Estimation of surface tension for high temperature melts of the binary Ag-X alloys

ABSTRACT

Surface tension is a key property to materials. In this work, the surface tension of the binary alloys Ag-X (Au, Cu, Ce, Bi, Sn, Sb, In, Ni, Y, Pd) is carried out by using Butler Model over enter composition ratio at a certain temperature. According to calculation results, the increasing surface tension of the Ag-X (Cu, Au, Ni, Y, Pd) alloy is accompanied by the composition increases. For Ag-Sn alloy, the surface tension calculated by Butler model is consistent with the experimental result at temperature 1273?K. However, other Ag-X alloys can’t be compared due to the lack of the related experimental data. Although the experimental data about surface tension of the Ag-X alloy are limited, we are possible to make a comparison between the calculated results for the surface tension in this study and the available experimental data. Taken together, the surface tension calculated by Butler model that especially the Ag-Sn alloy are consistent with the experimental results at temperature 1273?K.     

Surface tension and density of liquid Sn-Cu alloys

The surface tension and density of Sn-Cu liquid alloys were measured with the sessile drop method, in a broad range of temperature. Total of seven compositions were investigated in the range from 0.018 to 0.5 mole fraction of Cu. With increasing concentration of Cu, both density and the surface tension are increased. With increasing temperature the density decreases linearly for all of the compositions. The surface tension exhibits similar behavior for most of the compositions, except for the alloy of 0.5 mole fractions of Cu, in which case the increase of the surface tension is observed. The obtained results are compared with existing literature data and Butler model calculations, and a relatively good agreement is observed.     

Surface tension and density of liquid Sn-Ag alloys

The surface tension and density measurements for Sn-Ag alloys were carried out with the sessile drop method. Seven different compositions were investigated in the range from 0.011 to 0.5 mole fraction of Ag, in a broad range of temperature. With increasing concentrations of Ag, both density and the surface tension are increased. With increasing temperature the density decreases for all of the alloys. A decrease of the surface tension is observed for most of the composition except for the alloy of 0.5 mole fractions of Ag. The obtained results are compared with existing literature data and Butler model calculations and relatively good agreement is observed.     

Surface properties of liquid In-Zn alloys

The measurements of surface tension and density of zinc, indium and liquid In-Zn alloys containing 0.9, 0.85, 0.75, 0.70, 0.60, 0.40, 0.25 and 0.10 mole fraction of In were carried out using the method of maximum pressure in gaseous bubbles (MBP) as well as dilatometric technique. The technique of sessile drop was additionally applied in the measurements of surface tension for pure indium and zinc. The measurements were performed at temperature range 474-1151 K. The isotherms of surface tension calculated based on Butler's equation at 700 and 1100 K corresponded well with the experimental values for zinc content lower than 0.6 mole fraction. The surface tension calculated for alloys of higher zinc concentrations (0.6 < X_Zn < 0.95) had a positive value of the surface tension temperature coefficient (dσ/dT), which did not coincide with the experimental results. The density as well as molar volume of liquid In-Zn alloys showed almost identical behaviour like the ideal solutions. The observed little deviations were contained within assessed experimental errors.     

The surface tension of liquid Cu-Fe-Sb alloys

The results of study on the influence of temperature and iron and antimony on the surface tension of liquid ternary Cu-Fe-Sb systems are presented. The measurements were carried out with the sessile drop method, in a broad range of the alloy additions concentration (Fe and Sb). It was demonstrated that the surface tension varies as a linear function of temperature and concentration of iron. It was also demonstrated that antimony, in examined alloys, shows the properties characteristic of a surface-active substance, significantly reducing the surface tension value. The changes of the surface tensions as a function of concentration of antimony were described with the Szyszkowski's equation. Composition of surface layer, enriched with an antimony, was determined basing on the model, which used data regarding properties of binary systems. The surface tension values of Cu-Fe-Sb systems was also computed from model and compared with experimental data. A good agreement was obtained.     

Calculation of the surface tension of liquid Ga-based alloys

As known, Eyring and his collaborators have applied the structure theory to the properties of binary liquid mixtures. In this work, the Eyring model has been extended to calculate the surface tension of liquid Ga–Bi, Ga–Sn and Ga–In binary alloys. It was found that the addition of Sn, In and Bi into Ga leads to significant decrease in the surface tension of the three Ga-based alloy systems, especially for that of Ga–Bi alloys. The calculated surface tension values of these alloys exhibit negative deviation from the corresponding ideal mixing isotherms. Moreover, a comparison between the calculated results and corresponding literature data indicates a good agreement.     

Surface and transport properties of Au-In liquid alloys

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 = 1273-1493 K. 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.     

