One-dimensional model of formation of dislocation matrix structure and temperature dependence of size of vein pattern

A simplified model is developed for the mechanism governing the early stage of matrix structure formation, and to predict the dependence of the characteristic length scale of the vein pattern on the mean size of the loops. The matrix structure pattering is interpreted as a result of a redistribution of loops by a self-organization process. It is assumed that the loops and their size distribution are determined by the mechanism of their generation and the sweeping and drift of loops are dominant in the early pattering. All four types of loops, vacancy and interstitial types of two possible polarizations, are treated the same way as in the first approximation, the sweeping and drift of a loop is independent of the loop type.