Measurement and modeling of Alloy-Spinel-Corundum equilibrium in the Ni-Mn-Al-0 system at 1873 K

The oxygen content of liquid Ni-Mn alloy equilibrated with spinel solid solution, (Ni,Mn)O. (1 +x)A1₂O₃, and α-Al₂O₃ has been measured by suction sampling and inert gas fusion analysis. The corresponding oxygen potential of the three-phase system has been determined with a solid state cell incorporating (Y₂O₃)ThO₂ as the solid electrolyte and Cr + Cr₂O₃ as the reference electrode. The equilibrium composition of the spinel phase formed at the interface of the alloy and alumina crucible was obtained using EPMA. The experimental data are compared with a thermodynamic model based on the free energies of formation of end-member spinels, free energy of solution of oxygen in liquid nickel, interaction parameters, and the activities in liquid Ni-Mn alloy and spinel solid solution. Mixing properties of the spinel solid solution are derived from a cation distribution model. The computational results agree with the experimental data on oxygen concentration, potential, and composition of the spinel phase.     

Measurement and modeling of Alloy-Spinel-Corundum equilibrium in the Ni-Mn-Al-0 system at 1873 K

The oxygen content of liquid Ni-Mn alloy equilibrated with spinel solid solution, (Ni,Mn)O. (1 +x)A1₂O₃, and α-Al₂O₃ has been measured by suction sampling and inert gas fusion analysis. The corresponding oxygen potential of the three-phase system has been determined with a solid state cell incorporating (Y₂O₃)ThO₂ as the solid electrolyte and Cr + Cr₂O₃ as the reference electrode. The equilibrium composition of the spinel phase formed at the interface of the alloy and alumina crucible was obtained using EPMA. The experimental data are compared with a thermodynamic model based on the free energies of formation of end-member spinels, free energy of solution of oxygen in liquid nickel, interaction parameters, and the activities in liquid Ni-Mn alloy and spinel solid solution. Mixing properties of the spinel solid solution are derived from a cation distribution model. The computational results agree with the experimental data on oxygen concentration, potential, and composition of the spinel phase.     

Alloy/oxide equilibria in Fe—V—O and Fe—Nb—O systems

An experimental characterization of three-phase equilibria in Fe—V—O and Fe—Nb—O systems at 1 823, 1 873, and 1 923 K has been carried out using a solid state cell and by analysis of quenched samples. The oxygen potentials corresponding to these three-phase equilibria were monitored by a solid state cell incorporating Y₂O₃ doped ThO₂ with Cr + Cr₂O₃ as reference electrode. Similar measurements were carried out for Fe—Nb—O alloys in equilibrium with a mixture of FeNb₂O₆ and NbO₂. These measurements permit evaluation of interaction parameters (e^v_o= -6590/T+2.892 and e^Nb_o = -4066/T+1.502) and activity coefficients of vanadium and niobium in dilute solution (In y^o_v = -35320/T+12.68 and In y^o_Nb = - 12386/T+ 4.34) in liquid iron. The results obtained in this study resolve a number of discrepancies in thermodynamic data reported in the literature, especially regarding the activity coefficients of V and Nb and the stability ranges for V₂O₃ and VO_1+x.     

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.     

Thermodynamics of oxygen behaviour in cobalt-nickel alloys

In this study the concentration and chemical potential of oxygen in liquid Co-Ni alloys equilibrated with cobalt-nickel aluminate spinel solid solutions and alumina have been determined at 1773, 1823 and 1873K as a function of nickel concentration. The oxygen content of the melt has been measured by suction sampling and inert gas fusion analysis. The corresponding oxygen potential has been determined with the following solid state cell: Mo, Mo+MoO₂ | (MgO)ZrO₂ | (Co, Ni) melt + AI₂O₃ + (Co, Ni)O·(1+x)Al₂O₃, Mo. The effect of nickel on the activity coefficient of oxygen in Co-Ni alloys has been determined. The results for the activity coefficient have been modelled with Wagner's interaction parameters and also the more recent exponential method of St. Pierre et al. at the three temperatures.     

