecular dynamics calculations","volume":"52","year":"1983","journal-title":"J.\u00a0Comput. Phys."},{"key":"2026102008020370600_c30","doi-asserted-by":"publisher","first-page":"1226","DOI":"10.1016\/j.bpj.2016.02.017","article-title":"A method for molecular dynamics on curved surfaces","volume":"110","year":"2016","journal-title":"Biophys. J."},{"key":"2026102008020370600_c31","volume-title":"Differential Geometry of Curves and Surfaces","year":"1976"},{"key":"2026102008020370600_c32","doi-asserted-by":"publisher","first-page":"015012","DOI":"10.1088\/0965-0393\/18\/1\/015012","article-title":"Visualization and analysis of atomistic simulation data with ovito\u2014The open visualization tool","volume":"18","year":"2009","journal-title":"Modell. Simul. Mater. Sci. Eng."}],"container-title":["The Journal of Chemical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0357442\/21175244\/154905_1_5.0357442.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0357442\/21175244\/154905_1_5.0357442.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,20]],"date-time":"2026-10-20T12:02:08Z","timestamp":1792497728000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/165\/15\/154905\/3406838\/Defect-organization-in-coexisting-hexagonal-and"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,20]]},"references-count":32,"journal-issue":{"issue":"15","published-print":{"date-parts":[[2026,10,21]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0357442","relation":{},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,10,21]]},"published":{"date-parts":[[2026,10,20]]},"article-number":"154905"}}