Length scales and pinning of interfaces

Area of Science:

• Materials Science
• Condensed Matter Physics
• Solid Mechanics

Background:

• Interface pinning by defects and heterogeneities is crucial in phenomena like grain growth, phase transitions, ferroelectricity, dislocations, and fracture.
• Understanding the influence of length scales on pinning behavior is essential for controlling material properties.

Purpose of the Study:

• To investigate the role of length scale in the pinning of interfaces by heterogeneities.
• To determine how the relative width of an interface compared to heterogeneity length scale affects pinning and hysteresis.

Main Methods:

• Theoretical exploration of interface pinning dynamics.
• Analysis of pinning behavior across different length scales of heterogeneities relative to interface width.

Main Results:

• Large heterogeneities cause strong pinning and can lead to stick-slip behavior.
• Small heterogeneities may result in insignificant pinning.
• An intermediate regime shows complex interactions, yielding a non-monotone relationship between heterogeneity size and critical depinning stress.

Conclusions:

• The length scale of heterogeneities relative to interface width critically influences pinning and hysteresis.
• Introducing small-scale heterogeneities offers a strategy for developing materials with reduced hysteresis.
• Complex pinning behaviors emerge when heterogeneity and interface width scales are comparable.