Metallurgical and Materials Transactions A

, Volume 34, Issue 2, pp 367–382 | Cite as

Growth of solutal dendrites: A cellular automaton model and its quantitative capabilities

  • Lazaro Beltran-Sanchez
  • Doru M. Stefanescu


A model based on the cellular automaton (CA) technique for the simulation of dendritic growth controlled by solutal effects in the low Péclet number regime was developed. The model does not use an analytical solution to determine the velocity of the solid-liquid (SL) interface as is common in other models, but solves the solute conservation equation subjected to the boundary conditions at the interface. Using this approach, the model does not need to use the concept of marginal stability and stability parameter to uniquely define the steady-state velocity and radius of the dendrite tip. The model indeed contains an expression for the stability parameter, but the process determines its value. The model proposes a solution for the artificial anisotropy in growth kinetics valid at zero and 45° introduced in calculations by the square cells and trapping rules used in previous CA formulations. It also introduces a solution for the calculation of local curvature, which eliminates mesh dependency of calculations. The model is able to reproduce qualitatively most of the dendritic features observed experimentally, such as secondary and tertiary branching, parabolic tip, arms generation, selection and coarsening, etc. Computation results are validated in two ways. First, the simulated secondary dendrite arm spacing (SDAS) is compared with literature values. Then, the predictions of the classic Lipton-Glicksman-Kurz (LGK) theory for steady-state tip velocity are compared with simulated values as a function of melt undercooling. Both comparisons are found to be in very good agreement.


Material Transaction Cellular Automaton Solid Fraction Dendritic Growth Local Curvature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© ASM International & TMS-The Minerals, Metals and Materials Society 2003

Authors and Affiliations

  • Lazaro Beltran-Sanchez
    • 1
  • Doru M. Stefanescu
    • 1
  1. 1.the Department of Metallurgical and Materials EngineeringThe University of AlabamaTuscaloosa

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