2022 Fiscal Year Annual Research Report
Development of Kirkwood-Buff integral theory for crystalline matter
| Project/Area Number |
19K05383
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| Research Institution | Chiba University |
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Principal Investigator |
KRUEGER PETER 千葉大学, 大学院工学研究院, 教授 (30706362)
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| Project Period (FY) |
2019-04-01 – 2023-03-31
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| Keywords | ナノ構造 / 統計力学 |
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| Outline of Annual Research Achievements |
In this project our goal was to generalize Kirkwood-Buff integral (KBI) theory to solids. By the end of the four year project, we have achieved most of our goals.
1) We have used the finite-volume KBI theory (that we have developed in 2013) to compute the Madelung constants of ionic crystals. We have shown that this "ensemble averaged" method does not suffer from the usual convergence problem and has a universal size dependence from which the surface energy of ionic crystals can be estimated.
2) We have succeeded in applying KBI theory to solids for the first time. We have solved the divergence problem and have computed thermodynamic quantities such as the compressibility and partial molar volumes from the KBI for the following systems (a) a harmonic crystal by an analytical calculation of the pair distribution functions (PDF) (b) solid argon where the PDF was obtained from Monte-Carlo simulations (c) the first solid solution namely a Ar-Xe mixture.
3) In the 4th year we found that for systems of finite volume, the compressibility equation does not hold when the usual definition of PDF is used i.e. the particle number fluctuations do not give the correct compressibility. We have shown that this problem can be solved by a redefinition of the PDF where the excluded volume is explicitly taken into account. This result has been presented at a conference and will soon be published.
During the project, we published six peer-reviewed papers and held an international workshop on KBI theory in Dijon, France in September 2021.
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