Thermodynamics of the system NaF-AlF3: Part VII. Non-stoichiometric solid cryolite

Earlier data are recalculated to give the boundaries of the homogeneous field of solid cryolite. The equilibrium constant

Thermodynamics of the system NaF-AlF3. Part III: Activities in liquid mixtures

Measurements have been made of a) the sodium content of aluminum in contact with NaF-AlF₃ melts at 1020° and 1080°C, and in contact with liquid-solid mixtures along the cryolite liquidus, b) the position of the A1F₃ liquidus line, and c) the electromotive force of solid-electrolyte cells with one side in the NaF-Na₃AlF₆ two-phase region and the other on the cryolite liquidus. With previously determined data for the activity coefficient of sodium in aluminum and for ΔH°_298f for cryolite, activities of NaF and A1F₃ are calculated. As a limiting condition the melts conform to a regular solution model withRTlnγ’₁ = ∔12,200(1 − n’₁)² cal where γ’₁=a₁/n’₁ and n’₁ the molar fraction of either NaF or NaAlF₄ calculated with them as species. This model breaks down progressively as the NaAlF₄ composition is approached, the deviations starting earlier at higher temperatures. The most plausible explanation is the disproportionation equilibrium 2A1F-₄ ⇌ A1₂F-₇ + F^-, stoichiometric NaAlF₄ containing about 70 pct AlF^- ₄ at 1020° to 1080°C. The hypothetical undisproportionated NaAlF₄ has a free energy of formation from NaF(I) and AlF₃(s) of ΔG° = •101,235 + 32.085T + 5.929 × 10⁷/T. This equation, together with that above for γ’NaAlF₄, defines α AlF₃ in all regions where the regular solution model holds. Solutions of sodium in aluminum are found to conform to Henry’s law in the range 100 to 2 ppm, contrary to recent suggestions.     

Thermodynamics of the system NaF-AlF3. Part IV: The cryolite liquidus curve

The theory of the variation of activity of a binary compoundAXB with composition in a $$a_{A_x B} = {\text{ }}K \cdot a_A^x \cdot a_B $$ the activity coefficient should be defined as $$\gamma _{A_x B} {\text{ = }}K \cdot \gamma _A^x {\text{ }} \cdot {\text{ }}\gamma _B {\text{ = }}a_{A_x B} {\text{/(}}n_A^x {\text{ }} \cdot {\text{ }}n_B {\text{)}}$$ K is chosen so that^aA_xb is unity in the stoichiometric liquid (or, if preferred, so that γA_XB is unity). Such an activity coefficient possesses the property of approaching a limiting value at the stoichiometric composition, and the analog of Raoult’s law is^aA_xB∝ n_A ^x nB From this it follows that a plot of log (n_A ^x nB) against 1/T should show the same limiting tangent for points on both sides of the liquidus curve. Data for Na₃AlF₆ do not pass this test. With the aid of previously measured activities the discrepancy can be resolved if it be assumed that the solid material separating has a composition (2.824 ±0.005)NaF A1F₃; the calculated enthalpy of fusion of this material is 24,270 cal/gfw, and the standard deviation of the liquidus points from the least-squares line is ±2.3 deg.     

Thermodynamics of the system NaF-AIF3: Part VI. revision

Literature data are reviewed to derive enthalpies and entropies of Na₃AlF₆ and NaF, and they are combined with electrochemical and equilibrium data to yield free energies of formation of Na₃AlF₆ from the constituent fluorides. Liquidus data and measurements of the Na content of Al in equilibrium with the melts then enable the calculation of the free energy of formation, enthalpy, and entropy of all mixtures liquid at 1293 K. In stoichiometric Na₃AlF₆ at 1293 K, a_NaF =0.37 and a_{AlF 3} = 4.9 × 10⁻⁴. The activity coefficient of Na in dilute solution in Al is given byRT ln γ_Na = (40 967 + 9.480 T) J. At 1293 K the partial pressure of NaAlF₄ is given by pNaA1F₄/bar = 27a_NaF . a_{Aif 3}- A heavier species— suggested to be NaAl₃F₁₀—is present in the vapor above AlF₃-rich melts.     

