Computer analysis of phase diagrams and thermodynamic properties of cryolite based systems: I. The AIF3-LiF-NaF system

Calculations of the phase diagram of the AlF₃-LiF-NaF system up to 35 mol pct A1F₃ and of the binary subsystems are presented. For the binary LiF-NaF, AlF₃-NaF, AlF₃-LiF, and the quasibinary Li₃AlF₆-Na₃AlF₆ systems, thermodynamic properties of the unary and binary phases are used to numerically generate the corresponding phase diagram. The calculated and measured values are in good agreement. The broad data base thus constructed is used with equations from the conformai ionic solution theory to derivea priori phase equilibria of the AlF₃-LiF-NaF system. Ternary liquidus temperatures are calculated covering compo-sitions outside the range of measurements.     

Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the CaO-Al2O3, Al2O3-SiO2, and CaO-Al2O3-SiO2 systems

All available thermodynamic and phase diagram data have been critically assessed for all phases in the CaO-Al₂O₃, Al₂O₃-SiO₂, and CaO-Al₂O₃-SiO₂ systems at 1 bar pressure from 298 K to above the liquidus temperatures. All reliable data for the binary systems have been simultaneously optimized to obtain, for each system, one set of model equations for the Gibbs energy of the liquid slag and all solid phases as functions of composition and temperature. The modified quasichemical model was used for the slag. With these binary parameters and those from the optimization of the CaO-SiO₂ system reported previously, the quasichemical model was used to predict the thermodynamic properties of the ternary slag. Two additional small ternary parameters were required to reproduce the ternary phase diagram and ternary activity data to within experimental error limits. The calculated optimized phase diagram and thermodynamic properties are self-consistent and are the most reliable currently available estimates of the true values.     

Computer study of structure, thermodynamic, and electrical transport properties of Na3AlF6-Al2O3 and CaF2-Al2O3 melts

Structure, thermodynamic, and electrical transport properties of Na₃AlF₆-Al₂O₃ and CaF₂-Al₂O₃ melts were examined by molecular dynamics. Ionic models were constructed for Na₃AlF₆-Al₂O₃ and CaF₂-Al₂O₃ melts at 1283 and 2000 K, respectively. It was found that in the Na₃AlF₆-Al₂O₃ melts, stable aluminum-fluorine-oxygen groups are formed. Although bonds between F⁻ and Al³⁺ ions in the first coordination shell are weaker than between O²⁻ and Al³⁺ ions, very stable negatively charged AlF ₆ ³⁻ groups are formed at low oxygen concentrations in the Na₃AlF₆-Al₂O₃. This results in migration of aluminum to the anode in an external electric field. In the CaF₂-Al₂O₃ melts, positively charged aluminum-oxygen groups dominate. This results in migration of aluminum to the cathode at almost all Al₂O₃ concentrations. Therefore, in Na₃AlF₆-Al₂O₃ melts, the Al³⁺ ion as a component of the complex anion has a negative partial conductivity and the O²⁻ ion has positive partial conductivity; in CaF₂-Al₂O₃ melts, Al³⁺ has a positive transport number while O²⁻ has a negative transport number.     

Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the CrO-Cr2O3-SiO2-CaO system

Available thermodynamic and phase diagram data have been critically assessed for all phases in the CrO-Cr₂O₃-SiO₂-CaO system from 298 K to above the liquidus temperatures at all compositions under reducing conditions and at low CaO concentrations under oxidizing conditions. All reliable data have been simultaneously optimized to obtain one set of model equations for the Gibbs energy of the liquid slag and all solid phases as functions of composition and temperature. The modified quasichemical model was used for the slag. The models permit phase equilibria to be calculated for regions of composition, temperature, and oxygen potential where data are not available.     

Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the MnO-TiO2, MgO-TiO2, FeO-TiO2, Ti2O3-TiO2, Na2O-TiO2, and K2O-TiO2 systems

All available thermodynamic and phase diagram data have been critically assessed for all phases in the MnO-TiO₂, MgO-TiO₂, FeO-TiO₂, Ti₂O₃-TiO₂, Na₂O-TiO₂, and K₂O-TiO₂ systems at 1 bar pressure from 298 K to above the liquidus temperatures. All reliable thermodynamic and phase diagram data have been simultaneously optimized to obtain, for each system, one set of model equations for the Gibbs energy of the liquid slag as a function of composition and temperature and equations for the Gibbs energies of all compounds as functions of temperature. The modified quasichemical model was used for the molten slag phases.     

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.     

