Self-diffusion of copper in Cu−Al solid solutions

Self-diffusion coefficients of copper in Cu?Al solid solutions in the concentration interval 0 to 19 at. pct Al and in the temperature range 800° to 1040°C have been determined by the residual activity method using the isotope Cu⁶⁴. The values of the self-diffusion coefficients in the concentration interval 0 to 14.5 at. pct Al satisfy the Arrhenius relation and their temperature dependence can be expressed by the following equations $$\eqalign{ & D_{Cu}^{Cu} = \left( {0.43_{ - 0.11}^{ + 0.15} } \right) exp \left( { - {{48,500 \pm 700} \over {RT}}} \right) cm^2 /\sec \cr & D_{Cu - 2.80 at. pct Al}^{Cu} = \left( {0.46_{ - 0.16}^{ + 0.23} } \right) exp \left( { - {{48,000 \pm 900} \over {RT}}} \right) cm^2 /\sec \cr & D_{Cu - 5.50 at. pct Al}^{Cu} = \left( {0.30_{ - 0.07}^{ + 0.09} } \right) exp \left( { - {{47,000 \pm 600} \over {RT}}} \right) cm^2 /\sec \cr & D_{Cu - 8.83 at. pct Al}^{Cu} = \left( {0.46_{ - 0.09}^{ + 0.11} } \right) exp \left( { - {{47,100 \pm 500} \over {RT}}} \right) cm^2 /\sec \cr & D_{Cu - 11.7 at. pct Al}^{Cu} = \left( {0.61_{ - 0.13}^{ + 0.17} } \right) exp \left( { - {{47,200 \pm 600} \over {RT}}} \right) cm^2 /\sec \cr & D_{Cu - 14.5 at. pct Al}^{Cu} = \left( {4.2_{ - 1.5}^{ + 2.2} } \right) exp \left( { - {{51,110 \pm 1000} \over {RT}}} \right) cm^2 /\sec \cr} $$ An analysis of the results leads to the conclusion that, in the concentration interval 0 to 11.7 at. pct Al, the frequency factor and activation enthalpy concentration dependences can be described by the following equations whereD _0Cu ^Cu and ΔH _Cu ^Cu are diffusion characteristics for self-diffusion in pure copper,X _Al is the atomic percent of aluminum, andK andB are experimental constants.     

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. $$\begin{gathered} \log {\text{ }}\gamma _{{\text{Pb}}} {\text{ = - 0}}{\text{.255 }}N_{Bi}^2 {\text{ }}N_{{\text{Bi}}} {\text{< 0}}{\text{.8}} \hfill \\ \log {\text{ }}\gamma _{{\text{Tl}}} {\text{ = - 0}}{\text{.805 }}N_{Bi}^2 {\text{ }}N_{{\text{Bi}}} {\text{< 0}}{\text{.7}} \hfill \\ \end{gathered} $$      

The Solubility and Diffusivity of Fluorine in Solid Copper from Electrochemical Measurements

The solubility and diffusivity of fluorine in solid copper were determined electrochemically using the double solid-state cell $$Ni + NiF_2 \left| {CaF_2 } \right|Cu\left| {CaF_2 } \right|Ni + NiF_2 .$$ In the temperature range 757 to 920°C, the diffusivity of fluorine in solid copper was found to be $$D_F \left( {{{cm^2 } \mathord{\left/ {\vphantom {{cm^2 } s}} \right. \kern-\nulldelimiterspace} s}} \right) = 9.32 \times 10^{ - 2} \exp \left( {\frac{{ - 98,910 {J \mathord{\left/ {\vphantom {J {mole}}} \right. \kern-\nulldelimiterspace} {mole}}}} {{RT}}} \right).$$ . The results obtained for the dissolution of fluorine as atoms in solid copper showed large scatter. However, the equilibrium dissolution of fluorine follows Sieverts’ law. Above the melting point (770°C) of CuF₂, the mean solubility of fluorine in solid copper, for the equilibrium Cu(s)+ CuF ₂(l), follows the relationship $$N_F^s (atom fraction) = 0.98 \exp \left( {\frac{{ - 79,500 {J \mathord{\left/ {\vphantom {J {mole}}} \right. \kern-\nulldelimiterspace} {mole}}}} {{RT}}} \right).$$      

Influence of chromium and nickel on the dissociation of CO2 on carbon-saturated liquid iron

