Degenerate Ising model for atomistic simulation of crystal-melt interfaces

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Materials Science

Background:

• First-order phase transitions are fundamental in nature.
• Microscopic models are crucial for understanding complex phenomena like nucleation.
• Lattice models provide a simplified yet powerful framework for studying phase transitions.

Purpose of the Study:

• To simulate a minimal Ising-type lattice model for thermally driven first-order phase transitions.
• To investigate the influence of model parameters on nucleation barriers and interface properties.
• To analyze equilibrium crystal-melt coexistence and detect phenomena like negative heat capacities.

Main Methods:

• Utilizing rejection-free canonical and microcanonical Monte Carlo algorithms for simulation.
• Applying the model to square (2D) and face-centred cubic (3D) lattices with periodic boundary conditions.
• Analyzing caloric curves, heat capacity plots, and crystal-melt interface dynamics.

Main Results:

• Precisely adjusted bulk latent heat and communal entropy, independent of interface properties.
• Tuned crystal nucleation barriers at fixed undercooling, verifying dimension-dependent scaling.
• Detection of negative heat capacities in the microcanonical ensemble, particularly when interface entropy dominates.
• Observation of smooth negative heat capacity branches linked to varying interface-area-to-volume ratios.
• Simulation of microcanonical crystal nucleation and relaxation to equilibrium Wulff shapes.

Conclusions:

• The minimal model effectively tracks crystal-melt interfaces at the atomistic level.
• The study validates classical nucleation theory predictions and reveals insights into negative heat capacity phenomena.
• The findings contribute to a deeper understanding of phase transitions and crystal growth dynamics.