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This review represents the state of the art in the thermophysical properties of liquid Ag-Sn alloys highlighting the surface and wetting properties of Ag-Sn eutectic solder. It includes an atomistic approach developed within the framework of statistical mechanical theory in conjunction with a Quasi Lattice Theory that, through a rigorous mathematical formalism, provides exact relationships between the properties in terms of classical thermodynamics. The model predicted property values are substantiated by available experimental data. Based on the phase diagram evidence about the existence of ε-Ag3Sn intermetallic compound, the surface (surface tension and surface composition), transport (viscosity and diffusivity) properties and microscopic functions (concentration fluctuations in the long-wavelength limit and chemical short-range order parameter) have been studied using the Compound Formation Model in a weak interaction approximation and Quasi Chemical Approximation for regular solutions. A case study of Ag-Sn eutectic alloy is presented. Taking into account its importance for design and development of lead free solder alternatives, the literature data on the wettability and the phases formed at the interface between Ag-Sn eutectic alloy and different substrates (Cu, Ni, Au, Pd) have also been analysed. [ABSTRACT FROM AUTHOR]

The experimental investigation of the Ag-Ge-Zn phase diagram was performed by using combined microstructural and Differential Scanning Calorimeter (DSC) analyses. The samples were subjected to thermal cycles by a heat-flux DSC apparatus with heating and cooling rate of 0.5 or 0.3 °C/min. The microstructure of the samples, both after annealing and after DSC analysis, was studied by optical and scanning electron microscopy coupled with EDS (Energy Dispersive Spectroscopy) analysis. Considering the slow heating and cooling rate adopted, the isothermal section at room temperature was established. No ternary compounds were observed. On the basis of the experimental investigations the invariant reactions were identified. Combining the thermodynamic data on the Ag-Ge, Ag-Zn and Ge-Zn liquid phases by means of Butler's model the surface tension of Ag-Ge-Zn alloys was calculated. [ABSTRACT FROM AUTHOR]

The knowledge of thermophysical properties of liquid Co-Si alloys is a key requirement for manufacturing of composite materials by infiltration method. Despite this need, the experimental and predicted property data of the Co-Si system are scarce and often inconsistent between the various sources. In the present work the mixing behaviour of Co-Si melts has been analysed through the study of the concentration dependence of various thermodynamic, surface (surface tension and surface composition) and structural properties (concentration fluctuations in the long-wavelength limit and chemical short-range order parameter) in the framework of the Compound Formation Model (CFM) and Quasi Chemical Approximation for regular solutions (QCA). In addition, the surface tension of the Co 22·5 Si 77.5 (in at%) eutectic alloy, that is proposed to be used as the infiltrant, has been measured by the pendant drop method at temperatures ranging from 1593 to 1773 K. The results obtained were discussed with respect to both, temperature and concentration, and subsequently compared with the model predictions and literature data. [ABSTRACT FROM AUTHOR]

The energetics of mixing in the Fe–Cr liquid phase has been analysed through the study of the concentration dependence of various thermodynamic, structural, surface (surface tension and surface segregation) and transport properties (diffusivity and viscosity) by the first or the Quasi-Chemical Approximation (QCA) for regular solutions, developed by Bhatia and Singh, in the framework of statistical mechanical theory in conjunction with the Quasi-Lattice Theory (QLT). There is some disagreement regarding the assessments of the Fe–Cr phase diagram available in the literature, but all versions reported indicate the presence of a σ intermediate phase in the solid state. Since the arrangement of molecules in a liquid alloy is in some respects similar to that of a crystal, at least near to its melting temperature, the complex formation phenomenon in Fe–Cr melts has been described in terms of the microscopic functions (concentration fluctuations in the long-wavelength limit and chemical short-range order parameter). [ABSTRACT FROM AUTHOR]

