2019 Fiscal Year Research-status 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 |
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| Outline of Annual Research Achievements |
The aim of this project is to generalize Kirkwood-Buff (KB) theory, which is widely used for liquids and solutions, to crystalline solids. In the first year we have achieved the following two major goals.
1) We have used the finite-volume KB formalism to calculate the Madelung energy of ionic crystals. The new method is quite efficient and converges for any structure. We have shown that the leading surface term, which can be interpreted as the orientation averaged surface energy of ionic solids, has a simple, universal (i.e. structure independent) expression. The results of this study have been submitted for publication in Phys. Rev. B [P. Krueger, "Ensemble averaged Madelung energies of finite volumes and surfaces", https://arXiv.org/abs/2003.03721].
2) We have successfully applied, for the first time ever, KB theory to crystals (solid Ar). For the perfect crystal, where the exact result is known, we have shown that the finite volume KB integral converges to the correct result (while the usual, so-called running KB integral, diverges severely). This proves that our new KB theory can indeed be used to study crystalline solids. Second we have studied the temperature dependence of the KB integrals of solid Argon numerically using pair-distribution functions obtained by Monte-Carlo simulations. From this the compressibility of solid Argon has been obtained and the result was found in good agreement with the value obtained by other methods.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
The project makes progress as planned and we have not encounter any trouble so far. The research is carried out in good cooperation with groups in France and The Netherlands. One of my 4th year student has written his Bachelor thesis in the field of this project and in 2019 he has spend a 1-month research internship in the partner group in France to learn Monte-Carlo simulation methods.
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| Strategy for Future Research Activity |
a) Analytical proof that the KBI method gives correct results for ionic crystals with harmonic interaction by comparison with a phonon calculation (manuscript in preparation)
b) Computation of the pair-distribution function of solid Argon by Monte-Carlo simulations. The compressibility as a function of temperature and defect concentration will then be obtained by applying the novel Kirkwood-Buff integral theory. Speeding up convergence as a function of system size is the major challenge.
c) Computation of the Madelung energy in solid solutions as a function of the order parameter, i.e. comparison between random and ordered solid solutions. For the random case this problem has not yet been solved beyond the so-called CPA approximation (to the best of our knowledge).
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