Thermodynamic assessment of the Nd–Zn binary system

On the basis of available experimental information, the Nd–Zn binary system has been thermodynamically optimized using the CALPHAD method. The solution phases, liquid, bcc and dhcp, were treated as substitutional solutions, while the intermediate compounds, NdZn, NdZn₂, NdZn₃, Nd₃Zn₁₁, Nd₁₃Zn₅₈, Nd₃Zn₂₂, Nd₂Zn₁₇ and NdZn₁₁, were described as stoichiometric phases. A set of self-consistent parameters formulating the Gibbs energies of various phases in this binary system was obtained. Most of experimental data on thermochemistry and phase diagram reported in the literatures were satisfactorily reproduced.     

Thermodynamic assessment of the Ni-Sb binary system

The Ni-Sb binary alloy system was thermodynamically assessed using CALPHAD approach in this article.Excess Gibbs energies of solution phases,liquid and fcc phases,were formulated using the Redlich-Kister expression.The intermediate phases were modeled by the sublattice model with (Ni,Va)0.5(Ni,Sb)0.25(Ni)0.25 for Ni3Sb_HT phase and (Ni,Va)0.3333(Sb)0.3333(Ni,Va)0.3333 for NiSb phase.The other phases including Ni3Sb,Ni7Sb3,and NiSb2 were treated as stoichiometric compound owing to their narrow composition ranges.Based on the reported thermodynamic properties and phase diagram data,the thermodynamic parameters of these phases were optimized,and the obtained values can reproduce the available experimental data well.     

Thermodynamic modeling of the Al–Cr system

By means of calculation of phase diagram (CALPHAD) technique, the Al–Cr system was critically assessed. Three solution phases (liquid, body-centered cubic, face-centered cubic) were modeled with the Redlich–Kister equation. The intermetallic compounds Al₇Cr, Al₁₁Cr₂, Al₄Cr, Al₈Cr₅, AlCr₂, which have a homogeneity range, were treated as the formulae Al₇(Al,Cr), Al₁₁(Al,Cr)₂, Al₄(Al,Cr), (Al,Cr)₈(Al,Cr)₅, (Al,Cr)(Al,Cr)₂ using two-sublattice model, respectively. A set of self-consistent thermodynamic parameters describing the Gibbs energy of each individual phase as a function of composition and temperature for the Al–Cr system was obtained.     

Fe-C-Ta三元系相关系的实验测定与热力学计算

采用差热分析(DTA)测定了Fe-C-Ta三元系中Fe-XC-0.1Ta和Fe-XC-0.5Ta 2个垂直截面,并选取Fe-2.93C-0.1Ta和Fe-2.31C-0.5Ta 2种合金,对其相变过程进行了分析。利用CALPHAD方法,并结合实验数据对该体系的相关系进行了热力学优化。结果表明,计算结果与实验结果符合较好。该体系富铁角的液相面投影存在4个四相恒温反应:Liquid+bcc?fcc+Ta C,Liquid?bcc+Fe_2Ta+Ta C,Liquid?Fe_3C+Ta C+fcc,Liquid+Ta_2C?Ta C+Fe_2Ta,反应温度分别为1443.26、1413.90、1122.42及1508.64℃。Fe-XC-0.1Ta合金和Fe-XC-0.5Ta合金在726.6℃发生共析反应。     

Thermodynamic optimization of the Cu-Nd system

The thermodynamic constraints to eliminate artificial phase relations were introduced with the Cu-Nd system as an example. The enthalpies of formation of the compounds Cu₆Nd, Cu₅Nd, Cu₂Nd and αCuNd are calculated using density functional theory. Taking into account all the experimental data and the first-principles calculated enthalpies of formation of these compounds, the thermodynamic optimization of the Cu-Nd system was performed under the proposed thermodynamic constraints. It is demonstrated that the thermodynamic constraints are critical to obtain a set of thermodynamic parameters for the Cu-Nd system, which can avoid the appearance of all the artificial phase relations.     

