Many-particle surface diffusion coefficients near first-order phase transitions at low temperatures

Area of Science:

• Surface Science
• Physical Chemistry
• Statistical Mechanics

Background:

• Understanding surface diffusion is crucial for processes like thin-film growth and catalysis.
• First-order phase transitions involve abrupt changes in material properties, including diffusion.
• Previous studies often focused on supercritical temperatures, leaving subcritical behavior less explored.

Purpose of the Study:

• To analyze chemical (D(c)) and jump (D(J)) surface diffusion coefficients near a first-order phase transition.
• To derive approximate analytical formulas for these coefficients under subcritical conditions.
• To investigate the dependence of diffusion on surface coverage (θ) and system size (N).

Main Methods:

• Utilized the local equilibrium approximation for theoretical analysis.
• Derived approximate analytical formulas for diffusion coefficients in different regimes.
• Employed a lattice-gas model on a triangular lattice for illustration and specific case studies.

Main Results:

• In the two-phase regime, D(c) and D(J) exhibit hyperbolic dependence on coverage relative to transition points.
• Diffusion coefficients show a rapid change when transitioning from two-phase to single-phase regimes.
• Crossover behavior between regimes is described by complex formulas involving the Lambert function.

Conclusions:

• The study provides a detailed theoretical framework for surface diffusion near subcritical first-order phase transitions.
• The derived formulas offer quantitative predictions for diffusion behavior as a function of coverage and system size.
• The findings are illustrated with specific examples from a lattice-gas model, validating the general approach.