At 1600 °C, under conditions where the rate was not significantly affected by liquid-phase or gasphase mass transfer, the rate of dissociation of CO₂ was determined from the rate of decarburization of iron-based carbon-saturated melts containing varying amounts of chromium and nickel. The rate was determined by monitoring the change in reacted gas composition with an in-line spectrometer. The results indicate that neither chromium nor nickel had a strong effect on the kinetics of dissociation of CO₂ on the surface of the melt. Sulfur was found to significantly decrease the rate, as is the case for alloys without chromium or nickel, and the rate constant is given by $$k = \frac{{k^0 }}{{1 + K_s a_s }} + k_r $$ where k ⁰ denotes the chemical rate on pure iron, K _s is the adsorption coefficient of sulfur, a _s is the activity of sulfur corrected for Cr, and k _r represents the residual rate at a high sulfur level. The rate constants and adsorption coefficient were determined to be: $$\begin{array}{*{20}c} {k^0 = 1.8 \times 10^{ - 3} mol/cm^2 s atm} \\ {k_r = 6.1 \times 10^{ - 5} mol/cm^2 s atm} \\ {K_s = 330 \pm 20} \\ \end{array} $$ Experiments run at lower carbon contents showed that only a very small quantity of chromium was oxidized, immediately forming a protective layer. However, this oxidation occurred at a higher carbon content (2 pct) than what was expected from the thermodynamics.     

Kinetics and mechanism of the reduction of molten nickel sulfide by hydrogen

The kinetics and mechanism of the reduction of M₃S₂ by hydrogen have been investigated between 1133° and 1300°C. When high flow rates of hydrogen and argon or helium bubbling through the melt are maintained the rate-determining step is a chemical process which can be expressed by a rate law of the form $$\begin{gathered} r_{H_2 S} = k_{expt} (N_S - \alpha )^2 p_{H_2 }^{1/2} \hfill \\ p_{H_2 } \geqslant 0.88atm \hfill \\ \end{gathered} $$ where k_expt = 85.1 atm^-1/2 min^-1, α = 0.17 at 1250°C. The experimental activation energy for this process is 20.1 ±3.0 kcal per mole. These results are discussed in terms of possible catalysis by nickel.     

A mass-spectrometric study of the thermodynamics of the Fe−Cu and Fe−Cu−C(sat) systems at 1600°C

The Knudsen cell-mass spectrometer combination has been used to study the Fe?Cu and Fe?Cu?C_(sat) alloys at 1600°C. Activity coefficients in the Fe?Cu system are closely represented by the equations $$\begin{gathered} \ln \gamma _{Fe} = 1.86N_{Cu}^2 + 0.03, (0< N_{Fe}< 0.7) \hfill \\ \ln \gamma _{Cu} = 2.25N_{Fe}^2 - 0.19, (0.7< N_{Fe}< 1.0) \hfill \\ \end{gathered} $$ with an uncertainty in the quadratic terms of about 5 pct. For the iron-rich carbon-saturated alloys, the activity coefficient of copper is given by the equation $$\ln \gamma _{Cu} = 2.45(N'_{Fe} )^2 + 0.3N'_{Fe} + 0.03, (0< N'$$ to within an uncertainty of about 10 pct. N _Fe ^′ represents the fraction N_Fe/(N_Fe+N_Cu), etc. The activity coefficient of iron in this region is found to be essentially constant at 0.69±0.05.     

Reaction Mechanism and Kinetics of Enargite Oxidation at Roasting Temperatures

Roasting of enargite (Cu₃AsS₄) in the temperature range of 648?K to 898?K (375?°C to 625?°C) in atmospheres containing variable amounts of oxygen has been studied by thermogravimetric methods. From the experimental results of weight loss/gain data and X-ray diffraction (XRD) analysis of partially reacted samples, the reaction mechanism of the enargite oxidation was determined, which occurred in three sequential stages:

1. $4{\text{Cu}}_{ 3} {\text{AsS}}_{ 4} \left( {\text{s}} \right){\text{ + 13O}}_{ 2} \left( {\text{g}} \right){\text{ = As}}_{ 4} {\text{O}}_{ 6} \left( {\text{g}} \right){\text{ + 6Cu}}_{ 2} {\text{S}}\left( {\text{s}} \right){\text{ + 10SO}}_{ 2} \left( {\text{g}} \right) $
2. $ 6{\text{Cu}}_{ 2} {\text{S}}\left( {\text{s}} \right){\text{ + 9O}}_{ 2} \left( {\text{g}} \right){\text{ = 6Cu}}_{ 2} {\text{O}}\left( {\text{s}} \right){\text{ + 6SO}}_{ 2} \left( {\text{g}} \right) $
3. $ 6{\text{Cu}}_{ 2} {\text{O}}\left( {\text{s}} \right){\text{ + 3O}}_{ 2} \left( {\text{g}} \right){\text{ = 12CuO}}\left( {\text{s}} \right) $

