Strongly nonlinear theory of rapid solidification near absolute stability

Area of Science:

• Materials Science
• Physics
• Chemical Engineering

Background:

• Solidification of binary melts can lead to morphological instabilities.
• Understanding interface dynamics is crucial for controlling material properties.

Purpose of the Study:

• Investigate nonlinear evolution of solid-liquid interface deformation under rapid solidification.
• Analyze effects of interfacial disequilibrium and attachment kinetics.
• Characterize instabilities near absolute stability limits.

Main Methods:

• Derivation of nonlinear evolution equations for interface dynamics.
• Analysis of systems near equilibrium and disequilibrium conditions.
• Mathematical modeling of cellular and oscillatory instabilities.

Main Results:

• Disequilibrium introduces oscillatory instabilities and deep-rooted interface structures.
• Asymmetry and root deepening increase with departures from equilibrium.
• Time-periodic oscillations occur only for small initial amplitudes.

Conclusions:

• Interfacial disequilibrium significantly impacts solidification morphology.
• Non-periodic growth and deep-rooted structures are common under moderate disequilibrium.
• Understanding these nonlinear dynamics is key for materials design.