Thermodynamic analysis of the Zn−Pb−Cd system and interaction studies in ternary liquid dilute solutions

Dilute zinc solutions in the Zn−Pb−Cd system were investigated by an emf method with concentration cells to show the influence of variation in lead and cadmium concentrations on the zinc activity coefficients. Zinc concentrations were held in the mole fraction range 0.03≤X _Zn≤0.1 with measurements in the temperature range 714<T<877°K. The interaction parameters, ∈ _Zn ^Pb and ∈ _Cd ^Zn , were deduced from plots of (ln γ_Zn) _{X Zn→0} vsX _Pb. 3 The limiting values of zinc activity coefficients for other ternary systems previously investigated were analyzed using Krupkowski's method and the random solution model of Alcock and Richardson. Experimental data for ∈ ₁ ² and ∈ ₁ ³ (where 1=Zn and 2, 3 are components of investigated ternaries) are compared also with the values obtained from limiting activity coefficients of the particular binary systems.     

Lattice spacings and stacking fault probabilities in Ag−Cd−In alloys

Lattice spacing values in ternary Ag−Cd−In alloys containing 5 to 30 at. pct Cd and 5 to 15 at. pct In have been determined from X-ray powder patterns using the Nelson-Riley extrapolation procedure. The values are shown to lie, in a ternary plot, on iso-parameter lines obtained by joining equal lattice spacing values in the relevant binary alloys. The intrinsic stacking fault probabilities (α) in these alloys obtained from measurement of X-ray peak displacements are found to follow the empirical relation α=α₀ expk|ΔZ|p, where α₀ is the intrinsic fault probability in Ag, |ΔZ| is the weighted mean of solvent-solute valence differences,p is the combined solute content, andk is a constant approximately equal to 0.08 in agreement with the value found earlier for binary alloys based on silver.     

A thermodynamic study of copper-iron and copper-cobalt liquid alloys by mass spectrometry

The thermodynamic activities in the liquid Cu-Fe and Cu-Co binary systems were measured by a high temperature mass spectrometric technique. From the obtained data, the heats of mixing in the Cu-Co liquid binary were calculated. Both the Cu-Fe and Cu-Co systems are thermodynamically similar, with large positive deviations from ideality in the activities. The activity coefficients in the liquid Cu-Co system at 1823 K were found to be symmetrical and can be expressed by lnγ_Cu= 1.76X _Co ² The heat of mixing in the liquid Cu-Co system was found to be described by a cubic function δH_m = −17.9 _Co ³ − 7.6X _Co ² + 25.5_Co (kJ/mol) The activity coefficients in the liquid Cu-Fe system at 1873 K were found to satisfy two quadratic formalisms in the binary In γ_Cu = 2.10X _Fe ² − 0.13 0.65 ≤X _Fe ≤ 1 In γ_Fe = 1.79X _Cu ² + 0.04 0 ≤X _Fe ≤ 0.65     

Activities in the spinel solid solution Fe X Mg1−X Al2O4

Activities in the spinel solid solution Fe _X Mg_1−X Al₂O₄ saturated with α-Al₂O₃ have been measured for the compositional range 0<X<1 between 1100 and 1350 K using a bielectrolyte solid-state galvanic cell, which may be represented as Pt, Fe + Fe _X Mg_1−X Al₂O₄+α-Al₂O₃//(Y₂O₃)ThO₂/(CaO)ZrO₂//Fe + FeAl₂O₄+α-Al₂O₃, Pt Activities of ferrous and magnesium aluminates exhibit small negative deviations from Raoult’s law. The excess free energy of mixing of the solid solution is a symmetric function of composition and is independent of temperature: ΔG ^E=−1990 X(1−X) J/mol. Theoretical analysis of cation distribution in spinel solid solution also suggests mild negative deviations from ideality. The lattice parameter varies linearly with composition in samples quenched from 1300 K. Phase relations in the FeO-MgO-Al₂O₃ system at 1300 K are deduced from the results of this study and auxiliary thermodynamic data from the literature. The calculation demonstrates the influence of intracrystalline ion exchange equilibrium between nonequivalent crystallographic sites in the spinel structure on intercrystalline ion exchange equilibrium between the monoxide and spinel solid solutions (tie-lines). The composition dependence of oxygen partial pressure at 1300 K is evaluated for three-phase equilibria involving the solid solutions Fe + Fe _X Mg_1−X Al₂O₄+α-Al₂O₃ and Fe + Fe _y Mg_1−Y O+Fe _X Mg_1−X Al₂O₄. Dependence of X, denoting the composition of the spinel solid solution, on parameter Y, characterizing the composition of the monoxide solid solution with rock salt structure, in phase fields involving the two solid solutions is elucidated. The tie-lines are slightly skewed toward the MgAl₂O₄ corner.     

