Roughness exponents and grain shapes

Abstract

In surfaces with grainy features, the local roughness w shows a crossover at a characteristic length rc, with roughness exponent changing from α1≈1 to a smaller α2. The grain shape, the choice of w or height-height correlation function (HHCF) C, and the procedure to calculate root-mean-square averages are shown to have remarkable effects on α1. With grains of pyramidal shape, α1 can be as low as 0.71, which is much lower than the previous prediction 0.85 for rounded grains. The same crossover is observed in the HHCF, but with initial exponent χ1≈0.5 for flat grains, while for some conical grains it may increase to χ1≈0.7. The universality class of the growth process determines the exponents α2=χ2 after the crossover, but has no effect on the initial exponents α1 and χ1, supporting the geometric interpretation of their values. For all grain shapes and different definitions of surface roughness or HHCF, we still observe that the crossover length rc is an accurate estimate of the grain size. The exponents obtained in several recent experimental works on different materials are explained by those models, with some surface images qualitatively similar to our model films.