Abstract
The elaborated in [R. V. Chepulskii, Analytical method for calculation of the phase diagram of a two-component lattice gas, Solid State Commun. 115:497 (2000)] analytical method for calculation of the phase diagrams of alloys with pair atomic interactions is generalized to the case of many-body atomic interactions of arbitrary orders and effective radii of action. The method is developed within the ring approximation in the context of a modified thermodynamic perturbation theory with the use of the inverse effective number of atoms interacting with one 1ixed atom as a small parameter of expansion. By a comparison with the results of the Monte Carlo simulation, the high numerical accuracy of the generalized method is demonstrated in a wide concentration interval.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
R. V. Chepulskii, Analytical method for calculation of the phase diagram of a two-component lattice gas, Solid State Commun. 115:497 (2000).
T. D. Lee and C. N. Yang, Statistical theory of equations of state and phase transitions. II. Lattice gas Izing model, Phys. Rev. 87:410 (1952).
R. V. Chepulskii and V. N. Bugaev, Analytical methods for calculation of the short-range order in crystal compounds. I. General theory, J. Phys.: Condens. Matter 10:7309 (1998); R. V. Chepulskii and V. N. Bugaev, Analytical methods for calculation of the short-range order in crystal compounds. II. Numerical accuracy study, J. Phys.: Condens. Matter 10:7327 (1998).
R. V. Chepulskii, Analytical description of the short-range order in crystal compounds with many-body atomic interactions II, J. Phys.: Condens. Matter 11:8645 (1999); R. V. Chepulskii, Effect of nonpair atomic interactions on the short-range order in disordered crystal compounds, J. Phys.: Condens. Matter 11:8661 (1999).
K. Binder and D. W. Heermann. Monte Carlo Simulation in Statistical Physics: an Introduction, Springer, Berlin (1988).
D. de Fontaine, Configurational thermodynamics of solid solutions, Solid State Physics 34:73 (1979).
V. N. Bugaev and R. V. Chepulskii, The symmetry of interatomic lattice potentials in general crystal structures. 1. Basic theory, Acta Cryst. A 51:456 (1995).
R. V. Chepulskii, to be published.
R. Brout. Phase Transitions, Benjamin, New York (1965).
A. G. Khachaturyan, Ordering in substitutional and interstitial solid solutions, J. Prog. Mat. Sci. 22:1 (1978).
J. G. Kirkwood, Order and disorder in binary solid solutions, J. Chem. Phys. 6:70 (1938).
R. Kubo, Generalized cumulant expansion method, J. Phys. Soc. Japan 17:1100 (1962).
A. Finel and F. Ducastelle, On the phase diagram of the FCC Ising model with antiferromagnetic first-neighbour interactions, Europhys. Lett. 1:135 (1986).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer Science+Business Media, Inc.
About this chapter
Cite this chapter
Chepulskii, R.V. (2005). Calculation of the Phase Diagrams of Alloys with Nonpair Atomic Interactions within the Ring Approximation. In: Turchi, P.E.A., Gonis, A., Rajan, K., Meike, A. (eds) Complex Inorganic Solids. Springer, Boston, MA. https://doi.org/10.1007/0-387-25953-8_10
Download citation
DOI: https://doi.org/10.1007/0-387-25953-8_10
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-24811-0
Online ISBN: 978-0-387-25953-6
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)