STUDY ON PHASE TRANSITION OF Si (111) 7x7 STRUCTURE BY MONTE-CARLO SIMULATION

&lt；1&gt；7x7结构的建模根据每个单元的两种状态来描述表面结构，每个单元被定义为7x7单元单元的三角形一半。在格子气体模型中，两个态，一个是堆积断层结构，另一个是‘1x1’结构，用一个数值算符来表示。系统的哈密顿量由数算符的泛函给出。我们推导了7x7结构组元的In相互作用与形成能之间的关系，发现存在一种三体相互作用。考虑到‘1x1’结构是一组无序态，我们引入了简并。&lt；2&gt；数值计算。我们用蒙特卡罗模拟对上述模型进行了数值计算。结果表明：(1)该结构在实验过程中经历了一级相变；(2)较好地再现了淬火表面F级、U级、阶地生长模式的特征；(3)淬火表面成核临界尺寸随温度的变化与实验结果定性一致。每个阶段的结果都发表在福冈理工学院的研究公报上，并在日本物理学会的几次会议上进行了报告。现在，我们将向一些科学期刊提交一篇包含新成果的论文。

<1> Modeling of 7x7 structureThe surface structure is described in terms of two states of each unit which is defined as a triangular half of the 7x7 unit cell. The two states ; one a stacking-faulted structure and the other '1x1' structure, is expressed by a number operator in the lattice gas model. The Hamiltonian of the system is given by a functional of the number operators. We derive relations between the in interactions and formation energies of components of 7x7 structure and find existence of a type of three-body interaction. Considering the '1x1' structure a set of disordered states, we introduce the degeneracy.<2> Numerical calculationWe performed numerical calculations for the above model by Monte-Calro simulation. It results that(1) the structure undergoes the first order transition as the experiments (2) the characteristic features of growing patterns from F-step, U-step, terrace on the quenched surface are well reproduced (3) the temperature dependence of the critical size for nucleation on the quenched surface is qualitatively in agreement with the experimental result.<3> Publication of resultsThe above results have been got by various trials. The result in each stage was published in reported in Research Bulletin of Fukuoka Institute of Technology and reported in several meetings of Physical Society of Japan. Now, we are going to submit a paper which include the new results to some scientific journal.