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.     

Thermodynamic Database and the Phase Diagrams of the (U,Th, Pu)-X Binary Systems

A thermodynamic database for nuclear materials, including U-Th, U-Pu, Th-Pu, and (U, Th, Pu)-X (X = Al, Co, Cr, Cu, Fe, Ga, Mg, Mn, Mo, Nb, Ni, Si, Ta, W, Zr) binary system has been developed by the Calculation of Phase Diagrams (CALPHAD) method. Thermodynamic parameters describing Gibbs free energies of different phases have been evaluated by optimizing experimental data on phase equilibria and thermodynamic properties. The present thermodynamic database can provide much-needed information such as stable and metastable phase equilibria, phase fractions, and various thermodynamic quantities that is important to the design of nuclear materials. This database is also an essential starting point to construct thermodynamic databases for the multicomponent systems.     

The development of the COST 531 lead-free solders thermodynamic database

The methods for modeling the thermodynamic properties of multicomponent systems are described in this article. The rules for creating a consistent database for muticomponent systems are described in general terms and documented in relation to the thermodynamic database for lead-free solders, developed within the scope of European Cooperation in the Field of Scientific and Technical Research Action 531. New assessments and reassessments of the Bi-Sn-Zn, Cu-Ni-Sn, and Ag-Cu-Sn systems are shown as examples illustrating the application of the database for the modeling of lead-free solder materials.     

Computational thermodynamics and the kinetics of martensitic transformation

To assist the science-based design of alloys with martensitic microstructure, a multicomponent database kMART (kinetics of MARtensitic Transformation) encompassing the components Al, C, Co, Cr, Cu, Fe, Mn, Mo, N, Nb, Ni, Pd, Re, Si, Ti, V, and W has been developed to calculate the driving force for martensitic transformation. Built upon the SSOL database of the Thermo-Calc software system, a large number of interaction parameters of the SSOL database have been modified, and many new interaction parameters, both binary and ternary, have been introduced to account for the heat of transformation, T ₀ temperatures, and the composition dependence of magnetic properties. The critical driving force for face-centered cubic (fcc) → body-centered cubic (bcc) heterogeneous martensitic nucleation in multicomponent alloys is modeled as the sum of a strain energy term, a defect-size-dependent interfacial energy term, and a composition-dependent interfacial work term. Using our multicomponent thermodynamic database, a model for barrierless heterogeneous martensitic nucleation, a model for the composition and temperature dependence of the shear modulus, and a set of unique interfacial kinetic parameters, we have demonstrated the efficacy of predicting the fcc → bcc martensitic start temperature (M _s ) in multicomponent alloys with an accuracy of ± 40 K over a very wide composition range.     

Development of Co-Cr-based longitudinal magnetic recording media:Thermodynamic consideration

This paper reviews our recent work on development of Co-Cr-based longitudinal magnetic recording media through the point of view of thermodynamics. It focuses on our experimental finding on the miscibility gap in the fcc α-Co phase region of the Co-Cr binary system, and on the predictions on the improvements of magnetic properties of many Co-Cr-Z ternary systems by thermodynamic computing on the basis of the newly-assessed Co-Cr binary thermodynamic parameters. Good agreement in the phase separation behavior of many Co-Cr-Z (Z=Pt, Ta, Ge)alloy systems between the calculation and the experiments has been achieved, as discussed in detail in the full paper.By the same token, many other elements, such as Ir, P, B, Mo, Zr, Nb, have been predicted to improve the magnetic grain isolation of the potential Co-Cr-Z multicomponent magnetic recording media in the future.     

Homogenization of multicomponent alloys via partial melting

A practically important case, when homogenization of multicomponent alloys is achieved through partial melting, is analyzed. In the course of this process, liquid pools, initially formed from interdendritic material after re-heating, shrink continuously, change their composition, and finally disappear to leave an inhomogeneous solid solution behind. To tackle this diffusion-controlled isothermal process, a comprehensive mathematical model was developed to couple thermodynamic properties and kinetic characteristics. In particular, a numerical solution of the transient liquid phase problem for the multicomponent case is presented. The model was applied to simulate homogenization processes in Cu-Ni-Sn commercial alloys. Since the validity of quantitative estimations and predictions obtained with this model depend on the reliability of input thermodynamic information, the properties of the liquid and FCC phases in the Ni-Sn and Cu-Ni-Sn systems were re-assessed using the CALPHAD method.     

Homogenization of multicomponent alloys via partial melting

A practically important case, when homogenization of multicomponent alloys is achieved through partial melting, is analyzed. In the course of this process, liquid pools, initially formed from interdendritic material after re-heating, shrink continuously, change their composition, and finally disappear to leave an inhomogeneous solid solution behind. To tackle this diffusion-controlled isothermal process, a comprehensive mathematical model was developed to couple thermodynamic properties and kinetic characteristics. In particular, a numerical solution of the transient liquid phase problem for the multicomponent case is presented. The model was applied to simulate homogenization processes in Cu-Ni-Sn commercial alloys. Since the validity of quantitative estimations and predictions obtained with this model depend on the reliability of input thermodynamic information, the properties of the liquid and FCC phases in the Ni-Sn and Cu-Ni-Sn systems were re-assessed using the CALPHAD method.     

Computational thermodynamics and the kinetics of martensitic transformation

To assist the science-based design of alloys with martensitic microstructure, a multicomponent database kMART (kinetics of MARtensitic Transformation) encompassing the components Al, C, Co, Cr, Cu, Fe, Mn, Mo, N, Nb, Ni, Pd, Re, Si, Ti, V, and W has been developed to calculate the driving force for martensitic transformation. Built upon the SSOL database of the Thermo-Calc software system, a large number of interaction parameters of the SSOL database have been modified, and many new interaction parameters, both binary and ternary, have been introduced to account for the heat of transformation, T ₀ temperatures, and the composition dependence of magnetic properties. The critical driving force for face-centered cubic (fcc) → body-centered cubic (bcc) heterogeneous martensitic nucleation in multicomponent alloys is modeled as the sum of a strain energy term, a defect-size-dependent interfacial energy term, and a composition-dependent interfacial work term. Using our multicomponent thermodynamic database, a model for barrierless heterogeneous martensitic nucleation, a model for the composition and temperature dependence of the shear modulus, and a set of unique interfacial kinetic parameters, we have demonstrated the efficacy of predicting the fcc → bcc martensitic start temperature (M _s ) in multicomponent alloys with an accuracy of ± 40 K over a very wide composition range.     

Thermodynamic assessment of systems of actinide or rare earth with Cd

A pyrometallurgical process is being developed for recycling nuclear reactor fuels. Thermodynamic information on multicomponent systems of actinides and rare earths (REs) with liquid Cd is very useful in the design of a process in which a liquid Cd electrode is used for the selective recovery of Pu and U, and a reductive extraction process using a molten salt/liquid Cd system for the recovery of minor actinides, such as Np, Pu, etc. A key issue in the design of these processes is a variation in solubility or activity of actinides or REs in multielement systems. In the present study, phase diagrams of U-Cd, Pu-Cd, Np-Cd, Y-Cd, La-Cd, Ce-Cd, Pr-Nd, Nd-Cd, and Gd-Cd were optimized by the CALPHAD method. For these systems, thermodynamic data, such as the activity of solutes in liquid Cd and the Gibbs energies of formation of the intermetallic compounds as well as the phase diagram data were available for the optimization. For optimization, the calculated primary results were entered into a database. Then, some ternary systems were preliminarily assessed through the use of the optimized data for the binary systems. Two extreme conditions were assumed: one condition was complete miscibility between the compounds that have the same mole ratio between solutes and Cd; the other condition was no solid solubility between the compounds. The results indicated the tendencies toward solubility and activity of actinides and REs in multielement systems.     

