Computing the crystal growth rate by the interface pinning method.

Area of Science:

• Materials Science
• Computational Physics
• Chemical Engineering

Background:

• Crystal growth kinetics are crucial for material properties.
• The kinetic coefficient relates supercooling to growth velocity.
• Existing methods for calculating this coefficient can be complex.

Purpose of the Study:

• To develop a novel, efficient method for computing the kinetic coefficient.
• To validate the method using simulations and first-principles calculations.
• To demonstrate its applicability to real elements.

Main Methods:

• Utilizing an interface pinning method within a single equilibrium simulation.
• Employing a spring-like bias field coupled to an order parameter to stabilize two-phase configurations.
• Analyzing the crystal growth rate via the exponential relaxation of the order parameter, treating crystal growth as a Smoluchowski process.

Main Results:

• The kinetic coefficient was successfully computed for the Lennard-Jones model.
• A scaling relationship was identified: the kinetic coefficient is inversely proportional to the square-root of temperature at high temperatures.
• The method was practically demonstrated for Sodium (Na) and Silicon (Si) using first-principles calculations.

Conclusions:

• The interface pinning method provides an efficient route to determine crystal growth kinetic coefficients.
• The findings offer insights into temperature-dependent growth kinetics.
• The generalized method holds potential for calculating crystal nucleation rates and other rare events.