| 研究実績の概要 |
In this 3rd year of the project we have made substantial progress and achieved our goals.
First we have demonstrated theoretically that Kirkwood-Buff theory can be applied to solids and that it gives exact results in the case of harmonic crystal and the Debye approximation. We have calculated analytically the pair distribution function (PDF) and from that we have computed the Kirkwood-Buff integrals (KBI) with our finite volume KBI theory. We obtained exact results for the compressibility, which proves that KBI is valid for crystals. [Publication: Peter Krueger, Phys. Rev. E 103, L061301 (2021)]. Next we have applied the theory to a real solid, namely fcc Argon. The PDF was obtained using Monte-Carlo simulations and the KBI was computed for temperatures up to the melting point. We devised new numerical methods (PDF convolution) to accelerate convergence of the KB integrals with system size. We obtained results in good agreement with experiment. This was the first application of KBI theory to solids. [Publication: M. Miyaji, B. Radolo, J.-M. Simon, P. Krueger, J. Chem. Phys. 154, 164506 (2021)].
We have also applied the theory to a solid solution (Ar-Xe) and obtained good results, which we have written in a publication which was submitted in March 2022.
In 2021/9/20-22, P. Krueger has also co-organized an international scientific workshop, entitled "CECAM: Recent progress in the statistical mechanics of solutions through Kirkwood-Buff integrals and related approaches" at Dijon University, France, on with about 40 participants, all expert researchers in KBI theory.
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| 今後の研究の推進方策 |
In the last year of the project we continue applying the novel Kirkwood-Buff integral (KBI) theory to solid solutions. Moreover, we want to solve two theoretical questions/problems. First, in the case of solid Ar, we found that the compressibility calculated from KBI was considerably smaller than the experimental value. We are trying to find the reason for this error and to correct the theory accordingly. Second, in finite volume KBI theory (for liquids or solids) one can compute intensive thermodynamic quantities (such as the compressibility) for open systems of finite size. When using the standard definition of the pair distribution function (PDF), the computed compressibility strongly depends on size, which seems unphysical. We are currently examining this problem and are working on a new definition of the PDF which takes account of the excluded volume of the particles. We hope that in this way, the unphysical size-dependence of intensive variables will disappear. It is planned to write a scientific publication on this subject.
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| 次年度使用額が生じた理由 |
In order to purchase a large computer, we decided to put together the budgets of year 3 (2021) and year 4 (2022). As a consequence, no expenses were done in 2021, but saved for the large expense planned in 2022.
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