Test of Some Statistical Approximations (Quasi Chemical, CVM) in BCC and FCC Binary Alloys by Monte Carlo Simulation. Va
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TEST OF SOME STATISTICAL APPROXIMATIONS (QUASI CHEMICAL, CVM) IN BCC AND FCC BINARY ALLOYS BY MONTE CARLO SIMULATION. VALIDITY RANGE OF THE CLAPP AND MOSS APPROXIMATION. P. CENEDESE*, J.P. GASPARD** * Institut Laue-Langevin, 156X, 38042 Grenoble Cedex, France. **Institut de Physique, Universitr de Liege, B-4000 Sart-Tilman,
Belgique.
ABSTRACT In the framework of regular solution model, we test the validity of some usual approximations (QC, CVM) of entropy in (disordered) binary alloys by Monte Carlo simulation. The validity range of these approximations are explored both in alternant and nonalternant lattice with ferro- and antiferromagnetic coupling. The CVM tetrahedron approximation is also analysed on a structure containing only tetrahedra : the 120 polytope [8] in 3d curved space.
INTRODUCTION The Monte-Carlo method has been largely used in the field of disordered systems (Binder [3 ]). Its help in the understanding of simple liquids (Binder [3])and the test of mean field theories (PY, HNC, WCA theory) has no longer to be demonstrated. The activity in the field of substitutional alloys is recently increasing. Indeed, after the pioneering work in the field of alloys by Fosdick [9] most work on computer simulation in alloys were oriented towards the important question of the determination of the critical properties of the transition (Tc, critical exponents) for which the limited size of the system and the small duration of the run (in real time for the system) is a severe limitation. Recently, a growing interest has been devoted to the alloys not too close to the critical temperature in order to check some of the approximations usually made in the study of the thermodynamical properties of substitutional alloys. The aim of this paper is to test the most widely used approximations in disordered alloys (quasi-chemical, CVM of various clusters). The test is made on different topologies compact (fcc) or semicompact (bcc) crystals and a polytope of tetrahedra (polytope 120). The Monte Carlo simulation results are considered.
MONTE CARLO METHOD The Monte Carlo method has been extensively developed in a series of review papers [3,4]. The aim of the Monte Carlo method is to calculate average values (here of short range order parameters) at the thermodynamic equilibrium, at a given temperature. The system is treated here in the regular solution model, energy of the binary alloy is EEm where NAB is
Res.
I (1)
the number of heteroatomic pairs and £ is £=
Mat.
==ONAB• AB2
Soc. Symp. Proc. Vol.
LAB
-
the mixing
AA+
the exchange energy
BB )/2
21 (1984) QElsevier science Publishing Co..
(2)
Inc.
52
The pair energies tAA, tBB and tAB are taken between nearest neighbours. The case £ < 0 corresponds to ordering (antiferro case) while 2 > Ocorresponds to demixion (ferro case). The relevant parameters of the different Monte Carlo runs are listed in Table I TABLE I Structure
FCC
BCC
Boundary condition
Periodic
Periodic
Number of atoms
1372 •
Temperature range T TTc
T >
Concentration
.5 (.1,
Energy pa
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