Thermodynamic assessment of systems of actinide or rare earth with Cd

A pyrometallurgical process is being developed for recycling nuclear reactor fuels. Thermodynamic information on multicomponent systems of actinides and rare earths (REs) with liquid Cd is very useful in the design of a process in which a liquid Cd electrode is used for the selective recovery of Pu and U, and a reductive extraction process using a molten salt/liquid Cd system for the recovery of minor actinides, such as Np, Pu, etc. A key issue in the design of these processes is a variation in solubility or activity of actinides or REs in multielement systems. In the present study, phase diagrams of U-Cd, Pu-Cd, Np-Cd, Y-Cd, La-Cd, Ce-Cd, Pr-Nd, Nd-Cd, and Gd-Cd were optimized by the CALPHAD method. For these systems, thermodynamic data, such as the activity of solutes in liquid Cd and the Gibbs energies of formation of the intermetallic compounds as well as the phase diagram data were available for the optimization. For optimization, the calculated primary results were entered into a database. Then, some ternary systems were preliminarily assessed through the use of the optimized data for the binary systems. Two extreme conditions were assumed: one condition was complete miscibility between the compounds that have the same mole ratio between solutes and Cd; the other condition was no solid solubility between the compounds. The results indicated the tendencies toward solubility and activity of actinides and REs in multielement systems.     

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.     

Integrating CALPHAD into Phase Field Simulations for Practical Applications

Phase field modeling is a powerful tool for simulations of the microstructure evolutions. Its applications to practical alloy systems, however, have been limited mostly due to difficulties in relating the energy functional to the thermodynamic properties of the systems and mobilities to kinetic properties of the alloy elements involved. A phase field modeling tool, PanROME (Research Of Microstructure Evolution), has been developed that offers capabilities to overcome these difficulties. It can use the thermodynamic and kinetic databases that are built based on the CALPHAD approach, thus making it suitable for simulations in multicomponent and multiphase systems. This phase field model integrates Kim-Kim-Suzuki (KKS) model which allows simulations in a practical length scale while maintaining a reasonable interfacial energy with a multiphase model that is applicable to multiphase systems. Several applications of the PanROME modeling tool to Ni-base superalloys are demonstrated in the present article.     

A general method for calculating deviation from local equilibrium at phase interfaces

A general method to calculate the deviation from local equilibrium at phase interfaces in multicomponent systems is suggested. The deviation is caused by solute drag and finite interfacial mobility. In the limit of low transformation rates the new method degenerates to the well-known local equilibrium condition. The phase interface is divided into three zones, each with a finite thickness. In each zone a variation in thermodynamic properties and diffusional mobilities is assumed.     

A phase-field model with antitrapping current for multicomponent alloys with arbitrary thermodynamic properties

The development of accurate and efficient computational tools for phase transformation is a prerequisite in order to predict the microstructure evolution during phase transformation in engineering alloys. Even though the antitrapping phase-field model (PFM) has been developed and is increasingly being used for this purpose, it has been limited to dilute binary alloys. In this study, the antitrapping PFM was extended to multicomponent systems with arbitrary thermodynamic properties. We showed that at the condition of vanishing chemical potential jump, the antitrapping term in the multicomponent diffusion equation remains unchanged with the case of binary dilute alloys. We then derived the relationship between the phase-field mobility and the real interface mobility at the thin interface limit, and showed that the multicomponent effect in the relationship can be expressed in a concise matrix form.     

A Semi-Empirical Atomistic Approach in Materials Research

With developments of semi-empirical interatomic potentials for realistic materials systems, atomistic approaches to a wide range of bulk and nanostructured materials become more and more feasible. This article outlines a recently developed semi-empirical interatomic potential model, the second nearest-neighbor modified embedded-atom method that shows a strong applicability to multicomponent systems. It is shown that the interatomic potentials can well reproduce fundamental physical properties of representative materials systems. Examples are used to illustrate the applications of the atomistic approach to calculation of fundamental physical properties of both nano and bulk structural materials such as thermodynamic, elastic, interface, and defect properties necessary to understand the materials behavior and to serve as input to larger-scale simulations.     

