The paper presents the possibility of application of the developed computer script which allows the assessment of non-equilibrium

solidification of binary alloys in the ThermoCalc program. The script makes use of databases and calculation procedures of the POLY-3

module. A solidification model including diffusion in the solid state, developed by Wołczyński, is used to describe the non-equilibrium

solidification. The model takes into account the influence of the degree of solute segregation on the solidification process by applying the

so-called back-diffusion parameter. The core of the script is the iteration procedure with implemented model equation. The possibility of

application of the presented calculation method is illustrated on the example of the Cr-30% Ni alloy. Computer simulations carried out

with use of the developed script allow to determine the influence of the back-diffusion parameter on the course of solidification curves,

solidus temperature, phase composition of the alloy and the fraction of each phase after the solidification completion, the profile of solute

concentration in liquid during solidification process, the average solute concentration in solid phase at the eutectic temperature and many

other quantities which are usually calculated in the ThermoCalc program.

A numerical model of binary alloy crystallization, based on the cellular automaton technique, is presented. The model allows to follow the

crystallization front movement and to generate the images of evolution of the dendritic structures during the solidification of a binary

alloy. The mathematic description of the model takes into account the proceeding thermal, diffusive, and surface phenomena. There are

presented the results of numerical simulations concerning the multi-dendritic growth of solid phase along with the accompanying changes

in the alloying element concentration field during the solidification of Al + 5% wt. Mg alloy. The model structure of the solidified casting

was achieved and compared with the actual structure of a die casting. The dendrite interaction was studied with respect to its influence on

the generation and growth of the primary and secondary dendrite arms and on the evolution of solute segregation both in the liquid and in

the solid state during the crystallization of the examined alloy. The morphology of a single, free-growing dendritic crystal was also

modelled. The performed investigations and analyses allowed to state e.g. that the developed numerical model correctly describes the

actual evolution of the dendritic structure under the non-equilibrium conditions and provides for obtaining the qualitatively correct results

of simulation of the crystallization process.

A similarity solution for conduction dominated solidification of a dilute binary isomorphous alloy has been developed. The effect solidification due to density change during phase transformation has been highlighted and investigated in detail. The governing equations for solid, liquid and mushy phase has been proposed, taking into account the effect of shrinkage or expansion due to density change during phase change. The thermo-physical properties (thermal conductivity and specific heat), equilibrium temperature and phase fraction are evaluated within the mushy zone using averaging technique. The effect of equilibrium and non-equilibrium solidification is investigated using Lever and Scheil’s rule models respectively. In addition, the effect of boundary and initial temperature on solidification behavior of the alloy is also addressed. It has been observed that the interface (liquidus and solidus) moves faster with increase in density ratio and decrease in boundary and initial temperature. No major changes in temperature distribution and interface position has been observed with variation partition coefficient and microscale behavior model (Lever rule and Scheil’s rule).