Keywords
Burton Cabrera Frank theory
Monte Carlo simulation of crystal growth
How to Cite
Abstract
Models that allow to obtain directional dependencies of normal velocity of a straight step on the (001) face of Kossel crystal and its edge free energy are reviewed. The dependencies were considered in a wide range of crystal growth conditions, which showed some significant discrepancies between the models and limitations in the scope of their applicability. The results presented concern on one-dimensional kinetic and thermodynamic models of a single step.
References
Frank F.C. 1949. The influence of dislocations on crystal growth.Disc. Faraday Soc. 5: 48-54.
Burton W.K., Cabrera N., Frank F.C. 1951. The growth of crystals and the equilibrium structure of their surfaces.Phil. Trans. R. Soc. Lond. A 243: 299-358.
Voronkov V.V. 1968. Non-equilibrium structureof anelementary step.Soviet Phys. Crystallogr.13: 13-28.
TemkinD.E. 1969. The structure and kinetics of advance of a monomolecular step on a crystalline surface.Soviet Phys. Crystallogr.14: 179-185.
Pfeifer H. 1981. Anisotropy of step motion.Phys. stat. sol. (a) 66: 165-173.
Esin V.O., Tarabaev L.P.1980.Kinetics of growth of a monoatomic layer on a crystallinesurface(in Russian).Kristallografiya 25:357-364.
van Veenendaal E., van Hoof P.J.C.M, van Suchtelen J., van Enckevort W.J.P., Bennema P. 1998. Kinetic roughening of the Kossel (100) surface: comparison of classical criteria with Monte Carlo results.Surface Science 417: 121-138.
van Veenendaal E., van Hoof P.J.C.M, van Suchtelen J., van Enckevort W.J.P., Bennema P. 1999. Kinetic roughening of the Kossel (100) surface.J. Cryst. Growth 198/199: 22-26.
Cuppen H.M., van Veenendaal E., van Suchtelen J., van Enckevort W.J.P., Vlieg E. 2000. A Monte Carlo study of dislocation growth and etching of crystals.J. Cryst. Growth 219: 165-175.
Schulze T.P., Kohn. R.V. 1999. A geometric model for coarsening during spiral-mode growth of thin films.Physica D 132: 520-542.
Smereka P. 2000. Spiral crystal growth.Physica D 138: 282-301.
Forcadel N., Imbert C., Monneau R. 2012. Uniqueness and existence of spirals moving by forced mean curvature motion. Interfaces Free Bound. 14: 365-400.
Forcadel N., Imbert C., Monneau R. 2015. Steady state and long time convergence of spirals moving by forced mean curvature motion. Commun. Part. Diff. Eq. 40: 1137-1181.
Ohtsuka T., Tsai Y.-H. R., Giga Y. 2015. A level set approach reflecting sheet structure with single auxiliary function for evolving spirals on crystal surfaces.J. Sci. Comput. 62: 831-874.
Müller-Krumbhaar H., Burkhardt T.W., Kroll D.M. 1977. A generalized kinetic equation for crystal growth.J. Cryst. Growth 38: 13-22.
Jackson K.A. 1958. Mechanism of growth,in: Liquid metals and solidification (Ed.Moddin M.), 174-186. Cleveland: Am. Soc.for Metals.
Bennema P. 1992. Growth forms of crystals: possible implications for powder technology. KONA Powder and Particle 10: 25-40.
Bennema P., Gilmer G.H. 1973. Kinetics of crystal growth,in: Crystal growth: an introduction (Ed. HartmanP.), 263-327. Amsterdam: North–Holland Publ.
Gilmer G.H., Bennema P. 1972. Simulation of crystal growth with surface diffusion. J. Appl. Phys. 43: 1347-1360.
Gilmer G.H., Bennema P. 1972. Computer simulation of crystal surface structure and growth kinetics. J. Cryst. Growth 13/14: 148-153.
Rak M., Izdebski M., Brozi A. 2001. Kinetic Monte Carlo study of crystal growth from solution. Comput. Phys. Commun. 138: 250-263.
van der Eerden J.P. 1993. In: Handbook of Crystal Growth (Ed. Hurle D.T.J.), Vol. la, North-Holland, Amsterdam, p. 307.
Binsbergen F.L. 1970. A revision of some concepts in nucleation theory. Kolloid Z. Z. Polym. 237: 289-297.
Binsbergen F.L. 1972. Computer simulation of nucleation and crystal growth. J.Cryst. Growth 16: 249-258.
Bennema P. 1984. Spiral growth and surface roughening: developments since Burton, Cabrera and Frank. J. Cryst. Growth 69: 182-197.
Załuska-Kotur M.A., Krzyżewski F., Krukowski S. 2011. Double step structure and meandering due to the many body interaction at GaN(0001)surface in N-rich conditions. J. Appl. Phys. 109: 023515-1–023515-9.