The structures expected in a simple ternary eutectic system: Part II. The Al-Ag-Cu ternary system

Ternary alloys of various compositions from the aluminum rich corner of the Al-Ag-Cu system were directionally solidified at several different growth rates ranging from 6.4 × 10⁻¹ mm·S⁻¹ to 5.6 × 10⁻³ mm· s⁻¹. The region of two phase coupled growth between α-Al and CuAl₂ was determined at a growth rate of 6.4 × 10⁻¹ mm· s⁻¹. The composition range over which a fully ternary eutectic structure formed was investigated for several different growth rates. The results are found to be consistent with the predictions of the competitive growth model set out in Part I,¹ and it would seem that the ternary eutectic composition of the published phase diagram may be incorrect. Scanning electron microscopy, using the backscattered electron signal, was used, together with optical microscopy, to study the microstructures formed. The ternary eutectic between α-Al, Ag₂Al, and CuAl₂ was found to be semiregular, and the unusual morphology of the two phase dendrites between α-Al and Ag₂Al is explained. Formerly with Alcan Laboratories Ltd., Banbury, Oxon, United Kingdom Formerly with Alcan Laboratories Ltd.     

The effect of chromium on the activity coefficient of sulfur in liquid Fe−Cr−S alloys

The effect of chromium on the activity coefficient of sulfur in the ternary system Fe−Cr−S has been determined in the temperature range 1525° to 1755°C for chromium concentrations of up to 40 wt pct, using a levitation melting technique in H₂−H₂S atmospheres. The first order free energy interaction coefficient,e _S ^Cr , which is derived on the assumption that the thermal diffusion error is constant for both binary Fe−S and ternary Fe−Cr−S melts under controlled levitation conditions, is given by the relationship:e _S ^Cr =−94.2/T+0.040 The first order enthalpy and entropy interaction coefficients are found to beh _S ^Cr =−430±70 ands _S ^Cr =−0.183±0.007 respectively. These results are in good agreement with recently published data.     

Thermodynamics of component interactions in Ge−Fe−Al liquid alloys

Partial enthalpies of mixing of aluminum in Ge−Fe−Al alloys along various radial sections in the ternary system with constant x_Ge/x_Fe ratio were determined with the aid of a high-temperature isoperibolic calorimeter. Integral heats of mixing were calculated from the partial heats for aluminum using Darken method. It was determined that alloy formation in the ternary system is accompanied by small exothermic heat effects. Component interactions in the binary Ge−Fe and Fe−Al systems have a marked effect on the thermodynamics of alloy formation in the ternary system. Taras Shevchenko National University, Kiev. Translated from Poroshkovaya Metallurgiya, Nos. 7–8(408), pp. 68–74, July–August, 1999.     

The activity coefficient of nitrogen in binary liquid metal alloys

Literature data for the limiting thermodynamic properties of nitrogen in liquid Fe, Co, Ni, and Cr, as well as in the six binary alloys consisting of two of the above elements, are critically evaluated. The ternary data are evaluated in terms of the Wagner model for quasi-interstitial liquid alloys and values of the Wagner parameter h are obtained for each system. The correlation formulated by Chiang and Chang between the Wagner parameter h and the relevant binary thermodynamic properties for oxygen in binary alloys has been found to be equally valid for nitrogen in binary alloys. From this correlation, a value of h may be predicted in the absence of any ternary experimantal data. Utilizing the Wagner model and the value of h obtained for each system, values for the first-order and second-order Gibbs energy interaction parameters ∈N(s) and ρsujN(s) are derived.. The parameters are expressed as a linear function of the reciprocal temperature, i.e. ∈^jN(s) =α + β/T and.ρ^jN_(s) = α′ + β′/T. A linear correlation found by Chipman and Corrigan between β and ∈^jN(s) for systems where Fe is the solvent is also valid for systems with non-ferrous solvents. A linear correlation between β′ and ρ^jN_(s) is also found in the present study.     

