Tuned Mullins-Sekerka instability: exact results

Area of Science:

• Materials Science
• Physics of Crystal Growth
• Fluid Dynamics

Background:

• Mullins-Sekerka instability is a key phenomenon in crystal growth from undercooled melts.
• Previous studies often relied on quasisteady approximations, potentially overestimating instability.
• Understanding 3D self-similar growth is crucial for controlling crystal morphology.

Purpose of the Study:

• To investigate the Mullins-Sekerka instability in three-dimensional (3D) self-similar growth of spherical seed crystals.
• To obtain an exact solution for the linearized stability problem.
• To compare the exact solution with conventional quasisteady approximations.

Main Methods:

• Analytical solution of the linearized stability problem for 3D self-similar spherical crystal growth.
• Analysis of the temporal evolution of unstable modes.
• Comparison of exact solutions with quasisteady approximation results.

Main Results:

• The exact solution reveals a significantly weaker instability than predicted by quasisteady approximations.
• Unstable modes exhibit power-law growth, not exponential growth, over time.
• Relative growth rates of modes are time-dependent and influenced by initial amplitudes.

Conclusions:

• The exact analysis provides a more accurate description of Mullins-Sekerka instability in 3D growth.
• The observed power-law growth and time-dependent mode behavior allow for controlled manipulation of crystal shape.
• This offers potential for tailoring crystal morphology by controlling individual mode growth.