Solubility and activity of oxygen in liquid manganese

The oxygen concentration of liquid manganese in equilibrium with MnAl_2+2xO_4+3x and α−Al₂O₃ has been determined in the temperature range 1520 to 1875 K. The oxygen content of quenched samples, wrapped in oxygen-free nickel foil, was determined by an inert gas fusion technique. The results are combined with accurate data now available on the Gibbs energies of formation of MnO and Al₂O₃−saturated MnAl_2+2xO_4+3x to derive the oxygen content of liquid manganese in equilibrium with MnO and the Gibbs energy of solution of diatomic oxygen gas in liquid manganese. The enthalpy and entropy of solution of oxygen in manganese are compared with similar data on other metal-oxygen systems.     

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.     

Phase relations and gibbs energies in the system Mn-Rh-O

Phase relations in the system Mn-Rh-O are established at 1273 K by equilibrating different compositions either in evacuated quartz ampules or in pure oxygen at a pressure of 1.01 × 10⁵ Pa. The quenched samples are examined by optical microscopy, X-ray diffraction, and energy-dispersive X-ray analysis (EDAX). The alloys and intermetallics in the binary Mn-Rh system are found to be in equilibrium with MnO. There is only one ternary compound, MnRh₂O₄, with normal spinel structure in the system. The compound Mn₃O₄ has a tetragonal structure at 1273 K. A solid solution is formed between MnRh₂O₄ and Mn₃O₄. The solid solution has the cubic structure over a large range of composition and coexists with metallic rhodium. The partial pressure of oxygen corresponding to this two-phase equilibrium is measured as a function of the composition of the spinel solid solution and temperature. A new solid-state cell, with three separate electrode compartments, is designed to measure accurately the chemical potential of oxygen in the two-phase mixture, Rh + Mn_3−2xRh_2xO₄, which has 1 degree of freedom at constant temperature. From the electromotive force (emf), thermodynamic mixing properties of the Mn₃O₄-MnRh₂O₄ solid solution and Gibbs energy of formation of MnRh₂O₄ are deduced. The activities exhibit negative deviations from Raoult’s law for most of the composition range, except near Mn₃O₄, where a two-phase region exists. In the cubic phase, the entropy of mixing of the two Rh³⁺ and Mn³⁺ ions on the octahedral site of the spinel is ideal, and the enthalpy of mixing is positive and symmetric with respect to composition. For the formation of the spinel (sp) from component oxides with rock salt (rs) and orthorhombic (orth) structures according to the reaction, MnO (rs) + Rh₂O₃ (orth) → MnRh₂O₄ (sp),ΔG° = -49,680 + 1.56T (±500)J mol⁻¹ The oxygen potentials corresponding to MnO + Mn₃O₄ and Rh + Rh₂O₃ equilibria are also obtained from potentiometric measurements on galvanic cells incorporating yttria-stabilized zirconia as the solid electrolyte. From these results, an oxygen potential diagram for the ternary system is developed.     

Thermodynamics on the formation of spinel (MgO·Al<Subscript>2</Subscript>O<Subscript>3</Subscript>) inclusion in liquid iron containing chromium

The stability diagram of MgO, spinel solid solution (MgO·(Al _X Cr_1−X )₂O₃), and sesquioxide solid solution ((Al _Y Cr_1−Y )₂O₃) as a function of Mg, Al, and O contents at a constant chromium content (18 mass pct) in liquid iron is drawn at 1873 K. The interaction parameters between Mg and other solutes (Al, Cr, Ni, Ti, Si, and C) are determined by the experimental method, which assures equilibrium between Mg vapor and liquid iron, were applied to calculate the diagram. Titanium deoxidation is not recommended for the prevention of spinel formation, because Ti accelerates Mg dissolution from refractory or slag due to its high affinity for Mg (e _Mg ^Ti = − 0.64). The standard Gibbs free energies of formation for the three inclusions (periclase, spinel, and sesquioxide solid solutions) and the tielines between two solid solutions were calculated with the aid of the regular solution model and the thermochemical F*A*C*T database computing system, respectively. The phase stability regions and oxygen content in steel for the current Fe-Mg-Al-Cr (18 mass pct)-O system are compared with those of the previous non-Cr system. Detailed information on the spinel composition according to Mg and Al contents is also available from the present stability diagram.     

