[Paper Review] Low artificial anisotropy cellular automaton model and its applications to the cell-to-dendrite transition in directional solidification

Lei Wei, Xin Lin+2 more|arXiv (Cornell University)|Oct 15, 2014

Solidification and crystal growth phenomena1 references3 citations

TL;DR

This paper presents a low artificial anisotropy cellular automaton (CA) model with a limited neighbor solid fraction (LNSF) capture rule to simulate microstructure evolution during directional solidification. It reveals that the cell-to-dendrite transition velocity (Vcd) transitions from scaling with k₀ (Vcd ∝ Vc/k₀) to a constant value (Vcd = 8Vc) when the solute partition coefficient k₀ exceeds a critical threshold of 0.125, validated by simulations and experimental data for SCN-ace and SCN-camphor systems.

ABSTRACT

A low artificial anisotropy cellular automaton (CA) model is developed for the simulation of microstructure evolution in directional solidification. The CA model's capture rule was modified by a limited neighbor solid fraction (LNSF) method. Various interface curvature calculation methods have been compared. The simulated equilibrium shapes agree with the theoretical shapes, when the interface energy anisotropy coefficient is ε=0.01, ε=0.03 and ε=0.05, respectively.The low artificial anisotropy CA model is used in the numerical simulation of the cell-to-dendrite transition (CDT) in directional solidification. The influence of physical parameters (Γ, Dl, k0, ml) on CDT has been investigated. The main finding in this paper is the discovery of the changing behavior of the Vcd when the solute partition coefficient k0 is larger than a critical value. When k0 is less than 0.125, the Vcd follows the Kurz and Fisher criterion Vc/k0; while when k0>0.125, the Vcd equals to 8Vc. The experimental data of succinonitrile-acetone (SCN-ace, k0=0.1) and SCN-camphor (k0=0.33) support the conclusion from CA simulations.

Motivation & Objective

• To develop a cellular automaton model with minimal artificial anisotropy for accurate microstructure simulation in directional solidification.
• To investigate the influence of key physical parameters (Γ, Dl, k₀, ml) on the cell-to-dendrite transition (CDT).
• To clarify the transition behavior of the cell-to-dendrite transition velocity (Vcd) as a function of the solute partition coefficient k₀.
• To validate the simulation results against experimental data from succinonitrile-based systems with varying k₀ values.

Proposed method

• A limited neighbor solid fraction (LNSF) method is implemented to modify the CA capture rule, reducing artificial anisotropy in the model.
• Multiple interface curvature calculation methods are evaluated and compared to ensure accuracy in simulating dendritic growth.
• The model is calibrated using theoretical equilibrium shapes at low anisotropy coefficients (ε = 0.01, 0.03, 0.05), confirming good agreement with theory.
• Numerical simulations of the cell-to-dendrite transition are performed across a range of physical parameters, including k₀, Dl, ml, and Γ.
• The model is applied to simulate directional solidification in systems with k₀ = 0.1 (SCN-ace) and k₀ = 0.33 (SCN-camphor), matching experimental observations.

Experimental results

Research questions

• RQ1 How does the solute partition coefficient k₀ influence the cell-to-dendrite transition velocity (Vcd) in directional solidification?
• RQ2 What is the critical value of k₀ at which the Vcd behavior transitions from Vc/k₀ scaling to a constant value?
• RQ3 To what extent does the low artificial anisotropy CA model accurately reproduce theoretical equilibrium shapes at low anisotropy?
• RQ4 How well do the simulated Vcd values match experimental data for SCN-ace and SCN-camphor systems?
• RQ5 What is the role of interface energy anisotropy (ε) in the stability and morphology of growing dendrites?

Key findings

• The model successfully reproduces theoretical equilibrium shapes at low anisotropy coefficients (ε = 0.01, 0.03, 0.05), confirming minimal artificial anisotropy.
• When k₀ < 0.125, the cell-to-dendrite transition velocity (Vcd) follows the Kurz and Fisher criterion, scaling as Vc/k₀.
• For k₀ > 0.125, the Vcd stabilizes at a constant value of 8Vc, indicating a distinct transition in growth dynamics.
• The simulated Vcd values for SCN-ace (k₀ = 0.1) and SCN-camphor (k₀ = 0.33) align with experimental observations, supporting the model's validity.
• The transition at k₀ = 0.125 marks a critical shift in the growth mechanism, from solute-diffusion-limited to thermodynamically controlled behavior.