Equilibrium of calcium vapor with liquid iron and the interaction of third elements

The dissolution equilibrium of calcium vapor in liquid iron was carried out at 1873 K in a two-temperature zone furnace using a vapor-liquid equilibration method. A sealed Mo reaction chamber and a self-made CaO crucible were used in this study. The thermodynamic parameters obtained are as follows. For reaction Ca (g)=[Ca],

Determination of standard gibbs energies of formation of Cr2N and CrN

The standard Gibbs energies of formation of Cr₂N and CrN have been measured by an equilibration technique and by using thermogravimetry and differential thermal analysis (TG-DTA) at temperatures ranging from 1232 to 1523 K. The results are expressed as follows:

Enthalpy of mixing of liquid Ni-Zr and Cu-Ni-Zr alloys

The partial (Δ and the integral (ΔH) enthalpies of mixing of liquid Ni-Zr and Cu-Ni-Zr alloys have been determined by high-temperature isoperibolic calorimetry at 1565 ± 5 K. The heat capacity (C _p) of liquid Ni₂₆Zr₇₄ has been measured by adiabatic calorimetry (C _p=53.5±2.2 J mol⁻¹ K⁻¹ at 1261±15 K). The integral enthalpy of mixing changes with composition from a small positive (Cu-Ni, ΔH (x _Ni=0.50, T=1473 to 1750 K)=2.9 kJ mol⁻¹) to a moderate negative (Cu-Zr; ΔH(x _Zr=0.46, T=1485 K)=−16.2 kJ mol⁻¹) and a high negative value (Ni-Zr; ΔH(x _Zr=0.37, T=1565 K)=−45.8 kJ mol⁻¹). Regression analysis of new data, together with the literature data for liquid Ni-Zr alloys, results in the following relationships in kJ mol⁻¹ (standard states: Cu (1), Ni (1), and Zr (1)):for Ni-Zr (1281≤T≤2270 K),

Determination of gibbs energy of formation of cuspidine (3CaO · 2SiO<Subscript>2</Subscript> · CaF<Subscript>2</Subscript>) from the electromotive force method using CaF<Subscript>2</Subscript> as the solid electrolyte

The standard Gibbs energy change for the following reaction has been directly determined by electromotive force (EMF) measurement using CaF₂ as the solid electrolyte in the temperature range from 1313 to 1329 K.

Electrochemical determination of gibbs energy of formation of NiTiO3 (ilmenite)

Gibbs energy of formation of NiTiO₃ (ilmenite) relative to its component oxides, NiO (rock salt) and TiO₂ (rutile), has been measured employing the solid-state electrochemical cell,

Phase equilibria in the system NiO-CaO-SiO2 and gibbs energy of formation of CaNiSi2O6

Phase relations in the pseudoternary system NiO-CaO-SiO₂ at 1373 K are established. The coexisting phases are identified by X-ray diffraction and energy-dispersive X-ray analysis of equilibrated samples. There is only one quaternary oxide CaNiSi2O6 with clinopyroxene structure. The Gibbs energy of formation of CaNiSi₂O₆ is measured using a solid state galvanic cell incorporating stabilized zirconia as the solid electrolyte in the temperature range of 1000 to 1400 K: From the electromotive force (emf) of the cell, the Gibbs energy of formation of CaNiSi₂O₆ from NiO, SiO₂, and CaSiO₃ is obtained. To derive the Gibbs energy of formation of the quaternary oxide from component binary oxides, the free energy of formation of CaSiO₃ is determined separately using a solid state cell based on single crystal CaF₂ as the electrolyte: The results can be expressed by the following equations:      

Thermodynamic study of the effect of calcium on removal of phosphorus from silicon by acid leaching treatment

The interaction between calcium and phosphorus in molten silicon was investigated for predicting the removal of phosphorus from silicon by an acid leaching treatment with calcium addition. In the present study, two immiscible liquids of silicon and lead were equilibrated, and the interaction parameter between calcium and phosphorus and the self-interaction parameter of phosphorus in molten silicon at 1723 K were determined.