Thermodynamics of iron-manganese aluminate spinel inclusions in steel

The effect of manganese on the residual oxygen concentrations of liquid iron in equilibrium with alumina saturated iron-manganese aluminate spinel solid solutions was investigated at temperatures of 1550, 1600, and 1650°C. The relationship between the equilibrium concentrations of manganese and oxygen in iron melts containing up to 6 wt pct manganese has been established. The compositions of the spinel deoxidation products, (Fe _x Mn _j-x ) O · Al₂O₃, which were formed during equilibration with the iron melts were determined with electron microprobe and neutron activation analysis. From these results, new thermodynamic data pertaining to galaxite formation reactions have been derived and their implications with respect to the deoxidation of aluminum semikilled, silicon free, steels have been discussed.     

Activities of Phosphorus in Copper‐Iron Liquid Alloys Saturated with Copper‐Iron Solid Solutions

In order to determine the activities of phosphorus and iron in liquid {Cu‐Fe‐P} alloys, the two coexisting phases of liquid {Cu‐Fe‐P} alloys + <Cu‐Fe‐P> solid solutions were brought into equilibrium with a mixture of Al₂O₃ + AlPO₄ + Fe_xAl₂O₄ at temperatures of 1416K and 1526K. The oxygen partial pressures were measured with the aid of a solid‐oxide galvanic cell of the type: (+)Mo / Mo + MoO₂/ ZrO₂(MgO) / {Cu‐Fe‐P} + <Cu‐Fe‐P> + <Al₂O₃> + <AlPO₄> + <FeAl₂O₄> / Fe(‐) The equilibrium reactions underlying the experiments can be expressed by 2[P]_cu + (5/2) (O₂) + <Al₂O₃> = 2 <AlPO₄> and x[Fe]_Cu + (1/2) (O₂) + <Al₂O₃> = <Fe_xAl₂O₄> The Henrian activity coefficient referred to 1 wt pct solution in pure liquid copper could be well expressed by the formula log f_P° = (4.46±0.40) ‐ (8.67±0.59)/(T/K). The iron activities referred to pure solid iron could be formulated as log a_Fe =‐ (0.37 ± 0.12) + (500 ±200) /(T/K).     

Phase relations and thermodynamics of the system Fe-Cr-0 in the temperature range of 1600 °C to 1825 °C (1873 to 2098 K) under strongly reducing conditions

Equilibrium relations involving alloy and oxide phases in the system Fe-Cr-O were determined in the temperature range from 1600 °C to 1825 °C (1873 to 2087 K). Compositions of coexisting alloy and spinel phases were established as a function of oxygen pressure by equilibrating liquid Fe-Cr alloys with iron chromite (Fe_3-xCr_xO₄) solid solutions at 1600 °C and 1700 °C. Combinations of these experimental data and thermodynamic calculations were used to construct composition-oxygen pressure diagrams for the system at 1600 °C and 1700 °C. Additional runs for selected mixtures were made at still higher temperatures (1700 °C to 1825 °C), and thermodynamic parameters were derived for spinel-containing phase assemblages at temperatures up to 1865 °C. The spinel phases occurring in the present system are typically in the high-chromium range of the solid-solution series Fe₃O₄-Cr₃O₄,i.e., in the range between stoichiometric iron chromite (FeCr₂O₄) and Cr₃O₄. The activities of the various oxide components of the spinel solid solution at 1600 °C were calculated from experimentally determined parameters for coexisting alloy and spinel phases, as well as by statistical-mechanical modeling of the same spinel solid solution based on crystal-chemical considerations. The agreement between the two sets of results was excellent. Temperature variation of parameters characterizing the univariant equilibria spinel + Cr₂O₃ + alloy and spinel + alloy + liquid oxide was established. The univariant curves were found to display temperature maxima of 1715 °C ± 5 °C and approximately 1865 °C, respectively. In analogy with relations in the Cr-O system, the increase in divalent chromium of the liquid oxide phase with decreasing oxygen potential was identified as the main cause of the sharp decrease in liquidus temperatures of chromites in contact with Fe-Cr alloys of high Cr contents. Formerly Graduate Research Assistant, Department of Metallurgy, The Pennsylvania State University L.S. DARKEN and ARNULF MUAN, formerly Professors of Geochemistry and Materials Science, The Pennsylvania State University, University Park, PA 16802, are deceased.     

