Growth with surface curvature on quenched potentials

Area of Science:

• Physics
• Materials Science
• Surface Science

Background:

• Understanding surface evolution in disordered materials is crucial for predicting material properties.
• Previous models often simplify the complex dynamics of interfaces in random media.

Purpose of the Study:

• To investigate a discrete growth model driven by surface curvature in quenched random media.
• To determine the scaling behavior of interface width and the dynamic critical exponent.

Main Methods:

• Simulated a discrete growth model incorporating the Laplacian of surface curvature.
• Analyzed interface width (W) in the saturated regime against system size (L).
• Measured autocorrelation functions from initial sine wave conditions to determine the dynamic critical exponent (z).

Main Results:

• Observed interface width scaling W ~ L^alpha with alpha approximately 2.3.
• Determined the dynamic critical exponent z approximately 3.1.
• The model's behavior aligns with predictions from the quenched Mullins-Herring equations.

Conclusions:

• The discrete growth model accurately captures interface dynamics in quenched random media.
• The identified scaling exponents and dynamic critical exponent provide insights into the growth mechanism.
• The findings support the applicability of the quenched Mullins-Herring equations to this model.