Correlation between liquid structure and glass forming ability in glassy Ag-based binary alloys

The atomic structures of liquid Ag-based binary alloys have been investigated in the solidification process by means of X-ray diffraction. The results of liquid structure show that there is a break point in the mean nearest neighbor distance r1 and the coordination number Nmin for glass-forming liquid, while the correlation radius rc and the coordination number Nmin display a monotone variational trend above the break point. It means glass-forming liquids have a steady changing in structure above liquidus a...     

Liquid surface and liquid/liquid interface energies of binary subregular alloys and wetting transitions

Energetics and chemistry of liquid surfaces and liquid/liquid interfaces of binary A-B alloys are calculated using a subregular solution model. In this model, two macroscopic energetic parameters are used to produce an asymmetric miscibility gap. They are related to two microscopic parameters which describe the interaction energy between two atoms as a function of the composition of the first coordination shell of each atom. The impact of the asymmetry of the A-B interactions on the surface and interfacial energies and adsorption are analyzed by comparing the results obtained with this subregular model to those calculated for a regular solution. The role of the asymmetry on the prewetting and wetting transitions are also discussed. Calculations performed in the Co-Cu system are in good agreement with experimental data of surface energy.     

The surface tension and density of the Cu-Ag-In alloys

The surface tension and the densities of the Cu-Ag-In alloys have been measured by means of the sessile drop method. The density of these alloys depends linearly on temperature in the case of all the investigated compositions. The surface tension shows a linear dependence on temperature except for the lowest temperatures. For most of the alloys, the surface tension at the lowest temperature is lower than that predicted by the straight line. The experimental values of the surface tension of the Cu-Ag-In alloys are compared with those computed from the model, and quite good agreement is observed.     

Investigation of surface properties of liquid transition metals: Surface tension and surface entropy

In the present study, surface properties namely surface tension and surface entropy of liquid transition metals have been reported. The surface entropy of liquid Fe, Co and Ni metals has been investigated using the expression derived by Gosh et al. [R.C. Gosh, A.Z. Ziauddin Ahmed, G.M. Bhuiyan, Eur. Phys. J. B 56 (2007) 177]. To describe interionic interaction the pseudopotential approach has been used and radial distribution functions have been determined from the solution of Ornstein-Zernike integral equation. The calculated values of surface tension and surface entropy agree well with experiment. The present study shows that the expression derived by Gosh et al. leads to a good estimation for the surface entropy.     

Model calculation of the surface tension of liquid Ga-Bi alloy

A convenient model, based on some assumptions, for calculating the composition and temperature dependence of the surface tension of binary liquid alloys is reported. The theoretical calculations of the surface tension of gallium-rich-bismuth alloys are presented. The calculated results are compared with the reported experimental data. A relatively good agreement with experimental behavior of the composition dependence of the surface tension was found, but a disagreement was observed with experimental temperature behavior of the surface tension of these alloys. The calculations were conducted in the temperature range from almost 320 K to about 800 K. The surface tension was calculated from eutectic composition (x_Bi = 0.0022) to x_Bi = 0.1, and worked out by linear equations. The model calculation and analysis indicate a first order surface phase transition in this system, which is in accord with experimental findings. For this system, γ decreases linearly with increasing temperature at fixed Bi mole fraction x_Bi, and thus, suggesting a positive surface excess entropy. It is also found that the surface tension isotherms show the linear dependence on the concentration, in the logarithm scale of x_Bi, in the very narrow concentration range.     

Energy of formation for and liquid binary alloys

We have investigated the free energy of formation for Ag_xIn_1-x and Ag_xSn_1-x liquid binary alloys at temperatures 1173 and 1250 K, respectively. A microscopic theory based on the first order perturbation has been applied. The interionic interaction and a reference liquid are the fundamental components of the theory. The interionic interaction is described by a local pseudopotential. A liquid of hard spheres (HS) of two different effective diametres and charges is used to describe the reference system. The results of the calculations for energy of formation agree very well with the available experimental data. Our calculations also reveal that a simple perturbative approach along with appropriate effective pair potentials can produce nearly quantitative results for the concerned alloys.     

Thermodynamics and surface properties of liquid Cu–B alloys

The study of the thermodynamic and the surface properties of liquid Cu–B alloys can help better understanding of a complex interfacial chemistry related to liquid Cu–brazes in contact with boride substrates. Despite a simplicity of the Cu–B phase diagram, only a few thermodynamic data are available in the literature, while in the case of the surface properties a complete lack of data is evident. The quasi-chemical approximation (QCA) for the regular solution has been applied to describe the mixing behaviour of liquid Cu–B alloys in terms of their thermodynamic and surface properties as well as the microscopic functions. In view of joining processes related to liquid Cu–brazes/solid boride systems a particular attention is paid to the surface properties of the Cu-rich part of the system and the calculated values are substantiated by the new surface tension experimental data of liquid Cu and Cu–10 at.% B alloy. The tests have been performed by the sessile-drop method under the same experimental conditions. Considering the experimental uncertainties, the effect of oxygen on the surface tension of liquid Cu and Cu–10 at.% B alloy has been analysed by simple model that combines the physical property data included in Butler’s equation with the oxygen solubility data and it gives the same results as Belton’s adsorption equation.     

