Abstract
We study theoretically two types of kinetic models of a binary alloy at zero temperature. In the phase separation model, a nearest-neighbor interchange can occur if the fraction of AB bonds (where A and B denote distinct species of atoms in a binary alloy) is thereby decreased. The crystallization model is defined by the opposite evolution rule. We examine these models in one dimension and obtain exact analytical results for the densities of domain walls, defects, and for a number of other correlators. Nonergodic zero-temperature dynamics leads to final states strongly dependent on initial conditions. For generalized models, in which nearest-neighbor interchange is also performed if the portion of AB bonds is not changed, a very rich kinetic behavior is observed.
Similar content being viewed by others
References
A. Levy, S. Reich, and P. Meakin,Phys. Lett. A 87:248 (1982).
P. Meakin and S. Reich,Phys. Lett. A 92:247 (1982).
R. G. Palmer and H. L. Frisch,J. Stat. Phys. 38:867 (1985).
Y. Elskens and H. L. Frisch,J. Stat. Phys. 48:1243 (1987).
E. L. Hinrichsen, J. Feder, and T. Jossang,J. Stat. Phys. 44:793 (1986).
J. D. Sherwood,J. Phys. A 23:2827 (1990); G. Tarjus, P. Schaaf, and J. Talbot,J. Stat. Phys. 63:167 (1991).
G. Tarjus, P. Schaaf, and J. Talbot,J. Chem. Phys. 93:8352 (1990).
M. C. Bartelt and V. Privman,Int. J. Mod. Phys. B 5:2883 (1991), and references therein.
I. R. Epstein,Biopolymers 18:765 (1979).
J. Feder,J. Theor. Biol. 87:237 (1980).
B. Widom,J. Chem. Phys. 44:3888 (1966).
J. J. Gonzalez, P. C. Hemmer, and J. S. Hoye,Chem. Phys.,3:228 (1974), and references therein.
N. O. Wolf, J. W. Ewans, and D. K. Hoffman,J. Math. Phys. 25:2519 (1984).
J. J. Gonzalez and K. W. Kehr,Macromolecules 11:996 (1978).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Krapivsky, P.L. Kinetic models of a binary alloy at zero temperature. J Stat Phys 74, 1211–1225 (1994). https://doi.org/10.1007/BF02188224
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02188224