1990 Fiscal Year Final Research Report Summary
Study on Foundation and Applications of the Cluster Variation Method (CVM) and Path Probability Method (PPM)
| Project/Area Number |
01044006
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| Research Category |
Grant-in-Aid for international Scientific Research
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| Allocation Type | Single-year Grants |
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| Section | Joint Research |
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| Research Institution | Hokkaido University |
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Principal Investigator |
WADA Koh Department of Physics, Faculty of Science, Hokkaido University, 理学部, 助教授 (50000857)
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| Co-Investigator(Kenkyū-buntansha) |
FONTAINE D. De Department of Materials Science and Mineral Engineering, University of Californi, バークレー校・材料科学科(米), 教授
SATO Hiroshi School of Materials Engineering, Purdue University, 材料工学科(米), 名誉教授
KIKUCHI Ryoichi Department of Materials Science and Engineering, UCLA, ロサンゼルス校・材料科学工学科(米), 教授
ISHII Tadao Faculty of Engineering, Okayama University, 工学部, 助教授 (90033240)
MOHRI Tetsuo Department of Metallugical Engineering, Hokkaido University, 工学部, 助教授 (20182157)
KABURAGI Makoto College of Liberal Arts, Kobe University., 教養部, 助教授 (40093504)
ISHIKAWA Takuma Department of Materials Science, Iwaki-Meisei University, 理工学部, 助教授 (80016138)
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| Project Period (FY) |
1989 – 1990
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| Keywords | Cluster Variation Method (CVM) / Path Probability method (PPM) / Crystal Statistical Method / Variational Systematic Approximation / Phase Transition / Transport Phenomena / Phase Diagram |
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| Research Abstract |
The main achievements concerning the project "Study on Foundation and Applications of the Cluster Variation Method (CVM) and Path Probability Method (PPM)" are itemized in the following ;
(1) Interaction energies derived from the first-principle total energy calculation were used together with the CVM to study phase diagrams, ordering instability and the Fourier spectrum of the short range order parameters for noble metal alloys. The correct features of the k-space fluctuation spectrum is obtained in the tetrahedron-octahedron approximation of the CVM compared with the tetrahedron approximation.
(2) The surface structure change of a growing crystal under the MBE (molecular beam epitaxy) condition is studied on the solid-on-solid (SOS) model in the pair approximation of the PPM. The average number of atom-vacancy pairs is found to change periodically, reflecting the layer-by-layer completion.
(3) The CVM is applied to the multi-components system with random interaction. The glass transition is obtained under a certain condition in the three components system.
(4) The relaxation process of spin system was investigated in the tetrahedron approximation of the PPM. In an isothermal development an order phase different from the final equilibrium one appears transiently. The concept of the "pseud-stable state" is proposed.
(5) The ionic conductivity of 1D hopping model is studied. The Monte Carlo simulation method for the frequency dependent conductivity is developed and compared with the results obtained by the PPM.
(6) The critical exponents of second order phase transition in the D (=2, 3, 4) dimensional cubic lattice Ising model was analytically studied on the basis of the coherent anomaly method (CAM) by using the pair, the square-cactus and the square approximation of the CVM and the PPM. These simple approximations give reasonable values of critical exponents and correct transition temperature.
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Research Products
(44 results)