The three reactions occurred sequentially, each with constant rate, and they were affected significantly by temperature and partial pressure of oxygen. The kinetics of the first stage were analyzed by using the model X?=?k ₁ t. The first stage reaction was on the order of 0.9 with respect to oxygen partial pressure and the activation energy was 44?kJ/mol for the temperature range of 648?K to 898?K (375?°C to 625?°C).     

Thermodynamics of the system NaCl-AlCl3

Heat capacities of melts were measured in the range 400 to 1100 K and 0.48 < N_AlCl3 < 0.62, the results being expressed by C_p = 40.96 – 0.0295T + 2.01 × 10^?5 T ² J K^?1 g·atom^?1 i.e., AlCl₃ contains 4 atoms, and so forth). This equation was used in interpreting literature vapor pressure data. Measurements were made of the emf of the concentration cell $$AL\left| {_{AlCl_3 }^{NACl(sat)} } \right.\left| {_{(Na^ + )}^{Pyrex} } \right.\left| {_{AlCl_3 }^{NACl(sat)} } \right.\left| {_{AlCl_3 }^{NACl} } \right.\left| {AL} \right. $$ at temperatures 473 to 623 K, and the results were correlated with the vapor pressure data to yield activities of NaCl and AlCl₃. Measurements with a sodium electrode confirmed the accepted values for the free energy of formation of A1C1₃ within about 1.5 kJ mol^?1. The activities were used to analyze the phase diagram. Direct measurement of the eutectic temperature with a concentration-cell technique (which avoids supercooling) gave 386 K; the eutectic composition is 60.0 mol pct A1C1₃. The standard entropy of NaAlCl₄(s) is S _298.15 ^° = 199.1 J K^?1 mol^?1. The free energy for NaAlCl₄(l) = NaAlCl₄(g) is ΔG° = 82740 ?63.66T J mol^?1 at around 950 K.     

Investigation of the Oxidation Kinetics of Fe-Cr and Fe-Cr-C Melts under Controlled Oxygen Partial Pressures

In the current work, oxidation kinetics of Fe-Cr and Fe-Cr-C melts by gas mixtures containing CO₂ was investigated by Thermogravimetric Analysis (TGA). The experiments were conducted keeping the melt in alumina crucibles, allowing the alloy melt to get oxidized by an oxidant gas. The oxidation rate was followed by the weight changes as a function of time. The oxidation experiments were conducted using various mixtures of O₂ and CO₂ with $ P_{{{\text{O}}_{2} }} $ ?=?10^?2 to 10^4?Pa. In order to understand the mechanism of oxidation, the wetting properties between the alumina container and the alloys used in the thermogravimetric analysis (TGA) experiments and the change of the alloy drop shape during the course of the oxidation were investigated by X-ray radiography.The experiments demonstrated that the oxidation rate of Fe-Cr melt increased slightly with temperature under the current experimental conditions, but it is strongly related to the Cr-content of the alloy as well as the oxygen partial pressure in the oxidant gas mixture, both of which caused an increase in the rate. For the Fe-Cr-C system, the oxidation rate has a negative relationship with carbon content, viz. with increasing carbon, the oxidation rate of the alloy melt slightly decreased. The chemical reaction was found to be the rate determining step during the initial stages, whereas as the reaction progressed, the diffusion of oxygen ions through slag phase to the slag?Cmelt interface was found to have a strong impact on the oxidation rate. The overall impact of different factors on the chemical reaction rate for the oxidation process derived from the current experimental results can be expressed by the relationship: $ k_{1} = \frac{{dm}}{{dt}} = \Uplambda {\text C}_{\text{Cr}}^{0. 2 3} {\text{C}}_{{\text{CO}}_{ 2} } ^{ 0. 4 1}{\text{exp}}(\frac{{{{ - E}}_{\text{a}} }}{{{\text{R}}T}} ). $ A model for describing the kinetics of oxidation of Fe-Cr and Fe-Cr-C alloys under pure CO₂ was developed. Simulation of the oxidation kinetics using this model showed good agreement with the experimental results.     

