A mathematical model of solidification of an iron-based binary alloy (Fe-C) modified with nanosize high-refractory particles is proposed. The processes of alloy heterogeneous nucleation on the surface of nanosize particles and those of alloy crystallization in a cylindrical mold are described. For liquidus temperature, a linear approximation of the concentration of dissolved carbon is adopted; the law of change of this temperature obeys the non-equilibrium lever rule. The volume of the solid phase formed around a nucleus during the crystallization determines the characteristic size of the grain structure in the solidified alloy. Numerical simulation of melt solidification in a cylindrical crucible was carried out, and the kinetics of heterogeneous nucleation and growth of the solid phase was analyzed. It was found that the conditions for nucleation and crystallization differ substantially within the casting. It is shown that, as the melt undergoes cooling, volume-sequential crystallization gets established.

提出了一种用纳米高难熔颗粒改性的铁基二元合金（Fe-C）凝固的数学模型。描述了在纳米颗粒表面上合金异质成核的过程以及在圆柱形模具中合金结晶的过程。对于液相线温度，采用溶解碳浓度的线性近似。该温度的变化规律遵循非平衡杠杆法则。在结晶过程中围绕核形成的固相的体积决定了凝固合金中晶粒结构的特征尺寸。进行了圆柱坩埚中熔体凝固的数值模拟，并分析了异相形核和固相生长的动力学。发现铸件内成核和结晶的条件基本上不同。结果表明，随着熔体的冷却，建立了体积顺序的结晶。