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Interfacial contribution to cluster free energy
A328 Surface Science 144 (1984) 53-66 North-Holland, Amsterdam
53
INTERFACIAL CONTRIBUTION TO CLUSTER FREE ENERGY A. P E R I N I and G. J A C U C C I Istituto per la Ricerca Scientifica e Tecnologica in Trento, I- 38050 Pooo, Italy
and G. M A R T I N Section de Recherches de Mbtallurgie Physique, C E N - Saclay, F- 91191 Gif - sur- Yvette Cedex, France Received 15 November 1983; accepted for publication 30 December 1983 The Monte Carlo technique of "overlapping distributions" is used for computing directly the free energy difference FN+ 1 -- F~ between two clusters containing respectively N + 1 and N solute atoms, in the square and the simple cubic Ising model with nearest neighbour interactions. High accuracy results are obtained within reasonable computer times. The capillarity approximation gives a good fit to the data, provided the following is taken into account: (i) the specific bulk and surface energies are given their macroscopic equilibrium values; (ii) a curvature correction to the surface specific energy has to be introduced: it is positive for two dimensions and negative for three dimensions; (iii) a size independent term is to be added in three dimensions; it may be viewed as a corner contribution; (iv) the coefficient of the logarithmic term is given its more recent value. When introduced in the master equation which describes the kinetics of the cluster population, within the simplifying assumptions of the classical nucleation theory, good agreement is found, for the shapes of the cluster size distributions, with the numerical experiments on the kinetic Ising model in two dimensions. However, the time scales of both computations do not match linearly. Possible reasons for this discrepancy are discussed.
Surface Science 144 (1984) 67-76 North-Holland, Amsterdam
67
RELATIONS BETWEEN INTERGRANULAR DIFFUSION AND STRUCTURE: A MOLECULAR DYNAMICS STUDY M. G U I L L O P E Centre d'Etudes Nuclbaires de Saclay, S R M P , F-91191 Gif-sur-Yvette Cedex, France
G. C I C C O T T I lnstituto di Fisica G. Marconi, Universit~ degli Studi di Roma, 1-00185 Roma, Italy
and V. PONTIKIS Centre d'Etudes Nuclbaires de Saclay, S R M P , F-91191 Gif -sur- Yvette Cedex, France Received 3 January 1984; accepted for publication 16 January 1984 The high temperature ( T > 0.5Tin) structure of the previously studied fcc (310)[001] ~ = 5 grain boundary is reinvestigated in order to determine the nature of the diffusion mechanism. The obtained results confirm our earlier conclusion that the grain boundary remains crystalline, but highly disordered, up to the melting point. In addition, we explored the diffusion mechanisms in the fcc (210)[001] Z = 5 grain boundary. As expected, diffusion occurs mainly by the vacancy migration. The j u m p frequencies determined by the molecular dynamics simulation have been used to evaluate the tracer correlation factor and the anisotropy of the intergranular diffusion coefficient through a random walk model simulation of the vacancy migration.
53
INTERFACIAL CONTRIBUTION TO CLUSTER FREE ENERGY A. P E R I N I and G. J A C U C C I Istituto per la Ricerca Scientifica e Tecnologica in Trento, I- 38050 Pooo, Italy
and G. M A R T I N Section de Recherches de Mbtallurgie Physique, C E N - Saclay, F- 91191 Gif - sur- Yvette Cedex, France Received 15 November 1983; accepted for publication 30 December 1983 The Monte Carlo technique of "overlapping distributions" is used for computing directly the free energy difference FN+ 1 -- F~ between two clusters containing respectively N + 1 and N solute atoms, in the square and the simple cubic Ising model with nearest neighbour interactions. High accuracy results are obtained within reasonable computer times. The capillarity approximation gives a good fit to the data, provided the following is taken into account: (i) the specific bulk and surface energies are given their macroscopic equilibrium values; (ii) a curvature correction to the surface specific energy has to be introduced: it is positive for two dimensions and negative for three dimensions; (iii) a size independent term is to be added in three dimensions; it may be viewed as a corner contribution; (iv) the coefficient of the logarithmic term is given its more recent value. When introduced in the master equation which describes the kinetics of the cluster population, within the simplifying assumptions of the classical nucleation theory, good agreement is found, for the shapes of the cluster size distributions, with the numerical experiments on the kinetic Ising model in two dimensions. However, the time scales of both computations do not match linearly. Possible reasons for this discrepancy are discussed.
Surface Science 144 (1984) 67-76 North-Holland, Amsterdam
67
RELATIONS BETWEEN INTERGRANULAR DIFFUSION AND STRUCTURE: A MOLECULAR DYNAMICS STUDY M. G U I L L O P E Centre d'Etudes Nuclbaires de Saclay, S R M P , F-91191 Gif-sur-Yvette Cedex, France
G. C I C C O T T I lnstituto di Fisica G. Marconi, Universit~ degli Studi di Roma, 1-00185 Roma, Italy
and V. PONTIKIS Centre d'Etudes Nuclbaires de Saclay, S R M P , F-91191 Gif -sur- Yvette Cedex, France Received 3 January 1984; accepted for publication 16 January 1984 The high temperature ( T > 0.5Tin) structure of the previously studied fcc (310)[001] ~ = 5 grain boundary is reinvestigated in order to determine the nature of the diffusion mechanism. The obtained results confirm our earlier conclusion that the grain boundary remains crystalline, but highly disordered, up to the melting point. In addition, we explored the diffusion mechanisms in the fcc (210)[001] Z = 5 grain boundary. As expected, diffusion occurs mainly by the vacancy migration. The j u m p frequencies determined by the molecular dynamics simulation have been used to evaluate the tracer correlation factor and the anisotropy of the intergranular diffusion coefficient through a random walk model simulation of the vacancy migration.