| Project/Area Number |
19K05383
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 32010:Fundamental physical chemistry-related
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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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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2022: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2021: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 統計力学 / 粒子個数ゆらぎ / 固体 / 溶液 / 圧縮率方程式 / マーケティング定数 / 積分発散 / ナノ構造 |
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| Outline of Research at the Start |
The aim of this project is to apply the Kirkwood-Buff theory, which is widely used for liquids and solutions, to crystalline solids.
Previously, Kirkwood-Buff theory could not be applied to crystals because of integral divergence problem. We have solved this problem recently [P. Krueger et al, J. Phys. Chem. Lett. 4, 235 (2013), idem, Phys. Rev. E 97, 051301 (2018)]. In the first year we shall use Kirkwood-Buff theory to calculate the Madelung energy of ionic systems (both crystalline and disordered) which is a mathematically challenging problem.
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| Outline of Final Research Achievements |
(1) We have proposed the new, ensemble averaged method for the calculation of the Coulomb energy of ionic crystals. We proved that the surface term of the ensemble averaged Madelung energy is independent of crystal structure. (2) We have succeeded in applying Kirkwood-Buff integral (KBI) theory to solids for the first time. In harmonic crystals, we could calculate the pair distribution function (PDF) analytically and proved that the compressibility equation also holds for crystals. In the case of solid argon and a Ar-Xe solid solution, we computed the PDF by simulation and calculated the compressibility, partial molar volumes etc, from the KBI. (3) We discovered that in finite volumes, the compressibility cannot be calculated exactly from the particle number fluctuations, when the usual definition of the PDF is used. We succeeded in correcting the error by a new definition of the PDF which takes account of the excluded volume of the particles.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究はKirkwood-Buff積分(KBI)理論を固体に拡張することを目標をし、その目標を達成した。通常の計算法を用いると固体のKBIが発散し、計算できない。一方、我々が2013年に開発した有限体積KBI理論を使って、固体のKBI理論が収束し、初めて計算することを成功した。そこから、固体の統計力学で使用できる様々の数値法を開発した。
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