| 研究実績の概要 |
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 second year we have achieved the following two major results.
1) We have successfully applied, for the first time, KB theory to crystals, namely solid argon. While the usual, so-called running KB integral, diverges severely, we have shown that the finite volume KB integral always converges. We have thus shown how KB theory can be used to study crystalline solids. At zero temperature, we recover the exact result. We have studied solid Argon at finite temperature numerically, using Monte-Carlo and Molecular Dynamics simulations. We have developed an integral conserving convolution of the pair-distribution function in order to speed up the (slow) convergence of the KB integrals with systems size. Thereby we obtain converged integrals with usual simulation box sizes of a few thousand particles. This has been published in: M. Miyaji, B. Radola, J.-M. Simon and P. Krueger, J. Chem. Phys. 154, 164506 (2021).
2) We have shown that the compressibility equation, a fundamental equation of the statistical mechanics of fluids, is also valid in solids, if and only if the finite volume KB theory is used. This was proved rigorously for a solid with harmonic interactions, through an analytical phonon calculation. We have also derived an analytic expression of the peak shape function of the pair distribution function. These results put the new theory on a solid theoretical basis. A paper is submitted (preprint at arXiv:2101.03515)
|
| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
The project makes progress essentially as planned. Some numerical issues took us a bit more time than we expected, and some of these problems are still to be solved, but this is quite normal. We have not encountered any major trouble so far. The international cooperation with groups in France and The Netherlands is good, despite the Corona-Virus.
|
| 今後の研究の推進方策 |
a) We have managed to calculate the compressibility of solids for the first time using Kirkwood-Buff theory. When the pair-distribution function (PDF) is obtained by numerical simulation, we obtained very good temperature dependence, but the absolute values are systematically underestimated by 40-50%. Now we need to find corrections to the numerical PDF which reduce this error as much as possible.
b) We next focus on mixtures, i.e. solid solutions and alloys. This will be done both using simple models that can be solved analytically (or with little numerical effort) as well as with Monte-Carlo and Molecular dynamics simulations. The first system to be studied is the Ar-Xe mixture, which is used for radiation detection, both in medical and astrophysical applications. The precise phase diagram and the solid-liquid equilibrium is under debate. We will study it with our new theory.
c) The theory will be extended to two-dimensional systems. This is important for better understanding the finite-size effects in numerical simulation and for applying the theory to self-assembled adsorbed monolayers, which often present rich phase-diagrams with a liquid and several crystal phases.
|
