PanEngine for Thermodynamic Calculation
In Pandat, thermodynamic calculations are all performed by PanEngine. In
the CALPHAD approach the Gibbs energies of phases in an alloy system are
described by different thermodynamic models such as the random
substitutional solution model, the stoichiometric compound model and the CEF.
In addition to these commonly used models, PanEngine can also deal with both
ideal and non-ideal gases, the ionic liquid model, the associate solution
model, the CEF with ionic species and the more advanced Cluster/Site
Approximation (CSA).
In order to solve the phase equilibrium problem for a multi-component
system, minimization of the Gibbs energy functions described with different
thermodynamic models is a pre-requisite. However, due to the possible
presence of multiple solutions and the complexity of the models, the
algorithms available in most commercial software packages provide no
guarantee of obtaining the correct solution for the general phase
equilibrium problem. This situation is exaggerated if a more complicated
model such as the CEF with ionic species or the CSA is used in a
multi-component system. Faced with this problem, special global optimization
algorithms were implemented in PanEngine with great successes. For more
information, please refer to [2002Che
]
for discussions of this topic and [2008Cao
]
for recent improvements and benchmarks of the algorithms.
A number of examples are given as follows (diagrams from
2008Cao
).
Figure 1. PANDAT point calculation results of alloy 625
(a) in a list table and (b) in a grid table (customizable); an extended grid
table is automatically generated by a PANDAT point calculation.
Figure 2. Line calculation results of alloy 718 from 1500C
to 600C.
Figure 3. The calculated binary Ni-Al phase diagram.
Figure 4. The calculated isopleth for Ni-Al-Pt system with
the mole fraction of Pt being fixed at 0.05.
Figure 5. The calculated isothermal section for Ni-Al-Ru
system at 1523K compared with the experimental data.
Figure 6. The liquidus projection for Ni-Al-Ir system.
Figure 7. The calculated solidification paths for a
niobium alloy (Nb-22Ti-2Hf-4Cr-3Al-16Si in at%) using PANDAT under Lever
Rule and Scheil conditions.
Figure 8. The calculated binary Fe-O phase diagram.
Figure 9. The calculated isothermal section of Fe-Cr-O
system at 1573 K.
Figure 10. The calculated stability diagram of Fe-Cr-O
system at 1573 K.