Ba-eu (barium-europium)

Several thermodynamic models for calculating binary phase diagrams published in the literature have been reevaluated. Problems in some of these models are already evident in the models themselves and may also be seen in the resulting calculated phase diagrams. When a calculation is attempted, thermodynamic models with quite different formulations may result in very similar proposed phase diagrams. In such cases, if experimental data of a binary phase diagram can be represented reasonably well by several different thermodynamic models, a simpler model often provides the clearest insight into the basic properties of the system. If a calculated phase diagram results in unusual phase relationships, the adopted thermodynamic model may be inappropriate or may involve unrealistic parameters. If the thermodynamic model is clearly unrealistic and yet the calculated phase diagram appears to be normal, errors in calculation or in interpretation may be suspect. Various examples of unlikely combinations of thermodynamic models and phase diagrams are discussed.     

guidelines for binary phase diagram assessment

The recent publication of Binary Alloy Phase Diagrams,2nd ed, [90Mas] and our extensive screening of phase diagram graphics for this edition has revealed many phase diagram features, which while not explicitly violating phase diagram rules, are to a lesser or greater extent unlikely to represent thermodynamically acceptable conditions. In two previous papers, several thermodynamically improbable features or boundaries in binary phase diagrams were pointed out [91Oka2], and some unlikely thermodynamic models were shown to be unrealistic, or in error [91Okal]. In the present paper, we discuss some of the unlikely features in more detail in order to develop a set of guidelines that may be useful for checking future proposed phase diagram boundaries, or some specific phase diagram features resulting from both experimental and theoretical work, including also phase diagram assessments.     

guidelines for binary phase diagram assessment

The recent publication of Binary Alloy Phase Diagrams,2nd ed, [90Mas] and our extensive screening of phase diagram graphics for this edition has revealed many phase diagram features, which while not explicitly violating phase diagram rules, are to a lesser or greater extent unlikely to represent thermodynamically acceptable conditions. In two previous papers, several thermodynamically improbable features or boundaries in binary phase diagrams were pointed out [91Oka2], and some unlikely thermodynamic models were shown to be unrealistic, or in error [91Okal]. In the present paper, we discuss some of the unlikely features in more detail in order to develop a set of guidelines that may be useful for checking future proposed phase diagram boundaries, or some specific phase diagram features resulting from both experimental and theoretical work, including also phase diagram assessments.     

Critical evaluation and optimization of the thermodynamic properties and phase diagrams of the Al-Mg, Al-Sr, Mg-Sr, and Al-Mg-Sr Systems

All available thermodynamic and phase diagram data were critically assessed for all phases in the Al-Mg, Al-Sr, and Mg-Sr systems at 1 bar pressure from room temperature to above the liquidus temperatures. For these systems, all reliable data were simultaneously optimized to obtain a set of model equations for the Gibbs energy of the liquid alloy and all solid phases as functions of composition and temperature. The modified quasi-chemical model was used for the liquid. The Al-Mg-Sr ternary phase diagram was calculated from the optimized thermodynamic properties of the binary systems. Since no reliable ternary data were available, three assumptions were made: no ternary terms were added to the model parameters for the thermodynamic properties of the liquid, no ternary solid solutions are present in the system, and no ternary compound is present in the system. The calculated ternary phase diagram is thus a first approximation, which can be improved by the addition of new experimental data and can be used as a base for the calculation of phase diagrams of multicomponent systems.     

Influence of coupling with calculation of phase diagrams on microsegregation forming simulation of Al-4.5%Cu alloy

The effect of coupling with calculation of phase diagrams on microsegregation forming simulation was investigated. The traditional simplified phase diagram and calculated phase diagram were introduced into the numerical models respectively and simulation on microsegregation forming of the Al-4.5%Cu alloy ingot was also presented. The simulation results were both compared with the experiment results. The results show that the calculated sencondary arm spacing with these two kinds of phase diagram are almost the same because relationship between the coarsening model and the information of phase diagram is not close. The calculated eutectic phase volume fractions of different locations in the ingot coupled with different phase diagrams are discrepant. The calculated volume fractions are consistent with the experiment results when calculated phase diagram couples, but are far from the experiment results and obviously inacceptable when traditional simplified phase diagram couples. So, coupling with accurate calculated phase diagrams is very significant for microsegregation forming simulation since much information of the phase diagram is used in the models and it can improve the precision of simulation results.     

Thermodynamic optimization of the boron-cobalt-iron system

A thermodynamic optimization of the boron-cobalt-iron ternary system is performed based on thermodynamic models of the three constitutional binary systems and the experimental data on phase diagrams and thermodynamic properties of the ternary system. The liquid, fcc_A1, bcc_A2 and hcp_A3 solution phases are described by the substitutional solution model. The three intermediate line compounds, (Co,Fe)B, (Co,Fe)₂B and (Co,Fe)₃B, are described by the two sublattice model. A set of thermodynamic parameters are obtained. The calculated phase diagram and thermodynamic properties are in reasonable agreement with most of the experimental data.     

