Nizovtseva I G, Starodumov I O, Alexandrov D V
Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Ekaterinburg, 620000, Russia. Friedrich-Schiller-Universität Jena, Otto Schott Institute of Materials Research, D-07743 Jena, Germany.
J Phys Condens Matter. 2020 Jul 15;32(30):304003. doi: 10.1088/1361-648X/ab83b3. Epub 2020 Mar 26.
The process of directional crystallization with a quasi-equilibrium mushy region is considered in the steady-state conditions with allowance for the non-linear phase diagram. A complete analytical solution of model equations is found in a parametric form by introducing a new variable-the solid phase fraction in the mushy layer. The temperature and solute concentration, as well as the solid fraction in the mushy layer, its boundaries, and the crystallization velocity, are determined analytically. It is shown that a non-linear phase diagram substantially influences the behavior of solutions obtained.
在考虑非线性相图的稳态条件下，研究了具有准平衡糊状区的定向结晶过程。通过引入一个新变量——糊状层中的固相分数，以参数形式得到了模型方程的完整解析解。通过解析确定了温度、溶质浓度、糊状层中的固相分数、其边界以及结晶速度。结果表明，非线性相图对所得解的行为有显著影响。
