PHASE COMPETITION AND DIFFUSION PATH SELECTION IN REACTIVE DIFFUSION IN A MODEL TERNARY SYSTEM

Abstract

Reactive diffusion in multicomponent systems often leads to complex phase formation scenarios that are significantly more difficult to predict than in binary systems. In binary diffusion couples any phase predicted by the equilibrium phase diagram will eventually appear during interdiffusion, although its formation may be delayed by the growth of other phases. In ternary and multicomponent systems, however, the situation is fundamentally different: several diffusion paths are possible, and each path may correspond to a different sequence of phases and morphologies formed in the diffusion zone. Therefore, the actual phase composition and morphology depend not only on the initial compositions but also on the diffusion path selected by the system during the reaction.

In the present work we investigate the competition between phases and the selection of diffusion paths during reactive diffusion in a model ternary A-B-C system. The study focuses on diffusion couples of the type A-(B+C), where the reaction may lead to the formation of two ordered intermediate phases, AB and AC. The goal of the work is to analyze how the interplay between thermodynamic interaction parameters and the initial alloy composition influences the morphology of the reaction zone and the diffusion path in the concentration triangle.

Two simulation approaches were employed. The first is the Stochastic Kinetic Mean-Field (SKMF) method, which describes the system evolution through time-dependent probabilities of site occupation by atoms of different types. In this framework, atomic transport is represented by direct exchanges between neighboring atoms, while the configuration energy of each atom is calculated as a sum of pair interactions with atoms in the first and second coordination shells. The second approach is lattice Monte Carlo simulation using the Metropolis algorithm, where the system evolves through discrete atomic exchanges determined by the change in configurational energy.

The model system considered in this work represents a two-dimensional section of an f.c.c. lattice (the (001) plane). Interatomic interactions are introduced for the first and second coordination shells. Two sets of interaction parameters were analyzed. In the first (symmetric) set, the interactions between A-B and A-C atoms are identical, resulting in a degenerate phase diagram where the ordered phases AB and AC are energetically equivalent. In the second (asymmetric) set, the A-C interaction is stronger than the A-B interaction, which leads to a non-degenerate phase diagram with two distinct three-phase regions involving the ordered compounds.

The simulations show that the combination of negative mixing energies in the first coordination shell and positive mixing energies in the second shell promotes the formation of nearly stoichiometric ordered phases AB and AC with narrow composition ranges. The resulting phase diagrams obtained from simulations reproduce the expected equilibrium phase relations qualitatively.

Reactive diffusion between A and the B-C alloy was simulated for different initial compositions B(x)|C(1-x). The evolution of the system was analyzed in terms of phase maps and diffusion paths constructed in the concentration triangle. The results demonstrate that the morphology of the reaction zone strongly depends on the relative stability of the competing ordered phases and on the B⁄C ratio in the initial alloy.

Within the SKMF simulations several characteristic regimes of phase formation were observed. When possible, the system tends to avoid the formation of a wide two-phase region containing numerous interfaces. Instead, it often forms a sequential phase arrangement, where layers of the AB and AC phases appear one after another. In such cases the diffusion path in the concentration triangle exhibits a segment approximately parallel to the tie lines between the two ordered phases, followed by a jump from one side of the tie-line region to the other.

However, when the initial B and C concentrations approach the equiatomic composition, the formation of a genuine two-phase region becomes unavoidable. In this regime the diffusion path may split into two branches, corresponding to the coexistence of the AB and AC phases within the reaction zone.

The asymmetry in interaction parameters also significantly influences the diffusion path. When the ordered AC phase is energetically more stable than AB, the diffusion path tends to shift toward the AC side of the concentration triangle even for compositions where the average alloy composition would suggest a trajectory closer to the AB side. This effect reflects the thermodynamic driving force favoring the formation of the more stable ordered phase.

Monte Carlo simulations performed with the same interaction parameters reveal qualitatively similar trends but also important differences. In particular, the tendency toward a strictly sequential phase arrangement is less pronounced in the Monte Carlo results. This difference is attributed to stronger local fluctuations and a less planar interface morphology, which allows the competing phases to interpenetrate and locally form elements of a parallel phase arrangement.

Overall, the results demonstrate that the morphology of the diffusion zone and the selected diffusion path in ternary reactive diffusion are governed by a complex interplay between thermodynamic interaction parameters and the initial composition of the reacting alloys. The comparison between SKMF and Monte Carlo simulations highlights the role of concentration fluctuations and local interface roughness in determining the final morphology of the reaction zone.

The developed modeling approach provides a useful framework for studying phase competition and diffusion path selection in multicomponent systems and may contribute to a better understanding of phase formation processes in reactive diffusion.