Thermodynamic studies of liquid copper alloys by electromotive force method: Part II. The Cu−Ni−O and Cu−Ni systems

Oxygen activities in liquid Cu?Ni melts have been measured at 1100°, 1200°, and 1300°C by the solid electrolyte electromotive force method. Addition of nickel lowers the activity coefficient of oxygen in liquid copper. The temperature dependence of \( \in _{\rm O}^{(Ni)} \) can be represented as follows: 1 $$ \in _{\rm O}^{(Ni)} = 17.0 - (3.60 \times 10^4 / T)$$ The solubility and activity of oxygen in liquid Cu?Ni alloys in equilibrium with NiO were measured at 1400°C. Oxygen solubility decreases with increasing nickel in the alloys. Nickel activities in the liquid Cu?Ni system were also calculated from the electromotive force data. Copper activities were evaluated by the Gibbs-Duhem integration. Activities of copper and nickel deviate positively from ideality. The activity coefficient of nickel in the liquid Cu?Ni system at 1400°C can be represented by the Darken's formulation: In 2 $$\gamma _{Ni} = 1.323 (1 - N_{Ni} )^2 ; N_{Ni} = 0.55 to 0.77$$ In 3 $$\gamma _{Ni} = 1.000 (1 - N_{Ni} )^2 + 0.005; N_{Ni} = 0.0 to 0.3$$ Excess entropies in the liquid Cu?Ni system are less than 0.1 eu. A complete set of thermodynamic properties of the system can be calculated by combining the free energy data of this study with the estimated enthalpy data from literature sources.     

Chemical potentials of oxygen for mixtures of CaO (s) + Ca4P2O9 (s) + {CaO + P2O5 + FexO} melts and Ca4P2O9 (s) + Ca3P2O8 (s) + {CaO + P2O5 + FexO} melts

Electrochemical measurements involving stabilized zirconia as solid electrode and Mo + MoO₂ as reference electrode were conducted in order to determine the chemical potentials of oxygen for threephase assemblages of CaO (s) + Ca₄P₂O₉ (s) + liquid and Ca₄P₂O₉ + Ca₃P₂O₈ + liquid within the system CaO + Fe_xO + P₂O₅. The results for the former are $$\log (P_{O_2 } /atm) = 6.22 - 27,900 (T/K)$$ while for the latter, $$\log (P_{O_2 } /atm) = 6.35 - 27,600 (T/K)$$      

The diffusion and solubility of oxygen in solid nickel

Solid-state electrochemical measurements using various experimental procedures were made with the double cell: $$ Ni + NiO|ZrO_2 + Y_2 O_3 |Ni + \underline O |ZrO_2 + Y_2 O_3 |Ni + NiO $$ to determine the diffusivity and thermodynamic functions of oxygen dissolved in solid nickel. Non-steady state diffusion of oxygen in the specimen was caused by applying a preselected potential between the reference and specimen electrodes and was monitored by measuring time-dependent potentials and/or currents. The following results were obtained for the diffusivity of oxygen and the solubility of oxygen in nickel in equilibrium with NiO: $$D{\text{ = 4}}{\text{.9 }} \times {\text{ 10}}^{{\text{ - 2}}} {\text{ exp}}\left( {{\text{ - }}\frac{{{\text{164 kJ/mole}}}}{{{\text{R}}T}}} \right){\text{cm}}^{\text{2}} /{\text{sec (850 to 1400 }}{}^{\text{o}}{\text{C)}}$$ $$C_{\text{O}}^s {\text{ = 8}}{\text{.3 exp}}\left( { - \frac{{55{\text{kJ/mole}}}}{{{\text{R}}T}}} \right){\text{at}}{\text{. pct (800 to 1000 }}{}^{\text{o}}{\text{C)}}$$ The thermodynamic and transport behaviors of oxygen in solid nickel were fairly well described by a simple quasi-regular model and an interstitial diffusion model, respectively.     

