Review and modeling of viscosity of silicate melts: Part I. Viscosity of binary and ternary silicates containing CaO, MgO, and MnO

A structurally related model for the calculation of the viscosity of silicate melts is proposed based on the general behavior of the viscosity of binary silicate melts. It relates viscosity to the degree of polymerization, as represented by the three types of oxygen in the melts. The model parameters for binary systems were optimized to give best fit to the experimental values. For ternary systems, it was assumed as a first approximation that the model parameters were linear functions of the parameters of the two binary silicate systems. The model has been applied to the CaO-SiO₂, MgO-SiO₂, and MnO-SiO₂ binary systems and the CaO-MgO-SiO₂ and CaO-MnO-SiO₂ ternary systems. Good agreement was obtained between calculated values and experimental data over the composition and temperature ranges in which experimental data exist. Comparison was made between the present model and the Urbain model. The present model has the capability of representing changes in viscosity due to substitution of cation species in silicate melts.     

Calculation of phase equilibria in the Ga-Bi and Ga-P-Bi systems based on a theory of regular associated solutions

A new theory of regular associated solutions (RAS) has been formulated to provide a consistent representation of binary and ternary phase equilibria in the Ga-P-Bi system. The key postulate of the theory is that the major species in liquid alloys are Ga, P, and Bi atoms and Bi₂ dimers. At first, the gross component activities in the Ga-Bi binary system are approximated from the dimer dissociation constant,K, and the activity coefficients of the three species (identified here with the coefficients for a ternary regular solution). The accord observed between the form of the isothermal activity data and the theory permits the determination ofK and the Ga-Bi interchange energy. These parameters are then employed in the calculation of the enthalpy and entropy of mixing and the prediction of the liquidus curve and asymmetric miscibility gap for the Ga-Bi system, all of which are in good agreement with the experimental findings. Generalization of the enthalpy and entropy of mixing for a binary RAS facilitates the derivation of the activities in the ternary system. Knowledge of the activities leads to the evaluation of the ternary liquidus isotherms over the entire composition range, since the Bi-P interchange energy can be obtained from the GaP-Bi pseudobinary liquidus data. It is found that along the pseudobinary the standard error between calculated and experimental liquidus points is 7° C. Furthermore, in P-rich liquid solutions, at any temperature below ≈R 1380°C, an open miscibility gap intersects the primary liquidus isotherms of Bi-doped GaP. The predicted miscibility gap in the Bi-P system is consistent with the fragmentary evidence. Finally, the paper discusses extensions of the RAS model to other ternary systems involving compound semiconductors wherein association in the liquid is likely.     

M-Si-B合金非晶形成能力的CALPHAD模式评估

Evaluation of the amorphous-forming ability of M-Si-B ternary alloys using CALPHAD approach@長谷部光弘$日本九州工业大学 @OHTANI Hiroshi$Department of Materials Science and Engineering, Kyushu Institute of Technology @HASEBE Mitsuhiro$Department of Materials Science and Engineering, Kyushu Institute of Technology…     

Relation between the Full and effective solidification ranges and the hot cracking of multicomponent aluminum-based alloys

The relation between the calculated full and effective solidification ranges (FSR and ESR) and the experimentally determined hot-cracking index (HCI) for standard industrial and experimental cast aluminum alloys of various systems is analyzed. It is established that the ESR and the HCI correlate well only for alloys belonging to the same doping system. It is concluded that the ESR is not the only (and possibly not the main) factor determining the HCI. It is shoESRwn that there is virtually no correlation between the FSR and the HCI for the investigated multicomponent alloys.     

Experimental and Calculated Ag + Au + Ge Phase Diagram

The investigation of the equilibrium phase diagram of the Ag + Au + Ge system has been carried out by the following ways: (a) the location of equilibrium surfaces was determined on the whole composition range by high temperature isoperibolic calorimetry and differential thermal analysis; (b) the equilibrium temperatures of the ternary system were calculated from the equilibrium temperatures and the thermodynamic functions referring to the three limiting binary alloys Ag + Au, Ag + Ge, Au + Ge. A satisfactory agreement was found between the calculated liquidus and the one obtained by calorimetry and thermal analysis. In the course of a systematic thermodynamic investigation of ternary alloys based on gold, silver, and a IV b metal, the three systems Ag + Au + Si, Ag + Au + Ge, and Ag + Au + Sn were examined; the molar enthalpies of formation of the liquid mixtures were obtained on the one hand and the equilibrium phase diagrams on the other.^1,2,3 This paper focuses on the latter topics for the ternary alloys Ag + Au + Ge; a comparison is carried out between the equilibrium temperatures measured by differential thermal analysis at the laboratory S.E.T.T. in Marseille and those calculated at the Royal Institute of Technology in Stockholm. This calculation is based on the thermodynamic data published for the limiting binary systems and also on the ternary enthalpies measured by calorimetry at very high temperature.     

