A Unified Theory of Melting, Crystallization and Glass Formation

In recent years, dislocations have been involved in theories of melting, in models of the liquid state, and in calculations of the viscosity of glasses. Particularly noteworthy are the Mott-Gurney model of a liquid as a polycrystal with a grain size (i. e. a dislocation network size) of near-atomic dimensions, and the demonstration by Kotze and Kuhlmann-Wilsdorf that the solid-liquid interfacial energy is proportional to the grain boundary energy for a number of elements. These developments suggest the possibility of a relatively simple picture of crystallization and glass formation. In the liquid state dislocations, at the saturation density, are in constant motion and the microscopic grain boundary structure that they form is constantly changing due to dislocation-dislocation interaction. As the liquid is cooled below the melting point the free energy favors the crystalline form and grains larger than the critical nucleation size at any given temperature will grow at the expense of the surrounding grains. If this process does not occur the dislocations will remain and a glass will be formed. Just which of these alternatives will actually be observed for a given material will depend especially on the amount of dislocation motion that can take place during the critical period when nucleation and growth becomes favored thermodynamically. Thus the glassy form will have a better chance of being formed if either the liquid is particularly viscous or if the cooling rate is particularly rapid.