The glass-liquid and solid-jelly transition temperatures

The supercooled liquid undergoes a “glass transition” in whichC _p (I) decreases rapidly and approaches that ofC _p (s). The theoretical glass transition temperature T_{g,theoretical} is defined as the temperature below the melting point, whereS (l-s) = 0. Similarly, the overheated solid will undergo a transition, where the lattice softens, as the structure cannot support vibrations with larger and larger amplitudes.S (l-s), the entropy difference between liquid and solid, andG (l-s), the Gibbs energy difference between liquid and solid, cross the zero line above the melting point. WhereS (l-s) crosses the zero line, the entropy of the liquid becomes less than that of the superheated solid. We call this pointT _jS_theoretical. At a higher temperature, G (l-s) crosses the zero line, where the superheated solid becomes stable with respect to the liquid. We call this pointT _jG_theoretical. We do not know yet which of the two are technologically important. For example, what influence does 7T_jS_theoretical, orT _jG_theoretical have on the behavior of aluminum, which melts at a low temperature but is used up to very high temperatures in various alloys. We obtained (T _g, T_jS, andT _jG all theoretical) $$T_g /T_{mp} = (0.4018 \pm 0.1601) + (8.53 \pm 2.68) \cdot 10^{--5} \cdot T_{mp} , R = 0.5228;$$ $$T_g /T_{max} = (0.3816 \pm 0.1074) + (7.47 \pm 1.80) \cdot 10^{--5} \cdot T_{mp} , R = 0.6249;$$ $$T_g /T_j S = (0.1749 \pm 0.1023) + (7.55 \pm 1.71) \cdot 10^{--5} \cdot T_{mp} , R = 0.6470;$$ $$6S_{mp} /d = - (2.08 \pm 2.80) \cdot 10^{10} + (3.84 \pm 0.47) \cdot 10^{--7} \cdot T_{mp} , R = 0.8446;$$ $$T_{bp} /T_j S = 1.066 \pm 0.325;$$ $$T_{bp} /T_j G = 0.703 \pm 0.214$$ whereT _mp is the temperature of the standard melting point,T _bp is the standard boiling point, T_max is the temperature whereS (l-s) is maximum and C_p(l-s) = 0, andR is the regression coefficient.     

Thermodynamic properties of the Cu−Sn and Cu−Au systems by mass spectrometry

The activities and partial molar heats of mixing have been determined in the liquid Cu?Sn system at 1320°C and the liquid Cu?Au system at 1460°C. The experimental technique consisted of the analysis of Knudsen cell effusates with a T.O.F. mass spectrometer. The ion current ratio for the alloy components was measured for each system over a range of temperature and composition and the thermodynamic values calculated by a modified Gibbs-Duhem equation. Both systems exhibited negative deviations from ideal behavior. The results can be partially represented by the equations $$\begin{gathered} \log \gamma _{Cu} = - 0.0175x^2 _{Sn} - 0.302 (0 \leqslant x_{Cu} \leqslant 0.20) \hfill \\ log \gamma _{Sn} = - 0.342x^2 _{Cu} + 1.084(0 \leqslant x_{Sn} \leqslant 0.20) \hfill \\ \end{gathered} $$ for the Cu?Sn system at 1320°C and by $$\begin{gathered} \log \gamma _{Cu} = - 0.703x^2 _{Au} - 0.083(0 \leqslant x_{Cu} \leqslant 0.52) \hfill \\ \log \gamma _{Au} = - 1.057x^2 _{Cu} + 0.098(0 \leqslant x_{Au} \leqslant 0.47) \hfill \\ \end{gathered} $$ for the Cu?Au system at 1460°C.     

Thermodynamic properties of the liquid Sn−Ge and Sn−Au systems by mass spectrometry

The activities and partial molar heats of mixing have been determined for the liquid Sn?Ge system at 1773 K and the liquid Sn?Au system at 1873 K. The experimental technique consisted of analyzing Knudsen cell effusates with a TOF mass spectrometer. The ion current ratios for the monomeric vapor species were measured as a function of temperature and composition and the thermodynamic properties calculated using a modified form of the Gibbs-Duhem equations. In addition to exhibiting very slight positive deviation from ideal behavior, the Sn?Ge system displayed parabolic solution behavior over the entire composition range. The results for the excess partial molar free energies and partial molar heats of mixing for the Sn?Ge system can be represented by $$G_1^E = 3.06X_2^2 kJ/g \cdot mol$$ and $$H_1^M = 5.86X_2^2 kJ/g \cdot mol$$ at 1773 K. The Sn?Au system exhibited negative deviation from ideal behavior and the results can be partially represented by $$\begin{gathered} \log _{10} \gamma Au = - 0.388 - 0.650 X_{Sn}^2 (0.00 \leqslant X_{Au} \leqslant 0.30) \hfill \\ \log _{10} \gamma Sn = 0.658 - 2.63 X_{Au}^2 (0.00 \leqslant X_{Sn} \leqslant 0.25) \hfill \\ \end{gathered} $$ and $$H_1^M = - 61.7 X_2^2 kJ/g \cdot mol$$ at 1873 K. Comparison of the results with other investigations indicates the heat of mixing for the system becomes more exothermic with increasing temperature above 1100 K. An experimental technique is presented for determining the effect of dissociative ionization of molecular species on the activity coefficient. The effect of dissociative ionization of the molecular species present in the Knudsen cell effusate was determined to be negligible.     

