Nonlinear effects in periodic surface limited grain growth

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Several of the characteristic features of periodic behavior in surface limited grain growth have been quantitatively described for the first time using an analytical solution to the nonlinear, governing partial differential equation. This analysis in this paper reproduces the experimental observations of a correlation between surface groove depth and surface groove spacing, the asymmetry of the surface groove, and aperiodic groove depth within a group of parallel surface grooves. The results of this analysis suggests each of these features is associated with the nonlinear interaction of the time dependent velocity perturbation with the time dependent slope perturbation. It is apparent from the analysis presented here that the depth of the surface grooves and the spacing of the surface grooves are both proportional to the inverse of √V. This prediction shows reasonable agreement with the experimental observations as shown in Figure 2. The model presented in this paper also shows qualitative agreement with the experimentally observed asymmetry of the surface grooves originally described by Mullins. The nonlinear model also predicts a time dependent subharmonic resonance which causes a halving of the period predicted by the linear model in (2). This resonance is consistent with the experimentally observed aperiodic behavior of surface groove image widths within some groups of parallel surface grooves.

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Scripta Materialia