Solubility of oxygen in Fe–Co melts containing titanium

Solutions of oxygen in Fe–Co melts containing titanium are subjected to thermodynamic analysis. The first step is to determine the equilibrium reaction constants of titanium and oxygen, the activity coefficients at infinite dilution, and the interaction parameters in melts of different composition at 1873 K. With increase in cobalt content, the equilibrium reaction constants of titanium and oxygen decline from iron (logK(FeO · TiO₂) =–7.194; logK(TiO₂) =–6.125; logK(Ti₃O₅) =–16.793; logK(Ti₂O₃) =–10.224) to cobalt (logK(CoO · TiO₂) =–8.580; logK(TiO₅) =–7.625; logK(Ti₃O₅) =–20.073; logK(Ti₂O₃) =–12.005). The titanium concentrations at the equilibrium points between the oxide phases (Fe, Co)O · TiO₂, TiO₂, Ti₃O₅, and Ti₂O₃ are determined. The titanium content at the equilibrium point (Fe, Co)O · TiO₂ ? TiO₂ decreases from 1.0 × 10^–4% Ti in iron to 1.9 × 10^–6% Ti in cobalt. The titanium content at the equilibrium point TiO₂?Ti₃O₅ increases from 0.0011% Ti in iron to 0.0095% Ti in cobalt. The titanium content at the equilibrium point Ti₃O₅ ? Ti₂O₃ decreases from 0.181%Ti in iron to 1.570% Ti in cobalt. The solubility of oxygen in the given melts is calculated as a function of the cobalt and titanium content. The deoxidizing ability of titanium decline with increase in Co content to 20% and then rise at higher Co content. In iron and its alloys with 20% and 40% Co, the deoxidizing ability of titanium are practically the same. The solubility curves of oxygen in iron-cobalt melts containing titanium pass through a minimum, whose position shifts to lower Ti content with increase in the Co content. Further addition of titanium increases the oxygen content in the melt. With higher Co content in the melt, the oxygen content in the melt increases more sharply beyond the minimum, as further titanium is added.     

Thermodynamics of the oxygen solutions in Fe-Ni-Ti melts

The oxygen solutions in Fe-Ni melts containing up to 3% titanium are analyzed thermodynamically. The results of the works that determined the fields of the oxide phases in iron and nickel deoxidized by titanium are generalized. The proposed calculation model is shown to adequately describe the titanium deoxidation of iron-nickel alloys. The deoxidizing capacity of titanium decreases as the nickel content in the melt increases to 40% and, then, increases sharply as the nickel content increases further. The oxygen solubility curves pass through a minimum, whose position changes from 0.5644% Ti for pure iron to 0.6332% Ti for pure nickel. The points of equilibrium between the TiO₂, Ti₃O₅, and Ti₂O₃ oxide phases are determined for six alloy compositions at 1873 K. The titanium deoxidation of Fe-40% Ni melts is experimentally studied, and the calculated and experimental results are in good agreement.     

Transient Behavior of Inclusion Chemistry,Shape, and Structure in Fe-Al-Ti-O Melts: Effect of Titanium Source and Laboratory Deoxidation Simulation

During ladle processing of interstitial-free (IF) steel melts, it is possible for transient titanium-containing oxides to be formed if the local titanium/aluminum (Ti/Al) ratio is locally and temporarily increased after aluminum killing. The phase stability diagrams suggest that if the Ti/Al ratio is increased, then Al₂TiO₅ and/or a liquid Al-Ti-O region can become stable, and eventually at even higher Ti/Al ratios, Ti₃O₅ becomes stable. In this study, the Ti/Al ratio was successively altered to investigate (1) how the inclusions evolved after titanium addition to aluminum-killed iron melts and (2) whether the inclusions present after sufficient time were those predicted by thermodynamics. When the Ti/Al ratio was maintained at 1/4, such that Al₂O₃ is the only thermodynamically stable oxide, the results show that transient titanium-containing oxides exist temporarily after titanium addition, but with time, the predominant inclusion was Al₂O₃, which would generate little shape change and produce transient stage inclusions with less titanium contents. When the Ti/Al ratio was increased to 1/1 (Al₂O₃ still being the only thermodynamically stable oxide), the results show a more distinct increase in the titanium content of the transient inclusions. The transient reaction was, in this case, accompanied by an irreversible shape change from spherical to irregular inclusions. When the Ti/Al ratio in the melt was increased to 15/1 within the Al₂TiO₅ stable phase region, the inclusion population evolved from spherical-dominant ones to irregular ones. It was found that the final inclusion chemistry has more titanium but less aluminum content compared with the expected from the Al₂TiO₅ chemistry. Besides, the transmission electron microscopy (TEM) results showed the existence of Ti₂O. When the Ti/Al ratio in the melt was increased such that Ti₃O₅ is the thermodynamically stable inclusion (Ti/Al ratio of 75/1 or ∞), the inclusions evolved after titanium addition toward TiO_x inclusions, which is accompanied by a shape change from spherical to irregular. The TEM results revealed and confirmed the existence of metastable Ti₂O besides the thermodynamically stable Ti₃O₅, and it was consistent with the results based on oxidation studies of thin layers of titanium with Al₂O₃ substrate. It was discovered that Ti₂O has the tendency of transforming into the thermodynamically stable phase Ti₃O₅ under certain conditions.     

