Numerical Simulation Of Two-dimensional Crystal Growth

The phase field crystal method is an important method to study crystal growth and crystal defects.The spatial scale can be described to the nanometer scale.The phase field crystal method is often used to simulate the structural evolution of nanomaterials mainly applied to the study of dislocation motion and decomposition,crystal and quasi-crystal growth,grain boundary deformation,etc.In this paper,Since we study the growth of two-dimensional crystals and quasi-crystals,we choose the CahnHilliard type dynamic equations with periodic boundary conditions,so we can choose Fourier pseudo-spectral method to solve them numerically in space,on the time scale,we choose semi-implicit scheme,Fourier quasi-spectral method is often used to study the periodic problem.The main findings are as follows:1.In this paper,phase field crystal model is used to study the growth of hexagonal crystal seeds under the two-scale model.In one case the growth of quasi-crystals is slow,but in the other case the compressed crystal is formed first and then the quasi-crystals.2.The growth of a 6-fold crystal seed and a twelve-turn quasi-crystal was studied by using a phase-field crystal model.The effects of model coefficients,average density and seed rotation angle on the formation of phase structure were investigated,including: Fluid Phase,six-phase Crystal Phase,twelve-phase quasi-crystal,lamellar phase,crystal and lamellar phase coexistence phase.3.It is also found that when the seed of the six-rotating crystal is placed in the background of the quasi-crystal,three kinds of phase structures can be obtained when the seed of the six-rotating crystal changes the crystal radius,including 6-fold crystal,12-fold quasi-crystal and coexisting quasi-crystal,the three phase structures are distributed regularly.Thee growth of two-dimensional quasi-crystals with different initial values has been simulated reasonably,and the whole process of crystal growth has been shown vividly.