Interdiffusivities matrix of CaO-Al2O3-SiO2 melt at 1723 K to 1823 K

Ternary oxide mixtures of lime, alumina, and silica were premelted and quenched to produce glassy cylinders. A diffusion couple was selected from the mixtures of six different compositions in such a way that the average composition could be 40 wt pct CaO-20 wt pct A1₂O₃ = 40 wt pct SiO₂. Penetration curves of the components were measured with a X-ray microprobe analyzer. The interdiffusivities matrix defined with the Matano interface has been obtained from 52 successful diffusion runs at 1723 K to 1823 K as follows; 1 $$\begin{gathered} \tilde D_{10 - 10}^{30} = 8.9 \times 10^{ - 11} \exp ( - \frac{{253,700}}{{RT}})(m^2 /s) \hfill \\ \tilde D_{10 - 20}^{30} = - 2.5 \times 10^{ - 11} \exp ( - \frac{{194,300}}{{RT}})(m^2 /s) \hfill \\ \end{gathered} $$ 2 $$\begin{gathered} \tilde D_{20 - 10}^{30} = - 4.0 \times 10^{ - 11} \exp ( - \frac{{177,600}}{{RT}})(m^2 /s) \hfill \\ \tilde D_{20 - 20}^{30} = 6.12 \times 10^{ - 11} \exp ( - \frac{{318,400}}{{RT}})(m^2 /s) \hfill \\ \end{gathered} $$ where symbols, 10, 20, and 30 mean CaO, A1₂O₃, and SiO₂, respectively, and the activation energies are in Joules per mole. The diffusion composition paths obtained are discussed in relation to Cooper’s parallelogram. The composition dependency of the above interdiffusivities is estimated from the quasibinary interdiffusivities in all composition ranges of the present oxide system in liquid state.     

Nitrogen diffusion and solubility in tungsten

The diffusion and solubility of nitrogen in tungsten were determed using an ultrahigh vacuum-and mass-spectrometric technique capable of measuring concentrations of 10^?2 ppm and degassing rates of 10^?3 ppm N per hr. The technique is based on measuring the degassing rate of nitrogen as a function of time from a resistivity heated tungsten wire previously engassed with nitrogen between 1 and 25 torr. The diffusion and solubility constants between 1000° and 1800°C may be summarized by $$D = (2.37 \pm 0.43) \times 10^{ - 3} \exp [( - 35,800 \pm 3900)/RT] cm^2 /\sec ,$$ , and $$S = (0.21 \pm 0.06) \exp [( - 17,600 \pm 5900)/RT] torr \cdot liter cm^{ - 3} torr^{ - 1/2} .$$ . The concentration of nitrogen in tungsten at 760 torr according to these results are 0.4 and 9.2 ppm at 1000° and 2000°C, respectively. The expression for the permeation constants calculated fromD andS is $$K = 5 \times 10^{ - 4} \exp ( - 53,400/RT) torr \cdot liter cm^{ - 1} sec^{ - 1} torr^{ - 1/2} .$$ .     

