2次元における正常粒成長のモンテカルロシミュレーション Monte Carlo simulation of normal grain growth in two dimensions
Monte Calro simulations on the basis of the Potts model have been carried out to study normal grain growth in two dimensions. A microstructure of a polycrystalline aggregate can be represented by means of mapping onto a discrete lattice of which site is assigned an orientation number from 1 to <i>Q</i>. The following three lattice models were used in this simulation: triangular lattice (with first nearest neighbor site interactions), square lattice I (with first nearest neighbor site interactions) and square lattice II (with first and second nearest neighbor site interactions). The simulations were performed under constant temperature conditions (0≤<i>T</i><<i>T<sub>c</sub></i>) quenched from an initial high temperature (<i>T</i>»<i>T<sub>c</sub></i>) state. Obtained microstructures are evolved keeping asimilar form of a grain boundary network. The microstructures produced especially on the triangular lattice model are in good correspondence with those in cross-sections of annealed metals and ceramics and with those of nearly monomineralic metamorphic rocks. These simulations show that the representing grain area linearly increases with time after an initial transient, which is independent of lattice model, temperature and total number of allowed grain orientation (<i>Q</i>). This means that the grain growth exponent value <i>m</i> is universally 2 and agrees with the various theories of normal grain growth. The grain size distribution function scaled by a representative size approaches a limiting form for Q≥256 region, in which grains of like orientation rarely impinge. Both the grain size distribution function and the grain growth rate are found to be inconsistent among the three lattice models for lower temperature simulations but the differences are reduced with increasing temperature.
- 岩鉱 : 岩石鉱物鉱床学会誌 : journal of mineralogy, petrology and economic geology
岩鉱 : 岩石鉱物鉱床学会誌 : journal of mineralogy, petrology and economic geology 91(9), 339-351, 1996-09-05
Japan Association of Mineralogical Sciences