{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T20:33:36Z","timestamp":1760646816271,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,4,5]],"date-time":"2018-04-05T00:00:00Z","timestamp":1522886400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"the Fundamental Research Funds for the Central Universities"},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51631004","61674069","51275201"],"award-info":[{"award-number":["51631004","61674069","51275201"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Program for Innovative Research Team (in Science and Technology) of the University of Jilin Province"},{"name":"the Program for JLU Science and Technology Innovative Research Team","award":["2017TD-09"],"award-info":[{"award-number":["2017TD-09"]}]},{"name":"the National Key Research and Development Project of China","award":["2016YFB0400100"],"award-info":[{"award-number":["2016YFB0400100"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A formula has been established, which is based on the size-dependence of a metal\u2019s melting point, to elucidate the atomic diffusion coefficient of nanostructured materials by considering the role of grain-boundary energy. When grain size is decreased, a decrease in the atomic diffusion activation energy and an increase in the corresponding diffusion coefficient can be observed. Interestingly, variations in the atomic diffusion activation energy of nanostructured materials are small relative to nanoparticles, depending on the size of the grain boundary energy. Our theoretical prediction is in accord with the computer simulation and experimental results of the metals described.<\/jats:p>","DOI":"10.3390\/e20040252","type":"journal-article","created":{"date-parts":[[2018,4,5]],"date-time":"2018-04-05T16:50:58Z","timestamp":1522947058000},"page":"252","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Modeling of the Atomic Diffusion Coefficient in Nanostructured Materials"],"prefix":"10.3390","volume":"20","author":[{"given":"Zhiqing","family":"Hu","sequence":"first","affiliation":[{"name":"Roll Forging Research Institute, Jilin University, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhuo","family":"Li","sequence":"additional","affiliation":[{"name":"School of Materials Science and Engineering, Jilin University, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kai","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Materials Science and Engineering, Jilin University, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zi","family":"Wen","sequence":"additional","affiliation":[{"name":"School of Materials Science and Engineering, Jilin University, Changchun 130022, China"},{"name":"Key Laboratory of Automobile Materials, Ministry of Education, Jilin University, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongfu","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Materials Science and Engineering, Jilin University, Changchun 130022, China"},{"name":"Key Laboratory of Automobile Materials, Ministry of Education, Jilin University, Changchun 130022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,4,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S1359-6454(99)00285-2","article-title":"Nanostructured materials: Basic concepts and microstructure","volume":"48","author":"Gleiter","year":"2000","journal-title":"Acta Mater."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/j.pmatsci.2008.08.001","article-title":"Thermo-mechanical behavior of low-dimensional systems: The local bond average approach","volume":"54","author":"Sun","year":"2009","journal-title":"Prog. 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