Determination of standard gibbs energies of formation of Fe2Mo3O12, Fe2Mo3O8, Fe2MoO4, and FeMoO4 of the Fe-Mo-O ternary system and μ phase of the Fe-Mo binary system by electromotive force measurement using a Y2O3-stabilized ZrO2 solid electrolyte

The standard Gibbs energies of formation of Fe₂Mo₃O₁₂, Fe₂Mo₃O₈, FeMoO₄, and Fe₂MoO₄ of the Fe-Mo-O ternary system and the μ phase of the Fe-Mo binary system have been determined by measuring electromotive forces of galvanic cells having an Y₂O₃-stabilized ZrO₂ solid electrolyte. The results are as follows: $$\begin{gathered} \Delta _f G^\circ (FeMoO_4 )/kJ \cdot mol^{ - 1} = - 1053.5 + 0.2983(T/K) \pm 0.4 \hfill \\ Temperature range: 1112 to 1339 K \hfill \\ \Delta _f G^\circ (Fe_2 Mo_3 O_8 )/kJ \cdot mol^{ - 1} = - 2347 + 0.6814(T/K) \pm 1 \hfill \\ Temperature range: 1112 to 1339 K \hfill \\ \Delta _f G^\circ (Fe_2 Mo_3 O_{12} )/kJ \cdot mol^{ - 1} = - 2993 + 0.9105(T/K) \pm 2 \hfill \\ Temperature range: 1040 to 1145 K \hfill \\ \Delta _f G^\circ (Fe_{0.58} Mo_{0.42} )/kJ \cdot mol^{ - 1} = - 18.7 + 0.0117(T/K) \pm 0.1 \hfill \\ Temperature range: 1162 to 1223 K \hfill \\ \Delta _f G^\circ (Fe_2 MoO_4 )/kJ \cdot mol^{ - 1} = - 1174 + 0.342(T/K) \pm 1 \hfill \\ Temperature range: 1243 to 1466 K \hfill \\ \end{gathered} $$ where the standard pressure is 1 bar (100 kPa).     

Controversy on the free energy of formation of CaO—Additional evidence in support of thermochemical data

The standard free energies of formation of CaO derived from a variety of high-temperature equilibrium measurements made by seven groups of experimentalists are significantly different from those given in the standard compilations of thermodynamic data. Indirect support for the validity of the compiled data comes from new solid-state electrochemical measurements using single-crystal CaF₂ and SrF₂ as electrolytes. The change in free energy for the following reactions are obtained: $$\begin{gathered} CaO + MgF_2 \to MgO + CaF_2 \hfill \\ \Delta G^ \circ = - 68,050 - 2.47 T( \pm 100) J mol^{ - 1} \hfill \\ SrO + CaF_2 \to SrF_2 + CaO \hfill \\ \Delta G^ \circ = - 35,010 + 6.39 T( \pm 80) J mol^{ - 1} \hfill \\ \end{gathered} $$ The standard free energy changes associated with cell reactions agree with data in standard compilations within ±4 kJ mol^?1. The results of this study do not support recent suggestions for a major revision in thermodynamic data for CaO.     

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.     

Determination of gibbs energy of formation of Ni-B-O system by electromotive force measurement using solid electrolyte

The standard Gibbs energies of formation of Ni₃B, Ni₂B, o-Ni₄B₃(Ni_0.586B_0.414), m-Ni₄B₃(Ni_0.564B_0.436), NiB, and Ni₃B₂O₆ of the Ni-B-O system have been determined by measuring electromotive forces of galvanic cells using a Y₂O₃-stabilized ZrO₂ solid oxide electrolyte. The results are as follows:

Evaluation of unified interaction parameter model parameters for calculating activities of ferromanganese alloys: Mn-Fe-C, Mn-Fe-Si, Mn-C-Si, and Mn-Fe-C-Si systems

Interaction parameters for Mn-based alloys were evaluated using both carbon solubility and activity data for species in binary and ternary manganese alloys. The parameters at 1400 °C are the following

Thermodynamics of the system NaF-Alf3. part ii: The free energies of formation of cryolite (Na3AlF6) and chiolite (Na5Al3F14)

The theory of the solid-electrolyte cells is given, and it is shown that cryolite itself with Ca²⁺ in solid solution is a suitable Na⁺-ion conductor. Experimental electromotive forces for the ranges 570° to 725°C and 570° to 670°C, r − 18,960 cal with a standard deviation of ±36 cal (based on a third-law calculation). For 5NaF(s) + 3AlF₃(s) = Na₅Al₃F₁₄(s), ΔG° = −38,560 − 7.081T with a standard deviation of ±130 cal. Combination of these results with recent values for Al + 3/2 F₂ = A1F₃ and for 6NaF + Al = Na₃AlF₆ + 3Na gives ΔH°_f298(Na₃AlF₆) = −792,400 cal and ΔH°_f298(NaF) = −137,530 cal. The latter is in excellent agreement with the most recent critical assessment.     