On composite-structure weaknesses: Part II. Computer experiments,identification, and correlation

Part II of this article concerns correlating the composite-structure weaknesses (CSWs) with the local microstructure of simulated short-fiber-reinforced metal-matrix composite (MMC) samples. The proposed analytically-numerically-based approach was employed for numerical computation of the mesoscopic stress distribution in short fibers. Nine local microstructure-related parameters are defined, which incorporate local elastic and thermal anisotropies into presentation of a local microstructure. It is found that the nine defined parameters are adequate physical parameters, which also account for synergetic interactions due to orientation-induced local anisotropies, either elastic anisotropy or thermal expansion anisotropy. By using the defined physical parameters, CSWs can be correlated with the local microstructure of simulated MMC samples. A database which collects numerical correspondences between the orientation and geometry of composite constituents and CSWs has been established for a number of simulated MMC samples. Computer experiments confirm that not only the stiffness mismatch between fiber and matrix materials, but also orientation-induced local anisotropies, exert decisive influence on the distribution of CSWs in short-fiber composites. The mesoscopic stress and strain distributions within a short fiber are critically dependent on the local evolution of elastic and thermal anisotropies of surrounding grains. Whether a CSW may become a failure origin must be evaluated in conjunction with a local damage mechanism.     

Sn-C and Al-Sn-C phase diagrams and thermodynamic properties of C in the alloys: 1550 °C to 2300 °C

In research conducted by the United States Bureau of Mines, the Sn-C and Al-Sn-C phase diagrams were determined over the temperature range of 1550 °C to 2300 °C by chemical anal-ysis of alloys saturated with carbon within sealed graphite crucibles. Carbon forms a dilute solution in tin described by log [at. pct C] = 2.9767-12,082.35/T, whereT is temperature in Kelvin. Isothermal sections for the ternary system were determined at intervals of 150 °C over the range of temperatures investigated. The univariant points on the 1700 °C, 1850 °C, and 2000 °C isotherms were determined by metallographic examination of rapidly cooled alloys to be about 34Al-66Sn-0.1C, 49.7Al-49.7Sn-0.5C, and 70Al-27Sn-2.8C, respectively, where all concentrations are atomic percent. Graphite and A1₄C₃ (decomposition temperature 2156 °C) were the only solid phases observed at these temperatures. The excess partial Gibbs energy for dissolved C in liquid Al-Sn-C solutions in equilibrium with C, as calculated from the experi-mental solubilities, is G _C ^e = -RT ln x = y²[176.860 - 55.42T - (224,200 - 110.84T)x] + (231,400 - 18.700T)z₂ + yz[151,860 - 8.423T + (19,400 - 8.4867)z + (56,100 - 57.6577)yz - (39,800 - 40.904T)yz²], J/g · atom where R is the gas constant,T is the temperature in Kelvin, andx, y, and z are the atomic fractions of C, Al, and Sn, respectively. The equation also is a good approximation for liquid solutions in equilibrium with A1₄C₃ within about 100 °C of the decomposition temperature.     

Thermodynamics and phase relationships of transition metal-sulfur systems: IV. thermodynamic properties of the Ni-S liquid phase and the calculation of the Ni-S phase diagram

An associated solution model is applied to describe the thermodyanmic properties of the liquid Ni-S phase. This model assumes the existence of ‘NiS’ (l) species in the liquid in addition to Ni(l) and S(l). With two solution parameters for the binaries Ni-‘NiS’ and ‘NiS’-S, this model is able to describe the thermodynamic behavior of the liquid phase over a wide range of temperature and composition. Using this model for the liquid phase, a statistical thermodynamic model for the monosulfide phase and empirical thermodynamic equations for β₁-Ni₃S₂ and β₂-Ni₄S₃, the Ni-S phase diagram is calculated. The calculated diagram is in excellent agreement with the available experimental data with the exception that the eutectic composition for the equilibrium L₁ + δ + η and those of the two liquids for the equilibriumL ₁ + L ₂ + η differ from the experimental data by more than 2 at. pct S. Formerly Post-Doctorl Research Associate, University of Wisconsin-Milwaukee is now Lecturer, Department of Metallurgical Engineering, Indian Institute of Technology, Kanpur, India     

The thermodynamic properties of UFe2:Agreement with the campbell correlation of laves phase compounds

The reported value of the heat of formation of UFe₂ determined by acid solution calorimetry¹ and the Gibbs energy of formation determined by high temperature emf cells² seem to give results that are in unreasonably poor agreement. It was recently discovered³ that a well defined correlation exists between the heat of formation and the unalloyed radius ratio of AB₂ type Laves compounds. When this test is applied it is found that the emf data of Yoshihara and Kauno for UFe₂ gives very good correlation with the compounds formed between Pu and the Group Villa metals as shown in Fig. 1. Although these authors did not indicate that heats or entropies of formation could be calculated from their data, a third law calculation using Kopp’s law of the additivity of heat capacity⁴ shows that the entropy term derived from the observed Gibbs energy of formation     

Thermodynamic properties of molten sulfides: Part II. The system Co-S

The equilibrium partial pressure of sulfur vapor over Co-S melts has been determined by equilibrating the melts with H₂S-H₂ gas mixtures at temperatures ranging from 1378 to 1617 °C and for melt compositions ranging from approximately cobalt saturation up to about 31 wt pct sulfur. As in a previous publication from these laboratories, an optical interferometer was employed to monitor the system’s approach to equilibrium and to analyze the composition of the equilibrium gas phase. A correlation based on the experimental data and that of other investigators is described. The correlation is based on the assumption of species in solution, and reproduces well all thermodynamic properties of Co-S melts. Formerly Graduate Student, Henry Krumb School of Mines, Columbi University. Formerly Graduate Student, Henry Krumb School of Mines, Columbi University.     