Thermodynamic assessment of ZnO-SiO2 system

ZnO-containing slags are common in pyrometallurgical processing of the base metals and steel. This caused the interest to the thermodynamics of the ZnO-SiO₂ system. A complete literature survey, critical evaluation of the available experimental data and a thermodynamic optimization of the phase equilibria and thermodynamic properties of the system ZnO-SiO₂ at 1.013×10⁵ Pa are presented. The molten oxide was described as an associate solution. The properties of liquid were reassessed and enthalpy term of the Gibbs energy of solid Zn₂SiO₄ was re-fitted to be compatible with the new data in the willemite primary phase field. The thermodynamic data set agrees well with the recent experimental observations. It can be used for predicting, e.g., the thermodynamic properties and the domains of the phase diagram, like critical point of the liquid miscibility gap, with a better accuracy than using the previous assessments. A set of optimized model parameters were obtained, reproducing the reliable thermodynamic and phase equilibrium data within their experimental errors from 298 K to liquidus temperatures, over the entire composition range. The created database can be used in a Gibbs energy minimization software to calculate the thermodynamic properties and the phase diagram sections of interest.     

Au-Ag-Al系相图的热力学优化和计算

使用计算相图方法(CALPHAD)计算Au-Ag-Al的三元相图时,三个边际二元相图(Au-Al,Au-Ag,Ag-Al)的准确性对三元相图的计算有很大的影响,目前Au-Al边际二元相图存在着一定的矛盾。在综合评估Au-Al体系实验数据的基础上,优化和计算了Au-Al合金体系的平衡相图,使用置换式溶体溶液模型描述Au-Al体系中液相、Bcc和Fcc相的吉布斯自由能,分别用亚点阵模型(Al)(Au)4、(Al)3(Au)8、(Al)(Au)2、(Al)(Au)和(Al,Au)2(Al,Au)描述AlAu4、Al3Au8、AlAu2、AlAu和Al2Au相,通过Pandat软件优化得到一组各相的热力学参数,计算得到的Au-Al相图与实验数据和热力学数据相吻合。结合Au-Ag和Ag-Al的热力学参数,计算了Au-Ag-Al液相面投影图和等温截面图,液相面投影图显示该三元系存在8个四相平衡反应,对Au-Ag-Al合金的研究具有指导意义。     

Thermodynamic modeling of the Ca–Ag binary system

The Ca–Ag binary system has been assessed with CALPHAD approach based on experiment information about phase diagram and thermodynamic properties. The excess Gibbs energies of the solution phases including liquid, bcc and fcc were formulated with Redlich–Kister polynomial functions. The intermetallic compounds Ca₂Ag₉, Ca₂Ag₇, CaAg₂, CaAg, Ca₅Ag₃ and Ca₃Ag were treated as stoichiometric phases. Self-consistent thermodynamic parameters have been obtained and the calculated results agree well with most literature data. Several diagrams and tables concerning the Ca–Ag system are presented.     

Thermodynamic modeling of the Ru–Zr system

The Ru–Zr system has been critically assessed by means of the CALPHAD technique. Based on the experimental data, the solution phases (liquid, body-centered cubic, hexagonal close-packed) were initially modeled with the Redlich–Kister equation. It was shown that this model had a definite temperature range beyond which the liquid became unstable. To tackle the problem, the solution phases were modeled with a new semi-empirical equation, which was recommended by Kaptay. A two-sublattice model (Ru, Zr)_0.5(Ru, Zr)_0.5 is applied to describe the compound RuZr in order to deal with the order–disorder transition between body-centered cubic solution (A2) and RuZr with CsCl-type structure (B2). Another two-sublattice model (Ru, Zr)_0.6667(Ru, Zr)_0.3333 is applied to describe the compound Ru₂Zr in order to cope with the order–disorder transition between hexagonal close-packed (A3) and Ru₂Zr with MgZn₂-type structure (C14). A set of self-consistent thermodynamic parameters of the Ru–Zr system was obtained.     

Thermodynamic assessment of Cu-Cd system

A thermodynamic assessment of the Cu-Cd system has been carried out by CALPHAD technique.The liquid phase, FCC_A1(Cu)and HCP_A3(Cd)terminal phases are described by a simple substitutional model,their excess Gibbs energy is formulated with the Redlich-Kister expression.The system contains four intermediate compounds,includingβ(Cu2Cd),γ(Cu4Cd3), δ(Cu5Cd8)andε(Cu3Cd10).Theδphase is described by a two-sublattice model and the other three intermediate phases are treated as stoichiometric phases.The optimization is carried out in the Thermo-Calc package.A set of self-consistent thermodynamic parameters are obtained.The calculated phase diagram and thermodynamic properties agree well with the available experimental data.     

