A self-consistent model for predicting interaction parameters in multicomponent alloys

Several models have been proposed to predict interaction parameters in multicomponent alloys from the physical characteristics of constituent elements. But all these models are not self-consistent, i.e., they do not meet the basic requirement of the reciprocal relation, ε _i ^j =ε _j ⁱ , automatically. In this article, a new and self-consistent model is proposed by coupling Chou’s geometric solution model with Miedema’s model on the enthalpy of mixing for binary alloys. The new model is applied to the calculation of interaction parameters in a large number of iron-based alloys, and the agreement between calculation and experimental data is found to be reasonable.     

The unified interaction parameter formalism: Thermodynamic consistency and applications

In a recent article, we proposed modifications to the standard interaction parameter formalism. The modified formalism, known as the “Unified Interaction Parameter Formalism,” is discussed in the present article with respect to thermodynamic consistency at finite concentrations in binary, ternary, and multicomponent systems. A new method, which is independent of integration paths, is proposed to derive the equations of the formalism by differentiation of the integral Gibbs energy expression. It is shown that the formalism is thermodynamically exact in both dilute and nondilute composition regions. It is also shown that the formalism reduces to Wagner’s formalism at infinite dilution and to Darken’s quadratic formalism in dilute solutions. Examples are presented and methods are discussed for determining the parameters of the formalism from thermodynamic data.     

A model for calculating interaction coefficients between elements in liquid and iron-base alloy

A new model for predicting ln γ _i ⁰ and an activity interaction coefficient ɛ _i ^j has been proposed by use of free volume theory, Miedema’s semiempirical formation enthalpy model for binary alloys, and the Toop model. The results calculated are in good agreement with experimental values except for the systems which contain nitrogen and hydrogen gas elements.     

Evaluation of the methods for calculating the concentration-dependent diffusivity in binary systems

Boltzmann and Matano developed a procedure for the solution to Fick’s second law when the diffusivity is a function of concentration. The procedure requires the determination of the so-called Matano interface. The accuracy of the resulting solution depends heavily on the precise location of the Matano interface, the determination of which is laborious and often inaccurate. Three alternative procedures by Sauer and Freise, Wagner, and den Broeder, modifications to the original Boltzmann-Matano (B-M) method, were developed such that the diffusivity can be calculated without having to determine the location of the Matano interface. However, none of these derivations quantifies the extent to which the modified methods arrive at the same result as that obtained from the standard B-M analysis. This article serves to apply the B-M method, and the modification suggested by den Broeder, to various analytical concentration profiles containing different degrees of noise and to compare the results quantitatively. In addition to these analytical functions, concentration profiles obtained from interdiffusion experiments were studied. The two methods are shown to be equivalent in terms of the accuracy of the result. The advantages or disadvantages of one method over the other are illustrated with examples.     

On the gibbs energy interaction parameters of oxygen and nitrogen in liquid alloys

A number of theoretical models reported in the literature for predicting the values of the Gibbs energy interaction parameters of oxygen and nitrogen in liquid alloys is briefly reviewed. The validity of these models is tested using the large number of experimental data available in the literature. It is found that the Wagner model together with the correlations proposed by Chang and coworkers predict values in best agreement with the experimental values. Formerly Graduate Research Assistant, Materials Department, College of Engineering and Applied Science, University of Wisconsin-Milwaukee     

A nonmetal interaction model for the segregation of trace metals during solidification of Fe-Ni-S,Fe-Ni-P,and Fe-Ni-S-P alloys

As nonmetals are added to the Fe-Ni system, segregation coefficients(k) of trace constituents change dramatically. For example, as the S content of the metallic liquid increases from 0 to ≈31 wt pct, the molar k(Ge) between solid and liquid metal increases from 0.6 to ~120. Little of this change can be ascribed to temperature. Also, these changes are not linear. In the case of the Fe-Ni-S system, the largest changes are seen between 20 and 30 wt pct S. Here we present a model for the interaction of nonmetals with other species in metallic systems. The model assumes that the nonmetal either repels or attracts tracers (E) in the metallic liquid, causing those tracers to either segregate strongly into the solid metal or to have enhanced solubility in the liquid. Examples of both types of behavior are given. The model predicts that the activity coefficient of the tracer (γ_E) should correlate linearly with (1 - αnX_N @#@), where X_N is the mole fraction of the nonmetal in the metallic liquid,n is a stoichiometry factor related to the speciation of N in the liquid, and a is a constant. Indeed, good linear correlations of n(k) vs n (1 -αnX_N @#@) are found for all elements where there is a measurable effect. Thus, if the composition of the metallic liquid is known, a segregation coefficient of a trace constituent may be pre-dicted— even if the temperature, exact Fe/Ni ratio, and information about the activity coef-ficient in the solid phase are unknown. The nonmetal interaction model presented here can be related to more traditional methods of modeling activity coefficients(i.e., power law expan-sions) and can be shown to be a special case of this type of parameterization. Comparison of model predictions of first-order (sulfur-E) interaction coefficients (ε) to measured values yields acceptable agreement for some elements, such as P and Ge, and all elements except Ni agree to within a factor of 3. The predictive model described above, based on equilibrium experi-ments, may be used to evaluate the segregation coefficients extracted from the dynamic (“plane front solidification”) experiments of Sellamuthu and Goldstein.^[10,11] Contrary to claims, reliable segregation coefficients are not extractable from dynamic experiments.     