Unidirectionally solidified Ti−TiB and Ti−Ti5Si3 eutectic composites

Induction melting and electron beam melting techniques were employed in the production of unidirectionally solidified eutectic composites of Ti-1.7 wt pct B and Ti-8.5 wt pct Si. The grown eutectics were reinforced by 7.7 volume pct of TiB fibers and 31 volume pct of Ti₅Si₃ fibers respectively. Controlled dendritic solidification of a hypereutectic composition of Ti-12 wt pct Si was also accomplished. Tensile, compressive, creep, and stress rupture specimens were cut from the eutectic composites and tested with reinforcing fibers parallel to the load axis. Ti?TiB eutectic was found to have less than the critical volume fraction of fibers necessary for reinforcement, while Ti?Ti₅Si₃ composite attained a compressive yield strength of 275,000 psi and a compressive Young's modulus of 30×10⁸ psi after heat treatment. The 500 and 4000 hr stress rupture properties of Ti?Si eutectic were superior to commercial titanium alloys at 1000° and 1200°F. The minimum creep rate of Ti?Ti₅Si₃ eutectic composite was lower than all other titanium alloys at 1000°F. Tensile, compressive, and creep properties of the Ti-8.5 wt pct Si eutectic are discussed in terms of the current theories of composite behavior.     

Thermodynamics of Oxygen Solution in Fe–Ni Melts Containing Boron

Fe–Ni alloys are widely used in engineering today. They are sometimes alloyed with boron. Oxygen is a harmful impurity in Fe–Ni alloys. It may be present in dissolved form or as nonmetallic inclusions. The presence of oxygen in Fe–Ni alloys impairs their performance. Research on the thermodynamics of oxygen solutions in Fe–Ni melts containing boron is of considerable interest in order to improve alloy production. The present work offers a thermodynamic analysis of solutions of oxygen in Fe–Ni melts containing boron. The equilibrium constant of the reaction between boron and oxygen dissolved in the melt in such systems is determined. The activity coefficients at infinite dilution and the interaction parameters in melts of different composition are also calculated. When boron reacts with oxygen in Fe–Ni melts, the oxide phase contains not only B₂O₃ but also FeO and NiO. The mole fractions of B₂O₃, FeO, and NiO in the oxide phase are calculated for different boron concentrations in Fe–Ni melts at 1873 K. For iron melts with low boron content, the mole fraction of boron oxide is ~0.1. With increase in the nickel and boron content in the melts, the boron-oxide content in the oxide phase increases. Its mole fraction is close to one for pure nickel. The solubility of oxygen in Fe–Ni melts is calculated as a function of the nickel and boron content. The deoxidizing ability of the boron improve significantly with increase in nickel content in the melt. The curves of oxygen solubility in Fe?Ni melts containing boron pass through a minimum, which is shifted to higher boron content with increase in nickel content in the melt. The boron content at the minima on the curves of oxygen solubility are determined, as well as the corresponding minimum oxygen concentrations.     

