Fanyou Xie

Diffusion coefficients of some solutes in fcc and liquid Al: critical evaluation and correlation

The diffusion coefficients of several transition elements (Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn) and a few non-transition elements (Mg, Si, Ga, and Ge) in fcc and liquid Al are critically reviewed and assessed by means of the least-squares method and semi-empirical correlations. Inconsistent experimental data are identified and ruled out. In the case of the elements, for which plentiful experimental data are available in the literature, the least-squares analysis gives rise to the activation energies and pre-exponential factors in an Arrhenius equation. For the elements with limited experimental data or no data at all, the diffusion parameters are estimated from two semi-empirical correlations. In one correlation, the logarithmic pre-exponential factors are plotted against the activation energies for various elements in Al. In the other correlation, the activation energies are shown as a function of valences relative to Al. The diffusion coefficients calculated by using the evaluated diffusion parameters agree reasonably with the reliable experimental data. The proposed semi-empirical correlations are used to predict the diffusion coefficients of a few elements in liquid Al. A satisfactory agreement between the predicted and measured diffusion coefficients is obtained.

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.

Phase diagram calculation: past, present and future

The past, present and future of phase diagram calculations for multicomponent alloys are reviewed and assessed. The pioneering studies of Van Laar and Meijering in the first half of the 20th century led to the use of phase equilibrium information as a supplement to single phase thermodynamic property data in these calculations. The phenomenological modeling or the Calphad approach is the primary focus of this review due primarily to its great success in calculating multicomponent phase diagrams for technological applications. In this approach, thermodynamic descriptions of multicomponent alloys are obtained by appropriate extrapolations of descriptions obtained for the lower order systems, viz., the constituent binaries and ternaries. Some shortcomings of the Calphad route to obtaining phase diagrams are pointed out. These include (a) the inability of first generation software to always automatically calculate the stable phase diagram of a system given a thermodynamic description and (b) the use of some inappropriate thermodynamic models, particularly those used for ordered phases. The availability of second generation software eliminates the first shortcoming and a physically more realistic model, the cluster/site approximation, has been formulated which is more suitable for describing the thermodynamics of ordered alloys. The results obtained to-date using the new software and the new model open up new avenues for calculating more reliable multicomponent phase diagrams for technological applications.

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.

Microsegregation in Al–4.5Cu wt.% alloy: experimental investigation and numerical modeling

Abstract Microsegregation in Al–4.5 wt.%Cu alloy was investigated experimentally using directional solidification and electron probe microanalysis (EPMA). The degrees of dendrite tip undercooling were measured for growth rates from 0.0038 to 0.2 mm s−1 with a temperature gradient of 50°C cm−1 at the liquid–solid interfaces. A modified Scheil model incorporating back diffusion, undercooling and dendrite arm coarsening was used to calculate the degrees of microsegregation. The partition coefficients obtained from the thermodynamic models of the solid and liquid phases and the measured cooling curves were used as the inputs to carry out the microsegregation calculation. While the calculated results using the Scheil model deviate significantly from the experimental data, those from the modified Scheil model are much better. Out of the three geometrical models, i.e. plate, sphere and cylinder, to approximate the shapes of the dendrites, the sphere is the best. However, the calculated results using the spherical model is near accord with the data for small fractions of solids and those using the cylinder is better at large fractions of solids. Two different thermodynamic descriptions of the Al–Cu system were used to demonstrate the importance of reliable phase diagram data in studying the degree of microsegregation.

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.

Thermodynamic description of the Al-Fe-Mg-Mn-Si system and investigation of microstructure and microsegregation during directional solidification of an Al-Fe-Mg-Mn-Si alloy

Abstract The thermodynamic database for the Al –Fe–Mg–Mn– Si system is developed based on the constituent binary, ternary, and quarternary systems. The computed phase diagrams agree well with the experimental data. The obtained database is used to describe the solidification behavior of Al 356.1 (91.95Al–0.46Fe–0.3Mg–0.32Mn–6.97Si, in wt.%) and Al 356.2 (92.77Al–0.08Fe–0.35Mg–6.8Si, in wt.%) under equilibrium and Gulliver–Scheil non-equilibrium conditions. The reliability of the established thermodynamic database is also verified by the good agreement between calculation and experiment for both equilibrium and Gulliver–Scheil non-equilibrium solidifications. Microstructure and microsegregation of the directionally solidified Al 356.1 alloy are investigated with a growth rate of 0.04445 cm s–1 and a temperature gradient of 45 K cm–1. Fractions of solids formed are measured by using quantitative image analysis of back-scattered electron, and solute redistribution in the primary (Al) is determined by means o...

Vacancy concentrations in the B2 intermetallic phase PdIn at 900°C

Abstract X-ray and bulk densities of PdIn were determined. These measurements were made at room temperature on samples annealed at 900°C and quenched in water/ice mixtures. On the basis of these measurements, the vacancy concentrations in this intermetallic phase were obtained. These data can be described quantitatively by a thermodynamic model derived from the existence of triple-defects in the lattice. The vacancy data show that the predominant point defects in PdIn are not of the Schottky type as reported in a recent publication. However, they are consistent with the triple-defect type which exists in many similar intermetallic phases such as NiAl.

Predicting Microstructure and Microsegregation in Multicomponent Aluminum Alloys

Accurate predictions of microstructure and microsegregation in metallic alloys are highly important for applications such as alloy design and process optimization. Restricted assumptions concerning the phase diagram could easily lead to erroneous predictions. The best approach is to couple microsegregation modeling with phase diagram computations. A newly developed numerical model for the prediction of microstructure and microsegregation in multicomponent alloys during dendritic solidification was introduced. The micromodel is directly coupled with phase diagram calculations using a user-friendly and robust phase diagram calculation engine-PANDAT. Solid state back diffusion, undercooling and coarsening effects are included in this model, and the experimentally measured cooling curves are used as the inputs to carry out the calculations. This model has been used to predict the microstructure and microsegregation in two multicomponent aluminum alloys, 2219 and 7050. The calculated values were confirmed using results obtained from directional solidification.