Surface pattern formation and scaling described by conserved lattice gases

Area of Science:

• Condensed Matter Physics
• Materials Science
• Surface Science
• Computational Physics

Background:

• Surface diffusion is crucial for understanding crystal growth and material properties.
• Existing models often simplify complex surface dynamics.
• The interplay between diffusion and deposition processes dictates surface morphology.

Purpose of the Study:

• To extend a discrete growth model with conserved, local exchange dynamics for surface diffusion.
• To investigate the competition between surface diffusion and deposition processes.
• To analyze pattern formation and scaling laws in nonequilibrium growth systems.

Main Methods:

• Extension of a 2+1-dimensional discrete growth model incorporating octahedra exchange dynamics.
• Mapping surface slopes to particles, creating a 2D nonequilibrium binary lattice model.
• Numerical simulations on large scales to analyze surface width scaling and pattern evolution.

Main Results:

• Demonstrated Mullins-Herring or molecular-beam epitaxy class scaling for surface width.
• Observed pattern formation (dots or ripples) from the competition between diffusion and deposition (Kardar-Parisi-Zhang process).
• Confirmed the stability of Kardar-Parisi-Zhang scaling against surface diffusion and identified logarithmic growth for strong diffusion.

Conclusions:

• The extended model accurately describes surface diffusion and its impact on growth dynamics.
• The competition between surface diffusion and deposition leads to diverse morphological patterns.
• Kardar-Parisi-Zhang scaling is robust, and strong diffusion leads to logarithmic growth, consistent with mean-field behavior.