Enthalpy of mixing of liquid Cu-Ti-Zr alloys

The enthalpy of mixing of liquid Cu-Ti-Zr ternary alloys is studied by high-temperature isoperibolic calorimetry at 1873 K along three ray sections characterized by the ratios x _Zr: x _Cu = 3: 7, x _Ti: x _Cu = 3: 7, and x _Zr: x _Ti = 1 at x _Cu = 1?0.4. The isotherm of the integral enthalpy of mixing of these melts is described in terms of the Redlich-Kister-Muggianu model. Along with the substantial contributions of binary copper-titanium and copper-zirconium interactions, the contribution of a ternary interaction to the enthalpy of mixing of liquid Cu-Ti-Zr alloys also exists. The first partial enthalpies of mixing of Ni, Al, Si, Sn, and Y with the melts are studied to determine the character of the interaction between the ternary Cu-Ti-Zr melts and metal additions that facilitate amorphization upon melt quenching. The introduction of these metals into the ternary melts is shown to increase their thermodynamic stability.     

Understanding the Magnesiothermic Reduction Mechanism of TiO<Subscript>2</Subscript> to Produce Ti

Titanium dioxide (TiO₂) powders in the mineral form of rutile were reduced to metallic and an intermediate phase via a magnesiothermic reaction in molten Mg at temperatures between 973 K and 1173 K (700 °C and 900 °C) under high-purity Ar atmosphere. The reaction behavior and pathway indicated intermediate phase formation during the magnesiothermic reduction of TiO₂ using XRD (X-ray diffraction), SEM (scanning electron microscope), and TEM (transmission electron microscope). Mg/TiO₂ = 2 resulted in various intermediate phases of oxygen containing titanium, including Ti₆O, Ti₃O, and Ti₂O, with metallic Ti present. MgTi₂O₄ ternary intermediate phases could also be observed, but they were dependent on the excess Mg present in the sample. Nevertheless, even with excessive amounts of Mg at Mg/TiO₂ = 10, complete reduction to metallic Ti could not be obtained and some Ti₆O intermediate phases were present. Although thermodynamics do not predict the formation of the MgTi₂O₄ spinel phase, detailed phase identification through XRD, SEM, and TEM showed significant amounts of this intermediate ternary phase even at excess Mg additions. Considering the stepwise reduction of TiO₂ by Mg and the pronounced amounts of MgTi₂O₄ phase observed, the rate-limiting reaction is likely the reduction of MgTi₂O₄ to the Ti_tO phase. Thus, an additional reduction step beyond thermodynamic predictions was developed.     

Thermodynamic behavior of Na2O-B2O3 melt

The activity of Na₂O in a Na₂O-B₂O₃ melt was measured at 1373 K by a chemical equilibration technique to understand the thermodynamic behavior of this slag system. Also, the activity coefficient of Na in Ag was preliminarily measured as fundamental thermodynamic data, to estimate the activity of Na₂O in the slag. Sodium in the silver melt, within the present concentration range, exhibits the Henrian behavior, and the Henrian activity coefficient of Na in Ag (γ ⁰ _Na) is estimated to be 37.5 at 1373 K, indicating a positive deviation from ideality. The activity of Na₂O in the slag varies from 1.86×10⁻⁶ to 4.99×10⁻⁴ when its content is increased from 11.0 to 64.9 mol pct; this indicates a significant negative deviation from ideality. The excess stability does not exhibit any pronounced peak, despite being drastically changed at specific slag compositions. Comparing the molar Gibbs free energy of mixing in various binary slags, Na₂O was considered to be more basic than BaO (CaO) was, followed next by MgO; also, P₂O₅ would be significantly more acidic than SiO₂ would be, followed next by B₂O₃. Comparing the heats of formation of solid compounds in binary slags, the larger the differences in the electronegativity values between slag components, the more the relative ionic characters of the melts seemed to be.     

Electron Microscopic Study on the Suction Cast In Situ Ti-Fe-Sn Ultrafine Composites