Fe-Ti二元体系的热力学重新优化(英文)

为提高Fe-Ti二元系外推到三元或多元体系的能力,应用CALPHAD方法重新优化了该二元系。与前人的优化工作相比,重点放在对两个二元金属间化合物Fe2Ti和FeTi的热力学描述上。因目前普遍采用双亚点阵模型来描述C14_Laves相,所以采用双亚点阵模型来描述Fe2Ti相。通过检验包含Fe-Ti二元系的三元体系Fe-Ti边界上Fe2Ti相的均匀化范围进一步证实了Fe2Ti相的相边界。FeTi相具有BCC_B2晶体结构,因而将其处理成为BCC_A2相的有序相,并且用统一的Gibbs 能函数来描述有序和无序相。另外一个特别关注的方面就是重现这两个化合物的实测热容。计算结果与有关相图和热力学性质实验结果的广泛对比显示两者符合得很好,从而证明了所得热力学描述的有效性。     

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.     

热力学优化Bi-Ni二元系

基于文献报导的实验数据,采用相图计算（CALPHAD）方法,热力学优化了Bi-Ni二元系相图。该二元系的液相、fcc_A1（Ni）相和rhombohedral_A7（Bi）相用替换溶液模型来描述,其过剩吉布斯自由能用Redlich-Kister多项式来表达。考虑到晶体结构（NiAs型）以及与多组元体系热力学数据库的兼容性,中间化合物BiNi相采用亚点阵模型：（Bi）（Ni,Va）（Ni,Va）;Bi3Ni相处理为化学计量比化合物。最后,通过优化该二元系实测的相图和热力学数据,获得一组能够表达各相吉布斯自由能的自洽的热力学参数。根据这些热力学参数计算的相图和热力学数据与报导的实验数据吻合良好。     

Cu-Ni-Sn三元系相平衡的热力学计算

基于Cu-Ni-Sn三元系的相平衡和热力学的实验信息,采用亚正规溶体模型描述液相和fcc相的Gibbs自由能,为了预测该体系中bcc相的A2-B2有序-无序转变,bcc相的Gibbs自由能采用双亚点阵模型进行描述.利用CALPHAD(相图计算)方法评估了Cu-Ni-Sn三元系各相的热力学参数,计算的富Cu侧相图和热力学性质与实验数据比较一致.并对该三元系中bcc相的A2-B2有序-无序转变及fcc相的溶解度间隙进行了计算.这些计算结果对利用析出强化以及Spinodal分解开发高强度和高导电性的新型Cu基合金的组织设计具有一定的指导意义.     

Thermodynamic database of the phase diagrams in the Mg-Al-Zn-Y-Ce system

The Mg-Al-Zn-Y-Ce system is one of the key systems for designing high-strength Mg alloys. The purpose of the present article is to develop a thermodynamic database for the Mg-Al-Zn-Y-Ce multicomponent system to design Mg alloys using the calculation of phase diagrams （CALPHAD） method, where the Gibbs energies of solution phases such as liquid, fcc, bcc, and hcp phases were described by the subregular solution model, whereas those of all the compounds were described by the sublattice model. The thermodynamic parameters describing Gibbs energies of the different phases in this database were evaluated by fitting the experimental data for phase equilibria and thermodynamic properties. On the basis of this database, a lot of information concerning stable and metastable phase equilibria of isothermal and vertical sections, molar fractions of constituent phases, the liquidus projection, etc., can be predicted. This database is expected to play an important role in the design of Mg alloys.     

Thermodynamic analysis and assessment of the Ce–Ni system

An optimised set of thermodynamic parameters for the Ce–Ni system has been obtained using the CALPHAD approach. A thorough thermodynamic analysis of the system has been carried out using different calorimetric techniques and the data have been used in the assessment. The free energy of the liquid phase has been described as a function of temperature and composition using a Redlich–Kister polynomial. Solid compounds have been considered as stoichiometric with the exception of the Laves phases. The phase diagram and thermodynamic quantities calculated from assessed parameters agree well with experimental data.     

Co-Cr-W三元系相平衡的热力学计算

用CALPHAD方法评估了Co-Cr-W三元系,计算了1000,1200和1350℃的相平衡。采用亚正规溶体模型描述了液相,fcc相,bcc相和hcp相。σ相,μ相,R相分别用模型（Co,W）8（Cr,W）4（Co,Cr,W）18,（Co,Cr,W）7W2（Co,Cr,W）4和（Co,W）27（Cr,W）14（Co,Cr,W）12来表示;得到了自洽的热力学相互作用参数。计算的1000,1200和1350℃的相图与实验数据吻合。