Quadtree Grids And Dendritic Growth

As technology advances, there has been an increased desire from the energy and aerospace industries to predict crystalline microstructures in designing solidification methodologies for advanced materials. Polycrystalline materials such as most metals, are commonly made of dendritic crystals on the micrometer scale. It is the characteristics of these crystals, such as their size and shape, that significantly impact the physical, mechanical and electrical properties of the material. When a liquid metal is cooled, it crystallizes. The environmental parameters of this process, such as cooling rate and temperature gradient, determine the characteristics of the crystals. Complete understanding of this subject would result in the ability to manipulate  these characteristics by controlling the environmental parameters. Ultimately this would allow for the properties of a metal to be tailored to specific applications. Currently, much about this subject is still unknown and experiments are time consuming and expensive. My lab is developing a numerical method and computer simulation that attempts to accurately model the dendritic growth of crystals. The numerical method organizes the calculated data in a quadtree grid format. The variable resolution of this format decreases the computational time of the simulation by a factor of up to forty. In our simulation, the characteristics and properties of the crystals are easily measured. If our simulation proves accurate and reliable, it has the potential to vastly improve the efficiency of research of dendritic growth.