The activity coefficient of oxygen in binary liquid metal alloys

The Wagner model with one energy parameter,h, for describing the effect of alloying elements on the activity coefficients of nonmetallic solutes in liquid metals is extended to have two energy parameters,h ₁andh ₂. The validity of both the Wagner one-parameter equation and the newly derived two-parameter equation is tested using data available in the literature for twelve ternary metal-oxygen systems. In order to have consistent thermodynamic data, all the relevant binary, as well as the twelve ternary metal-oxygen systems are evaluated using the same thermodynamic values for the reference materials which were used in carrying out the experimental measurements. It is found that the twoparameter equation is capable of quantitatively accounting for the compositional dependences of the activity coefficients of oxygen in all twelve ternary systems while the Wagner one-parameter equation is not. A correlation between the Wagner parameter,h, and the thermodynamic properties of the respective binary metal-oxygen and binary metals systems is found, from which the value of this parameter may be predicted without referring to any ternary data. Accordingly, the two-parameter equation is more useful in evaluating ternary experimental data while the Wagner one-parameter equation in connection with the correlation betweenh and binary data is capable of predicting ternary data without any experimental investigation in the ternary region. Based on the one-parameter and the two-parameter equations, theoretical equations for the first-order and second-order free energy interaction parameters,(∈ ₀ ^j )_sand(ρ ₀ ^j )_s, are derived in terms of the model parameters. The values of(∈ ₀ ^j )_s and(ρ ₀ ^j )_s for all the systems are derived and are found to vary linearly with the reciprocal of temperature. Furthermore, linear relationships between these two interaction parameters and their slopes with 1/T are found, from which the temperature dependence of the interaction parameters may be estimated in the absence of experimental data.     

Experimental study and thermodynamic calculation of Lu_2O_3-SiO_2 binary system

As a binary system of BaO-Lu_2O_3-SiO_2 ternary system, Lu_2O_3-SiO_2 system was optimized and calculated by CALPHAD approach based on available phase diagram and relevant thermodynamic data of RE_2O_3-SiO_2(RE=Lu,Yb,Y) binary systems as well as our experimental data of Lu_2O_3-SiO_2 system obtained by quenching experiment. The Gibbs free energy of high temperature solution was described by an ionic two-sublattice model as(Lu~(3+))P(O~(2-), SiO_2~0)Q. The calculated phase diagram below 1873 K was in good agreement with experimental data at 1573, 1773 and 1873 K. The calculated Gibbs energies of two intermediate phases Lu_2SiO_5 and Lu_2Si_2O_7, the activity of Lu_2O_3 and SiO_2 and specific heat capacities of intermediate phases agreed well with experimental results of Y_2O_3-SiO_2 system. This tentative study will offer help for the research of single-phase phosphor and related metallurgical slags, refractories, high-temperature superconductivity material systems.     

Prediction of Activities in Fe-Based Ternary Liquid Alloys by Hoch-Arpshofen Model

 Thermodynamic properties for an alloy system play an important role in the materials science and engineering. Therefore, theoretical calculations having the flexibility to deal with complexity are very useful and have scientific meaning. The Hoch-Arpshofen model was deduced from physical principles and is applicable to binary, ternary and larger system using its binary interaction parameters only. Calculations of the activities of Fe-based liquid alloys are calculated using Hoch-Arpshofen model from data on the binary subsystems. Results for the activities for Fe-Au-Ni, Fe-Cr-Ni, Fe-Co-Cr and Fe-Co-Ni systems at required temperature are presented by Hoch-Arpshofen model. The average relative errors of prediction are 78%, 45%, 49% and 27%, respectively. It shows that the calculated results are in good agreement with the experimental data except Fe-Au-Ni system, which exhibits strong interaction between unlike atoms. The model provides a simple, reliable and general method for calculating the activities for Fe-based liquid alloys.     

