Critical exponents in percolation model of track region

Abstract

Numerous experiments on defect formation in insulators, metals, alloys, and amorphous semiconductors have shown that these materials are sensitive to track formation when they are bombarded by swift heavy ions (SHI). Detail understanding of the basic processes of materials modification by SHI will help to construct materials with preassigned properties. Tracks were examined like a chain of deal spherical regions; it was assumed that each incident ion creates one such chain. In this model, we assume that the track is formed randomly, but in that place of the ion path, where the energy value, which loses each ion to the unity of the way, is above some threshold value. As a result of irradiation the number of tracks will continue to grow, areas of the single tracks modified substance continue to overlap, form of modified matter becomes more complicated, creating branched structure. Based on the scaling hypothesis large-scale curve were constructed, critical exponents for this percolation model was established. Two such curves were evaluated: in the case of non-equiprobable distribution of tracks regions in depth with ratio of critical exponents ( / )s 0.68 and in the case with equiprobable distribution of tracks regions in depth, so-called model of continuous percolation with ratio of critical exponents ( / )e 0.41. Differences between critical exponents of this model and the continuous percolation model indicate that the dependence of the modified structure area on the dose and the angle related with the correlation between individual tracks. It results in next effect: angular dependence of the surface area of the branched structure has maximum value at certain «critical» angle of ions incidence.