The thermodynamic properties of liquid Fe−Si alloys

The thermodynamic properties of liquid Fe?Si alloys have been determined electrochemically by use of the following galvanic cells: $$\begin{gathered} Cr - Cr_2 O_3 (s)|ZrO_2 (CaO)|Fe - Si(l), SiO_2 (s) \hfill \\ Cr - Cr_2 O_3 (s)|ThO_2 (Y_2 O_3 )|Fe - Si(l), SiO_2 (s) \hfill \\ \end{gathered} $$ The free energy of formation of SiO₂ was measured and is ?139.0 and ?134.3 kcals per mole at 1500° and 1600°C, respectively. The activity coefficients of iron and silicon for the atom fraction of siliconN _Si<0.35 at 1600° and 1500°C can be represented by the quadratic formalism. $$\begin{gathered} \left. {\begin{array}{*{20}c} {log \gamma _{Fe} = - 2.12 N_{Si}^2 } \\ {log \gamma _{Si} = - 2.12 N_{Fe}^2 - 0.22} \\ \end{array} } \right\}1600^ \circ C (2912^ \circ F) \hfill \\ \left. {\begin{array}{*{20}c} {log \gamma _{Fe} = - 2.50 N_{Si}^2 } \\ {log \gamma _{Si} = - 2.50 N_{Fe}^2 - 0.13} \\ \end{array} } \right\}1500^ \circ C (2732^ \circ F) \hfill \\ \end{gathered} $$ The results indicate that an excess stability peak occurs at about the equimolar composition. Combining the heats of solution determined in this study with previous data indicates that the heats also follow the quadratic formalism. The partial molar heats, \(\bar L_{Si} \) and \(\bar L_{Fe} \) , are represented by $$\begin{gathered} \bar L_{Si} = - 31 N_{Fe}^2 - 4 kcals per mole \hfill \\ \bar L_{Fe} = - 31 N_{Si}^2 kcals per mole \hfill \\ \end{gathered} $$ ForN _Si less than 0.35 and by $$\begin{gathered} \bar L_{Si} = - 22 N_{Fe}^2 \hfill \\ \bar L_{Fe} = - 22 N_{Fe}^2 - 7.0 \hfill \\ \end{gathered} $$ forN _Fe less than 0.35. There is an inflection point in the transition region similar to an excess stability peak for the excess free energies. At 1600°C the ThO₂(Y₂O₃) electrolyte exhibited insignificant electronic conductivity at oxygen partial pressures as low as that in equilibrium with Si?SiO₂ (2×10^?16 atm).     

Mass-spectrometric determination of activities in Fe−Cr and Fe−Cr−Ni alloys

The Knudsen cell-mass spectrometer combination has been used to study the Fe?Cr system and some Fe?Cr?Ni liquid alloys. The Fe?Cr liquid alloys at 1600°C are found to be essentially ideal when referred to pure liquids as standard states. Phase equilibria over a limited composition range for this system are derived from the behavior of the ion-current ratios. The necessary equations are derived to apply the integration technique to the measured ion current ratios in a ternary system and the method is applied to the Fe?Cr?Ni system at 1600°C. The results are represented, within experimental error, by the following equations: forN _Fe≥0.6, $$\begin{gathered} ln \gamma _{Fe} = - 0.08 N_{Ni}^2 \hfill \\ \ln \gamma _{Cr} = 0.09 - 0.08 N_{Ni}^2 \hfill \\ \ln \gamma _{Ni} = - 0.26 - 0.08(1 - N_{Ni} )^2 \hfill \\ \end{gathered} $$ forN _Fe=0.45, $$\begin{gathered} \ln \gamma _{Fe} = - 0.20 N_{Ni}^2 \hfill \\ \ln \gamma _{Cr} = 0.09 - 0.20 N_{Ni}^2 \hfill \\ \ln \gamma _{Ni} = - 0.19 - 0.20(1 - N_{Ni} )^2 \hfill \\ \end{gathered} $$      

Electrical conductivity of molten cryolite-based mixtures obtained with a tube-type cell made of pyrolytic boron nitride