Experimental determination of thermodynamic and thermophysical properties of both solid and, in particular, liquid alloys at high temperatures is often technically difficult or even impossible, and therefore theoretical models can be used to estimate missing property values. Preliminary inspection of the literature related to the Cr-Nb-Re system and its binary subsystems reveals mainly theoretical results obtained in the framework of different theories, but the corresponding experimental property data are still sparse. The energetics of mixing in liquid Cr-Nb, Cr-Re and Nb-Re systems has been analysed through the study of the concentration dependence of various thermodynamic, surface (surface tension and surface composition) and structural properties (concentration fluctuations in the long-wavelength limit and chemical short-range order parameter) by the first or the quasi-chemical approximation for regular solutions, developed by Bhatia and Singh, in the framework of statistical mechanical theory in conjunction with the quasi-lattice theory. The results obtained for these binary systems have been extended to study the thermodynamics and surface properties of ternary Cr-Nb-Re liquid alloys. [ABSTRACT FROM AUTHOR]

Abstract: The systems containing highly reactive element such as Ti are the most difficult to be determined experimentally and therefore, it is often necessary to estimate the missing values by theoretical models. The thermodynamic data of the Al–Ti system are scarce, its phase diagram is still incomplete and there are very few data on the thermophysical properties of Al–Ti melts. The study on surface, dynamic and static structural properties of liquid Al–Ti alloys has been carried out within the framework of the Compound Formation Model. In spite of the experimental difficulties, the surface tension of liquid Al–2at.%Ti alloy has been measured over a temperature range by the pinned drop method. [Copyright &y& Elsevier]

Abstract: The mixing behaviour of liquid Sb–Sn alloys has been described in terms of energetics and structure through the study of their thermodynamic, surface, transport and structural properties by using the Complex Formation Model (CFM) in the weak interaction approximation and by postulating SbSn chemical complexes as energetically favoured. The new Sb–Sn surface tension experimental data, obtained by the pinned drop method at temperatures ranging from 513 to 1023K, have been analysed in the framework of the CFM and compared with the calculated values as well as with the corresponding literature data. The structural characteristics of Sb–Sn melts are described by the two microscopic functions, i.e. the concentration fluctuations in the long-wavelength limit and the Warren–Cowley short-range order parameter. [ABSTRACT FROM AUTHOR]

Abstract: The energetics of mixing in Al–Nb and Nb–Ti liquid alloys have been analysed through the study of surface properties (surface tension and surface segregation), dynamic properties (chemical diffusion) 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 quasi-lattice theory (QLT). The phase diagram of the Al–Nb system exhibits three intermetallic compounds in the solid state, while a relatively simple phase diagram of the Nb–Ti system indicates nearly ideal mixing behaviour in the liquid phase and two stable solid phases. Since the structure of a liquid alloy is in some respects similar to that of a crystal, the complex formation phenomenon in Al–Nb melts has been analysed by a quasi-lattice structural model for chemical complexes. The energetics and structural arrangement in Nb–Ti melts have been studied by the quasi-chemical approximation (QCA) for the regular solution model. [ABSTRACT FROM AUTHOR]

The surface tension and density of three liquid AlTi-based alloys (AlTiV, AlTiNb, and AlTiTa) have been measured using electromagnetic levitation as a tool for containerless processing. Surface tension has been determined by the oscillating-drop method, while the density was measured using a shadowgraph technique. Both quantities were determined over a wide temperature range, including the undercooled regime. In addition, sessile-drop and pendant-drop experiments to determine the surface tension were performed in a recently built high-temperature furnace. The measured data were compared to thermodynamic calculations using phenomenological models and the Butler equation. Generally, good agreement was found. [ABSTRACT FROM AUTHOR]

The density and the surface tension of binary Sn–Sb and ternary Sn–Sb–Cu liquid alloys have been measured over a wide temperature range by the sessile-drop method. The experimental data for the surface tension were analyzed by the Butler thermodynamic model. Investigations of the wetting behavior of these alloys on the Cu and Ni substrates in a vacuum were also performed. [ABSTRACT FROM AUTHOR]