The liquidus surfaces of ternary systems involving compound semiconductors: II. Calculation of the liquidus isotherms and component partial pressures in the Ga−As−Zn and Ga−P−Zn systems

The previously derived liquidus equation for anAB compound (GaAs or GaP) incorporating a dilute solute (zinc) in equilibrium with a ternary regular melt was applied to the available liquidus data in the Ga?As and Ga?As?Zn and in the Ga?P and Ga?P?Zn systems. The ternary interchange energies for both systems were computed by the method of multidimensional leastsquares. Utilizing these interchange energies, the liquidus isotherms in the Ga?As?Zn and Ga?P?Zn systems were calculated over a wide temperature range from the nonlinear liquidus equation by a numerical method. By a combination of the ternary regular activity coefficients with the vapor pressures of the pure components and the liquidus isotherms, the component partial pressures along the liquidus isotherms were determined. The ternary liquidus and partial pressure isotherms are in good agreement with the experimental data of Panish, Koster and Ulrich, and Shihet al. It is further shown that in the binary limit, the results of these calculations are also in accord with liquidus and partial pressure measurements for the Ga?As and Ga?P systems.     

Model prediction of thermodynamic properties of Co-Fe-Ni-S mattes

The modified quasichemical model for short-range ordering has been used to predict the thermodynamic properties of liquid Fe-Co-S, Ni-Co-S, and Fe-Ni-S solutions based only upon parameters obtained from critical optimization of data for the corresponding metal-sulfur and metal-metal binary systems. Calculated equilibrium sulfur pressures over the ternary solutions and calculated tie-lines between the ternary solutions and the solid alloy phases agree with measurements, within experimental error limits, over a wide range of compositions and temperatures.     

LiF-NaF-KF体系的相图计算

基于CALPHAD技术首先评估了LiF-NaF和LiF-KF两个二元熔盐体系,液相和端际固溶体Halite相均采用Redlich-Kister多项式置换熔体模型描述,模型参数的优化选取实验相平衡数据和热化学数据以及本文根据第一性原理预测的数据.结合文献中已报道的NaF-KF体系的热力学参数,用Muggianu模型扩展至LiF-NaF-KF三元体系,根据三元共晶点的实验数据调整三元交互参数.最终的相图计算结果与绝大部分实验数据和第一原理计算数据吻合较好,由此获得了一套自洽且可靠的热力学参数,其能够准确描述LiF-NaF-KF体系的相平衡与热力学性质.      

Phase relationships in the fe-cr-mn-ni-c system at solidification temperatures

The phase relationships between the liquid phase and the primary solid phases were investigated in the iron-rich corner of the quinary system Fe-Cr-Mn-Ni-C. Of the five quaternary systems that comprise the quinary system, this study was limited to the three quaternary systems which contain both carbon and iron as two of the components;viz.: Fe-Cr-Mn-C, Fe-Cr-Ni-C, and Fe-Mn-Ni-C, as well as all of the binary and ternary subsystems that have iron as a component. This paper discusses the modeling efforts for these systems, with particular emphasis on the ternary systems Fe-Cr-Mn and Fe-Mn-Ni and the quaternary systems Fe-Cr-Mn-C and Fe-Mn-Ni-C. The experimental investigation consisted of measurements of tie-lines for the liquid-delta (bcc) and the liquid-gamma (fcc) equilibria in the iron-rich corner of the Gibbs simplex bounded by 0 to 25 wt pct Cr, 0 to 12 wt pct Mn, 0 to 25 wt pct Ni, and 0 to 1.2 wt pct C (bal. Fe). The temperature ranged from 1811 to about 1750 K. Compositions for the tie-lines were obtained from liquid-solid equilibrium couples, and the temperatures for the equilibrium by differential thermal analysis (DTA). Parameters were selected in a thermodynamic model of the alloy system to minimize the square of the difference between experimentally and calculated tie-lines, the latter being implicitly a function of the derived parameters in the model. Binary and higher-order parameters were generally required. Ternary parameters were obtained on ironcarbon base alloys Fe-Cr-C, Fe-Mn-C, and Fe-Ni-C, and for the Fe-Cr-Ni system, but not for the Fe-Cr-Mn and Fe-Mn-Ni systems. Of the quaternary systems investigated, quaternary parameters were required only for theL/δ equilibrium in the Fe-Cr-Ni-C system; the Fe-Cr-Mn-C and Fe-Mn-Ni-C systems were found to be represented adequately by employing only binary and ternary parameters.     

The activity coefficient of nitrogen in binary liquid metal alloys

Literature data for the limiting thermodynamic properties of nitrogen in liquid Fe, Co, Ni, and Cr, as well as in the six binary alloys consisting of two of the above elements, are critically evaluated. The ternary data are evaluated in terms of the Wagner model for quasi-interstitial liquid alloys and values of the Wagner parameter h are obtained for each system. The correlation formulated by Chiang and Chang between the Wagner parameter h and the relevant binary thermodynamic properties for oxygen in binary alloys has been found to be equally valid for nitrogen in binary alloys. From this correlation, a value of h may be predicted in the absence of any ternary experimantal data. Utilizing the Wagner model and the value of h obtained for each system, values for the first-order and second-order Gibbs energy interaction parameters ∈N(s) and ρsujN(s) are derived.. The parameters are expressed as a linear function of the reciprocal temperature, i.e. ∈^jN(s) =α + β/T and.ρ^jN_(s) = α′ + β′/T. A linear correlation found by Chipman and Corrigan between β and ∈^jN(s) for systems where Fe is the solvent is also valid for systems with non-ferrous solvents. A linear correlation between β′ and ρ^jN_(s) is also found in the present study.     

