Surfaces,interfaces and phase transitions in Al–In monotectic alloys

Surface and bulk liquid phase transitions are measured by a unique method currently used to determine surface and interfacial tension of liquid alloys. Focusing on the Al–In system, the location of the liquid miscibility gap was determined from the critical to the monotectic temperatures. The surface tensions of nine liquid alloys, the interfacial tension between coexisting liquids and their densities were measured as a function of temperature. Implementing the bulk data extracted from the asymmetric miscibility gap into a sub-regular model reproduced the experimental surface and interfacial tensions. The wetting temperature was estimated to lie well below the monotectic temperature. The micrometer thickness of the In-rich films which wet the surface of the Al-rich liquid phase after solidification is suggested to be due to the growth of the equilibrium wetting film by diffusion from the Al-rich phase during cooling.     

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.     

Phase transformations in ternary monotectic aluminum alloys

Monotectic aluminum alloys are of interest for the development of new alloys for technological applications such as self-lubricating bearings. In contrast to the well-known binary phase diagrams, many of the ternary systems are not well established. Moreover, in a ternary monotectic alloy one may encounter the four-phase equilibrium L′+L″+solid₁+solid₂, whereas in a binary system only a three-phase equilibrium L′+L″+solid₁ is possible. This opens a window for generating entirely new monotectic microstructures. The basis for such developments is the knowledge of the ternary phase diagrams and the conditions under which such four-phase reactions or different extensions of the binary monotectic reactions may form. This work presents a systematic classification of monotectic ternary aluminum alloys, illustrated by real systems. The study employs thermodynamic calculations of the ternary phase diagrams. For more information contact Rainer Schmid-Fetzer, Institute of Metallurgy, Clausthal University of Technology, D-38678 Clausthal-Zellerfeld, Germany. Fax +49-5323-723120; e-mail schmidfetzer@tu-clausthal.de     

Solidification paths of multicomponent monotectic aluminum alloys

Solidification paths of three ternary monotectic alloy systems, Al–Bi–Zn, Al–Sn–Cu and Al–Bi–Cu, are studied using thermodynamic calculations, both for the pertinent phase diagrams and also for specific details concerning the solidification of selected alloy compositions. The coupled composition variation in two different liquids is quantitatively given. Various ternary monotectic four-phase reactions are encountered during solidification, as opposed to the simple binary monotectic, L′ → L′′ + solid. These intricacies are reflected in the solidification microstructures, as demonstrated for these three aluminum alloy systems, selected in view of their distinctive features. This examination of solidification paths and microstructure formation may be relevant for advanced solidification processing of multicomponent monotectic alloys.     

Anomalous temperature dependence of the surface tension in liquid silver–lead alloys

The surface tension of liquid silver–lead alloys is discussed with special emphasis on the unusual temperature coefficients apparent at certain concentrations. In contrast to most other liquid alloys silver-rich mixtures of silver–lead adopt positive temperature coefficients. This anomalous behaviour is found to be well explained in terms of Butler's model of surface tension. The phenomenological approach of Bhatia and March was applied in semi-empirical manner in order to achieve agreement with the experimental findings. In view of the high concentration fluctuations of the system – expressed in terms of S_cc(0) – the anomalous temperature coefficients find a plausible interpretation. A short critical assessment of the model's general applicability to systems with demixing properties is presented. Qualitatively, both treatments indicate that the unusual temperature dependence of the surface tension is the mere consequence of the thermodynamics of the system.     

Temperature dependence of the crystal–melt interfacial energy of metals

A model to express the dependence of the crystal–melt interfacial energy on the temperature for metals is proposed. The crystal–melt interfacial energies, the homogeneous nucleation undercoolings and the critical cooling rates to form ideal metallic glasses of silver, copper and nickel have been predicted according to the present model and simulated by the molecular dynamics method. The results show that the crystal–melt interfacial energy of metals increases nonlinearly with temperature. Over a wide temperature range from the melting point to the glass transition temperature the predicted results for the crystal–melt interfacial energy, the homogeneous nucleation undercooling and the critical cooling rate to form ideal metallic glasses from the present crystal–melt interfacial energy model are in good agreement with the experimental results reported, as well as the results of molecular dynamics simulations based on different EAM potentials of the metals.     