Effect of Ternary Alloying Elements Addition on the Order-Disorder Transformation Temperatures of B2-Type Ordered Fe-Al-X Intermetallics

The effect of alloying element additions on B2↔A2 order-disorder phase transformation temperatures of B2-type ordered Fe_0.5(Al_1−n X _n )_0.5 intermetallics (X = Cr, Ni, Mo, Ta, Mn, Ti, and W) that readily form single-phase solid solution for X = 1 at. pct were investigated experimentally. It was shown that the type of the ternary substitutional alloying elements have a profound effect on the variation of order-disorder transition temperature of Fe_0.5(Al_1−n X _n )_0.5 alloys. Based on the magnitude of partial ordering energies of the Al-X and Fe-X atomic pairs, predicted normalized transition temperatures, ∆T/T _o , were verified experimentally. Besides the normalized transition temperature, the relative partial ordering energy (RPOE) parameter, β, was also defined to estimate the extent of variation in B2↔A2 order-disorder phase transformation temperatures upon ternary alloying additions. The RPOE parameter, β, takes into account both the effects of magnitude of partial ordering energies of Al-X and Fe-X atomic pairs and also the lattice site occupation preferences of X element atoms over B2-type ordered Fe-Al sublattices. The alloying elements, which are preferentially distributed Fe sublattice sites, β > 0, and owing to β >> 1, are more effective in increasing order-disorder transformation temperature in Fe-Al (B2) intermetallics. On the contrary, alloying elements having β < 1 tend to decrease the transition temperature slightly relative to the binary FeAl intermetallic. The experimentally determined B2↔A2 order-disorder transition temperatures are in good qualitative or semiquantitative agreement with theoretical predictions for all X ternary alloying elements. Accordingly, the present experimental results confirm the validity of the theoretical model and calculations proposed in our previous study on the B2↔A2 order-disorder transition temperatures of single-phase Fe_0.5(Al_1−n X _n )_0.5 intermetallics.     

Thermodynamic properties of liquid Mg-ln-Cd ternary solutions

By means of concentration cells of the following type: Mg(s)∣MgCl₂ in (LiCl-KCl)_eut(l)∣Mg-In or Mg-ln-Cd(l), the partial thermodynamic data of Mg in Mg-ln and Mg-ln-Cd liquid solutions have been obtained in the composition range 0.1 ≤ X_Mg ≤ 0.7 for binary while for ternary alloys fort = 0.4, 0.6, and 0.8 (wheret = X_In/(X_In + X_Cd)) and at various mangesium concentrations 0.1≤ X_Mg ≤ 0.6. Both ternary and binary alloys were investigated at a temperature range 750 to 900 K. Experimental partial excess Gibbs energies of Mg were interpreted by the Pelton and Flengas method. Results for Mg-ln system show a slight difference in comparison with previously published data for the same system also from emf studies. Results of this study for Mg-ln system exhibit negative and positive excess entropies of magnesium and the same is observed in ternary system Mg-ln-Cd at the range of concentration close to Mg-ln.     

The effects of alkaline earth metal ions and halogen ions on the chromium oxide activities in alkaline earth metal oxide-halide-Cr2O3 system fluxes

The solid electrolyte cell — Mo|Cr + Cr₂O₃‖ZrO₂(MgO)‖{Cu-Cr}_alloy + (Cr₂O₃)_fluxes|Mo+ is used at 1673 K to determine Cr₂O₃ activities in MO-MX ₂-Cr₂O₃ (M = Ca²⁺, Ba²⁻, X = F⁻ or Cl⁻) ternary fluxes, which are in equilibrium with the copper-chromium binary alloy. The ternary isothermal phase diagrams of CaO-CaF₂-Cr₂O₃ and BaO-BaCl₂-Cr₂O₃ system fluxes are inferred on the basis of the experimental results and binary phase diagrams. The results indicate that Cr₂O₃ activities in all fluxes always decrease with the increase of the X _MO /X _MX2 ratio. Partial replacement of BaO in BaO-BaF₂-Cr₂O₃ fluxes by CaO is acceptable for economy and efficiency considerations. At the same time, partial substitution of BaO for CaO in CaO-CaF₂-Cr₂O₃ fluxes is advantageous for phosphorus removal and chromium retention as a result of the increased Cr₂O₃ activities, increased basicities, and widening of the liquid zones. Compared to those in BaO-BaF₂-Cr₂O₃ fluxes, Cr₂O₃ activities in CaO-CaF₂-Cr₂O₃ fluxes approximately follow the same curve as the former, although the position and the width of the liquid zones are considerably different, and activities in BaO-BaCl₂-Cr₂O₃ fluxes are higher at the lower Cr₂O₃ content, or vice versa. The activity coefficients of Cr₂O₃ in the fluxes decrease with the increase of the X _MO /X _{MX 2} ratios.     