The current investigation reports detailed study on the microstructural evolution in the suction cast hypereutectic Ti₇₁Fe_29?x Sn _x alloys during Sn addition with x = 0, 2, 2.5, 3, 3.85, 4.5, 6, and 10 at. pct and the solidification of these ternary alloys using SEM and TEM. These alloys have been prepared by melting high-purity elements using vacuum arc melting furnace under high-purity argon atmosphere. This was followed by suction casting these alloys in the water-cooled split Cu molds of diameters, ? = 1 and 3 mm, under argon atmosphere. The results indicate the formation of binary eutectic between bcc solid solution ??-Ti and B2 FeTi in all alloys. ??-Ti undergoes eutectoid transformation, ??-Ti ?? ??-Ti + FeTi, during subsequent solid-state cooling, leading to formation of hcp ??-Ti and FeTi. For alloys x < 2, the primary FeTi forms from the liquid before the formation of eutectic with minute scale Ti₃Sn phase. For alloys with 2 ?? x ?? 10, the liquid is found to undergo ternary quasi-peritectic reaction with primary Ti₃Sn, L+Ti₃Sn ?? ??-Ti+FeTi, leading to formation of another kind of FeTi. In all the other alloy compositions (3.85 ?? x ?? 10), Ti₃Sn and FeTi dendrites are observed in the suction cast alloys with profuse amount of Ti₃Sn being formed for alloys with x ?? 4.5. The current study conclusively proves that the liquid undergoes ternary quasi-peritectic reaction involving four phases, L + Ti₃Sn ?? ??-Ti + FeTi, which lies at the invariant point Ti_69.2±0.8Fe_27.4±0.7Sn_3.4±0.2 (denoted by P). Below P, there is one univariant reaction, i.e., L ?? ??-Ti + FeTi for all alloy compositions, whereas above P, liquid undergoes one of the univariant reactions, i.e., L + ??-Ti ?? Ti₃Sn (Sn = 2, 2.5, 3, and 4.5 at. pct) or L + FeTi ?? Ti₃Sn for alloys (Sn = 6, 10 at. pct). For alloy with Sn = 3.85 at. pct, the ternary quasi-peritectic reaction is co-operated by two monovariant eutectic reactions, i.e., L ?? ??-Ti + FeTi below P and L ?? FeTi + Ti₃Sn above P. Detailed microstructural information allows us to construct liquidus projection of the investigated alloys. The results are critically discussed in the light of available literature data.     

Activity of titanium in Fe-Cr melts

The activity of titanium in Fe-Cr melts was measured using a galvanic cell technique. By measuring the activity of oxygen in equilibrium with the molten metal and solid titanium oxide, in conjunction with the analysis of the samples for titanium, the activity coefficient of Ti was measured at 1873 K. Oxygen cells, comprised of a thoria-yttria electrolyte with a Cr-Cr₂O₃ reference electrode and an Al₂O₃ (ZrO₂)-Mo cermet tipped molybdenum lead wire, were used to take the electromotive force (EMF) measurements. The measured values of γ°_Ti and e _Ti ^Cr were 0.018 and 0.1032, respectively.     

Infrared Brazing Ti50Ni50 and Invar Using Ag-Based Filler Foils

Infrared brazing Ti₅₀Ni₅₀ and Invar using BAg-8 and Cusil-ABA foils was investigated. The Ag-Cu eutectic matrix dominates both brazed joints. The maximum shear strengths of the brazed joints using BAg-8 and Cusil-ABA fillers are 158 and 249 MPa. Failure of interfacial Fe₂Ti/Ni₃Ti reaction layers is responsible for the BAg-8 joint. In contrast, the Cusil-ABA brazed joint is fractured along the interfacial Fe₂Ti intermetallic compound. Both fractographs are characterized with cleavage dominated fracture.     

Infrared brazing Cu and Ti using a 95Ag-5Al braze alloy

Dynamic wetting angle measurements, microstructural evolution, reaction kinetics, and shear strength of infrared brazing Cu and Ti using a 95Ag-5Al braze alloy are evaluated. The specimen infrared brazed at 900 °C consists mainly of Cu₂Ti and Cu₄Ti. Both CuTi and Cu₄Ti₃ are observed at the interface between the braze and Ti substrate. Microstructures of Ti/95Ag-5Al/Cu joints infrared brazed at 830 °C and 850 °C are very different from that of the joint infrared brazed at 900 °C, because the dissolution of both substrates significantly decreased as the brazing temperature decreased. Specimens infrared brazed at 830 °C and 850 °C are primarily comprised of Ag-Cu eutectic and the Cu-rich phase. Two interfacial reaction layers, including Ti₂Cu and AlCu₂Ti, are found in the experiment. The shear strengths of infrared brazed specimens at 830 °C and 850 °C are between 160 and 198.5 MPa, and are fractured along the interfacial reaction layers, AlCu₂Ti and Ti₂Cu, between the braze alloy and Ti substrate. The use of the infrared brazing provides an effective way to inhibit the growth of intermetallics at the interface between the braze alloy and substrate.     