A pyrolytic boron nitride tube-type cell was used to measure the electrical conductivity for molten cryolite, for binary mixtures of cryolite with Al₂O₃, AlF₃, CaF₂, KF, Li₃AlF₆, and MgF2, and for ternary mixtures Na₃AlF₆-Al₂O₃-CaF₂ (MgF₂) and Na₃AlF₆-AlF₃-KF (Li₃AlF₆). The cell constant was about 40 cm^?t. The temperature and concentration dependence of the conductivity in the investigated concentration range was described by the equation $$\begin{gathered} \kappa /S cm^{ - 1} = 7.22 exp\left( { - 1204.3/T} \right) - 2.53\left[ {Al_2 O_3 } \right] - 1.66\left[ {AlF_3 } \right] \hfill \\ - 0.76\left[ {CaF_2 } \right] - 0.206\left[ {KF} \right] + 0.97\left[ {Li_3 AlF_6 } \right] - 1.07\left[ {MgF_2 } \right] \hfill \\ - 1.80\left[ {Al_2 O_3 } \right]\left[ {CaF_2 } \right] - 2.59\left[ {Al_2 O_3 } \right]\left[ {MgF_2 } \right] \hfill \\ - 0.942\left[ {AlF_3 } \right]\left[ {Li_3 AlF_6 } \right] \hfill \\ \end{gathered} $$ whereT represents the temperature in Kelvin and the brackets represent the mole fractions of the additions. The standard deviation was found to be 0.026 S cm^?1 (～1 pct). For practical reasons, it is often desired to express composition in weight percent. In that case, it holds that $$\begin{gathered} \ln \kappa = 1.977 - 0.0200\left[ {Al_2 O_3 } \right] - 0.0131\left[ {AlF_3 } \right] - 0.0060\left[ {CaF_2 } \right] \hfill \\ - 0.0106\left[ {MgF_2 } \right] - 0.0019\left[ {KF} \right] + 0.0121\left[ {LiF} \right] - 1204.3/T \hfill \\ \end{gathered} $$ whereT represents the temperature in Kelvin and the brackets denote the concentration of the additives in weight percent. However, in this case, the maximum relative error of the conductivity equation can reach up to 2.5 pct.     

Determination of diffusion coefficient of oxygen in γ-iron from measurements of internal oxidation in Fe-Al alloys

The internal oxidation of iron alloys containing between 0.069 and 0.274 wt pct aluminum was investigated in the temperature range from 1223 to 1373 K for the purpose of determining the diffusion coefficients in γ-iron as well as in the internal oxidation layer. A parabolic rate law is obeyed in the internal oxidation of the present alloys. The rate constant for penetration of the oxidation front, the oxide formed, and the concentration of aluminum in the oxidation layer were determined. Pronounced enrichment of aluminum in the oxidation layer was observed, resulting from the counterdiffusion of aluminum. The oxygen concentration at the specimen surface was determined by combining the thermodynamic data on the dissociation of FeO and the solution of oxygen in y-iron. The diffusion coefficient of oxygen in the internal oxidation layer,D _o ¹⁰ , was evaluated on the basis of the rate equation for internal oxidation.D _o ¹⁰ increases at a given temperature as the volume fraction of oxide,f ¹⁰, in the oxidation layer increases. The diffusion coefficient of oxygen in γ-iron,D _o, was determined by extrapolation ofD _o ¹⁰ = 0.D _o may be expressed as $$D_o = \left( {1.30\begin{array}{*{20}c} { + 0.80} \\ { - 0.50} \\ \end{array} } \right) \times 10^{ - 4} \exp \left[ { - \frac{{166 \pm 5(kJ \cdot mol^{ - 1} )}}{{RT}}} \right]m^2 \cdot s^{ - 1} .$$ D _o is close to the diffusion coefficients of carbon and nitrogen in γ-iron.     

Thermodynamic behavior in binary metallic solutions

The applicability of Krupkowski’s formalism $$\begin{gathered} ln \gamma _1 = \omega \left( T \right)\left( {1 - X_1 } \right)^m \hfill \\ ln \gamma _2 = \omega \left( T \right)\left[ {\left( {1 - X_1 } \right)^m - \frac{m}{{m - 1}}\left( {1 - X_1 } \right)^{m - 1} + \frac{1}{{m - 1}}} \right] \hfill \\ \end{gathered} $$ in interpreting experimental data is shown for several binary systems. Both dilute and concentrated solutions are considered. In dilute solutions (Henry’s law region) these equations exclude constant values of the activity coefficients. These formulae withm>1 satisfy Raoults law and Henry’s law as limiting cases. However, experimental data indicate that only in two systems, namely Zn-Sn and Zn-Bi,γ _Zn ⁰ =γ _Zn over a finite composition range. Whenm is close to unity, as is the case for the Zn-Sn and Zn-Bi systems Raoult’s law is not satisfied untilX _Zn is infinitesimally close to unity. Data for concentrated zinc solutions for both systems support this conclusion. A comparison of Krupkowski’s method with Darken’s quadratic formalism was also carried out, and it was shown that both methods give similar results whenm=2.     

