Z. Phys.B - CondensedMatter 55, 309-315 (1984) Condensed Zeitschrift Matter for Physik B 9 Springer-Verlag 1984 Dynamical Spinodal: The Transition between Nucleation and Spinodal Decomposition Dieter W. Heermann Institut fiir Festk/Srperforschung, Kernforschungsanlage Jiilich, Federal Republic of Germany Received March 22, 1984 The nonclassical regime in the two phase region between nucleation and spinodal decomposition of a binary model with medium range interaction has been investigated. The Monte Carlo results indicate a dynamical spinodal. At this dynamical spinodal a transient percolating structure occurs. However, the mean droplet size remains finite there. In experimental studies of quenched alloys [1,2] and unmixing of fluid mixtures [3, 4] it has been noted that the systems sometimes exhibited perco- lation-like structures. A similar effect has also been seen in a Monte Carlo study of the two dimensional Ising model [5]. There a percolation-like structure formed after quenching into the two phase region and dissolved again after some time. It is this effect which we study in this paper. Specifically, we will link this problem to the question of the existence of a spinodal which divides the two phase region into a region governed by nucleation and one governed by spinodal decomposition. For finite range interaction it has been argued that the spinodal singularity should be rounded [-6,7], i.e., that the correlation length does not diverge. In this case there would be a gradual transition. On the other hand the spinodal is well defined in the infinite range limit. Hence we will study a model with medium range interaction which interpolates between short and infinite range interaction and concentrate on the region between nucleation and spinodal decomposition. For this re- gion there exists yet no analytic theory and we therefore use the Monte Carlo technique to study the problem. The Model The model which we have studied by the Monte Carlo method consists of a simple cubic lattice where each lattice site is occupied by either an A or a B atom. The number of A and B atoms is fixed: Each lattice site interacts with q neighbors (q= 124) with equal interaction strength J/k~T=(9/4)(1/q), which gives a temperature TITs= 4/9. T c is the criti- cal temperature in the mean field approximation. This model interpolates between the nearest neigh- bor model and the infinite range interaction, i.e., mean field. Most of the Monte Carlo simulations reported here were done for a lattice of size N= 603 with periodic boundary conditions. Finite size effects were studied using lattices of size N= 303 and 1023. We have chosen three concentrations (c.f. Fig. 1) c =0.105, 0.1275 and 0.15 (c=(l+~, fl=(1/N)Ztli, where t/i= + 1 (A atom) or -1 (B atom)). P2 is the mean field spinodal concentration. P1 and P3 are concentrations to the left and right of P2 which lie, according to previous simulations I-8,9] and the criterion developed by Binder [10], in the region where the classical nucleation [11] and classical spi- nodal decomposition theory [12] break down. Initially a configuration was chosen at random. This corresponds to an infinite temperature. The tempera- ture was then set to T/Tc=4/9. The system, now in the two phase region, evolved through exchanges of unlike-nearest-neighbor atoms 1-13]. Time was mea- sured by the number of attempted exchanges. Per- iodically the system was frozen and the largest drop- let and its radius of gyration, percolation, i.e., does the largest droplet percolate the system, and the mean droplet size were computed. Here a droplet was not defined as the usual Ising