Abstract
Morphologies of grain growth are investigated using idealized three-dimensional models. The investigations are based on a body centred cubic (bcc) tetrakaidecahedra and allow either a single grain or one-half of the grains to grow. The polyhedra considered possess a high degree of symmetry which makes it easier to follow the path of the growing grain. The investigations are partly geometric and partly physical in nature. In the case of structures with planar interfaces, starting from the unimodular structure (bcc), by allowing one-half of the grains to grow, complex bimodular and trimodular structures are evolved. It is found that the sequence of grain growth from bcc to simple cubic is pseudo-cyclic and an analogy with the martensitic transformation from y-iron (fcc) to a -iron (bcc) has been noted. Using the appropriate ratios of the energies of grain boundary with different orientation the total energy remains constant, so that all these structures are in stable equilibrium. For structures with curved interfaces, using an isotropic grain boundary energy ratio and allowing one-half of the grains to grow, the total energy is found to decrease. Thus the unimodular array of tetrakaidecahedra is not in stable equilibrium and grain growth will occur. In the case of structures with a rogue grain, both planar and curved interfaces are considered. For the structures with planar interfaces the total energy again remains constant. For the growing grain and its nearest neighbours a relationship with the two-dimensional array of hexagons is suggested. However, in the case of structures with curved interfaces as the rogue grain is allowed to grow the energy increases. Therefore, in this case the unimodular structure, an array of tetrakaidecahedra, is the stable configuration. The investigations for structures with curved interfaces involve solving the equations of Laplace and Poisson when only a limited amount of information is available on the locations of the boundaries. The procedure developed to obtain these solutions provide the first advance on those used by Kelvin in the late 19th century. Many of the results are presented graphically using computer generated isometric projections. Unfortunately, little experimental work that can be compared directly with the present results has been carried out. However, the calculations of the thesis suggest some critical experiments which can now be usefully undertaken.