| For solidification system, different interior microcosmic structures of the material determine the different nature. In the development of the process of material, the evolution of the internal microcosmic structure and the outcome will directly affect the performance, so it is very important to study the internal microcosmic structure of the material by workers. In this paper, we study the crystal of the microstructure morphology by epitaxial growth and introduce several widely used method of solidification microstructure simulation. We propound the phase field model for epitaxial growth of island according to phase field principle. The basic movement of atomic surface and the structure information of atomic scale are included intently and simplely into the continuity equation, and the phase field control equation is solved by finite difference method. A MPI program of parallel calculation with FORTRAN language is designed to solve phase field model equation. We simulate the epitaxial growth for Fe/Fe(001) system. The topography are predicted and dynamically display the the island growth. We also build the related dynamical scale law and growth mechanism. We simulate the topography with the different growth condition, which is found to be in line with the experimental results. The conclusions are as follow.(a) We introduce the important application of thin films in actual use, the physical mechanisms of epitaxial growth thin films and the methods and Principle. We also presents the top methods of microstructure simulation such as Monte-Calor method, level-set method, front tracking method and so on, and analysis the strengths and weaknesses of every methods. The advantage of phase-filed method for epitaxial growth simulation are put forward.(b) We deduce the phase field equation based on Ginzburg–Landau theory, and build the phase field model epitaxial island growth according to the basic physical process of epitaxial growth. A MPI program of parallel calculation with FORTRAN language is designed to solve phase field model equation based on finite difference method on uniform grid.(c) We introduce the phase field control parameters in detail such as phase-field transition zones, the spacing of the spatial grids, time step, capillarity length, nucleation parameter, the characteristic time of attachment of adatoms at boundaries of islands, and their effect on the calculation results. We get the values range for all parameters based on theory deduction and actual calculation. We obtain the results that the grid length may get larger appropriately with the increase of the temperature; that we fix the largest time step and the relation between the the characteristic time of attachment of adatoms and nucleation parameter; that we can get reliable results when the values of phase-field transition zones range from 2a to 10a between 293K and 529K.(d) We simulate the epitaxial island growth with the phase field model. The topography are predicted and dynamically display the the island growth at different temperature to explain the physical mechanism. The effects of outside condition and phase field parameters on the micro System are researched. We arrive at that the numbers of island decrease, but the area of an island get larger, and the coverage is independent on the temperature, as the temperature increase.(f) We improve the phase field model for epitaxial island growth by introducing empirical equation between the island numbers and the local datom density in level-set method instead of the nucleation term of original equation. The improved phase field equation arrive at the the well known 1/3 scaling law of the diffusion rate/flux dependence of the density of islands.
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