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Natl. Acad. Sci. U.S.A."],"published-print":{"date-parts":[[2026,9,29]]},"abstract":"<jats:p>How crystals emerge from supercooled liquids remains a central problem in condensed-matter physics and a paradigm of first-order phase transitions under metastable conditions. Supercooled liquids often form crystal nuclei that are not the thermodynamically most stable solid, in a manner that cannot be attributed solely to statistical fluctuations, challenging the intuition that polymorph selection simply follows the free-energy hierarchy of crystalline phases. Using molecular-dynamics simulations of supercooled Cu, Al, and Lennard-Jones liquids, we show that polymorph selection at the onset of crystallization is biased by orientationally ordered precursor states in the liquid. Precursor components with greater spatial coherence and persistence increase the likelihood of nucleating symmetry-compatible crystal structures, or structures accessible through low-barrier cross-symmetry transformations, even when these structures do not correspond to the thermodynamically most stable bulk phase. Because these precursors lack translational order, they can possess orientational symmetries distinct from those of the equilibrium crystal in the liquid state, thereby creating precursor-mediated nucleation pathways that are not fully captured by macroscopic descriptions based only on bulk crystalline free energies and liquid\u2013crystal interfacial tensions. Subsequent growth and structural relaxation are then governed by translational ordering and further reduction of the free energy. Together, these findings show how the sequential coupling between orientational and translational order reorganizes crystallization pathways and identify liquid-state precursor symmetry, spatial coherence, and lifetime as important factors that bias early-stage polymorph nucleation.<\/jats:p>","DOI":"10.1073\/pnas.2601278123","type":"journal-article","created":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T16:25:03Z","timestamp":1790180703000},"update-policy":"https:\/\/doi.org\/10.1073\/pnas.cm10313","source":"Crossref","is-referenced-by-count":0,"title":["Liquid-state orientational precursors bias crystal polymorph nucleation"],"prefix":"10.1073","volume":"123","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6317-5700","authenticated-orcid":false,"given":"Simin","family":"An","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03sxpbt26","id-type":"ROR","asserted-by":"publisher"}],"name":"Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics","place":["Beijing, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7679-6768","authenticated-orcid":false,"given":"Pengfei","family":"Guan","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04tavf782","id-type":"ROR","asserted-by":"publisher"}],"name":"Beijing Computational Science Research Center","place":["Beijing, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0681-8201","authenticated-orcid":false,"given":"Xian","family":"Zhang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/025397a59","id-type":"ROR","asserted-by":"publisher"}],"name":"Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology","place":["Beijing, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bo","family":"Sun","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03sxpbt26","id-type":"ROR","asserted-by":"publisher"}],"name":"Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics","place":["Beijing, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haifeng","family":"Liu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03sxpbt26","id-type":"ROR","asserted-by":"publisher"}],"name":"Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics","place":["Beijing, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haifeng","family":"Song","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/03sxpbt26","id-type":"ROR","asserted-by":"publisher"}],"name":"Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics","place":["Beijing, China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4444-1890","authenticated-orcid":false,"given":"Hajime","family":"Tanaka","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/057zh3y96","id-type":"ROR","asserted-by":"publisher"}],"name":"Research Center for Advanced Science and Technology, The University of Tokyo","place":["Tokyo, Japan"]},{"id":[{"id":"https:\/\/ror.org\/057zh3y96","id-type":"ROR","asserted-by":"publisher"}],"name":"Department of Fundamental Engineering, Institute of Industrial Science, The University of Tokyo","place":["Tokyo, Japan"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"341","published-online":{"date-parts":[[2026,9,23]]},"reference":[{"key":"e_1_3_4_1_2","volume-title":"Metastable Liquids Concepts and Principles","author":"Debenedetti P. 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