2022 Fiscal Year Final Research Report
Development of Kirkwood-Buff integral theory for crystalline matter
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 |
Section | 一般 |
Review Section |
Basic Section 32010:Fundamental physical chemistry-related
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Research Institution | Chiba University |
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 | 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 |
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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Free Research Field |
物質科学
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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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