Quasicrystals,crystals and multiply twinned particles: A unified growth model

A recursive (R) quasicrystal growth model which unifies existing theories, including multiple twinning is presented. The model generates infinite, space-filling structures reproducing the structure of observed quasicrystals, crystals, multiply twinned particles and predicts the possible existence of incommensurate structures not observed yet. The R model is generalization of the crystal case where the structure is generated by periodic translations of the unit cell into any of its points. For quasicrystals, the unit cell is replaced by a star vector with icosahedral or decagonal symmetry and displacements are restricted to points belonging to the Coincidence Site (Quasi) Lattice.     

A unified resistor-capacitor model for impedance, dielectrophoresis, electrorotation, and induced transmembrane potential

Dielectric properties of suspended cells are explored by analysis of the frequency-dependent response to electric fields. Impedance (IMP) registers the electric response, and kinetic phenomena like orientation, translation, deformation, or rotation can also be analyzed. All responses can generally be described by a unified theory. This is demonstrated by an RC model for the structural polarizations of biological cells, allowing intuitive comparison of the IMP, dielectrophoresis (DP), and electrorotation (ER) methods. For derivations, cells of prismatic geometry embedded in elementary cubes formed by the external solution were assumed. All geometrical constituents of the model were described by parallel circuits of a capacitor and a resistor. The IMP of the suspension is given by a meshwork of elementary cubes. Each elementary cube was modeled by two branches describing the current flow through and around the cell. To model DP and ER, the external branch was subdivided to obtain a reference potential. Real and imaginary parts of the potential difference of the cell surface and the reference reflect the frequency behavior of DP and ER. The scheme resembles an unbalanced Wheatstone bridge, in which IMP measures the current-voltage behavior of the feed signal and DP and ER are the measuring signal. Model predictions were consistent with IMP, DP, and ER experiments on human red cells, as well as with the frequency dependence of field-induced hemolysis. The influential radius concept is proposed, which allows easy derivation of simplified equations for the characteristic properties of a spherical single-shell model on the basis of the RC model.     

Integral treatment for the representation of thermodynamic properties in multicomponent systems using interaction parameters

The partial thermodynamic functions of the solvent component of a ternary system have been deduced in terms of the interaction parameters by integration of several series which emerge from the Maclaurin infinite series based on the integral property of the system and subjected to appropriate boundary conditions. The series integration shows that the resulting partial functions are suitable for interpreting the thermodynamic properties of the system and are independent of compositional paths. In the present analysis, the higher order terms of these series are found to make insignificant contributions. Formerly Visiting Professor, Technical University Berlin     

Diffusion parameters of metal and alloys

Conclusions On the basis of general laws of motion and statistical regularities, a formula has been derived for the diffusion coefficient which is in good agreement with the well-known Dushman-Langmuir formula allowing for entropy of activation.An attempt has been made to elucidate the physical meaning of the preexponential factor D₀ and energy of activation A. The preexponential factor D₀ represents the averaged specific action of an elementary displacement of a diffusing atom and energy of activation A the averaged value of energy in the action of one mole of the diffusing substance.Translated from Poroshkovaya Metallurgiya, No. 8 (68), pp. 56–59, August, 1968.     

超高强铝合金铸造技术及装备控制系统的发展

超高强铝合金是是世界各国航空航天工业中的重要结构材料,随着现代航空航天工业的快速发展,已研制开发出多种使用性能很好的新型超高强铝合金.重点阐述了超高强铝合金铸造技术及装备控制系统的发展现状.     

A unified model of microsegregation and coarsening

Using a coordinate transform in a standard microsegregation model it is shown that the effect of coarsening on the dilution of the liquid phase can be accounted for by adding a dimensionless parameter α ^c to the back-diffusion Fourier number. Through theory, for the case of parabolic growth, and numerical experiments for the constant cooling rate, it is shown that a constant value of α ^c =0.1 is a sound choice across a wide range of casting and alloy conditions. This finding allows for the development of a unified model for microsegregation and coarsening. In particular, previous approximate microsegregation models can be readily modified to account for coarsening.     