Abstract: The mixing behaviour of liquid Bi–In alloys has been described in terms of energetics and structure through the study of their thermodynamic, surface and structural properties by using the Complex Formation Model (CFM) in the weak interaction approximation and by postulating BiIn-chemical complexes as energetically favoured. The new Bi, In and Bi–In surface tension experimental data set, obtained by the large drop method in the temperature range 553–873 K, has been analysed in the framework of the CFM and compared with the calculated values as well as with corresponding literature data. The structural characteristics of Bi–In melts are described by the two microscopic functions, i.e. the concentration fluctuations in the long-wavelength limit and the Warren–Cowley short-range order parameter. [Copyright &y& Elsevier]

Abstract: The thermodynamic properties of liquid In–Sn alloys indicate a weak interactions between unlike atoms. The new In, Sn and In–Sn surface tension experimental data set obtained by the large-drop method over the temperature range 523–923K together with the literature data on different thermophysical properties substantiate a nearly ideal mixing behaviour of these alloys. A low interaction energies do not effect the composition dependence of thermophysical properties, in particular the surface tension and the surface segregation. In order to estimate the effects of the short-range order phenomenon on the surface properties of In–Sn liquids, the QCA (quasi chemical approximation) for the regular solution model and the CFM (compound formation model) have been applied. In the same framework the transport properties and the structural characteristics of liquid In–Sn alloys have also been analysed. [Copyright &y& Elsevier]

Abstract: Thermodynamic quantities on Au–In liquid alloys have been used as the input data for the interaction parameter calculations in the framework of the complex formation model (CFM). Once the interaction energies are computed the surface (surface tension and surface composition) and transport properties (chemical diffusion and viscosity) as well as the microscopic functions (concentration fluctuations in the long-wavelength limit and chemical short-range order parameter) have been calculated. The concentration and temperature dependent surface tension values have been compared with our new set of experimental data, obtained by the large drop method in the temperature range of T =1273–1493K. The anomalous change of surface tension for some alloy compositions may be attributed to a retention of order in the Au–In melts which is similar to the atomic arrangement in solid Au–In. [Copyright &y& Elsevier]

Abstract: The present work is an experimentally based investigation of the applicability of the complex formation model (CFM) in the framework of statistical mechanical theory in conjunction with quasi-lattice theory (QLT) to describe the surface and transport properties of Au–Sn liquid alloys. Depending on melting temperatures, the surface tension of molten Au and Au–Sn alloys has been measured by the pinned-large drop method in the temperature range of T =1275–1493K. The calculations have been done with various objectives in view, i.e., to analyse existing thermodynamic data related to the peculiarities of the Au–Sn phase diagram, to use these data as the input for the interaction parameter calculations, to calculate the surface properties (surface tension and surface composition) and to compare the computed data with a new set of the surface tension experimental data as well as to predict the values of dynamic properties (chemical diffusion and viscosity). Some information on the structure of Au–Sn liquid alloys are given in terms of the microscopic functions (concentration fluctuations in the long-wavelength limit and chemical short-range order parameter). [Copyright &y& Elsevier]

Abstract: The thermodynamic data of the Ag–Ti and Ag–Hf systems as well as their phase diagrams are still incomplete. Moreover, up to now the phase diagram of the Ag–Hf system is not yet assessed. As concerns their thermophysical properties, a complete lack of experimental data is evident. Such a state of the art results from the experimental difficulties involved in high temperature measurements on highly reactive systems. Based on the experimental data on the existence of the AgTi, AgTi2, AgHf and AgHf2 intermetallic compounds in the Ag–Ti and Ag–Hf systems, respectively and our recently reported theoretical results on the Ag–Zr compound forming system, it is reasonable to expect similar mixing behaviour in these three alloy systems. The mixing behaviour of Ag–Ti and Ag–Hf has been analysed through the study of surface properties (surface tension and surface composition), transport properties (chemical diffusion and viscosity) and microscopic functions (concentration fluctuations in the long-wavelength limit and chemical short-range order parameter) in the frame of Quasi Lattice Theory (QLT) combined with a statistical mechanical theory. [Copyright &y& Elsevier]