渣成分对高温合金0Cr15Ni25Ti2MoAlVB 电渣重熔Ti烧损率和钢锭表面质量的影响

试验分析了2.5 t电渣炉使用4种成分熔渣重熔0Cr15Ni25Ti2MoAlVB合金时的Ti烧损率。试验结果表明,4种渣系中75%CaF₂-15%Al₂O₃-10%CaO三元提纯渣的Ti烧损率最低,为7.0%,并且避免了70%CaF₂-30%Al₂O₃的二元渣系重熔钢锭表面渣沟等缺陷。     

Computer analysis of phase diagrams and thermodynamic properties of cryolite based systems: Part II. The AIF3-CaF2-LiF,AIF3-CaF2-NaF,and CaF2-LiF-NaF systems

A computer-assisted critical analysis of available phase diagrams and thermodynamic data of the ternary AlF₃-CaF₂-NaF, AlF₃-CaF₂-LiF, and CaF₂-NaF-LiF systems up to 30 mol pct A1F₃, as well as of all binary subsystems was performed. Optimized mathematical expressions for the thermodynamic properties of all phases were obtained. In the case of the binary mixtures, the use of the F0rland equivalent fractions was shown to reduce the number of coefficients needed to represent analytically the enthalpies of mixing. The Conformai Ionic Solution Theory was applied with success to describe the thermodynamic properties of these ternary charge-asymmetrical systems. The binary and ternary phase diagrams were calculated and compared, wherever possible, with experimental investigations.     

Thermodynamics of B2 intermetallic compounds with triple defects: a Bragg-Williams model for (Ni,Co)Al

Applying the Bragg-Williams approximation, a pair interaction model has been developed for describing the composition and temperature dependence of thermodynamic properties of ternary intermetallic B2 phases. Taking the activities and the integral enthalpies of formation as input data, values for the enthalpy and the entropy of bonds between atoms have been obtained. An analytical expression has been derived for the dependence of the concentration of point defects (vacancies and antistructure atoms) on composition and temperature. The model has been applied successfully to the available experimental data for the Ni-Al, Co-Al, and Ni-Co-Al systems. It has been shown that the values calculated accordingly for the effective enthalpy (and entropy) of formation of vacancies agree well with those from experimental observations and theoretical ab initio calculations.     

Experimental investigation of the thermodynamics of Fe-Nb-C austenite and nonstoichiometric niobium and titanium carbides (T = 1273 to 1473 K)

The thermodynamics of Fe-Nb-C austenite and nonstoichiometric binary niobium carbide and titanium carbide in the temperature range of 1273 to 1473 K has been investigated using a dynamic gas equilibration technique. Methane-hydrogen mixtures have been used for fixing carbon potentials, and the carbon contents have been determined as dynamic weight changesvia a sensitive Cahn microbalance. The niobium-carbon interactions, similar to the titaniumcarbon interactions, are manifested as a minimum in the niobium carbide solubility in austenite, as increased amounts of dissolved carbon with niobium additions, and as the variation of solubility limit of the carbide with carbon content at high carbon levels. The results on the isoactivity measurements in the ternary Fe-Nb-C have been analyzed using the modified Wagner formalism, and the ternary interaction parameter ε _C ^Nb has been evaluated. The solubility of niobium carbide in Fe-Nb-C in austenite has been determined as the deflection in the variation of carbon content with Nb additions at constant carbon activity. The dissolution free energy of body-centered cubic (bcc) Nb in face-centered cubic (fcc) Fe has also been determined from the solubility data. Rational correlation between the dissolution free energies of transition metal solutes in fcc Fe and the group number in the Periodic Table has been shown to exist. A correlational relationship between the ternary interaction parameter and the free energy of formation of carbides has been established. These relationships are utilized in the assessment, as well as the systematization of thermodynamic data. The results on the activity-composition relationship in the binary niobium and titanium carbides have been analyzed using the sublattice-subregular model proposed by Hillert and Staffansson, [2] and the interaction parameters in the model were determined. The thermodynamic calculations based on this model and our experimental results were carried out, and very good agreement between experimental and calculated results was obtained. K. BALASUBRAMANIAN, Formerly with McMaster University,