Y. A. Chang

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.

Thermodynamic Assessment and Calculation of the Ti-Al System

A thermodynamic description of the Ti-Al system has been developed. Three different analytical descriptions were used to describe the three different types of phases occurring in the Ti-Al system: the stoichiometric compounds, the disordered solution phases, and the ordered inter-metallic compounds which have homogeneity ranges. A least-squares technique was used to optimize the thermodynamic quantities of the analytical description using experimental data available in the literature. The calculated phase diagram, as well as the thermodynamic func-tions, agree well with the critically evaluated experimental data from the literature.

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.

Correlation of the hardness and vacancy concentration in FeAl

Abstract Microhardness measurements of FeAl containing 40–51 at.% Al were carried out at ambient temperature on specimens which had been subjected to different heat treatments. The hardness values for specimens heat-treated at 500°C and water-quenched to ambient temperature increase slowly with composition until at about 48 at.% Al. At higher Al concentrations the hardness values increase more rapidly. For specimens heat-treated at temperatures higher than 700°C and water quenched to ambient temperature, the hardness values increase with Al concentration with little change in slope through the entire composition range of 40–51 at.% Al. The compositional dependences of the hardness values are similar to those of the vacancy concentrations in FeAl. The vacancy concentrations as a function of Al composition were obtained from a thermodynamic model and experimental data at the stoichiometric composition. The close resemblance of the shapes of the hardness curve and the vacancy concentration curve suggests that the hardness and thus the yield strength may be related to the presence of vacancies in the lattice. This conclusion is further supported by the evidence that the hardness of FeAl increases with the square root of the vacancy concentration. This type of relationship agrees well with established point-defect strengthening models, based on the interaction of a moving dislocation with a point defect.

Temperature Dependence of the Elastic Constants of Cu, Ag, and Au above Room Temperature

The adiabatic elastic constants c44, ½(c11−c12), and ½(c11+c12+2c44) have been measured for copper, silver, and gold over the temperature range from 300° to about 800°K using the conventional ultrasonic pulse‐echo technique. The room‐temperature values of the stiffness coefficients are shown to be in acceptable agreement with previously published data for the noble metals. Over the entire range from 300° to 800°K, it is found that, to a remarkably good approximation, the elastic constants for all three metals decrease linearly with temperature. Additional evidence is presented to show that the linear temperature dependence of the elastic constants for silver extends to at least 1000°K, i.e., to within 80% of the absolute melting temperature. The isothermal compressibilities calculated from the elastic constant data are used to evaluate the dilational term in the specific heat, Cdil=Cp−Cv, and it is established that the approximate Nernst‐Lindemann relation for estimating Cdil is valid for Cu, Ag, and Au a...

Thermodynamics of intermetallic phases with the triple-defect B2 structure

Abstract A theoretical model is developed which predicts the compositional dependence of the thermodynamic properties of intermetallic phases exhibiting the triple-defect B2 structure. This type of structure is typically formed between elements of Group VIIIB (A metal) and elements of Group IIIA (B metal). For the thermodynamic activity of the components A and B, the following simple expressions are obtained: ( a A a A,0 ) = ( α z ) and ( a B a{B,0} ) = ( z α ) , where z is the vacancy concentration at any composition and α, the disorder parameter, is the vacancy concentration at the stoichiometric composition. For the partial enthalpy, the model predicts a step function, with essentially constant values of the partial enthalpy, below and above the stoichiometric composition. The defect concentration as a function of composition is given by the equation: z2(z − 2χ) = α3, where z is the vacancy concentration and (z − 2χ) 2 is the concentration of anti-structure atoms. The parameter, χ = xB − 0.5, expresses the deviation from stoichiometry. The model is applied to the following systems for which thermodynamic data are available: FeAl, CoAl, CoGa, NiAl, NiGa, RuAl, RuGa, RhAl, PdAl, PdIn, IrAl. It is found in general that the theoretical expressions for activity, partial enthalpy and vacancy concentration agree well with the experimental data. The values of the disorder parameter, α, range from 1.3 × 10−4 for CoAl to 4 × 10−2 for CoGa. An equation for the temperature dependence of the disorder parameter is given and a relationship between the enthalpy of formation and the disorder parameter is derived.

