Some exactly solved models of steady crystal growth

Abstract

Crystal growth at the molecular level can be described by statistical models for the surface structure and for the capture and escape of molecules. For some models the steady growth can be analysed exactly, leading to exact expressions for growth rate and surface characteristics. These are expressed in terms of the dimensions and angles of the surface and the rates of molecular events. Two-dimensional models describe the growth of a single layer on the surface of a three-dimensional crystal and approximate the growth of lamellar polymer crystals. The well known growth regimes for polymer crystals can be derived exactly. A two-dimensional model that can generate a rougher edge and a porous structure provides some insights into fast growth and into deposition of thin films from the vapour. A terrace–step–kink growth model in three dimensions can be exactly solved. For some models that have not been solved exactly, one can find conditions on the rates of molecular capture and escape that ensure steady, stable crystal growth.