Effect of superheat on the solidification structures of AISI 310S austenitic stainless steel

An experimental study was carried out to investigate the evolution of macrostructure and microstructure in AISI 310S stainless steel during solidification. Experimental findings suggested that the macrostructure and the microstructure of the cast material responded differently to variations in casting temperature. As the casting temperature decreased, the macro structure was refined, as expected, but the microstructure coarsened. A relationship was established between the proportion of equiaxed zone and superheat as follows: pct equiaxed zone =a +b ln (1/ΔT) wherea andb are constants. The relationship between grain width and superheat could be expressed by the equation $$gw = e^{\left( {c + d/\Delta T} \right)} $$ wherec andd are constants determined by the distance from the edge of the ingot. The relationship between primary arm spacing and superheat could be expressed by the equation $$\lambda _1 = p + q \ln \left( {1/\Delta T} \right)$$ wherep andq are constants determined by the distance from the edge of the ingot. The parameter “grain width ratio” has been introduced to describe the relationship between the shape and the nucleation and growth kinetics of the columnar grains.     

Thermodynamic properties of the vapor transport reactions in the Au−Cl system by a transpiration-mass spectrometric technique

A new transpiration-mass spectrometric technique is described for the study of vapor transport reactions, whereby the vapor transport species can be identified and their partial pressures determined from mass spectrometer ion intensity data. The vapor transport species in the Au?Cl system at low temperature (T<450°C) has been identified as Au₂Cl_8(g). For the reaction $$2Au_{(c)} + 3Cl_{2(g)} = Au_2 Cl_{6(g)} $$ the following results were obtained $$\Delta G_R^\circ = - 24,600( \pm 4400) + 59.8( \pm 8.2) T; \pm 1200 cal$$ A vapor pressure diagram for the Au?Cl system has been constructed from the experimental results and selected data from the literature. A new vapor transport species Au FeCl_8(g) was identified when chlorine was passed over a mixture of iron and gold. Formation of the vapor complex gives rise to increased transport rates.     

Ti3Ga and αTi interdiffusion between 660° and 860°C

Diffusion experiments were conducted in vacuum with bimetallic couples of the Ti₃Ga (α₂) composition and unalloyed α titanium. The gallium-composition profiles after various timetemperature exposures were determined by microprobe analyzer transverses and evaluated by established techniques. Results from this evaluation include the definition of the α to α +α₂ and the α + α₂ to α₂ phase boundaries for the Ti?Ga system and the determination of the interdiffusion coefficients for gallium in the α Ti and Ti₃Ga (α₂) phases. The interdiffusion coefficients were found to conform to the relationships: $$\tilde D_{\alpha Ti} = 4.4 \times 10^{ - 4} \exp [ - (43.4 \pm 4.7)10^3 /RT]cm^2 /\sec $$ $$\tilde D_{\alpha Ti_3 Ga} = 7.4 \times 10^{ - 5} \exp [ - (43.8 \pm 10.7)10^3 /RT]cm^2 /\sec $$      

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.     

The self diffusion of iron in Fe2SiO4 and CaFeSiO4 melts

The self diffusion of iron in Fe₂SiO₄ and CaFeSiO₄ melts has been measured in the temperature range 1250° to 1540°C using Fe⁵⁹ as the radio tracer and the capillary-liquid reservoir method of diffusion measurement. The results obtained are represented by $$log D_{Fe} = - \frac{{3800 \pm 500}}{T} - 2.74 \pm 0.29$$ for Fe₂SiO₄, and $$log D_{Fe} = - \frac{{5450 \pm 620}}{T} - 1.93 \pm 0.37$$ for CaFeSiO₄. Excellent agreement is obtained with the self-diffusivity of iron calculated from the measured interdiffusivity of iron and oxygen in iron oxide melts.     

Thermodynamic properties of the liquid Ge-Cu and Ge-Au systems by mass spectrometry

The activities and partial molar heats of mixing have been determined for the liquid Ge-Cu system at 1525°C and the liquid Ge-Au system at 1400°C. The experimental technique consisted of analyzing Knudsen cell effusates with a TOF mass spectrometer. The ion current ratios for the monomeric vapor species were measured as a function of temperature and composition and the thermodynamic properties calculated using a modified form of the Gibbs-Duhem equations. Both systems exhibited negative deviations from ideal behavior. The results for the Raoultian activity coefficients can be partially represented by $$\begin{gathered} \log \gamma _{Ge} = - 2.521X_{Cu}^2 + 0.948 (0 \leqslant X_{Ge} \leqslant 0.2) \hfill \\ \log \gamma _{Cu} = - 0.048X_{Ge}^2 - 0.466 (0 \leqslant X_{Cu} \leqslant 0.2) \hfill \\ \end{gathered} $$ for the Ge-Cu system at 1525°C and by $$\begin{gathered} \log \gamma _{Ge} = - 2.327X_{Au}^2 + 0.465 (0 \leqslant X_{Ge} \leqslant 0.35) \hfill \\ \log \gamma _{Au} = - 0.510X_{Ge}^2 - 0.489 (0 \leqslant X_{Au} \leqslant 0.30) \hfill \\ \end{gathered} $$ for the Ge-Au system at 1400°C. An experimental technique is presented for determining the contribution of dissociative ionization of polymer species to the measured monomeric ion current ratio . The effect of dissociative ionization of the germanium polymer species present in the Knudsen ceil effusate was determined to be negligible.     

Solubility product of aluminum nitride in 3 percent silicon iron

The solubility product of aluminum nitride in 3 pct silicon iron was determined experimentally from 1273 to 1473 K with results described by the equation $$\begin{gathered} \log [pct \underline {Al} _{\alpha (3Si) } pct \underline N _{\alpha (3Si)} ] \hfill \\ = {\text{--11,900/}}T + 3.56 \hfill \\ \end{gathered} $$ whereT is in kelvins and concentrations are in weight percent. In the experiments the equilibrium distribution of nitrogen between purified gamma iron (fcc) and 3 pct silicon alpha iron (bcc) was determined between 1273 and 1523 K.     

Surface Tension of Liquid Fe-O Alloys: Revisiting Belton’s Two-Step Adsorption Model

The effect of oxygen adsorption on the surface tension of liquid iron was investigated using the constrained drop method. Experiments were carried out at 1823 K and 1873 K (1550 °C and 1600 °C) under a CO₂-H₂ gas mixture. The experimental results were interpreted using the Langmuir ideal adsorption model and Belton’s two-step adsorption model; the latter model showed better agreement with the experimental results. According to the two-step model, the surface tension of liquid Fe-O alloys at 1823 K and 1873 K (1550 °C and 1600 °C) can be respectively expressed as follows: $$ \sigma = 1882 - 260[0.25\ln (1 + 2407a_{\text{O}} ) + 0.75\ln (1 + 72a_{\text{O}} )]\quad \left[ {T = 1823\,{\text{K}}\left( {1550\,^\circ {\text{C}}} \right)} \right], $$ $$ \sigma = 1834 - 267[0.25\ln (1 + 1445a_{\text{O}} ) + 0.75\ln (1 + 46a_{\text{O}} )]\quad \left[ {T = 1873\,{\text{K}}\left( {1600\,^\circ {\text{C}}} \right)} \right]. $$      

Kinetics of the reaction of CH4 gas with liquid iron

In iron bath smelting and other processes that use coal, the effective use of volatile matter can improve the energy efficiency of the process. The reaction of simulated volatile (CH₄) with iron was studied. The rate of carburization of liquid iron by CH₄ gas was measured between 1400 °C and 1700 °C under conditions for which the effect of mass transfer can be corrected with reasonable accuracy. The rate was measured for partial pressures of CH₄ in Ar in the range of 0.02 to 0.06 atm and sulfur contents in the metal from 0.0006 to 0.5 mass pct. The results indicate that the rate of carburization may be controlled by the dissociation of CH₄ on the surface. Sulfur was found to decrease the rate, and the residual rate phenomenon was observed for high sulfur contents. The rate constant may be represented by the following equation: $$ k_C = \frac{{k^\circ }}{{1 + K_S a_S }} + \frac{{K_S a_S k_r }}{{1 + K_S a_S }}$$ wherek ^o ,k _r,K _s, anda _s are the bare surface rate constant, residual rate constant, adsorption coefficient for sulfur, and activity of sulfur in the metal, respectively. The second term in the rate equation represents the rate of dissociation on the adsorbed sulfur. The rate constants and adsorption coefficient were determined as functions of temperature to be $$\begin{gathered} log k^\circ = \frac{{ - 12,000}}{T} + 2.95 (mole/cm^2 s atm) \hfill \\ log k_r = \frac{{ - 14,000}}{T} + 3.45 (mole/cm^2 s atm) \hfill \\ log K_S = \frac{{ - 1800}}{T} + 1.04 \hfill \\ \end{gathered} $$      

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).