{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T19:35:12Z","timestamp":1790278512506,"version":"4.1.0"},"reference-count":56,"publisher":"AIP Publishing","issue":"18","funder":[{"DOI":"10.13039\/501100003246","name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","award":["OCENW.GROOT.2019.071"],"award-info":[{"award-number":["OCENW.GROOT.2019.071"]}],"id":[{"id":"10.13039\/501100003246","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,5,14]]},"abstract":"<jats:p>Almost all observed square\u2013triangle quasicrystals in soft-matter systems contain a large number of point-like defects, yet the role these defects play in stabilizing the quasicrystal phase remains poorly understood. In this work, we investigate the thermodynamic role of such defects in the widely observed 12-fold symmetric square\u2013triangle quasicrystal. We develop a new Monte Carlo simulation to compute the configurational entropy of square\u2013triangle tilings augmented to contain two types of irregular hexagons as defect tiles. We find that the introduction of defects leads to a notable entropy gain, with each defect contributing considerably more than a conventional vacancy in a periodic crystal. Intriguingly, the entropy gain is not simply due to individual defect types but is amplified by their combinatorial mixing. We then apply our findings to a microscopic model of core\u2013corona particles interacting via a square-shoulder potential. By combining the configurational entropy with vibrational free-energy calculations, we predict the equilibrium defect concentration and confirm that the quasicrystalline phase contains a higher concentration of point defects than a typical periodic crystal. These results provide a new understanding of the prominence of observed defects in soft-matter quasicrystals.<\/jats:p>","DOI":"10.1063\/5.0328844","type":"journal-article","created":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T11:38:49Z","timestamp":1778585929000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Vacancy defects in square\u2013triangle tilings and their implications for quasicrystals formed by square-shoulder particles"],"prefix":"10.1063","volume":"164","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4743-1081","authenticated-orcid":false,"given":"Alptu\u011f","family":"Ulug\u00f6l","sequence":"first","affiliation":[{"name":"Soft Condensed Matter and Biophysics Group, Debye Institute for Nanomaterials Science, Utrecht University 1 , Princetonplein 1, Utrecht 3584 CC,","place":["Netherlands"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5194-6064","authenticated-orcid":false,"given":"Giovanni","family":"Del Monte","sequence":"additional","affiliation":[{"name":"Soft Condensed Matter and Biophysics Group, Debye Institute for Nanomaterials Science, Utrecht University 1 , Princetonplein 1, Utrecht 3584 CC,","place":["Netherlands"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-0434-8617","authenticated-orcid":false,"given":"Eline K.","family":"Kempkes","sequence":"additional","affiliation":[{"name":"Soft Condensed Matter and Biophysics Group, Debye Institute for Nanomaterials Science, Utrecht University 1 , Princetonplein 1, Utrecht 3584 CC,","place":["Netherlands"]},{"name":"Computational Soft Matter Lab, Computational Chemistry Group and Computational Science Lab, Van \u2019t Hoff Institute for Molecular Sciences and Informatics Institute, University of Amsterdam 2 , Science Park 904, 1098 XH Amsterdam,","place":["The Netherlands"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9401-6067","authenticated-orcid":false,"given":"Frank","family":"Smallenburg","sequence":"additional","affiliation":[{"name":"Laboratoire de Physique des Solides, Universit\u00e9 Paris-Saclay 3 , Orsay 91405,","place":["France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9432-9680","authenticated-orcid":false,"given":"Laura","family":"Filion","sequence":"additional","affiliation":[{"name":"Soft Condensed Matter and Biophysics Group, Debye Institute for Nanomaterials Science, Utrecht University 1 , Princetonplein 1, Utrecht 3584 CC,","place":["Netherlands"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,5,11]]},"reference":[{"key":"2026051207384360900_c1","doi-asserted-by":"publisher","first-page":"1951","DOI":"10.1103\/physrevlett.53.1951","volume":"53","year":"1984","journal-title":"Phys. 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