Evolution of a grain system: From early to late stages

An analytical approach to the d-dimensional grain growth, which is a kind o f the heterogeneous nucleation-and-growth phase transformation, is offered. The system is assumed to be driven by capillary forces. Another important operative assumption is that the system evolves under preservation of its h ypervolume, which results in considering the process as a random walk in th e space of grain sizes. A. role of the initial condition imposed on the sys tem behaviour, and how does the system behave upon a prescribed initial sta te, have been examined. A general conclusion appears, which states that thi s prescription does not affect the asymptotic system behavior, but may be o f importance when inspecting the early-time domain more carefully, cf. the Weibull-type initial distribution. This study is addressed to some analogou s theoretical descriptions concerning polycrystals as well as bubbles-conta ining systems. Some comparison to another modeling, in which a crucial role of local material gradients (fluxes) was emphasized, has been attached.