Thermodynamic assessment of the Mo–Re binary system

The existing Mo–Re phase diagrams are reviewed and a thermodynamic calculation of the Mo–Re binary system is undertaken. The Gibbs energies are estimated for liquid, bcc (Mo), hcp (Re), σ and χ phases. The liquid, bcc (Mo) and hcp (Re) phases are described by a regular solution model, whereas the σ and χ phases are described respectively by three-sublattice models. For the σ phase, two thermodynamic models are used for calculations and the results are compared. The models take into account the crystallographic structure and similarity between the σ and χ phases. The calculated results remove the ambiguity of the existing phase diagram data and are compared with the experimental data in the literature.     

APPLICATION OF TWO-DIMENSIONAL BINARY SYSTEM TO STUDY CERTAIN PHASE DIAGRAMS

本文将二维系统的Collins模型推广到二元替换式系统,求出了它的Gibbs函数和自由能,得到了决定两相平衡曲线的方程,研究了几种常见的相图,并对“雪茄形”相图作了具体计算,所得结果与三维情况十分相似。     

Nacl—Bacl2—Srcl2三元熔盐相图的计算

本文运用作者提出的从三个对应的二元系的热力学性质预示三元溶液的热力学性质的新对称几何模型,推导得到三元溶液中三个组元的偏摩尔热力学性质的数学表达式。进而将这一结果应用于NaCl-BaCl_2-SrCl_2三元熔盐相图的计算中,得到此三元系的液相析出面及若干等温截面。计算所得结果与实测结果偏差小于5℃,说明此模型在一些熔盐体系中有较好的适用性。     

CALCULATION OF NaCl-BaCl_2-SrCl_2 PHASE DIAGRAM

The mathematical formulas are given for calculating the partial molar thermodynamic proper-ties in a ternary system from its three corresponding binary systems based on the new ternarysymmetric model presented by the authors in the foregoing paper.Applying this model toNaCl-BaCl_2-SrCl_2 system,the phase diagram of which as well as some isothermal sectionshave been calculated.The devations of temperature between the calculated and experimen-tal diagrams are less than five degrees.     

金属熔体凝固微观组织模拟的相场方法研究

全面阐述了现有的金属熔体凝固微观组织模拟的相场模型:纯物质、二元合金理想溶液或正规溶液和稀溶液相场模型,指出构造适合于具有复杂溶液模型的金属熔体凝固微观组织模拟相场模型的必要性.提出采用相图计算热力学模型构造相场模型中的体系自由能,并对相场参数做出相应修正,建立了能对具有复杂溶液模型的金属熔体凝固微观组织进行准确模拟的相场模型.利用该相场模型对Ti-Al金属熔体中晶体的自由生长和定向生长进行了模拟,得到许多与试验观察和理论分析相一致的结果.     

贵金属二元合金相图研究的新进展和展望

对贵金属二元合金相图研究现状及其可靠性进行了全面的分析,把贵金属与周期表中各元素的相互作用分成连续固溶体、简单包晶型、简单共晶型、简单偏晶型、生成化合物的复杂体系和在固态和液态都不互溶的6种类型,并把它们放在元素周期表中进行研究后,定性总结了它们的若干规律;评价了二元相图坐标的热力学表示原理;评价了二元相图的半径验计算法和中间相的IUPAC（国际理论化学和应用化学联合会）和MSIT（国际材料科学组织）表示法,强调半经验的热力学计算法比较成熟,而按第一原理的理论计算法尚处在快速发展中;展望了贵金属二元合金相图的发展方向。     

Thermodynamic Database for Phase Diagrams of Mn-RE Binary Alloy Systems

Thermodynamic assessment of Mn-RE (RE: Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu) binary systems has been carried out by means of the calculation of phase diagrams method on the basis of experimental data including phase equilibria and thermodynamic properties. The Gibbs free energies of liquid phase and solid solution phases in the Mn-RE systems were all described by the subregular solution model with the Redlich–Kister formulation, whereas those of intermetallic compounds were described by the sublattice model. Sets of thermodynamic functions with self-consistent parameters leading to satisfactory agreement between calculated results and experimental data were eventually obtained. A primary thermodynamic database for the phase diagrams of the Mn-RE (RE: Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, Yb, Lu) binary systems was developed from these essential thermodynamic parameters. This database can be used not only to calculate the phase equilibria and thermodynamic properties of binary Mn-RE systems but also to extrapolate to higher-order systems, which can provide theoretical guidance for design and development of high-performance Mn-RE alloy materials.     

