{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T07:39:53Z","timestamp":1768549193961,"version":"3.49.0"},"reference-count":42,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2018,9,7]],"date-time":"2018-09-07T00:00:00Z","timestamp":1536278400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2016YFB0301101"],"award-info":[{"award-number":["2016YFB0301101"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Hebei Provincial Science and Technology Program of China-Outstanding Young Talents Plan","award":["BJ2018026"],"award-info":[{"award-number":["BJ2018026"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>As temperature increases, the thermal vacancy concentration in pure metals dramatically increases and causes some strongly non-linear thermodynamic behaviors in pure metals when close to their melting points. In this paper, we chose body-centered cubic (bcc) W as the target and presented a thermodynamic model to account for its Gibbs energy of pure bcc W from 0 K to melting point by including the contribution of thermal vacancy. A new formula for interaction part was proposed for describing the quadratic temperature behavior of vacancy formation energy. Based on the experimental\/first-principles computed thermodynamic properties, all the parameters in the Gibbs energy function were assessed by following the proposed two-step optimization strategy. The thermodynamic behaviors, i.e., the strong nonlinear increase for temperature dependence of heat capacities at high temperatures and a nonlinear Arrhenius plot of vacancy concentration, in bcc W can be well reproduced by the obtained Gibbs energy. The successful description of thermal vacancy on such strongly non-linear thermodynamic behaviors in bcc W indicates that the presently proposed thermodynamic model and optimization strategy should be universal ones and are applicable to all other metals.<\/jats:p>","DOI":"10.3390\/ma11091648","type":"journal-article","created":{"date-parts":[[2018,9,7]],"date-time":"2018-09-07T11:47:41Z","timestamp":1536320861000},"page":"1648","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Effect of Thermal Vacancy on Thermodynamic Behaviors in BCC W Close to Melting Point: A Thermodynamic Study"],"prefix":"10.3390","volume":"11","author":[{"given":"Ying","family":"Tang","sequence":"first","affiliation":[{"name":"School of Materials Science and Engineering, Hebei University of Technology, Tianjin 300130, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5969-2406","authenticated-orcid":false,"given":"Lijun","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Powder Metallurgy, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,9,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.pmatsci.2009.08.001","article-title":"Vacancy mediated substitutional diffusion in binary crystalline solids","volume":"55","author":"Ven","year":"2010","journal-title":"Prog. 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