Thermodynamic properties of the Zn−Pb−In ternary system in dilute liquid zinc solutions

Electromotive force measurements were conducted on ternary Zn?Pb?In solutions having zinc concentrationsX _Zn=0.03, 0.05, 0.07, and 0.1. Special attention was paid to the effect of the addition of indium and lead on the Ln γ_Zn value at 714°, 757°, and 805°K. These data served to determine the interaction parameters ∈ _Zn ^In and ∈ _Pb ^Zn from the \((ln\gamma _{Zn} )_{X_{Zn} } \to _0 vs X_{Pb} \) plots over the indicated ranges of temperatures. The end points in ln γ_Zn vs X_Pb and \((ln\gamma _{Zn} )_{X_{Zn} } \to _0 vs X_{Pb} \) plots were taken from previous measurements on the Zn?In and Zn?Pb systems. The values of ln γ_Zn and \((ln\gamma _{Zn} )_{X_{Zn} } \to _0 \) in Zn?Pb?In dilute solutions were carried out by means of Krupkowski’s formulae. The influence of the Zn?Pb system in Zn?Pb-Me ternary solutions with a preponderant content of lead was analyzed whenMe=Bi, Cd, Sn, and Sb.     

Thermodynamics of iron-aluminum alloys at 1573 K

The activities of iron (Fe) and aluminum (Al) were measured in Fe-Al alloys at 1573 K using the ion-current-ratio technique in a high-temperature Knudsen cell mass spectrometer. The Fe-Al solutions exhibited negative deviations from ideality over the entire composition range. The activity coefficientsγ _Fe, andγ _A1 are given by the following equations as a function of mole fraction (x _Fe,x _Al): 1 $$\begin{gathered} 0< \chi _{A1}< 0.4 \hfill \\ ln \gamma _{Fe} = - 4.511 ( \pm 0.008)\chi _{A1}^2 \hfill \\ ln \gamma _{A1} = - 4.462 ( \pm 0.029)\chi _{Fe}^2 + 0.325( \pm 0.013) \hfill \\ 0.6< \chi _{A1}< 1.0 \hfill \\ ln \gamma _{Fe} = - 4.065 ( \pm 0.006)\chi _{A1}^2 + 0.099( \pm 0.003) \hfill \\ ln \gamma _{A1} = - 4.092 ( \pm 0.026)\chi _{Fe}^2 + 0.002( \pm 0.001) \hfill \\ \end{gathered} $$ The results showed good agreement with those obtained from previous investigations at other temperatures by extrapolation of the activity data to 1573 K.     

Correlation Between Viscosity and Electrical Conductivity of Aluminosilicate Melts

The linear relations between logarithm of viscosity and logarithm of electrical conductivity deduced in our previous paper for MO-SiO₂ (M = Mg, Ca, Sr, Ba) and M₂O-SiO₂ (Li, Na, K) melts are extended in this study. It is found that the linear law for MO-SiO₂ system is also followed for the melts of FeO-SiO₂ and MnO-SiO₂ (when electronic conduct can be neglected relative to ionic conduct). The relation between viscosity and electrical conductivity is mainly dependent on the valences of cations of basic oxides. For the $ \sum {{\text{M}}_{x} {\text{O-SiO}}_{2} } $ melt containing several basic oxides, there are two situations: In the case where all cations are divalent (or univalent), the relation is the same as that of MO-SiO₂ melt (or M₂O-SiO₂ melt); in the case of existing both divalent and univalent cations, the coefficients for the linear relation can be calculated based on the coefficients of MO-SiO₂ and M₂O-SiO₂ melts, with the weight factors from the renormalized mole fractions of $ \sum {\text{MO}} $ and $ \sum {{\text{M}}_{ 2} {\text{O}}} $ . It is also found that Al₂O₃ has little effect on the relation, and the law for $ \sum {{\text{M}}_{\text{x}} {\text{O-SiO}}_{ 2} } $ melt can be approximately applied to $ \sum {{\text{M}}_{\text{x}} {\text{O-Al}}_{ 2} {\text{O}}_{ 3} {\text{-SiO}}_{ 2} } $ melt.