Order-Disorder Transformation in Cu 3 Au: A Molecular Dynamics Study
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ORDER-DISORDER DYNAMICS STUDY
TRANSFORMATION
IN
Cu
3
Au:
A'
MOLECULAR
Fabrizio CLERI, Giorgio MAZZONE and Vittorio ROSATO ENEA, Divisione Scienza dei Materiali, C.R.E. Casaccia, 00100 ROMA A.D. (Italy)
CP2400,
ABSTRACT The order-disorder transformation in Cu 3 Au has been investigated using a combined Molecular Dynamics and Cluster Variation Method approach. Free energy minimization has been performed using the Natural Iteration technique. The calculated temperature dependence of enthalpy, lattice dynamics, short-range and longrange order parameters have been successfully compared with experimental data. INTRODUCTION Several alloys exhibit an order-disorder transformation at temperatures Tc below the melting temperatures Tm. The low temperature phase is characterized by an ordered arrangement of the atomic species on the lattice sites, while the high temperature state is characterized by a random arrangement of atoms. While the phase with the lowest enthalpy is stable at T=0, the competition between enthalpy and entropy determines the occurrence of structural transitions at higher temperatures. In the present approach the task of building the free energy functional required for the theoretical description of structural phase transitions has been accomplished via the development of a model of atomic interactions together with accurate approximation schemes for the configurational as well as for the other contributions to the system entropy [1]. The proposed scheme combines the Cluster Variation Method (CVM [2,3]) for the calculation of the configurational entropy and a Molecular Dynamics approach for the evaluation of enthalpy and vibrational entropy as a function of thermodynamic and structural variables (namely order parameters). All these quantities have been expressed as functions of CVM variables, in order to build a free energy functional which has been then minimized using the Natural Iteration technique [3].The model for MD simulations has been built up using many-body potentials able to reproduce metallic cohesion [4,5]. MODEL AND CALCULATIONS Cu 3 Au at low temperature has the cubic L12 structure (Au atoms on the cell corners and Cu atoms at the center of the faces) while, at high temperature, it transforms to an f.c.c. structure with Au and Cu atoms randomly distributed over the cell sites. The L12 structure naturally defines four sublattices: three of them, containing Cu atoms are equivalent, while the fourth contains Au atoms. Starting from a cubic lattice with N sites occupied according to the structure with the stoichiometry 25 7 5 CAu=0. and CCu=0. , the equilibrium behaviour of the system
Mat. Res. Soc. Symp. Proc. Vol. 291. 01993 Materials Research Society
532
at constant temperature and pressure value of the Gibbs free energy G(ai) = H{ail+T
[Sc(ai)
is
defined
+ Svfail]
by the minimum (1)
where H is the system enthalpy, Sc and Sv are the configurational and vibrational entropy terms, respectively (6]. These terms can be expressed as a function of a suitable set {ai} of independ
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