Spinel-corundum equilibria and activities in the system MgO-Al2O3-Cr2O3 at 1473 K

The tie-lines delineating intercrystalline ion-exchange equilibria between MgAl₂O₄-MgCr₂O₄ spinel solid solution and Al₂O₃-Cr₂O₃ solid solution with corundum structure have been determined at 1473 K by electron microprobe and X-ray diffraction (XRD) analysis of equilibrated phases. The tie-lines are skewed to the solid solution 0.7MgAl₂O₄-0.3MgCr₂O₄. The lattice parameters and molar volumes of both the solid solution series exhibit positive deviations from Vegard’s and Retger’s laws, respectively. Activities in the spinel solid solution are derived from the tie-line information and thermodynamic data on Al₂O₃-Cr₂O₃ solid solution available in the literature. Activities of Mg_0.5CrO₂ and Mg_0.5AlO₂ in the spinel solid solution exhibit strong positive deviations from Raoult’s law over most of the composition range. However, activity of Mg_0.5CrO₂ exhibits mild negative deviation for compositions rich in Mg_0.5CrO₂. The activity-composition relationship in the spinel solid solution is analyzed in terms of the intracrystalline exchange of cations between the tetrahedral and octahedral sites of the spinel structure. The intracrystalline ion exchange is governed by site preference energies of the cations. The difference between the Gibbs energy of mixing calculated using the cation mixing model and the experimental data is taken as a measure of the strain contribution arising from the difference in the radii of Al³⁺ and Cr³⁺ ions. The large positive strain enthalpy suggests the onset of immiscibility in the spinel solid solution at low temperatures. The computed critical temperature and composition for phase separation are 802 (±20) K and =0.46 (±0.02), respectively.     

Thermodynamics of iron alumino-chromite spinel inclusions in steel

The effect of chromium on the oxygen concentration of iron melts in equilibrium with various spinel reaction products has been determined. Alumina crucibles were used and experiments were performed at 1550, 1600, and 1650°C. Thermodynamic relationships between the equilibrium concentrations of chromium and oxygen in the iron melts have been established for chromium concentrations ranging up to 20 wt pct. Results from X-ray and electron microprobe analyses for the composition of the deoxidation products, together with solute activity relationships, indicate that the composition of the equilibrium spinel phase changes progressively from iron aluminate in the absence of chromium, through a series of aluminate-chromite solid solutions, FeO (Al _x Cr_1−x )₂O₃, (<0.5 pct chromium), to a complex chromite spinel, Fe₂Cr₇O₁₂, (0.5 to 3 pct chromium), and finally chromium oxide, Cr₃O₄ (>3 pct chromium). Deoxidation diagrams have been constructed and the effects of small amounts of alloying elements on the deoxidation behavior of aluminum interpreted in terms of buffered reactions which maintain oxygen concentrations in the melt at levels in excess of those normally associated with aluminum killed steel in equilibrium with alumina alone.     

Activities of Mn in solid and liquid Fe-Mn alloys

Activity measurements using solid state galvanic cells. Novel cell designs. Oxygen potential of Fe-Mn + MnO electrode between 1050 and 1174 K, and Fe-Mn + MnAl_2+2xO_4+3x + α-Al₂O₃ electrode at 1823 K, as a function of manganese concentration. Discussion of possible errors. Use of three phase equilibrium to minimize the effect of dissolved oxygen. Negative deviations from Raoult's law. Representation of data using subregular solution model. Comparison with literature and phase diagram.     