Experimental study of the ternary system Cd---Te---Zn

The ternary system Cd---Zn---Te has been studied by differential thermal analysis, differential scanning calorimetry and X-ray powder diffraction. A solid solution is observed between CdTe and ZnTe. At low temperature this quasi-binary section exhibits a miscibility gap. The liquid-liquid miscibility gap induced by the binary monotectic reaction extends within the ternary system and its boundary has been determined. The only ternary reaction existing in this system is a eutectic reaction at 265 °C and the corresponding composition is located in the very close neighbourhood of the binary eutectic Cd---Zn.     

On the application of modelling to study the surface and interfacial phenomena in liquid alloy–ceramic substrate systems

The wetting phenomena of molten alloy/ceramic substrate depend on the bonding characteristics of liquid alloys and ceramics as well as on the magnitude of interactive forces at the interface. According to this, the first step of this investigation is to determine the surface properties of Ag–Cu, Ag–Ti and Cu–Ti liquid alloys. The energetics of mixing in liquid alloys has been analysed through the study of surface properties (surface tension and surface composition) and microscopic functions (concentration fluctuations in the long-wavelength limit and chemical short-range order parameter) in the frame of statistical mechanical theory in conjunction with the quasi-lattice theory (QLT). The results obtained for these binary systems have been extended to the ternary Ag–Cu–Ti system. Combining the Young and the Dupré equations, the computed results of surface tension together with contact angle data have been used to calculate the work of adhesion and, in the case of non-reactive wetting, the interfacial tension between the solid substrate and the liquid alloys over the whole concentration range. The evaluation of the interfacial tension values is determined from calculated and measured data using solid surface tension data from literature. These results provide more information on the characteristics of metal–ceramic systems, and are therefore useful in guiding experiments, or in predicting the surface properties of metallic systems with similar characteristics as well as their wetting behaviour in contact with ceramic materials.     

Pb-Free solders: Part 1. Wettability testing of Sn−Ag−Cu alloys with Bi additions

Maximum bubble pressure, dilatometric, and meniscographic methods were used in the investigations of the surface tension, density, wetting time, wetting force, contact angle, and interfacial tension of liquid alloys of Sn−Ag−Cu eutectic composition with various additions of Bi. Density and surface tension measurements were conducted in the temperature range 250–900 °C. Surface tensions at 250 °C measured under a protective atmosphere of Ar−H₂ were combined with data from meniscographic studies done under air or with a protective flux. The meniscographic data with a nonwetted teflon substrate provided data on interfacial tension (solder-flux), surface tension in air, and meniscographic data with a Cu substrate allowed determinations of wetting time, wetting force, and calculation of contact angle. The calculated wetting angles from meniscographic studies for binary Sn−Ag eutectic and two ternary Sn−Ag−Cu alloys were verified by separate measurements by the sessile drop method under a protective atmosphere with a Cu substrate. Additions of Bi to both ternary alloys improve the wettability and move the parameters somewhat closer to those of traditional Sn−Pb solders.     

On the size dependence of a contact angle

A small drop on a flat solid surface is considered in this paper. In the framework of a unified approach (Gibbs dividing surface method), expressions for the interfacial tension at the liquid-vapor interface and for the contact angle were found. It is shown that introduction of the size dependence of the interfacial tension at a curved liquid-vapor interface is equivalent to using the concept of line tension on the three-phase solid-liquid-vapor boundary. It is noted that the calculations are in agreement with experimental data obtained using an atomic force microscope.     

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.     

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.     

Phase-field simulation of domain structure for PbTiO3/SrTiO3 superlattices

Phase-field modeling has been performed to study the domain morphologies of ferroelectric PbTiO₃/SrTiO₃ superlattice grown on SrTiO₃ substrates. Taking into account contributions of the interfacial and depolarization field effects, the polarization, phase transition temperature and critical thickness are calculated as functions of sample dimensions and temperature. The results show that interfacial and depolarization field effects are the main reasons behind the dependence of the domain structures and critical properties (i.e., the phase transition temperature and critical thickness) on the thicknesses of the constituent layers of the PbTiO₃/SrTiO₃ superlattices.     

