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Published on: February 22, 2018
Stability of a directional solidification front in subdiffusive media.
Mohammad Abu Hamed1, Alexander A Nepomnyashchy2
1Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel and Department of Mathematics, The college of Sakhnin-Academic College for Teacher Education, Sakhnin 30810, Israel.
Crystal growth instability in alloys is affected by anomalous diffusion, deviating from normal Brownian motion. This study generalizes the Mullins-Sekerka criterion for directional solidification under anomalous diffusion conditions.
Area of Science:
- Materials Science
- Solidification Physics
- Non-equilibrium Thermodynamics
Background:
- Crystal growth efficiency is often limited by morphological instability.
- This instability arises from a feedback loop between interface deformation and solute diffusion.
- Normal diffusion models assume Brownian motion, but anomalous diffusion occurs in complex media.
Purpose of the Study:
- To investigate the impact of anomalous diffusion on directional solidification fronts.
- To generalize the Mullins-Sekerka stability criterion for anomalous diffusion scenarios.
- To derive a nonlinear evolution equation describing interface cellular structures.
Main Methods:
- Linear stability analysis of a moving planar solidification front.
- Derivation of a generalized stability criterion.
- Asymptotic analysis to obtain a nonlinear evolution equation.
Main Results:
- A generalized Mullins-Sekerka stability criterion for anomalous diffusion was obtained.
- A Sivashinsky-type nonlinear evolution equation governing interface cellular structures was derived.
- The study demonstrates how anomalous diffusion modifies solidification front stability.
Conclusions:
- Anomalous diffusion significantly impacts crystal growth stability.
- The derived generalized criterion and evolution equation provide new tools for understanding alloy solidification.
- This work extends classical solidification theory to include memory effects from anomalous diffusion.