Enhancing the High Temperature Capability of Ti‐Alloys

Titanium is a widely used structural material for applications below approximately 500°C but right now it cannot be used at higher temperatures. Titanium forms a fast growing rutile layer under these conditions. Furthermore enhanced oxygen uptake into the metal subsurface zone leads to embrittlement which deteriorates the mechanical properties. To overcome this problem a combined Al‐ plus F‐treatment was developed. The combination of Al‐enrichment in the surface zone so that intermetallic Ti_xAl_y‐layers are produced which form a protective alumina layer during high temperature exposure plus stabilization of the Al₂O₃‐scale by the fluorine effect led to significantly improved resistance against increased oxidation and embrittlement in high temperature exposure tests of several Ti‐alloys. In this paper, the experimental procedures and achieved improvements are described. The results will be discussed for the use of Ti‐alloys at elevated temperatures.     

Evolution of microstructures in the nickel modified titanium trialuminides near the L12 phase field

This study focuses upon the evolution of microstructures during solidification processing of several intermetallic alloys around the Ll₂ phase in the Al-rich corner of the Al-Ti-Ni ternary system. The alloys were produced by double induction melting and subsequent homogenization followed by furnace cooling. The microstructure was characterized by means of optical and scanning electron microscopy with energy-dispersive spectroscopy (EDS) analysis and X-ray diffraction. The microstructural evolution in homogenized alloys was dependent on both nickel and titanium content. Very fine precipitates of Al₂Ti were observed within the Ll₂ phase in alloys containing 62 to 65 at. pct Al and at least 25 at. pct Ti. The Al₂Ti precipitates are stable at least up to 1000 °C and undergo complete dissolution at 1200 °C. In alloys containing around 66 at. pct Al and 25 to 31 at. pct Ti, phases such as Al₃Ti, Al₅Ti₂, and Al₁₁Ti₅ were observed. A modified room temperature isotherm in the Al-Ti-Ni ternary system is proposed, taking into account the existence of Al₂Ti, Al₁₁Ti₅, Al₅Ti₂, and Al₃Ti in equilibrium with the Ll₂ phase. It seems that at room temperature, the Ll₂ phase field for homogenized alloys is extremely small. It will be practically impossible to obtain a single-phase microstructure at room temperature in the Al-Ti-Ni ternary alloys after homogenization at 1000 °C followed by furnace cooling. S. BISWAS, formerly Graduate Student, Department of Mechanical Engineering, University of Waterloo     

Reaction layers and mechanisms for a Ti-activated braze on sapphire

A study was conducted to understand the wetting phenomena observed in brazing of a Ti-containing active filler metal on sapphire substrates. The goal of the study was to understand the interfacial reactions that permit wetting of commercial Ag-Cu-Ti active filler metal to pure alumina, despite the lower thermodynamic stability of TiO₂ relative to Al₂O₃. Based upon transmission electron microscope, electron microprobe, and Auger analyses, it is proposed that two coupled reactions and diffusion of reactants take place. The oxides TiO, Ti₂O, and Cu₃Ti₃O were observed at the braze/ceramic interface. It is suggested that the complex oxide Cu₃Ti₃O grows at its interface with TiO, and the oxide TiO is produced by reaction of Ti and sapphire and is subsequently consumed at its interface with Cu₃Ti₃O. It is also suggested that Ti₂O forms from Ti and TiO while cooling from the brazing cycle.     

Thermodynamics of the oxygen solutions in boron-containing Fe–Co melts

A thermodynamic analysis of the oxygen solutions in boron-containing Fe–Co melts has been performed. The equilibrium constant of reaction between boron and oxygen, which are dissolved in iron–cobalt melts; the activity coefficients at infinite dilution; and the interaction parameters for melts differing in composition have been determined. The oxide phase formed in the Fe–Co melts containing boron and oxygen comprises FeO and CoO along with the B₂O₃ phase. The oxide phase compositions over Fe–Co–B–O melts are calculated. As the cobalt and boron contents in the melts increase, the mole fraction of boron oxide increases; in the case of pure cobalt, it is close to unity. The dependences of the oxygen solubility on the cobalt and boron contents in the melts are calculated. The deoxidizing capacity of boron substantially increases as the cobalt content in a melt increases. The composition dependences of the oxygen solubility in boron-containing Fe–Co melts have a minimum, which shifts to a low boron content as the cobalt content in the melts increases. The boron contents corresponding to the minimum in the oxygen solubility curves and the minimum oxygen concentrations corresponding to the boron contents are determined.     