Solidification parameters,microstructures, and mechanical properties of rapidly solidified iron-based alloys

Cooling rate measurements were carried out using a computer controlled melt spinning unit for the production of rapidly solidified Fe 6.3 wt.% Si and Fe 3.2 wt.% C melt spun ribbons employing a wide range of process parameters. The cooling rates are mainly a function of the ribbon thickness, and are independent of the alloy composition and wheel material. The resulting microstructures have been characterized by light optical and electron microscopy (SEM and TEM) investigations and were found to be influenced by the cooling conditions during and after solidification. Grain sizes and secondary dendrite arm spacings are related to the cooling rates by means of exponential relationships. In addition to this, rapidly solidified eutectic Fe 4.2 wt. %C alloy powder was produced by argon melt-atomization. Powder particles of 20 μm to 80 μm size solidified microcrystalline and exhibit cementite, metastable γ-phase, and martensite. The cementite matrix is of dendritic structure. After consolidating the powder by hot pressing below A, the microstructure changes to the fine equiaxed grains containing about 66 Vol.% Fe₃C and a dispersoid of ferrite ≤1 μm within the cementite matrix. This material exhibits high tensile strength and wear resistance at room temperature. At elevated temperatures in the region between 650°C and 750°C, and at strain rates of ε ? 10^?4s^?1 the fine grained ceramic-like material reveals superplastic behaviour.     

Thermochemistry of binary liquid gold alloys: The systems Au-Ni,Au-Co,Au-Fe,and Au-Mn

In this paper we report enthalpy of mixing data for the liquid alloys of gold with manganese, iron, cobalt, and nickel obtained by a Calvet-type calorimeter at 1378 K. The enthalpies of mixing are compared with Gibbs energies calculated from earlier emf and vapor pressure studies to yield information on the excess entropies of mixing. The limiting enthalpies of solution of the liquid transition metals in liquid gold are compared with values predicted from the semi-empirical model of Miedemaet al. and with earlier data for the same transition metals in liquid copper. The calculated values of the excess entropy of solution in liquid gold are compared with the corresponding values in liquid copper near 1400 K. For Ni, Co, and Fe as solutes we observepositive shifts of 5 to 9 J K⁻¹ mol⁻¹ which are attributed to vibrational entropy terms. For Mn there is a strongnegative shift of about 35 J K⁻¹ mol⁻¹. This shift probably is due to “complex” or “associate” formation between gold and manganese atoms.     

Mass spectrometric determination of activities for alloys with complex vapor species: Bi-Pb and Bi-Tl

For solutions from which complex species vaporize (Bi₂, Si₂, Al₂O, Sb₄, and so forth) new methods of determining the thermodynamic properties from mass spectrometric data are demonstrated. In order to test the feasibility of these new techniques, experiments have been carried out on the liquid Bi-Pb and Bi-Tl systems for which adequate thermodynamic data are available. In evaluating the thermodynamic properties, the ion current ratiosI _Pb ⁺/IBi₂/+ andI _Tl ⁺/IBi₂/+ were employed,e.g. $$\log {\text{ }}\gamma _{{\text{Bi}}} {\text{ = - }}\mathop {\int {\frac{{N_{Pb} }}{{1{\text{ + }}N_{Pb} }}d} }\limits_{N_{Bi} = 1}^{N_{{\text{Bi}}} = N_{Bi} } {\text{ }}\left\{ {{\text{log}}\frac{{{\text{1}}_{{\text{Pb}}}^{\text{ + }} {\text{ }}N_{Bi}^2 }}{{I_{Bi2}^ + {\text{ }}N_{Pb} }}} \right\}$$ Measuring these particular ion current ratios eliminates errors resulting from the fragmentation of the complex vapor species in evaluating the thermodynamic properties. A dimer-monomer technique, which corrects for fragmentation, was also demonstrated. The results using these two independent approaches are in good agreement with each other as well as with previous investigations. The activity coefficients in both systems adhere to the quadratic formalism over large composition ranges,e.g. $$\begin{gathered} \log {\text{ }}\gamma _{{\text{Pb}}} {\text{ = - 0}}{\text{.255 }}N_{Bi}^2 {\text{ }}N_{{\text{Bi}}} {\text{< 0}}{\text{.8}} \hfill \\ \log {\text{ }}\gamma _{{\text{Tl}}} {\text{ = - 0}}{\text{.805 }}N_{Bi}^2 {\text{ }}N_{{\text{Bi}}} {\text{< 0}}{\text{.7}} \hfill \\ \end{gathered} $$      

A comparison of the molecular interaction volume model with the subregular solution model in multicomponent liquid alloys

The molecular interaction volume model (MIVM) is a two-parameter model, meaning it can predict the thermodynamic properties in a multicomponent liquid alloy system using only the coordination numbers calculated from the ordinary physical quantities of pure liquid metals and the related binary infinite dilute activity coefficients, γ _∞ ⁱ and γ _∞ ^j , which avoids somewhat adjustable fitting for the binary parameters of B _ji and B _ij. In comparison with the subregular solution model (SRSM), the prediction effect of the MIVM is of better stability and safety because it has a good physical basis.