Prediction of surface and interfacial tension based on thermodynamic data and CALPHAD approach

In this article, following a brief introduction concerning experimental measurements of surface and interfacial tensions, methods for calculating surface tension and surface segregation for binary, ternary, and multicomponent high-temperature melts based on Bulter＇s original treatment [ 1] and on available physical properties and thermodynamic data, especially excess Gibbs free energies of bulk phase and surface phase versus temperature obtained from thermodynamic databases using the calculation of phase diagram （CALPHAD） approach, with special attention to the model parameter β, have been described. In addition, the geometric models can be extended to predict surface tensions of multicom- ponent systems from those of sub-binary systems. For illustration, some calculated examples, including Pb-free soldering systems and phase-diagram evaluation of binary alloys in nanoparticle systems are given. On the basis of surface tensions of high-temperature melts, interracial tensions between liquid alloy and molten slag as well as molten slag and molten matter can be calculated using the Girifalco-Good equation [2]. Modifications are suggested in the Nishizawa＇s model [3] for estimation of interracial tension in liquid metal （A）/ceramics （MX） systems so that the calculations can be carried out based on the sublattice model and thermodynamic data, without deliberately differentiating the phase of MX at high temperature. Finally, the derivation of an approximate expression for predicting interfacial tension between the high-temperature multicomponent melts, employing Becker＇s model [4] in conjunction with Bulter＇s equation and inteffacial tension data of the simple systems is described, and some examples concerning pyrometallurgical systems are given for better understanding.     

Development of a diffusion mobility database for Ni-base superalloys

For the fcc phase of the Ni–Al–Co–Cr–Hf–Mo–Re–Ta–Ti–W system, diffusion data in various constituent binary systems were assessed to establish a multicomponent diffusion mobility database. The diffusion assessment relied on an existing thermodynamic database for the calculation of needed thermodynamic factors. The mobilities determined for the self-diffusion of the components in the fcc phase (a metastable state for some components) were consistent with the correlation of the diffusivity with the melting point. The general agreement of calculated and measured diffusion coefficients in the Ni–Co–Cr–Mo and Ni–Al–Cr–Mo quaternary systems demonstrated the ability of the database to extrapolate to higher order systems. Finally, the mobility database, in conjunction with an available thermodynamic database and a finite-difference diffusion code, was used to simulate a multicomponent diffusion couple between two commercial Ni-base superalloys.     

THE BASIC CONSIDERATIONS OF SELF-SReM AND SELF-BoSS MODELS

1. IntroductionComponent activity in metallurgical melts is one of the key projects in the investigationof thermodynamics. It is fully possible to apply the thermodyllamic principle for theoptimization or development of various metallurgical processes. However, the shortageof thermodynamic data in concentrated multicomponent systems frequently results in thelimitation of these applications.Traditionally, running experiment is the sole way to get the data of component activities on several poin…     

NaCl、NaBr、Nal在DMATk溶液中的电导率

钠盐在酰胺衍生物水混合溶剂中的电导率、摩尔电导率是研究溶液热力学性质的重要参数。它集中反映了指定溶剂中离子之间及离子与溶剂分子之间的相互作用。对离子溶剂化、离子缔合及溶液结构理论的研究与应用具有重要的意义。随着生物化工的发展,有机物水溶液热力学性质的测定及研究日益受到重视。为了更系统研究不同的取代基对迁移性质的影响,本文研究NaCl、NaBr、NaI与DMA（N,N-二甲基乙酰胺）水溶液的电导率,测定了NaCl、NaBr、Nal分别在浓度为0．1mol／L、0．2mol／L、0．3mol／L的DMA水溶液中,在298K、299K、300K、301K、302K五个温度下的电导率,根据公式Am=（λ液-λ剂）X10^-3／c计算NaCl、NaBr、NaI的摩尔电导率人。使用Origin软件进行线形分析,NaCl、NaBr、NaI在混合溶剂DMA和H20中随温度的增加,其摩尔电导率随之增加,且基本符合线性关系。