Kinetics of grain growth

Abstract

The two commonly used relations to describe isothermal grain growth in materials (dD/dt=KjD^m and D = βtⁿ , where D is the grain size, t growth time, and K, β, m and n are constants defined in the text) are considered and the correct grain growth equations consistent with the boundary conditions are derived. The criteria under which these equations can be simplified and the errors that would result when these criteria are violated are discussed. The relation between the parameters used in the two equations is derived and it is shown that the criteria under which the two equations can be simplified are the same in both cases. A graphical method of finding the solutions is given.