Computational Methods for Problems in Material Science

这个项目涉及到材料科学相关问题的有效数值方法的发展。研究人员研究了薄膜生长连续介质模型数值解的计算问题。其中许多模型考虑了表面扩散的影响，表面扩散是一种非线性的四阶项。因此，从计算的角度来看，这些模型是非常僵硬的。由于表面扩散项是非线性的，很难使用隐式方法。研究人员介绍了一种利用表面扩散求解运动的新的半隐式水平集方法。他使用这种新方法将表面扩散的影响纳入多晶薄膜的模型中。他还开发了一种计算岛屿动力学的新方法，其中阶地上的原子被视为连续场，而岛边缘的原子被离散处理。这种方法保留了连续介质方法的潜在优势，同时保留了孤岛动力学中存在的离散和随机效应。研究包括边缘扩散、表面张力、成核和弹性的影响。这个问题的一个重要计算方面是复数区域中扩散方程的数值解。这项研究为有效解决这一问题提供了新的方法。从轴承的涂层到半导体器件，薄膜在许多应用中都有应用。在许多情况下，这些薄膜不是单晶，而是多晶，薄膜的质量取决于它的结构。具有良好的双轴织构的薄膜接近于单晶，例如在超导带材的制造中有应用。决定织构演化的一个重要物理效应是表面扩散，但这很难在数值上实现，研究人员计划发展一种半隐式水平集方法来研究多晶薄膜的生长。这项工作有助于加深对这些薄膜的基本认识。分子束外延是制备薄膜的另一个重要过程。准确模拟这一过程的标准方法是动力学蒙特卡罗。在许多情况下，这种方法可能会很慢，而连续介质模型有可能极大地提高这种计算的速度。然而，连续介质模型忽略了离散和随机的影响。研究者开发了具有良好物理保真度但提供相当大计算速度的混合模型。

This project concerns the development of efficient numericalmethods for problems related to material science. Theinvestigator studies computational issues concerning thenumerical solution of continuum models for thin film growth. Manyof these models include effects for surface diffusion, which is anonlinear 4th order term. Consequently, these models are verystiff from a computational point of view. Because the surfacediffusion term is nonlinear, it is difficult to use implicitmethods. The investigator introduces a new semi-implicit levelset method for solving motion by surface diffusion. He uses thisnew method to incorporate the effects of surface diffusion intomodels of polycrystalline thin films. He also develops a newapproach for computing island dynamics, where the adatoms on theterraces are considered as a continuum field and the atoms on theedge of the island are treated discretely. This approach retainsthe potential advantage of continuum methods but at the same timepreserves the discrete and stochastic effects present in islanddynamics. The investigator includes effects of edge diffusion,surface tension, nucleation, and elasticity. An importantcomputational aspect of this problem is the numerical solution ofthe diffusion equation in a complex domain. The investigatorexamines new methods for the efficient solution of this problem. Thin films occur in a large number of applications, fromcoatings on bearings to semi-conductor devices. In many casesthese films are not single crystals but instead arepolycrystalline and the quality of the film can depend on itstexture. Films with good biaxial texture are close to being asingle crystal and have applications in the manufacture ofsuper-conducting tapes, for example. One important physicaleffect in determining the evolution of the texture is surfacediffusion, but this is difficult to implement numerically and theinvestigator plans to develop a semi-implicit level set method tostudy the growth of polycrystalline thin films. The work herecould help improve the fundamental understanding of these films.Another important process by which thin films are made ismolecular beam epitaxy. The standard method for accuratesimulation of this process is kinetic Monte Carlo. In manysituations this method can be slow, and continuum models have thepotential to greatly increase the speed of such computations.However, continuum models ignore discrete and stochastic effects.The investigator develops hybrid models that have good physicalfidelity but offer considerable computational speed.