Thermochemistry of binary liquid gold alloys: The systems gold-copper and gold-silver at 1379 K

The enthalpies of mixing of the binary liquid alloys of gold with copper and silver have been measured by high temperature reaction calorimetry. The experimental results are described by the following analytical expressions which were derived by a least squares treatment of the data: Au-Cu: ΔH_mix = X_AuX_Cu(-28,821 - 2,468 X^Au + 9,541 X_Au ²) J mol^-1 Au-Ag: ΔH_mix = X_AuX_Ag(-15,820 - 529 X_Au @#@) J mol^-1 The results are compared with excess Gibbs energy data from the published literature to yield approximate excess entropies of mixing. For the gold-copper system the observed parabolic dependence of the enthalpy interaction parameter on composition is well accounted for by the quasi-chemical theory.     

Enthalpy of formation and heat capacity of Fe-Mn alloys

The partial and integral enthalpies of mixing of liquid Fe-Mn alloys were measured as a function of the atomic fraction of iron (x) within the range of 0≤x≤0.45 at 1700±5 K, using a laboratory-built, high-temperature isoperibolic calorimeter. The minimum integral enthalphy of mixing at x=0.5 is about −820±45 J mol⁻¹. The enthalpy of formation of solid γ-Fe-Mn alloys with 30.0, 40.0, 50.0, and 57.0 at. pct Mn was determined indirectly, using the same calorimeter, by dissolving these alloys in liquid aluminium at 1409±3 K, and the minimum value amounts to −1940±70 J mol⁻¹ at x=0.5. The heat capacities of these alloys as well as the heat capacity of pure iron and α-Fe-Mn alloys with 0.95, 2.03, 2.73, and 4.30 at. pct Mn, were measured by a differential thermal analysis (DTA) technique and are described using a new analytical representation of the magnetic contribution. The composition dependencies of heat content, Curie and Neél temperatures, enthalpy of formation of α-Fe-Mn alloys, magnetic contribution to the enthalpy of pure Fe and its change due to the addition of Mn, as well as the change of enthalpy upon the γ → α transformation, were deduced from the experimental data. The results obtained were compared with experimental information available in the literature.     

Stable nonlinear relaxations in multiphase Al-Zn alloy

Experiment reveals the characteristics of stable damping in a multiphase Al-Zn eutectoid alloy as follows: (1) the whole damping (Q ⁻¹) has the same dependence on measuring frequency (f);i.e., Q ^-1 ∝f ⁻ⁿ , wheren is a parameter independent of temperature; (2) in a low-temperature (low-T) and low-strain-amplitude (low-A _ε) region,Q ⁻¹ = (B/f ⁿ) exp (-nH/kT) (whereB is a constant,H is the phase interface or interphase boundary atom diffusion activation energy,k is Boltzmann’s constant, andT is the absolute temperature);n andH are independent ofA _ε. The damping originates from an anelastic motion of phase interface; (3) in an intermediate region, including low-T and high-A _ε, middle-T and middle-A _ε, and high-T and low-A ^ε regions, we still have the equationQ ⁻¹ = (C/f ⁿ ) exp (-nH/kT), but the damping has a normal amplitude effect:C, n, andH all vary withA _ε. The damping results from a nonlinear relaxation of phase interface; and (4) in a high-T and high-A _ε region, there is no longer a linear relationship between InQ ⁻¹ and 1/T, whereas relationQ ⁻¹ ∝f ⁻ⁿ is still satisfied;n increases asA _ε increases; and the damping has a normal amplitude effect, but it is weaker than that in case (3). The damping may be attributed to another kind of nonlinear relaxation between phase interfaces.     

Thermodynamic calculation for alloy systems

The formulas for calculating the activity coefficient, γ _i, in the binary system and the activity coefficient of a solute at infinite dilution, γ _i ⁰ , as well as interaction parameters, ε _i ⁱ and ε _i ^j , in a metallic melt have been proposed on the basis of Miedema et al.’s model for the estimation of the heat of formation of binary alloys. The formulas can be used in both solid and liquid solutions and have been used in the calculation of both binary and ternary alloy systems taken from 75 elements. The results were compared with the experimental values.     

