The influence of spatial grain size correlation on normal grain growth in one dimension

In this paper we demonstrate that a size correlation between neighbouring grains will exist in a grain structure. Such a correlation is shown to prevail during coarsening of the grain structure and this will in turn influence the kinetics of the process and the size distribution. In this paper the phenomena has been investigated numerically in a one-dimensional grain structure. In the accompanying paper the treatment is extended to the two-dimensional case. In the one-dimensional case we demonstrate that a quasi stationary grain size function as well as a quasi stationary size correlation function exists in the system after a transient which depends markedly upon the initial conditions. The kinetics of the coarsening process has also been analysed analytically by means of a modification of Hillert's mean field theory.