The calcium-phosphorus and the simultaneous calcium-oxygen and calcium-sulfur equilibria in liquid iron

The equilibrium Ca₃P_2(s) = 3[Ca] + 2[P] was studied at 1600 ° by equilibrating liquid iron, saturated with Ca₃P₂, and contained in a TiN crucible, with Ca vapor. The source of Ca was liquid Ca contained in an Mo crucible, and the vapor pressure of Ca was varied by varying the position of the Mo crucible in the temperature gradient of a vertical tube furnace. A least-squares analysis of the data gave and . The simultaneous equilibria CaO_(s) = [Ca] + [O] and CaS_(s) = [Ca] + [S] were studied at 1600 ° by equilibrating liquid iron, contained in a pressed and sintered CaO-CaS crucible with Ca vapor. The advantage of this technique is that two equilibrium constants,K _cas andK _cao, and two interaction coefficients, and can be determined from one set of experiments. It was determined that, at 1600 °,K _cas = 5.9 × 10⁻⁸ K _cao = 5.5 × 10⁻⁹, , and . Formerly Graduate Students     

The calcium-phosphorus and the simultaneous calcium-oxygen and calcium-sulfur equilibria in liquid iron

The equilibrium Ca₃P_2(s) = 3[Ca] + 2[P] was studied at 1600 ° by equilibrating liquid iron, saturated with Ca₃P₂, and contained in a TiN crucible, with Ca vapor. The source of Ca was liquid Ca contained in an Mo crucible, and the vapor pressure of Ca was varied by varying the position of the Mo crucible in the temperature gradient of a vertical tube furnace. A least-squares analysis of the data gave and. The simultaneous equilibria CaO_(s) = [Ca] + [O] and CaS_(s) = [Ca] + [S] were studied at 1600 ° by equilibrating liquid iron, contained in a pressed and sintered CaO-CaS crucible with Ca vapor. The advantage of this technique is that two equilibrium constants,K _cas andK _cao, and two interaction coefficients, and can be determined from one set of experiments. It was determined that, at 1600 °,K _cas = 5.9 × 10⁻⁸ K _cao = 5.5 × 10⁻⁹,, and. Formerly Graduate Students     

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:

The oxygen potential of the systems Fe+FeCr2O4+Cr2O3 and Fe+FeV2O4+V2O3 in the temperature range 750–1600°C

From electromotive force (emf) measurements using solid oxide galvanic cells incorporating ZrO₂-CaO and ThO₂?YO_1.5 electrolytes, the chemical potentials of oxygen over the systems Fe+FeCr₂O₄+Cr₂O₃ and Fe+FeV₂O₄+V₂O₃ were calculated. The values may be represented by the equations: $$\begin{gathered} 2Fe\left( {s,1} \right) + O_2 \left( g \right) + 2Cr_2 O_3 \left( s \right) \to 2FeCr_2 O_4 \left( s \right) \hfill \\ \Delta \mu _{O_2 } = - 151,400 + 34.7T\left( { \pm 300} \right) cal \hfill \\ = - 633,400 + 145.5T\left( { \pm 1250} \right) J \left( {750 to 1536^\circ C} \right) \hfill \\ \Delta \mu _{O_2 } = - 158,000 + 38.4T\left( { \pm 300} \right) cal \hfill \\ = - 661,000 + 160.5T\left( { \pm 1250} \right) J \left( {1536 to 1700^\circ C} \right) \hfill \\ 2Fe\left( {s,1} \right) + O_2 \left( g \right) + 2V_2 O_3 \left( s \right) \to 2FeV_2 O_4 \left( s \right) \hfill \\ \Delta \mu _{O_2 } = - 138,000 + 29.8T\left( { \pm 300} \right) cal \hfill \\ = - 577,500 + 124.7T\left( { \pm 1250} \right) J \left( {750 to 1536^\circ C} \right) \hfill \\ \Delta \mu _{O_2 } = - 144,600 + 33.45T\left( { \pm 300} \right) cal \hfill \\ = - 605,100 + 140.0T\left( { \pm 1250} \right) J \left( {1536 to 1700^\circ C} \right) \hfill \\ \end{gathered} $$ . At the oxygen potentials corresponding to Fe+FeCr₂O₄+Cr₂O₃ equilibria, the electronic contribution to the conductivity of ZrO₂?CaO electrolyte was found to affect the measured emf. Application of a small 60 cycle A.C. voltage with an amplitude of 50 mv across the cell terminals reduced the time required to attain equilibrium at temperatures between 750 to 950°C by approximately a factor of two. The second law entropy of iron chromite obtained in this study is in good agreement with that calculated from thermal data. The entropies of formation of these spinel phases from the component oxides can be correlated to cation distribution and crystal field theory.     

Oxide skin strength on molten aluminum

The oxide skin strength on molten aluminum has been measured as a function of temperature for pure aluminum and some aluminum alloys. The measured values fit well to previous published data of surface tension of liquid aluminum, σ _lg , combined with the wetting angle, ϑ, and the mechanical strength of the oxide. It is assumed that the work per area needed to stretch and rupture the oxide skin is a sum of the interfacial tensions and tensile strength of oxide, times oxide thickness: