{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,3]],"date-time":"2026-11-03T22:47:08Z","timestamp":1793746028185,"version":"4.6.1"},"reference-count":44,"publisher":"IOP Publishing","issue":"29","license":[{"start":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T00:00:00Z","timestamp":1784851200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T00:00:00Z","timestamp":1784851200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["J. Phys.: Condens. Matter"],"published-print":{"date-parts":[[2026,7,24]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Liquid bismuth (Bi) exhibits an anomalous local structure that cannot be described by the hard-sphere model. It features a subpeak near 3\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mstyle scriptlevel=\"0\"\/>\n                          <mml:msup>\n                            <mml:mrow>\n                              <mml:mtext>\u00c5<\/mml:mtext>\n                            <\/mml:mrow>\n                            <mml:mrow>\n                              <mml:mo>\u2212<\/mml:mo>\n                              <mml:mn>1<\/mml:mn>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    in the structure factor and a shoulder over the range of 4 \u00c5\u20135.5 \u00c5 in the pair distribution function. This anomaly is associated with the Peierls distortion in the crystalline A7 structure. This study aims to clarify the structural origin in liquid Bi by comparing the liquid structure with the A7 structure via molecular dynamics (MD) simulations using a machine learning potential. The MD simulation performed at 573 K reproduced the static anomalies and the dynamic structure factor obtained experimentally by quasi-elastic neutron scattering. Analyses of the bond-length and angular limited triplet distribution functions revealed that the anomalous shoulder arises from a distinct angular correlation at approximately 45\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:msup>\n                            <mml:mi\/>\n                            <mml:mrow>\n                              <mml:mo>\u2218<\/mml:mo>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    within the geometrically accessible region. This geometry is defined as the minimal cluster, corresponding to a right-angled isosceles triangle. Simultaneously, equilateral triangular structures associated with dense packing arrangements were observed around 60\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:msup>\n                            <mml:mi\/>\n                            <mml:mrow>\n                              <mml:mo>\u2218<\/mml:mo>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    . A comparison with the A7 structure confirmed that the 60\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:msup>\n                            <mml:mi\/>\n                            <mml:mrow>\n                              <mml:mo>\u2218<\/mml:mo>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    arrangement emerges exclusively in the liquid phase. The coexistence of these distinct geometries was corroborated by polyhedral template matching and angular distribution function analyses. These analyses identified simple cubic-like environments reflecting the 90\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:msup>\n                            <mml:mi\/>\n                            <mml:mrow>\n                              <mml:mo>\u2218<\/mml:mo>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    minimal cluster and hexagonal close-packed-like environments corresponding to the 60\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:msup>\n                            <mml:mi\/>\n                            <mml:mrow>\n                              <mml:mo>\u2218<\/mml:mo>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    dense packing arrangements. These results suggest that the liquid Bi structure is characterized by the coexistence between the minimal cluster reflecting the A7 structure and dense packing arrangements.\n                  <\/jats:p>","DOI":"10.1088\/1361-648x\/ae8733","type":"journal-article","created":{"date-parts":[[2026,7,24]],"date-time":"2026-07-24T06:23:31Z","timestamp":1784874211000},"page":"295402","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Structure analysis of liquid bismuth using molecular dynamics simulation"],"prefix":"10.1088","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-5031-6281","authenticated-orcid":true,"given":"Masato","family":"Shiinoki","sequence":"first","affiliation":[{"name":"Waseda University"},{"name":"Waseda University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9940-6446","authenticated-orcid":false,"given":"Takayuki","family":"Nishiyama","sequence":"additional","affiliation":[{"name":"Japan Atomic Energy Agency"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1382-7184","authenticated-orcid":true,"given":"Tatsuya","family":"Kikuchi","sequence":"additional","affiliation":[{"name":"Japan Atomic Energy Agency"},{"name":"Sumitomo Rubber Industries, Ltd"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-2765-8648","authenticated-orcid":true,"given":"Yukinobu","family":"Kawakita","sequence":"additional","affiliation":[{"name":"Japan Atomic Energy Agency"},{"name":"Comprehensive Research Organization for Science and Society (CROSS)"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0476-2606","authenticated-orcid":false,"given":"Shinsuke","family":"Suzuki","sequence":"additional","affiliation":[{"name":"Waseda University"},{"name":"Waseda University"},{"name":"Waseda University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2026,7,24]]},"reference":[{"key":"cmae8733bib1","author":"Waseda","year":"1980","type":"book"},{"key":"cmae8733bib2","doi-asserted-by":"publisher","first-page":"3447","DOI":"10.1143\/JPSJ.53.3447","type":"journal-article","volume":"53","author":"Takeda","year":"1984","journal-title":"J. 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Published by IOP Publishing Ltd","name":"copyright_information","label":"Copyright Information"},{"value":"2026-04-01","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2026-07-07","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2026-07-24","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}