Calculation of phase diagrams for the FeCl2, PbCl2, and ZnCl2 binary systems by using molecular dynamics simulation

Recently, molecular dynamics (MD) simulation has been widely employed as a very useful method for the calculation of various physicochemical properties in the molten slags and fluxes. In this study, MD simulation has been applied to calculate the structural, transport, and thermodynamic properties for the FeCl₂, PbCl₂, and ZnCl₂ systems using the Born—Mayer—Huggins type pairwise potential with partial ionic charges. The interatomic potential parameters were determined by fitting the physicochemical properties of iron chloride, lead chloride, and zinc chloride systems with experimentally measured results. The calculated structural, transport, and thermodynamic properties of pure FeCl₂, PbCl₂, and ZnCl₂ showed the same tendency with observed results. Especially, the calculated structural properties of molten ZnCl₂ and FeCl₂ show the possibility of formation of polymeric network structures based on the ionic complexes of ZnCl ₄ ²⁻ , ZnCl ₃ ⁻ , FeCl ₄ ²⁻ , and FeCl ₃ ⁻ , and these calculations have successfully reproduced the measured results. The enthalpy, entropy, and Gibbs energy of mixing for the PbCl₂-ZnCl₂, FeCl₂-PbCl₂, and FeCl₂-ZnCl₂ systems were calculated based on the thermodynamic and structural parameters of each binary system obtained from MD simulation. The phase diagrams of the PbCl₂-ZnCl₂, FeCl₂-PbCl₂, and FeCl₂-ZnCl₂ systems estimated by using the calculated Gibbs energy of mixing reproduced the experimentally measured ones reasonably well.     

Freezing diagrams: Part II. Comparison with experimental observation and relevance to crystallization of metallic glass

The significance and limitations of the freezing diagram are discussed in terms of experimental observations reported in the literature. A freezing diagram constructed for the Cu−Ti system is shown to be an accurate predictor of metastable phase formation when the position of theT ₀ lines are known. Freezing diagrams also enable the construction of qualitative continuous cooling transformation diagrams for all alloy compositions, and these help in understanding the microstructure produced after cooling at a range of rates. The diagram further enables a prediction to be made of the subsequent crystallization of quenched-in glass or the decomposition of metastable phases, and this is verified by experimental observation. Liquid phase separation also is discussed in terms of freezing diagrams, and it is found that a reported case of liquidphase separation is more accurately described as primary crystallization resulting in liquid stabilization.     

Tensile properties of short fiber-reinforced SiC/Al composites: Part II. Finite-element analysis

The tensile properties of aluminum matrix composites containing SiC whiskers or particulate were investigated analytically and compared to experimental results. Two finite-element models were constructed and used for elastoplastic analysis. In both models, the SiC fibers are represented as longitudinally aligned cylinders in a three-dimensional array. The cylinder ends are transversely aligned in one model and staggered in the other. Using the models, the sensitivity of the predicted composite properties to the deformation characteristics of the matrix alloy was examined, and the general behavior of the models was validated. It was determined that both models are necessary to predict the overall composite stress-strain response accurately. The analytic results accurately predict: the observed composite stress-strain behavior; the experimentally observed increase in Young’s modulus and the work-hardening rate with increasing fiber volume content and aspect ratio; and the decrease and subsequent increase in proportional limit as the SiC volume fraction is increased. The models also predict that the transverse material properties should be insensitive to fiber aspect ratio. In addition, the model predicts the location of initial yielding and the propagation of the plastic region. These results offer insights into the deformation mechanisms of short fiber-reinforced composites.     

Thermodynamics and phase relationships of transition metal-sulfur systems: Part III. Thermodynamic properties of the Fe-S liquid phase and the calculation of the Fe-S phase diagram

An associated solution model is applied to describe the thermodynamic behavior of Fe-S liquid. This model assumes the existence of ‘FeS’ species in addition to Fe and S in the liquid. With two solution parameters for each of the binaries Fe-‘FeS’ and ‘FeS’-S, this model accounts for the compositional dependence of the thermodynamic properties of Fe-S liquid from pure Fe to pure S over a wide range of temperature. The binary Fe-S does not contribute significantly to the excess Gibbs energy of the liquid due to the rather small dissociation constant of ‘FeS’ to Fe and S. Using this model for the liquid phase and a defect thermodynamic model for the pyrrhotite phase, the Fe-S phase diagram is calculated. The calculated diagram is in excellent agreement with the experimental data, accounting for the range of homogeneity of pyrrhotite at all temperatures. Both the thermodynamic and phase diagram data are obtained from the literature. Formerly Post-Doctoral Research Associate, Materials Department, College of Engineering and Applied Science, University of Wisconsin-Milwaukee.