{"title":"Theoretical study of kinetic isotope effects for vacancy diffusion of impurity in solids","authors":"Yuxi Jing, Xuefang Li, Yun Liu","doi":"10.1007/s11631-024-00706-1","DOIUrl":null,"url":null,"abstract":"<div><p>Theoretical studies of the diffusional isotope effect in solids are still stuck in the 1960s and 1970s. With the development of high spatial resolution mass spectrometers, isotopic data of mineral grains are rapidly accumulated. To dig up information from these data, molecular-level theoretical models are urgently needed. Based on the microscopic definition of the diffusion coefficient (<i>D</i>), a new theoretical framework for calculating the diffusional isotope effect (DIE<sub>(v)</sub>) (in terms of <i>D</i><sup><i>*</i></sup><i>/D</i>) for vacancy-mediated impurity diffusion in solids is provided based on statistical mechanics formalism. The newly derived equation shows that the DIE<sub>(v)</sub> can be easily calculated as long as the vibration frequencies of isotope-substituted solids are obtained. The calculated DIE<sub>(v)</sub> values of <sup>199</sup>Au/<sup>195</sup>Au and <sup>60</sup>Co/<sup>57</sup>Co during diffusion in Cu and Au metals are all within 1% of errors compared to the experimental data, which shows that this theoretical model is reasonable and precise.</p></div>","PeriodicalId":7151,"journal":{"name":"Acta Geochimica","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Geochimica","FirstCategoryId":"89","ListUrlMain":"https://link.springer.com/article/10.1007/s11631-024-00706-1","RegionNum":4,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"GEOCHEMISTRY & GEOPHYSICS","Score":null,"Total":0}
引用次数: 0
Abstract
Theoretical studies of the diffusional isotope effect in solids are still stuck in the 1960s and 1970s. With the development of high spatial resolution mass spectrometers, isotopic data of mineral grains are rapidly accumulated. To dig up information from these data, molecular-level theoretical models are urgently needed. Based on the microscopic definition of the diffusion coefficient (D), a new theoretical framework for calculating the diffusional isotope effect (DIE(v)) (in terms of D*/D) for vacancy-mediated impurity diffusion in solids is provided based on statistical mechanics formalism. The newly derived equation shows that the DIE(v) can be easily calculated as long as the vibration frequencies of isotope-substituted solids are obtained. The calculated DIE(v) values of 199Au/195Au and 60Co/57Co during diffusion in Cu and Au metals are all within 1% of errors compared to the experimental data, which shows that this theoretical model is reasonable and precise.
期刊介绍:
Acta Geochimica serves as the international forum for essential research on geochemistry, the science that uses the tools and principles of chemistry to explain the mechanisms behind major geological systems such as the Earth‘s crust, its oceans and the entire Solar System, as well as a number of processes including mantle convection, the formation of planets and the origins of granite and basalt. The journal focuses on, but is not limited to the following aspects:
• Cosmochemistry
• Mantle Geochemistry
• Ore-deposit Geochemistry
• Organic Geochemistry
• Environmental Geochemistry
• Computational Geochemistry
• Isotope Geochemistry
• NanoGeochemistry
All research articles published in this journal have undergone rigorous peer review. In addition to original research articles, Acta Geochimica publishes reviews and short communications, aiming to rapidly disseminate the research results of timely interest, and comprehensive reviews of emerging topics in all the areas of geochemistry.