On the stability of crystal growth. (English) Zbl 1083.82523
Summary: We investigate properties of solid-on-solid models for crystal growth, involving general microscopic rates of capture of atoms by the crystal surface and of escape of atoms. The rates in this Markov process influence the stability of the growing surface. We prove, for various different ranges of the rate parameters, stability (i.e., ergodicity) and instability (i.e., nullity) of the growth process. Symmetry properties of the process, such as reversibility, dynamic reversibility, and reflection invariance, are proved or disproved under various conditions. We give a measure of surface smoothness that distinguishes between stable and unstable growth.
MSC:
| 82C24 | Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics |
| 82D25 | Statistical mechanics of crystals |
Keywords:
crystal growth; stability; Markov process; ergodicity; transience; null recurrence; dynamic reversibility; surface roughnessReferences:
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