Paper 1.9

ESTPHAD – a new and fast way to reproduce the results of CALPHAD calculations during simulation of phase transformations

Roósz A¹, Kaptay G.²

University of Miskolc. Faculty of Materials and Metallurgical Engineering

¹Department of Physical Metallurgy, ²Department of Physical Chemistry

The knowledge of equilibrium phase diagrams is necessary for the simulation of the phase transformations, such as solidification.  It is very difficult to use the phase diagrams determined by any experimental method (by thermal analysis, for example) because these diagrams are usually published in a graphical way. Moreover, in the case of three or more components, the partition coefficients can not be taken from ternary, or multi-component phase diagrams. 

The equilibrium phase diagrams, calculated by a CALPHAD software provide a better possibility, as both equilibrium temperatures and the partition coefficients are calculated numerically. The only disadvantage of a CALPHAD software, used as a sub-routine for a phase transformation simulation, is the long calculations times, being much higher compared to the phase transformation simulation software, itself.

In this lecture a new and simple method will be presented, allowing a fast reproduction of the transformation temperatures and the partition coefficients during simulation of phase transformations. The method is called by us ESTHPAD (Estimation of Phase Diagrams). ESTHPAD can use measured phase diagrams, or preferably data-files, calculated by a CALPHAD software, as initial data. The ESTHPAD algorithm is based on the same thermodynamic principles, as CALPHAD, except that the iteration steps are avoided by simplifying the original equations, using polynomials. The ESTHPAD algorithm is built in a hierarchical way: the coefficients obtained from the binary systems are used to describe the ternary systems, with some additional coefficients, being specific for the given ternary system, etc. The ESTPHAD algorithm is about 100 times faster compared to the CALPHAD algorithm.

The concentration dependence of an equilibrium temperature of phase transformation (T), based on the known value for a pure component A (T_A), and the partition coefficient of component J in the A-B-C-..J..-..-N system are calculated in the framework of the ESTPHAD algorithm by the following equations:

                                             (1) 

                        (2)

where  

,  are polynomials determined from the known AB and AC binary systems,

 and  are polynomials,  determined from the ternary ABC and from the n-component

 ABC…N systems,

 - the logarithm of the partition coefficient of component J in the AJ binary system, described by a

 polynomial,

,  …  are the additional polynomial terms, to be determined from the appropriate systems.

The application of the ESTPHAD algorithm to the data files, calculated by a CALPHAD software will be presented for the Al-Cu-Si and the Al-Si-Mg systems.