I. Crystal Surfaces in Equilibrium with the Surrounding Medium 117 The Surface Energy of Crystals 117 1. Kinks in Elementary Steps 117 2. Crystal Surface Energy. Herring's Formula 118 3. Corner Points in the Profiles of Crystal Surfaces 119 4. Surface Stability Conditions 120 5. The Equilibrium Shape of an Open Curve 121 II. Crystal Growth from Vapor 122 6. Particles Adsorbed on a Surface 123 7. The Motion of an Isolated Step 123 8. Parallel Sequences of Elementary Steps 124 9. The Normal Rate of Spiral Growth 124 10. The Motion of Macroscopic Steps 126 11. Some Experimental Results 128 12. Evaporation 129 III. Crystal Growth from the Solution and from the Melt 129 13. Introduction 129 14. The Motion of a Parallel Sequence of Elementary Steps 130 15. The Normal Growth Rate 131 16. Some Experimental Results 131 17. Growth from the Melt 132 18. The Diffusion Field and Rate of Advance of a Macroscopic Step 133 IV. The Interaction of Growing Crystals with Impurities 134 19. The Influence of Impurities on the Growth Rate 134 a) Strongly Adsorbed Impurities Captured by a Growing Crystal 135 b). Impurity Poisoning of Sinks 135 20. Nonequilibrium Capture of Impurities in Crystal Growth 137 21. Dislocation Production in Impurity Capture 139 V. Etching 139 VI. Collective Effects in the Movement of Steps 140 22. Shock Waves of Step Density 141 23. A Kinetic Equation for Steps 143 References 145

https://iopscience.iop.org/article/10.1070/PU1961v004n01ABEH003328/pdf

The spiral growth of crystals

Rapid growth of KDP-type crystals

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.

H. Emmett

Papers

Crystal growth from solution. I. Layer formation on crystal faces