Equlibrium between Liquid Fe‐Ti‐O Slags and Metallic Iron

The compositions of Fe‐Ti‐O melts in equilibrium with molten iron have been determined by melting mixtures of TiO₂, metallic iron and various additions of either Fe₂O₃ or metallic titanium in a high‐frequency induction furnace. The furnace had a vertically segmented water‐cooled copper crucible which enabled the mixture to be melted with vigorous stirring inside a freeze‐lining of about 1 mm thickness. The slag compositions were found to form a curved line in the ternary diagram FeTiO₃ – TiO₂ – Ti₂O₃ with its highest TiO₂ content slightly higher than the pseudobrookite (M₃O₅) composition FeTi₂O₅ ‐ Ti₃O₅. The slags were examined by X‐ray diffraction and microprobe analyses. For all slags the main phase was pseudobrookite (M₃O₅) solid solution with some rutile or Magnéli phase (Ti_nO_2n‐1). The most iron‐rich and the most titanium‐rich slags contained also some FeTiO₃, respectively Ti₂O₃ phase. A melting point diagram is suggested with a eutectic groove running between the M₃O₅ phase and the TiO₂ or Magnéli phase from about 1665°C for the iron‐free to the less than 1500°C for the titanium‐free slags.     

Oxygen activities in Cr-containing Fe and Ni-based melts

Plug-type, ZrO₂-based oxygen sensors have been used for long-term measurements of oxygen activity in Fe–O–Cr and Ni–O–Cr melts. In these melts, equilibrated with chromium oxide, oxygen activities a_O were determined as a function of Cr content. From the experimental results, data were derived for activity coefficients f_O and of 1st and 2nd order interaction parameters e_O^Cr and r_O^Cr. Cr₂O₃ has been identified as the oxide phase in equilibrium with the metal melt at ≥ 5 wt.% Cr in the case of iron and at ≥ 0.2 wt.% Cr in the case of nickel. Oxygen activities and oxygen contents in Cr-containing iron melts are lowered with increasing additions of nickel. Further investigations were directed to a_O determination in Fe–O–Cr–C and Fe–O–Cr–Al melts.     

Development of Al-Ti-C grain refiners containing TiC

Cast Al-Ti-C grain refiners were synthesized by reacting up to 2 pct graphite particles of 20 micron average size with stirred Al-(5 to 10) pct Ti alloy melts, which generated submicron-sized TiC particles within the melts, and their solidified structures showed preferential segregation of the carbide phase in the grain or cell boundary regions and occasional presence of free carbon whose amount exceeded equilibrium values. At the usual melt temperatures of below 1273 K, though, TiC formed first, but was subsequently found to react with the melt forming a sheathing of A1₄C₃ and Ti₃AlC which resulted into poisoning of the TiC particles. However, it was possible to reverse these reactions in order to regain the virgin TiC particles by superheating the melts in the temperature region where TiC particles are thermodynamically stable. Grain refining tests using the TiC master alloys produced fine equiaxed grains of cast aluminum whose sizes were comparable to that obtainable with the standard TiB₂ commercial grain refiner. TiC particles introducedvia the master alloys were found to occur in the grain centers, thereby confirming that they nucleated aluminum crystals. On leave from Regional Research Laboratory (CSIR), Bhopal, is Research Associate.     

Thermodynamic properties of aluminum, magnesium, and calcium in molten silicon

The thermodynamic properties of aluminum, magnesium, and calcium in molten silicon were investigated using a chemical equilibration technique at 1723 to 1848 K, 1698 to 1798 K, and 1723 to 1823 K, respectively. The activity coefficient of aluminum in molten silicon was determined by equilibrating molten silicon-aluminum alloys with solid Al₂O₃ and Al₆Si₂O₁₃, that of magnesium was determined by equilibrating molten silicon-magnesium alloys and MgO-SiO₂-Al₂O₃ melts doubly saturated with MgSiO₃ and SiO₂, and that of calcium was determined by equilibrating molten silicon-calcium alloys with SiO₂-saturated CaO-SiO₂ melts. The activity coefficients at infinite dilution relative to the pure liquid state were determined as follows: