S.-L. Chen

The PANDAT software package and its applications

Abstract PANDAT is a software package for multicomponent phase diagram calculation. Given a set of thermodynamic parameters for all phases in a system and a set of user constraints, PANDAT automatically calculates the stable phase diagram without requiring either prior knowledge of the diagram or special user skills. The features of PANDAT are discussed and some application examples presented. In addition to PANDAT, its calculation engine, PanEngine, is also discussed.

On the calculation of multicomponent stable phase diagrams

In a thermodynamic system, a stable phase diagram is uniquely determined by the thermodynamic parameters of each phase. A generalized phase equilibria calculation software package should enable the calculation of the phase diagram from the parameters automatically, without requiring either prior knowledge of the diagram or special user skills. Improvements to the existing software packages have been achieved in the new software package PANDAT. The approach used in this software is described briefly and some examples of its advantages are given.

A thermodynamic approach for predicting the tendency of multicomponent metallic alloys for glass formation

Abstract A thermodynamic approach has been used to predict the compositions of Zr–Ti–Cu–Ni alloys exhibiting low-lying-liquidus surfaces which favor glass formation. The idea is to build on all thermodynamic information from the lower order constituent binaries and ternaries to obtain the thermodynamic properties of the multicomponent alloys. These thermodynamic properties enable us to predict those alloy compositions with low-lying-liquidus surfaces. The predicted quaternary alloy compositions compare favorably with those determined experimentally for bulk glass formation. These results demonstrate that this approach can be used as a valuable tool for predicting alloy compositions of multicomponent systems as potential materials for glass formation.

Calculated phase diagrams of aluminum alloys from binary Al-Cu to multicomponent commercial alloys

Abstract More than three decades have passed since the publication of Alan Prince’s book on multicomponent phase equilibria. The most significant development in this time has been the use of a combined computational/experimental approach to calculate multicomponent phase diagrams. This has led to important advances in the design and processing of structural and functional materials for practical applications. In this paper, we present a few examples focusing on aluminum alloys from the classical Al–Cu binary to multicomponent alloys with a view toward practical applications.

Computational and experimental investigation of microsegregation in an Al-rich Al–Cu–Mg–Si quaternary alloy

Abstract A new micromodel was developed to predict the microstructure and microsegregation in multicomponent alloys during dendritic solidification. The micromodel was directly coupled with multicomponent phase diagram calculations using a user friendly and robust phase diagram calculation engine—PanEngine. Solid back diffusion, undercooling and coarsening effects were included in this model, and the experimentally measured cooling curves were used as the inputs to carry out the microsegregation calculations. Microsegregation in Al–4.5 wt%Cu–1 wt%Si–0.5 wt%Mg alloy was experimentally investigated from directional solidification and electron probe microanalysis. Calculated results using this model are in accord with the experimental data, while results from the Scheil model deviate significantly from the experimental data.

Phase equilibria of the cu-in system II: Thermodynamic assessment and calculation of phase diagram

The phases in the Cu-In binary were modelled thermodynamically using the Redlich-Kister expression for the Gibbs energies of the solution phases, the Wagner-Schottky model for those of the η (η)’)-Cu2ln phase (taking η and η)’ to be a single phase), and assuming line compound behavior for the other intermetallic phases. The model parameters were obtained using primarily the thermodynamic data, as well as the phase equilibrium data. The thermodynamic values for the various phases calculated from the models are in reasonable agreement with the experimentally determined thermodynamic data that are available in the literature. The entropies of melting for the intermetallic phases obtained from the models are in accord with the values calculated from the empirical formulas suggested by Kubaschewski.The calculated phase diagram is also in reasonable agreement with the experimentally determined diagram, with the calculated temperatures for all the invariant equilibria within 1°C of the experimental values. The discrepancies between the calculated and experimental phase boundaries at the invariant temperatures are less than 1 at.% except those involving βCu4Inn and γCu7ln3. These two phases were taken to be line compounds in the present study, although experimentally they exist over appreciable ranges of homogeneity.

Thermodynamic properties of the Al–Nb–Ni system

Abstract This paper provides a consistent thermodynamic data set for the whole Al–Nb–Ni ternary system via thermodynamic modeling. The order/disorder transitions between disordered bcc_A2 and ordered bcc_B2 phases as well as between disordered fcc_A1 and ordered L1 2 phases are treated using a two-sublattice model. The calculations indicate that the disordered and ordered phases can be described with a single equation. All of the experimental phase diagram data available from the literature are critically reviewed and assessed using thermodynamic models for the Gibbs energies of individual phases. Inconsistent experimental information is identified and ruled out. Optimal thermodynamic parameters are then obtained by considering reliable literature data. Comprehensive comparisons between the calculated and measured phase diagrams show that almost all the accurate experimental information is satisfactorily accounted for by the present thermodynamic description.

Modeling solidification of turbine blades using theoretical phase relationships

The solidification of hot-stage turbine blades made from René N4 nickel-base superalloy has been modeled to show the morphology of porosity and the local changes in solute concentration. The key task of the present study was the calculation of the solid-liquid phase equilibria of this 9-component nickel-base superalloy from the thermodynamic values of these phases. The Gibbs energies of the solid and liquid phases were obtained from those of the 36 binaries using the Muggianu and Kohler methods of extrapolation. The phase equilibrium data were then used to compute the change in fraction solid with temperature, initially using the complete mixing approximation (Scheil equation). The predicted freezing range was somewhat longer than measured. A modified Scheil equation was derived assuming incomplete mixing. Assuming 60 pct mixing of the solute, the calculated freezing range agreed with experiments. Fraction solid temperature allowed the detailed morphology of the“mushy”zone to be predicted. Using measured dendrite spacings and assuming the crystals to grow in a cubic array, the shape of the crystals and, consequently, the size of the liquid channels were predicted as a function of position. Hence, computation of the rate of fluid flow in the channels (from the known changes of temperature with time) allowed the pore morphology to be inferred.

Some problems arising from two sublattice modelling of ordered phases

Abstract Although two (or effectively two) sublattice modelling of ordered phases has been the norm in carrying out phase diagram assessments, it is argued that this kind of modelling should, in general, be discouraged for these phases. Two-sublattice modelling gives a Gibbs energy minimum (with reference states at the same temperature and with the same parent structure as the ordered phase) for every ordered phase, irrespective of its composition. In doing so, it fails to take into account that at most ordered phase compositions there are only kinks and not minima in the Gibbs energy-composition curve with respect to these reference states. Kinks can be obtained if the ordered phases are modelled with more than two sublattices. Because of the incorrect shape of the Gibbs energy-composition curve when two-sublattice modelling is used, there is an excessive but unnecessary demand on the sublattice L parameter terms in the excess Gibbs energy for the fitting of experimental results. This often leads to unreliable extrapolations of the Gibbs energy-composition curves.

Thermodynamic Analysis for the Solid-State Amorphization and Subsequent Crystallization of GaAs/Co

Phase equilibria along the CoGa-CoAs join were determined by DTA and metallography. On the basis of these data and the phase diagram of Co-Ga-As at 600 °C, thermodynamic values for the various phases along the GaAs-Co join were estimated. The Gibbs energy of the amorphous phase is approximated to be that of the supercooled liquid phase. These data were used to rationalize the amorphization process.