The mixing behaviour of Ga-Sn and Ga-Zn segregating alloy systems has been investigated by the Quasi-Chemical Approximation (QCA) in the frame of the Quasi-Lattice Theory (QLT) combined with a statistical mechanical theory. Assuming the order energy parameters as temperature dependent, various thermodynamic quantities are calculated at different temperatures. Thermodynamic properties of both systems deviate positively from the Raoult’s law. 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). Theoretical results are in a good agreement with the corresponding literature data and support a weak demixing tendency in Ga-Sn and Ga-Zn liquid alloys. [ABSTRACT FROM AUTHOR]

Abstract: The applicability of quasi-lattice theory (QLT) to describe surface and transport properties of Ag–Cu liquid alloys is substantiated by surface tension experimental data. The surface tension of molten Ag, Cu and Ag–Cu alloys has been measured by the pinned-sessile drop method over a temperature range. The results obtained are in good agreement with other reported measurements on pure elements and their alloys as well as with calculated surface tension values. The phase diagram of Ag–Cu system shows the existence of a simple eutectic indicating a tendency towards phase separation. The mixing behaviour of Ag–Cu regular alloys has been analysed through the study of surface properties (surface tension and surface composition), dynamic properties (chemical diffusion and viscosity) and microscopic functions (concentration fluctuations in the long-wavelength limit and chemical short-range order parameter) in the frame of quasi-lattice theory combined with a statistical mechanical theory. [Copyright &y& Elsevier]

Abstract: In the present work, the surface tension of liquid Si and Ge has been measured by the pendant/sessile drop combined method over the temperature range of 1723–1908K and 1233–1313K, respectively. The new surface tension data, the molar volumes and the melting temperatures of silicon and germanium as well as the excess Gibbs energy data of the Ge–Si liquid phase are the inputs for Calphad type modelling to study the mixing behaviour in alloy melts. The energetics of mixing in liquid Ge–Si system has been analysed through the study of the concentration dependence of various thermodynamic (activity, enthalpy of mixing, Gibbs energy of mixing), surface (surface tension and surface composition) and transport (diffusivity) properties as well as the microscopic functions (concentration fluctuations in the long-wavelength limit and chemical short-range order parameter) in the framework of statistical mechanical theory in conjunction with the Quasi-Lattice Theory (QLT). [Copyright &y& Elsevier]

Highlights: [•] The liquid phases of Co–Cr, Co–Ni and Cr–Ni were modelled by the Quasi Chemical Approximation for regular solutions. [•] The excess Gibbs free energy of mixing of the liquid Co–Cr–Ni phase is estimated by the three thermodynamic models. [•] Prediction of structure can compensate the lack of structural data of Co–Cr, Co–Ni and Cr–Ni melts. [•] Thermodynamic modelling of the surface properties of Co–Cr–Ni melts. [•] Weak effects of short range ordering among nearest neighbours in Co–Cr, Co–Ni and Cr–Ni liquid alloys can be deduced. [Copyright &y& Elsevier]

Abstract: The surface tension of liquid Cu–Ti alloys has been measured by using the containerless technique of electromagnetic levitation and theoretically calculated in the framework of the compound formation model. Measurements have been carried out on alloys covering the entire range of composition and over the temperature range 1275–2050K. For all investigated alloys the surface tension can be described by a linear function of the temperature with negative slope. Due to the presence of different intermetallic compounds in the solid state the surface properties of liquid Cu–Ti alloys are satisfactory described by the compound formation model. [Copyright &y& Elsevier]