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。     

Effect of Pd additions on the invariant reactions in the Ag−CuOx system

Palladium was added as a ternary component to a series of copper oxide-silver alloys in an effort to increase the use temperature of these materials for potential ceramic brazing applications. Phase equilibria at low palladium and copper oxide concentrations in the Pd−CuO_x−Ag system were determined experimentally using differential scanning calorimetry, microstructural analysis, and x-ray diffraction. Small additions of palladium were generally found to increase the temperature of the eutectic reaction present in the pseudobinary system but have little effect on a higher temperature monotectic reaction. However once enough palladium was added (≈5 mol%) to increase the new eutectic temperature to that of the original pseudobinary monotectic reaction, the pseu doternary monotectic temperature correspondingly began to move upward as well. The addition of palladium also forced the eutectic point to slightly lower silver concentrations, again causing a convergence with the former monotectic line. This paper was presented at the International Symposium on User Aspects of Phase Diagrams, Materials Solutions Conference and Exposition, Columbia, Ohio, 18–20 October, 2004.     

用冷却倾斜板技术制备Al-Pb偏晶合金的研究

利用冷却倾斜板技术制备Al-Pb轴瓦材料。在高于互溶温度下将偏晶合金液浇注到倾斜板上,利用倾斜板的激冷作用,使合金液的温度迅速降低,从而得到均质弥散分布的Al-Pb偏晶合金,并探讨了偏晶合金的凝固过程。结果表明,倾斜板的激冷作用可以使富Pb的液滴Stokes运动速度Us和Marongoni迁移速度Um相互作用并相互抵消,使得Al-Pb偏晶合金熔体在倾斜板上不发生严重的宏观偏析。然后经室温的金属型冷却,得到均质弥散分布的Al-Pb偏晶合金。     

Correlation between interfacial energy and phase diagram in ceramic-metal systems

Estimates of interfacial energies between ceramics (MX) and liquid metals (A) have been arrived at by employing an improved version of the Becker’s model for interfacial energy calculations at liquid metal-liquid metal interfaces to calculate the total energy of interatomic bonds across an interface. The results of such an approximation yield values that are very close to the experimental values; for instance, the estimated value for Al₂O₃/lFe is 2 J · m⁻², which compares well with the experimental data ranging from 1.9 to 2.3 J · m⁻². It is suggested that interfacial energies depend on two terms: (1) the formation energy of MX and (2) the pairwise interaction energies between M and A atoms and X atoms and vacant interstitial sites. It is also found that the calculated interfacial energies in eutectic systems (carbides-metal, etc.) are generally low, while those in the monotectic systems (oxides-metal, etc.) are generally high.     

NOTE ON THE Fe-Pb PHASE DIAGRAM

对 Pb 在 Fe 液中溶解度的实验数据进行评述,从而选出合理的数值,再通过简单的热力学处理,求出其与温度的依赖关系.将此关系与凝固点下降公式结合,算出 Fe-Pb 相图中偏晶点的成分和温度.对 Fe 在 Pb 液中溶解度的实验结果也作了适当的处理.在上述工作的基础上,给出了一个 Fe-Pb 相图.     

MEASUREMENT OF SURFACE TENSION OF Pb-Sb MELTS AND ITS TEMPERATURE COEFFICIENT

用卧滴法测定了液态Pb,Sb纯金属和Pb-Sb合金熔体的表面张力,其表面张力的温度系数均为负值。在同一温度下Pb-Sb熔体的表面张力值介于两纯金属值之间,其值随成分星非线性变化,且对“理想溶液”为负偏差。对液态二元共晶型合金,本文提出“液态类共晶原子团”的概念,并依此解释液态二元共晶型合金的表面张力现象。     

Correlation between interfacial energy and phase diagram in ceramic-metal systems

Estimates of interfacial energies between ceramics (MX) and liquid metals (A) have been arrived at by employing an improved version of the Becker’s model for interfacial energy calculations at liquid metal-liquid metal interfaces to calculate the total energy of interatomic bonds across an interface. The results of such an approximation yield values that are very close to the experimental values; for instance, the estimated value for Al₂O₃/lFe is 2 J · m⁻², which compares well with the experimental data ranging from 1.9 to 2.3 J · m⁻². It is suggested that interfacial energies depend on two terms: (1) the formation energy of MX and (2) the pairwise interaction energies between M and A atoms and X atoms and vacant interstitial sites. It is also found that the calculated interfacial energies in eutectic systems (carbides-metal, etc.) are generally low, while those in the monotectic systems (oxides-metal, etc.) are generally high.