The ternary Gd-Li-Mg system: Phase diagram study and computational evaluation

The binary Gd-Li and the ternary Gd-Li-Mg systems were studied experimentally by thermal analysis and phase equilibration and also by thermodynamic calculations using the CALPHAD method. Ternary phase equilibria at 250 °C were studied with 55 different alloys that were annealed for 400 h and analyzed by x-ray diffractometry. A thermodynamic assessment of the binary Gd-Li system was also performed and the calculated phase diagram is presented. In the Gd-Li-Mg system, ternary solubilities of Li in GdMg (up to 5 at.% Li), GdMg₂ (up to approximately 3 at.% Li), and GdMg₃ (up to 5 at.% Li) were found at 250 °C. No ternary compound was observed. Lattice parameters for different compositions are given for these phases. Thermal analysis using a ternary key sample of composition near the invariant reaction L′=L+(βGd)+GdMg provided the data that were needed to determine a thermodynamic parameter for the ternary liquid. Thermodynamic data sets for the ternary solid solution phases were also developed. Based on the present data sets and those of the binary Gd-Mg and Li-Mg systems from the literature, the phase equilibria in the entire ternary system were calculated. Isothermal and vertical sections of the phase diagram and the projection of the liquidus surface are shown. These calculated phase diagrams are well supported by the experimental data.     

Assessment of the Te-Tl (tellurium-thallium) system

The optimized thermodynamic data for the Te- TI binary system have been obtained by the computer operated least squares method from measured data. The Gibbs energy of the liquid phase was modeled as a two- sublattice model for ionic melt after Hillert.³¹ The intermediate compounds, Te₃Tl{2}and TeTl, were treated as stoichiometric phases, and the nonstoichiometric γ phase was expressed as a sublattice model. A strong tendency for chemical short- range order in the liquid state at the composition close to TeTh was confirmed by calculated results, but the existence of the TeTh phase was not justified. The experimental thermodynamic and phase diagram data were closely reproduced by the optimized thermodynamic data. Parameters describing the Gibbs energies of all the phases in this calculation and the calculated phase diagram and thermodynamic functions are presented and compared with experimental information.     

The ternary Gd-Li-Mg system: Phase diagram study and computational evaluation

The binary Gd-Li and the ternary Gd-Li-Mg systems were studied experimentally by thermal analysis and phase equilibration and also by thermodynamic calculations using the CALPHAD method. Ternary phase equilibria at 250 °C were studied with 55 different alloys that were annealed for 400 h and analyzed by x-ray diffractometry. A thermodynamic assessment of the binary Gd-Li system was also performed and the calculated phase diagram is presented. In the Gd-Li-Mg system, ternary solubilities of Li in GdMg (up to 5 at.% Li), GdMg₂ (up to approximately 3 at.% Li), and GdMg₃ (up to 5 at.% Li) were found at 250 °C. No ternary compound was observed. Lattice parameters for different compositions are given for these phases. Thermal analysis using a ternary key sample of composition near the invariant reaction L′=L+(βGd)+GdMg provided the data that were needed to determine a thermodynamic parameter for the ternary liquid. Thermodynamic data sets for the ternary solid solution phases were also developed. Based on the present data sets and those of the binary Gd-Mg and Li-Mg systems from the literature, the phase equilibria in the entire ternary system were calculated. Isothermal and vertical sections of the phase diagram and the projection of the liquidus surface are shown. These calculated phase diagrams are well supported by the experimental data.     

Assessment of the Te-Tl (tellurium-thallium) system

The optimized thermodynamic data for the Te- TI binary system have been obtained by the computer operated least squares method from measured data. The Gibbs energy of the liquid phase was modeled as a two- sublattice model for ionic melt after Hillert.³¹ The intermediate compounds, Te₃Tl{2}and TeTl, were treated as stoichiometric phases, and the nonstoichiometric γ phase was expressed as a sublattice model. A strong tendency for chemical short- range order in the liquid state at the composition close to TeTh was confirmed by calculated results, but the existence of the TeTh phase was not justified. The experimental thermodynamic and phase diagram data were closely reproduced by the optimized thermodynamic data. Parameters describing the Gibbs energies of all the phases in this calculation and the calculated phase diagram and thermodynamic functions are presented and compared with experimental information.     

THERMODYNAMIC CALCULATION MODELS FOR TiO_2-BASED SLAG MELTS

1.IntroductionTheincreasingdemandsf0rlownitrogensteelproductsgiveriset0greatenthusiaJsmtouseTiO2-basedfluxfordenitrogeniZationofsteel[1-3].ManyexperimentscondrmedthatTi0z-basedslagshavehighernitridecaPacitiesandaPpeartobeonekind0fthemosteffectivefiuxesf0rdeIiltrogenization.Butasfarastherm0dynamicstudiesareconcerned,littleworkhasbeenreported0nthethermodynamiccalculationm0delsforTiO2-base'slags[4],especiallyf0rmulticomponentslagswithtitania-Inadditi0n,aJsaresultofusingvanadium-bearingtitani…