An investigation of influencing of Sb and Bi contents on surface tensions associated with Pb-free Sn-Zn-Sb-Bi quaternary and sub-quaternary solder alloys

The surface tensions of ternary and quaternary systems of Sn-based Pb-free solder alloys have been calculated using geometric models, such as Muggianu, Kohler, Chou’s general solution model (GSM), Toop, Guggenheim, ideal Butler and Butler models. It is observed from the calculation carried out in the present work that Sb and Bi contents decrease the surface tension of the solder alloys Sn-Zn-Sb-Bi. It is inferred from the statistical analysis that the best agreement between the experimental results and the corresponding calculated values of the surface tensions is generally observed in GSM and Muggianu models among the geometric models. Whereas Muggianu model is the most appropriate. Relatively good agreements have been observed between models considered in this study and experimental data.     

Study of superconducting state parameters of alkali–alkali binary alloys by a pseudopotential

A detailed study of the superconducting state parameters (SSP) viz. electron–phonon coupling strength λ, Coulomb pseudopotential μ^*, transition temperature T_C, isotope effect exponent and effective interaction strength N_OV of ten alkali–alkali binary alloys i.e. Li_1−xNa_x, Li_1−xK_x, Li_1−xRb_x, Li_1−xCs_x, Na_1−xK_x, Na_1−xRb_x, Na_1−xCs_x, K_1−xRb_x, K_1−xCs_x and Rb_1−xCs_x are made within the framework of the model potential formalism and employing the pseudo-alloy-atom (PAA) model for the first time. We use the Ashcroft’s empty core (EMC) model potential for evaluating the superconducting properties of alkali alloys. Five different forms of local field correction functions viz. Hartree (H), Taylor (T), Ichimaru–Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) are used to incorporate the exchange and correlation effects. A considerable influence of various exchange and correlation functions on λ and μ^* is found from the present study. Reasonable agreement with the theoretical values of the SSP of pure components is found (corresponding to the concentration x = 0 or 1). It is also concluded that nature of the SSP strongly depends on the value of the atomic volume Ω₀ of alkali–alkali binary alloys.     

Surface oxidability of pure liquid metals and alloys

The analysis of the oxygen-liquid metal interaction is a topic of particular technological interest. A deep knowledge of the kinetics and transport mechanisms involved in the oxidation phenomena is necessary: the effect of oxidation reactions taking place in the gas phase and the evaporation of oxides must be considered.This paper aims to review our works in order to provide a systematic analysis of the oxidation of pure metals and determine the most likely to keeping oxygen-free the surface in a binary alloy.In addition, the upgrading of this theoretical approach, here briefly described, is addressed to give a contribution to a better understanding of the evolution of oxidation phenomena close to the solid-liquid-gas interfaces.     

Surface behaviour and undercooling in the liquid Ga—Bi binary system detected by optical second harmonic generation

We employ an optical second harmonic generation(SHG) technique to investigate the surface behaviours at the liquid(solid)/vapour interface of the Ga-Bi binary metallic system. In a heating and cooling cycle between 280℃ and room temperature, there is no change of the SH-intensity in the heating process, whereas there exists an abrupt and abnormal change of the SH-intensity in the cooling process. It is interesting to find that a macroscopic Bi-rich solid layer is floating on the surface of the Ga-rich liquid phase just below the monotectic temperature (222℃±2℃) in the cooling process, in spite of the Bi-rich phase being heavier than the Ga-rich phase. On the other hand, different undercooling behaviours are observed at the surface and in the bulk. The behaviours of surface solidification and surface melting are different from those in the bulk.     

Bulk and surface properties of liquid X-Zr (X=Ag, Cu) compound forming alloys

The phase diagrams of the Ag-Zr and Cu-Zr systems exhibit the existence of different intermetallic compounds in the solid state, and since the structure of a liquid alloy is in some respects similar to that of a crystal, the compound formation phenomenon in these liquid alloy systems 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 the compound formation model (CFM). Moreover, the associative tendency between unlike constituent elements qualitatively expressed by the microscopic functions indicates the glass-forming ability of both systems at higher Zr-concentrations. These results are in agreement with reported experimental data and confirm the applicability of a statistical mechanical theory in conjunction with the CFM to describe the mixing behaviour of compound forming alloys.