Crystal growth and dislocations

The theory of the growth of perfect crystals deriving from Gibbs and Volmer, shows that new crystal layers cannot be nucleated at an appreciable rate at low supersaturation. The essential truth of this theory is confirmed by the growth of crystals in polyhedra, which would otherwise be incomprehensible. But on this theory, by itself, the growth rate of such crystals would be virtually zero. This is not usually the case (though the necessary conditions have apparently been realized in Hawards experiments). The discrepancy is removed by considering that a real crystal contains dislocations and may therefore consist of only one layer of atoms perpetually overlapping itself. Such a crystal can grow to an unlimited size without any nucleation of new layers. The rate of growth of such a crystal can be calculated; it is proportional to the square of the supersaturation for low values and to the first power of the supersaturation for higher values in satisfactory quantitative agreement with the experimental results of Volmer and Schultze. The theory indicates that an almost flat crystal surface will show spiral growth steps, ending on dislocations. These are observed in many different cristals, confirming that this mode of growth is very common. Finally, some discussion is given to the way in which dislocations are produced in the growth process.