Thermodynamics of the system NaF-AlF3 Part I: The equilibrium 6NaF(s) + Al = Na3AlF6(s) + 3Na

The pressure of sodium existing over a mixture of aluminum and NaF has been measured by a gas-transference method over the range 635° to 816°C. The results (corrected for the presence of Na₂) give for the reaction 6NaF(s) + A1(l) =Na₃AlF₆(s) + 3Na(g) ΔH°₂₉₈ = +107,970 ± 220 cal (standard deviation) or ±60 cal (standard error). The corresponding activities of Na(l) may be expressed by log a_Na = −2,854/T − 0.853 log T + 4.303 The sodium content of aluminum in equilibrium with NaF(s) and Na₃AlF₆(s) has been determined over the range 679° to 876°C. The activity coefficient of sodium in aluminum is given byRT In γ_Na/n ₂ ^Al = 8290 + 3.73 T The present results are not consistent with the suggestion that Na₂F is an important gaseous species in this system.     

Thermodynamics of the System Fe−Mn−S: Part III. Equilibria Involving Solid and Liquid Phases in the Temperature Range 1100 to 1300°C

The equilibria between cubic (Fe,Mn)S solid solutions and sulfur rich liquid have been measured in the temperature range 1100 to 1300°C, and those between cubic (Fe,Mn)S and hexagonal ‘FeS’ at 1100°C. Gas phases consisting of H₂S-H₂ mixtures were used as atmospheres. Further, isosulfur-activity lines in the liquid phase region and the composition of the liquid at saturation with γ-iron were determined. The data were used to delineate the liquidus surfaces of γ-iron, (Fe,Mn)S, and ‘FeS’, and the location of the pertinent univariant lines in the 1100 to 1300γC range of the Fe?Mn?S system.     

Thermodynamics of the system Fe-Mn-S: Part I. activities in Iron sulfide-manganese Sulfide Solid Solutions in the Temperature Range 1100 to 1400°C

The equilibrium ratios pH₂S/ pH₂ of a gas phase coexisting with (Fe, Mn)S solid solutions of the system Fe-Mn-S and metallic iron have been determined in the temperature range 1100 to 1400°C. The activity of FeS in the sulfide solid solutions is proportional to pH₂S/ pH₂. The activity of MnS is obtained by a Gibbs-Duhem integration. The α-formalism is used to derive the analytical relationships between pH₂S/ pH₂ ora Mns, and composition of the solid solution.     

Study on Liquidus Temperature of NaF-KF-LiF-AlF3 System with Low Cryolite Ratio

Metallurgical and Materials Transactions B - Development of an energy-efficient method for aluminum manufacturing is the current research trend in the aluminum electrolysis industry. A...     

Thermodynamics of copper matte converting: Part I. Fundamentals of the noranda process

This paper presents a computer-oriented thermodynamic method to analyze copper matte smelting and converting, the system of which was ideally defined as consisting of five major components: Cu, Fe, S, O and SiO2. As an example of its application, the method was demonstrated in establishing a steady-state model for the Noranda Process producing either metallic copper or high grade matte. Process variables such as temperature, oxygen enrichment, charge (or concentrate) composition, matte grade and magnetite content of slag are integrated into one computer model. The model gives the chemical composition of metallic copper, matte and slag phases for any specified condition. Mathematical formulae accounting for physical entrainment in the melts are also presented to correlate the computed melt composition with that observed. The computer model can provide predictions as to the effects of operating and chemical parameters and can contribute to improved metallurgical control.     

Thermodynamics of copper matte converting: Part I. Fundamentals of the noranda process

This paper presents a computer-oriented thermodynamic method to analyze copper matte smelting and converting, the system of which was ideally defined as consisting of five major components: Cu, Fe, S, O and SiO2. As an example of its application, the method was demonstrated in establishing a steady-state model for the Noranda Process producing either metallic copper or high grade matte. Process variables such as temperature, oxygen enrichment, charge (or concentrate) composition, matte grade and magnetite content of slag are integrated into one computer model. The model gives the chemical composition of metallic copper, matte and slag phases for any specified condition. Mathematical formulae accounting for physical entrainment in the melts are also presented to correlate the computed melt composition with that observed. The computer model can provide predictions as to the effects of operating and chemical parameters and can contribute to improved metallurgical control.     

Solubility of Chromium(III) Oxide in the Molten Cryolite System

The solubility of Cr(III) species originating from dissolution of Cr₂O₃ in cryolite-based melts was studied in the temperature range 1173 K to 1293 K (900 °C to 1020 °C). The molar ratio n(NaF)/n(AlF₃) was in the range of 1.4 to 2.6. It was found that the solubility depends markedly on the molar ratio n(NaF)/n(AlF₃), high ratios resulting in higher solubility. A semi-empirical model describing the solubility of Cr₂O₃ was developed. The standard deviation between calculated and experimental data is 10 pm (ca 2.4 pct).     

