Competitive nucleation and the Ostwald rule in a generalized Potts model with multiple metastable phases

Abstract

We introduce a simple nearest-neighbor spin model with multiple metastable phases, the number and decay pathways of which are explicitly controlled by the parameters of the system. With this model, we can construct, for example, a system which evolves through an arbitrarily long succession of metastable phases. We also construct systems in which different phases may nucleate competitively from a single initial phase. For such a system, we present a general method to extract from numerical simulations the individual nucleation rates of the nucleating phases. The results show that the Ostwald rule, which predicts which phase will nucleate, must be modified probabilistically when the new phases are almost equally stable. Finally, we show that the nucleation rate of a phase depends, among other things, on the number of other phases accessible from it.

A note on the nucleation with multiple steps: Parallel and series nucleation

“…A qualitatively similar conclusion was reached by Sanders et al 24 using the artificially designed q-states Potts model. The probability is in fact proportional to the Boltzmann factor N * κ ∝ exp(−W * κ /kT ) from Eq.…”

Nucleation in a Potts lattice gas model of crystallization from solution

“…7,28,34,37 The Potts model 38 has been used as a phenomenological model of Ostwald's rule with each Potts orientation corresponding to a particular phase and with each phase preferentially giving birth to a particular phase through the introduction of an impurity 39 or a field favoring the new phase. 40 The Potts model has also been used by Sear 41 to study nucleation at interfaces. In a step toward using lattice models to describe specific molecular interactions, Jorge et al 42 developed a lattice model of the interactions between silica precursors and water molecules in zeolite synthesis.…”

Nucleation for One-Dimensional Long-Range Ising Models

“…The nucleation process of the critical droplet, i.e. the configuration triggering the crossover, has been indeed studied in different dynamical regimes: serial ( [8,17]) vs. parallel dynamics ( [2,11,13]); non-conservative ( [8,17]) vs. conservative dynamics ( [20,21,22]); finite ( [6]) vs. infinite volumes ( [7]); competition ( [14,15,23,29]) vs. non-competition of metastable phases ( [12,16]). All previous studies assumed that the microscopic interaction is of short-range type.…”