Equilibria involving the reciprocal spinel solid solution (Mg x Fe1−x ) (Al y Cr1−y )2O4: modeling and experiment

Developed in this article is a model for calculating cation distribution and activities in the reciprocal spinel solid solution (Mg _X Fe_1−X )(Al _Y Cr_1−Y )₂O₄ based on octahedral site preference energies of cations independent of composition and temperature, random distribution of ions on tetrahedral and octahedral sites, entropy of randomization of Jahn-Teller distortions associated with Fe²⁺ ions on the tetrahedral site, and the standard Gibbs energies of formation of the four pure spinel compounds. Enthalpy of mixing of this reciprocal solid solution caused by the large difference of ionic radii of Al³⁺ and Cr³⁺ present on the octahedral site was modeled based on experimental data on the binary systems. The tie-line compositions corresponding to the equilibria between the spinel solid solution and the sesquioxide solid solution (Al _Z Cr_1−Z )₂O₃ with corundum structure were computed. Values for activities in the corundum solid solution were taken from the literature. The oxygen potential corresponding to the three-phase equilibrium involving metallic iron, the spinel solid solution, and corundum solid solution was computed as a function of composition of the spinel solid solution. The computed results were verified by measurements on nine compositions inside the square representing the reciprocal system. The compositions of coexisting solid solutions were determined by electron-probe microanalysis (EPMA) and lattice parameter measurement using X-ray diffraction (XRD). The activities of FeAl₂O₄ and FeCr₂O₄ and oxygen potentials for three-phase equilibria were measured using two independent solid-state cells incorporating a bielectrolyte chain. Both cells gave consistent results within experimental error. The experimental results are in excellent agreement with the computed results, thus validating the model for the reciprocal spinel solid solution.     

A generalized approach to the flood-knapp structure based model for binary liquid silicates: Application and update for the PbO-SiO2 System

The nonideal activity of a metal oxide in a molten binary silicate system is described by treating the liquid as an ideal solution and by considering the formation of a few complexes. Application of this approach to the binary system PbO-SiO₂ shows that the experimentally determined activity of PbO(l) can be modeled by considering the lead silicate melt as an ideal solution of Pb²⁺ and O²⁻,SiO ₄ ⁴⁻ , Si₂O ₇ ⁶⁻ , Si₁₂O ₃₇ ²⁶⁻ , and Si₄O ₁₀ ⁴⁻ . The calculated Gibbs free energy values for the formation of the anionic complexes from O²⁻ and SiO ₄ ⁴⁻ are: ΔGℴ(Si₂O ₇ ⁶⁻ )/J · mol⁻¹ = 38977 − 30.909(T/K); ΔGℴ(Si₁₂O ₃₇ ²⁶⁻ )/J · mol⁻¹ = 200158 − 121.813(T/K); Δℴ(Si₄O ₁₀ ⁴⁻ )/J · mol⁻¹ = 104627 − 28.094(T/K). Values of Gibbs free energy of formation of the solid phases PbO, Pb₄Si0₆, Pb₂SiO₄, PbSiO₃, and SiO₂ which, together with the melt model data, give the best fit to experimental phase relations in the system PbO-SiO₂ were calculated. These values are all in good agreement with literature data.     

Variation of interface compositions during diffusion controlled precipitate growth in ternary systems

Isothermal diffusion controlled phase growth in ternary systems has been modeled using the Crank-Nicolson finite difference equations. Local equilibrium at phase boundaries and one dimensional growth are assumed. The model includes a method of determining phase growth velocity and interface compositions consistent with the diffusion rates of both elements. It also considers the effects of finite or overlapping diffusion fields (impingement). The growth of phosphide, (FeNi)₃P, in α ferrite in the Fe−Ni−P system was chosen for the simulation. Interface compositions are predicted to change with time, controlled by the necessity to balance the two solute (Ni and P) fluxes which cause the precipitate to grow. Diffusion controls the growth process although during initial growth interface structure may be important. The ratio of the major ternary coefficientsD _PP ^Fe /D _NiNi ^Fe controls the amount of shift of the precipitate interface composition from the tie line through the bulk composition. During the major period of growth the Ni interface compositions in phosphide and α remain constant and a square root of time,t ^1/2, dependence for growth is predicted. The practical, effect of impingement is to decrease phase growth and to allow the interface compositions to shift towards the tie line through the bulk composition.     

The Ce-Mg-Y system

On the basis of a critical assessment, the Ce-Mg-Y system has been investigated, employing X-ray diffraction (XRD), optical microscopy, and microprobe analyses. Phase relations have been determined in the complete isothermal section at 500 °C, revealing the existence of two novel ternary compounds: Ce_1−x Y _x Mg_5−y (0.39 ≤ x ≤ 0.84; 0 ≤ y ≤ 0.60) with the GdMg₅, or the defect Sm₁₁Cd₄₅-type and the cubic Laves phase Ce_1−x Y _x Mg₂ (x ≈ 0.67). The binary system Ce-Y has been reinvestigated, and a constitutional diagram, temperature vs concentration, has been proposed. In contrast to earlier versions, the so-called δ phase with the αSm-type has been shown to be metastable.