Thermodynamics and phase relationships of transition metal-sulfur systems: Part III. Thermodynamic properties of the Fe-S liquid phase and the calculation of the Fe-S phase diagram

An associated solution model is applied to describe the thermodynamic behavior of Fe-S liquid. This model assumes the existence of ‘FeS’ species in addition to Fe and S in the liquid. With two solution parameters for each of the binaries Fe-‘FeS’ and ‘FeS’-S, this model accounts for the compositional dependence of the thermodynamic properties of Fe-S liquid from pure Fe to pure S over a wide range of temperature. The binary Fe-S does not contribute significantly to the excess Gibbs energy of the liquid due to the rather small dissociation constant of ‘FeS’ to Fe and S. Using this model for the liquid phase and a defect thermodynamic model for the pyrrhotite phase, the Fe-S phase diagram is calculated. The calculated diagram is in excellent agreement with the experimental data, accounting for the range of homogeneity of pyrrhotite at all temperatures. Both the thermodynamic and phase diagram data are obtained from the literature.

A thermodynamic analysis of the NiAl system

Abstract Phase equilibrium and thermodynamic data of the binary NiAl system are analyzed using thermodynamic models. The liquid and fcc (γ) phases are treated as disordered solutions, the intermetallic compounds with appreciable ranges of homogeneity, i.e. γ′-(Ni3Al), B2-(NiAl) and Al3Ni2, are described by compound energy models, and the other intermetallic phases are taken to be line compounds. The phase equilibrium and thermodynamic properties calculated from the model parameters are in accord with most of the experimental data reported in the literature. For γ′-(Ni3Al) and B2-(NiAl), the model-calculated defect concentrations as functions of temperature and composition are in agreement with experimental data. In comparison to previous thermodynamic descriptions reported in the literature, the present one has fewer model parameters with more reasonable values. Despite this, the agreement between model-calculated thermodynamic values and phase boundaries and experimental data is as good as or better than that obtained in earlier studies.

The activity coefficient of oxygen in binary liquid metal alloys

The Wagner model with one energy parameter,h, for describing the effect of alloying elements on the activity coefficients of nonmetallic solutes in liquid metals is extended to have two energy parameters,h1andh2. The validity of both the Wagner one-parameter equation and the newly derived two-parameter equation is tested using data available in the literature for twelve ternary metal-oxygen systems. In order to have consistent thermodynamic data, all the relevant binary, as well as the twelve ternary metal-oxygen systems are evaluated using the same thermodynamic values for the reference materials which were used in carrying out the experimental measurements. It is found that the twoparameter equation is capable of quantitatively accounting for the compositional dependences of the activity coefficients of oxygen in all twelve ternary systems while the Wagner one-parameter equation is not. A correlation between the Wagner parameter,h, and the thermodynamic properties of the respective binary metal-oxygen and binary metals systems is found, from which the value of this parameter may be predicted without referring to any ternary data. Accordingly, the two-parameter equation is more useful in evaluating ternary experimental data while the Wagner one-parameter equation in connection with the correlation betweenh and binary data is capable of predicting ternary data without any experimental investigation in the ternary region. Based on the one-parameter and the two-parameter equations, theoretical equations for the first-order and second-order free energy interaction parameters,(∈0j)sand(ρ0j)s, are derived in terms of the model parameters. The values of(∈0j)s and(ρ0j)s for all the systems are derived and are found to vary linearly with the reciprocal of temperature. Furthermore, linear relationships between these two interaction parameters and their slopes with 1/T are found, from which the temperature dependence of the interaction parameters may be estimated in the absence of experimental data.

Point defect concentrations and hardening in binary B2 intermetallics

Point defect hardening in binary B2 intermetallic compounds with the anti-structure defect structure (FeCo and AuZn) and the triple defect structure (NiAl, FeAl, and CoAl) was investigated. Thermodynamic modeling combined with experimental measurements of lattice parameters and bulk densities were used to establish point defect concentrations as functions of composition and temperature. Microhardness measurements were made on samples of varying compositions and quenching temperatures. Solution hardening rates of vacancies were found to be significantly larger than those of anti-site defects. It was possible to relate the hardening rates of anti-site defects to the magnitude of the lattice dilation. This suggests that the elastic size effect was the primary hardening mechanism. No such correlation was found for vacancies.