Effects of lateral diffusion on morphology and dynamics of a microscopic lattice-gas model of pulsed electrodeposition

Abstract

The influence of nearest-neighbor diffusion on the decay of a metastable low-coverage phase (monolayer adsorption) in a square lattice-gas model of electrochemical metal deposition is investigated by kinetic Monte Carlo simulations. The phase-transformation dynamics are compared to the well-established Kolmogorov-Johnson-Mehl-Avrami theory. The phase transformation is accelerated by diffusion, but remains in accord with the theory for continuous nucleation up to moderate diffusion rates. At very high diffusion rates the phase-transformation kinetic shows a crossover to instantaneous nucleation. Then, the probability of medium-sized clusters is reduced in favor of large clusters. Upon reversal of the supersaturation, the adsorbate desorbs, but large clusters still tend to grow during the initial stages of desorption. Calculation of the free energy of subcritical clusters by enumeration of lattice animals yields a quasiequilibrium distribution which is in reasonable agreement with the simulation results. This is an improvement relative to classical droplet theory, which fails to describe the distributions, since the macroscopic surface tension is a bad approximation for small clusters.

Cluster evolution and critical cluster sizes for the square and triangular lattice Ising models using lattice animals and Monte Carlo simulations

“…For the square lattice, the values w b n can be found in literature up to n = 21, 9 for the triangular lattice, no relevant literature providing w b n values exists. Note that existing literature only provides data on the total number of configurations, polyominoes (polyiamonds, polyhexes), or lattice animals for a given n or provides data on the so-called perimeter polynomials.…”

“…For instance, for n = 19, 20, and 21, the number of clusters with the lowest energy (two lowest energies) is 8 (922), 2 (428), and 187 (7835), respectively. 9 Interesting work has been published recently on the validity of the classical nucleation theory for Ising models. 10 However, still the nucleation process is considered a 1D Markov.…”

“…[8][9][10][11][12][13][14]. Also, the present work is dedicated to this field of research by studying for the 2D square and triangular lattice Ising models the critical cluster for nucleation.…”

“…Although a complete picture of (both steady state and transient) nucleation is far from trivial in this one-dimensional case, 6 the complexity strongly increases when clusters with the same n can have a large variety in shapes and energies, as is already the case within the relatively simple 2D square lattice Ising model for n 6. [7][8][9] For example, for n = 19, 20, and 21, the total number of distinct cluster configurations on the 2D square lattice is over 5.9 × 10 9 , 22 × 10 9 , and 88 × 10 9 , respectively. 9 In principle, all possible transitions with their energies and probabilities between all configurations for such n − 1 ↔ n ↔ n + 1 have to be considered from n = 0 to n clearly larger than the critical nucleus size n * in order to arrive at a complete picture of nucleation.…”

“…[7][8][9] For example, for n = 19, 20, and 21, the total number of distinct cluster configurations on the 2D square lattice is over 5.9 × 10 9 , 22 × 10 9 , and 88 × 10 9 , respectively. 9 In principle, all possible transitions with their energies and probabilities between all configurations for such n − 1 ↔ n ↔ n + 1 have to be considered from n = 0 to n clearly larger than the critical nucleus size n * in order to arrive at a complete picture of nucleation. Fortunately, the situation simplifies at low temperatures, because cluster energy will prevail over entropy, and thus, for each n, only clusters with the lowest possible energies have to be considered.…”