Abstract
A Markov rate process whose transitions are captures and escapes of single atoms from the edge of a two-dimensional crystal is introduced. The stochastic equilibrium states of this process describe steady crystal growth, crystal-fluid equilibrium, and steady crystal decrescence. Exact and asymptotic growth rates are found. This extends recent results which dealt only with capture events. One application is to the growth of lamellar crystals from polymers.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C. H. Bennett, M. Bütticker, R. Landauer, and H. Thomas,J. Stat. Phys. 24:419–442.
W. Feller,An Introduction to Probability Theory and its Applications. I. 3rd ed. (Wiley, New York, 1968).
D. J. Gates and M. Westcott,Proc. R. Soc. Lond. A 416:443–461 (1988).
D. J. Gates and M. Westcott,Proc. R. Soc. Lond. A 416:463–476 (1988).
G. H. Gilmer,J. Crystal Growth 49:465–474 (1980).
G. H. Gilmer and K. A. Jackson, inCrystal Growth and Materials, E. Kaldis and H. J. Scheel, eds. (North-Holland, Amsterdam, 1976), pp. 80–114.
N. Goldenfeld,J. Phys. A 17:2807–2821 (1984).
K. A. Jackson,J. Crystal Growth 34:507–511 (1968).
F. P. Kelly,Reversibility and Stochastic Networks, (Wiley, New York, 1979).
D. M. Sadler,J. Chem. Phys. 87(3):1771–1783 (1987).
D. M. Sadler,Polymer 28:1440–1454 (1987).
P. Whittle, inPerspectives in Probability and Statistics, J. Gani, ed. (Academic Press, New York, 1975).
P. Whittle,Systems in Stochastic Equilibrium (Wiley, New York, 1986).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gates, D.J. Growth and decrescence of two-dimensional crystals: A Markov rate process. J Stat Phys 52, 245–257 (1988). https://doi.org/10.1007/BF01016412
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01016412