Thermodynamics and phase equilibria involving the spinel solid solution Fe X Mg1−X Cr2O4

Activities of FeCr₂O₄ in the spinel solid solutions Fe _X Mg_1−X Cr₂O₄ (0<X<1) in equilibrium with pure iron and Cr₂O₃ have been measured in the temperature range 1050 to 1350 K by employing a bielectrolyte solid-state galvanic cell of the type Pt, Fe + Fe _X Mg_1−X Cr₂O₄ + Cr₂O₃//(Y₂O₃) ThO₂/(CaO) ZrO₂//Fe + FeCr₂O₄ + Cr₂O₃, Pt Activities of both the components exhibit small negative deviation from the ideal behavior, characterized by the regular solution parameter Ω _s =−2260 (±200) J/mol. The lattice parameter of the spinel solid solutions quenched from 1200 K was found to obey Vegard’s law. The phase relations in the FeO-MgO-Cr₂O₃ system have been deduced from the results obtained in this study together with other relevant thermodynamic data from the literature. The tie-lines between the solid solutions with rock salt and spinel structures represent the influence of intercrystalline ion exchange. The tie-lines are skewed toward the FeCr₂O₄ corner, primarily because of the higher stability of FeCr₂O₄ compared to MgCr₂O₄, with respect to their component binary oxides. The oxygen partial pressure corresponding to the two three-phase regions, Fe + Fe _X Mg_1−X Cr₂O₄ + Cr₂O₃ and Fe + Fe _Y Mg_1−Y O + Fe _X Mg_1−X Cr₂O₄, have been evaluated as a function of composition at 1200 K.     

Oxygen and carbon sensing in Fe—O—C and Fe—O—C—Xn melts at elevated carbon contents

In the present study on solid electrolyte probes, the attempt was made to measure accurate and reproducible EMF values representing the extremely low oxygen activities in Fe—O—C melts at varying C contents. Various types of sensors were designed and successfully tested in laboratory experiments. Reliable oxygen activities were measured in Fe—O—C melts up to 4 wt. % C under pure CO gas, and f_o and f_c values were derived as a function of C content at 1 400 to 1 600°C. Further measurements were made in Fe—O—4 wt. % C—X_n melts at various contents of X_n (S_n = Si, Mn, Cr). Moreover, a solid oxide electrolyte probe with a CO gas channel to measure oxygen and carbon activities was developed and successfully tested in high-carbon iron melts.     

Thermodynamics of Mn–Fe–C and Mn–Si–C system

The solubility of C in Mn melts with different contents of Si and Fe at 1400 and 1500°C was determined. With these data the interaction coefficients e^Si_C, e^Fe_C, e^C_C as well as γ^o_C were evaluated. The standard free energy of solution of C in liquid Mn based on 1 wt.% solution standard at 1400 and 1500°C were calculated, respectively. The solubility of C in liquid Mn formulated in relation to temperature was made as to the conformability of the present results with those given in the literature.     

Chemical State, Site, Solid Solubility, and Magnetism of Fe in the Ferropericlase (Mg1–x Fe x )O Produced by Ball Milling of MgO and Fe

Ferropericlase (Mg_1–x Fe _x )O solid solution was prepared by ball milling of the mixture of MgO with a rock-salt structure and metal Fe powders in atmosphere and at room temperature. Differing from (Mg_1–x Fe _x )O prepared at high temperature by using MgO and FeO as starting materials, the solution of Fe in MgO is not continuous but limited in the ball milling process, and the solubility limit is less than 30 at. pct. About 92 pct of the Fe ions occupy the site of tetrahedral oxygen coordination in trivalent Fe (Fe³⁺) with high spin, whereas about 8 pct of the Fe ions occupy the site of octahedral oxygen coordination in bivalent Fe (Fe²⁺) with high spin. The Fe³⁺ and Fe²⁺ ions do not show a ferromagnetic but show a paramagnetic state. The as-milled (Mg_1–x Fe _x )O is metastable and decomposes to ferropericlase (Mg_1–y Fe _y )O (where y < x) and MgFe₂O₄ with spinel structure as annealed above 773 K (500  °C), and the content of Fe in the (Mg_1–y Fe _y )O increases with increasing annealing temperature. A bulk (Mg_1–x Fe _x )O was fabricated by annealing the as-milled (Mg_1–x Fe _x )O powders at 973 K (700  °C). It shows n-type conductivity, which is attributed to an electronic small polaron with an activation energy of 0.135 eV.