Computer simulation of a quenched binary alloy: cluster dynamics of a two-dimensional model system

Computer simulation of a quenched binary alloy: cluster dynamics of a two-dimensional model system

3. Aerosol Sci., 1976.Vol.7. pp. 509 to 510. PergamonPress. Printedin Great Britain. CURRENT WORK ON NUCLEATION Compiled by D. STAUFFER Institute o...

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3. Aerosol Sci.,

1976.Vol.7. pp. 509 to 510. PergamonPress. Printedin Great Britain.

CURRENT WORK ON NUCLEATION

Compiled by D. STAUFFER Institute of Theoretical Physics, University, 6600 Saarbriicken 11, GFR. Brief abstracts of work which have not yet been published may be submitted to the compiler for inclusion in this section. Nucleation Kinetics in condensed media. By D. PEAK;Physics Department, Union College, Schenectady, NY 12308, U.S.A., and J. W. CORBETT. We investigated the effects of a condensed solvent on the equilibrium state, and on the steady-state nucleation rate, of a model, supersaturated system. Our results emphasize the build-up of spatial correlation phenomena which occurs through the hierarchy of reactions leading to cluster formation. Droplet model and functional integral. By L. PICMAN; Department of Physics and J. Stefan Institute, University of Ljubljana, Ljubljana, Yugoslavia. An attempt is given of deriving the free energy for a droplet model of condensation from the functional integral representation of the partition sum. The energy functional is assumed to have the Landau-Girmburg form. From this it is possible to extract two parts: one corresponding to the mean field approximation, corrected for small fluctuations, and the other one representing large fluctuations of droplet type. The latter reveals the dimension d = 4 as a critical dimension. A particular attention is paid to the calculation of a droplet's entropy and comparison is given with a Fisher droplet model. It is found that in three dimensions the method gives the critical exponent 6 being close to 5 (6-t _~ 0.21). The critical temperature is determined by using the values of parameters from the Ising model, when it is found to lie only few percent below its mean field value. In two dimensions the results are less convincing, whereas in one dimension the method fails completely, due to the excluded volume effects. Size dependence of the lifetime of metastable states in the kinetic one-spin-flip Ising model. By E. P. STOLL and T. SCHNEIDER; IBM Zurich Research Laboratory, 8803 Riischlikon, Switzerland. Using the Monte Carlo technique we studied the relaxation of the order parameter after a sudden reversal of the applied field as a function of the size of the system. We considered square Ising models with nearest neighbour interaction subjected to periodic boundary conditions. For large systems the relaxation time was found to be independent of the size of the system. For small systems, however, the relaxation time decreases as the number of spins is reduced. In the intermediate range the relaxation time turned out to be inversely proportional to the number of spins. Computer simulation of a quenched binary alloy: cluster dynamics of a two-dimensional model system. By M. gAo, M. H. KALOS; Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, U.S.A., J. L. LEBOWITZ and J. MARRO. We present the results of a computer simulation of the time-development of a quenched two-dimensional (AB) alloy modelled as an Ising spin system with nearest neighbor exchanges. Of particular interest in this work is the study of the growth and evolution of microdomains of the minority phase following their nucleation, i.e. the coarsening of grains .... We also examine the nature of grains of critical size as discussed in nucleation theory .... Monte Carlo studies of percolation phenomena for a simple cubic lattice. By A. Stm, J. L. LEBOWITZ,J. MAP,SO; Belfer Graduate School of Science, Yeshiva University, New York; NY 10033, U.S.A., M. H. KALOS and S. KIRKPATRICK. The site-percolation problem on a simple cubic lattice is studied by the Monte Carlo method .... The shape of the clusters was also studied. The average "surface area" for clusters of size k was found to be close to its maximal value for the low concentration as well as for the high concentration region. The percentage of particles in clusters of different sizes k was found to have an exponential tall for large values of k for p below p~.... Exact distribution of cluster size and perimeter for two-dimensional percolation. By D. STAUH~It;Institute of Theoretical Physics, University, 6600 Saarbriicken 11, GFR. Exact series expansion data of Sykes et al. a r e used to calculate the average number c, and perimeter s, of clusters of size n _< 20 in the site percolation problem for the triangular, square, and honeycomb lattice .... This perimeter should not be interpreted as a cluster "surface" in the usual sense.... The asymptotic decay of the cluster numbers c, with n is consistent with the postulated asymmetry about p,: log c, oc - n ~ for n - - , ~ w i t h ~ - ~ 1 f o r p < p c a n d ~ 1/2 f o r p > p c . Temperature dependence of nucleation from sulfuric acid-water mixtures in air. By M. ITOH, T. TAKAHASHI and M. KASAHARA; Institute of Atomic Energy, Kyoto University, Uji, Kyoto 611, Japan. No abstract given; authors calculate the H2SO4-H20 binary nucleation rate for temperatures between 10 and 30°C. Variation of temperature has a minor effect on the nucleation rate if relative humidity or 509