Thermodynamics and phase relationships of transition metal-sulfur systems: Part V. A reevaluation of the Fe-S system using an associated solution model for the liquid phase

The relevant thermodynamic and phase equilibrium data for the Fe-S binary system have been reevaluated in light of more recent data. An associated solution model is used to describe the thermodynamic properties of the liquid phase as a function of composition and temperature. For the pyrrhotite phase, a statistical thermodynamic model based on the formation of Frenkel defects in the lattice is used. For the austenite and ferrite phases, the solute is assumed to follow Henry’s law, and pyrite is taken to be a stoichiometric compound. The model parameters for the various phases are obtained by evaluating all relevant experimental data reported in the literature. The calculated phase diagram is in good agreement with the experimental data. The calculated sulfur activity values for the liquid phase agree well with experimental values including those at higher sulfur concentrations. This is an improvement of an earlier evaluation by Sharma and Chang using the same model with the same number of parameters.     

Determination of the Cryolite Ratio of KF-NaF-AlF3 Electrolyte by Conductivity Method

Metallurgical and Materials Transactions B - The cryolite ratio (CR) is an important parameter for the electrolyte in aluminum reduction cells. The measurement method for the CR of the KF-NaF-AlF3...     

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.     

Y_(2-x)Sm_xW_3O_(12)固溶体的制备及热膨胀性能研究

采用二次固相反应法成功制备出Y2-xSm(xWO4)(3x=0.0,0.2)、(x=1.0,1.4,1.8,2.0)系列固溶体,低掺杂量Y2-xSm(xWO4)(3x=0.0,0.2)为单斜结构(空间群:P2/m),高掺杂量Y2-xSm(xWO4)(3x=1.0,1.4,1.8,2.0)为单斜结构(空间群:C2/c);热重分析表明低Sm掺杂Y2-xSm(xWO4)3具吸水性,且随Sm含量增加而含水量减少,当x≥1.0时,样品完全不吸水;SEM分析了样品的断口形貌与晶粒尺寸;热膨胀性能测试表明,Sm掺杂量(x=0.0,0.2)的Y2-xSm(xWO4)3排除水分子后,具有较强的负热膨胀特性,而掺杂量(x=1.0,1.4,1.8,2.0)的Y2-xSm(xWO4)3具有正膨胀性能。     

Thermodynamics of titanium-based melts: I. Thermodynamics of the dissolution of elements in liquid titanium

A method is described that involves the molar interaction parameters in liquid iron at a temperature of 1873 K, provides calculation of these parameters in liquid titanium at any temperature, and makes it possible to calculate the heats of dissolution of elements in liquid titanium and the activity coefficients of these elements. The changes in the Gibbs energy caused by the dissolution of some alloying and impurity elements in liquid titanium are calculated, and the activity coefficients of these elements are presented.     

水溶液中氯化铷与D-葡萄糖相互作用的热力学研究

采用数字式密度计测量了氯化铷-水、葡萄糖-水二元体系和氯化铷-葡萄糖-水三元体系在298.15K时的密度,通过实验设计,利用这一套密度数据获得了氯化铷和葡萄糖在氯化铷-葡萄糖-水三元体系中的表观摩尔体积及相应的标准偏摩尔体积。基于结构水化作用模型和Sav-age-Wood基团加合模型对氯化铷与葡萄糖在水溶液中的弱相互作用进行了分析,结果表明,氯化铷和葡萄糖相互作用的体积参数取决于金属阳离子与糖分子中的亲水基团(M -O)的相互作用。     

Thermodynamics of the System Fe-Mn-S: Part II. Solubility of Sulfur and Manganese in γ-Iron Coexisting with Sulfide in the Temperature Range 1100 to 1300°C

Iron platelets containing known contents of manganese were reacted with gas phases of controlled pH₂S/pH₂ ratios. After quenching, the sulfur contents of the samples were analyzed chemically, and the platelets were investigated microscopically to determine if sulfide inclusions had been formed. From the results, the sulfur potentials for incipient sulfide precipitation and the sulfur solubilities were established as a function of manganese content, in the temperature range 1100 to 1300°C. Additional data are presented for solubility of sulfur in pure γ-iron.