Memory of incomplete phase transitions from a random squares model.

Area of Science:

• Statistical physics
• Materials science
• Phase transitions

Background:

• Phase transitions exhibit complex memory phenomena, particularly in materials like shape memory alloys.
• Existing thermodynamic models for thermal memory effects can be intricate.
• A simplified, reproducible model is needed to understand these memory properties.

Purpose of the Study:

• To develop a simple two-dimensional statistical geometry model for phase transitions.
• To investigate the memory properties arising from incomplete transformations within this model.
• To demonstrate the model's relevance to thermal memory effects in shape memory alloys.

Main Methods:

• Modeling direct transformation via random placement and growth of square 'nuclei' on a surface.
• Incorporating 'interaction' rules where surrounding nuclei limit growth.
• Simulating incomplete ('arrested') reverse transformations and subsequent direct transformations to observe memory effects.

Main Results:

• The model naturally achieves near-equal area coverage for each square size after direct transformation.
• Arrested reverse transformations create memory, evidenced by size distribution imbalances in subsequent direct transformations.
• The model reproduces the 'hammer effect' and the memorization of multiple arrest points.

Conclusions:

• A statistical geometry approach can effectively model phase transition memory phenomena.
• The model simplifies the understanding of thermal memory effects without explicit thermodynamics.
• This simplified model offers a potentially easier framework for reproducing and studying memory effects in materials.