Butler Equation Research Articles

Surface tension and density of liquid Bi–Pb, Bi–Sn and Bi–Pb–Sn eutectic alloys

Surface tension and density measurement of liquid Bi 56Pb 44, Bi 43Sn 57 and Bi 46Pb 29Sn 25 eutectic alloys was carried out by using the large drop method over the temperature range of 380–750 K. The regular solution model has been used in conjunction with Butler's equation to calculate the surface tension of binary and ternary alloys of the Bi–Pb–Sn system, while the surface tension of ternary alloys has also been predicted by using geometric models. The new experimental results were compared with the calculated values of the surface tension as well as with the data available in the literature.

Modeling of the Thermodynamic Properties of Liquid Fe-Ni and Fe-Co Alloys From the Surface Tension Data

Modeling of the Thermodynamic Properties of Liquid Fe-Ni and Fe-Co Alloys From the Surface Tension DataRecently proposed method of modeling of thermodynamic properties of liquid binary alloys from their surface tension data is described. The method utilizes Melford and Hoar equation, relating surface tension with excess Gibbs free energy, combined with new description of the monatomic surface layer and β parameter. The method is tested on Fe-Ni and Fe-Co alloys and the obtained results show very good agreement with experimental thermodynamic data of other authors. The model allows also to calculate the surface tension from thermodynamic data, and it gives better agreement with experimental results than those modeled with the use of Butler equation and traditionally defined monatomic surface layer and β = 0.83.

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 0.10mole 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 474–1151K. The isotherms of surface tension calculated based on Butler's equation at 700 and 1100K corresponded well with the experimental values for zinc content lower than 0.6mole fraction. The surface tension calculated for alloys of higher zinc concentrations (0.6<XZn<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.

Computational Modelling of Oxide Surface Tensions in Secondary Metallurgy and Continuous Casting

AbstractTwo computational models were used to estimate the surface tensions of oxide systems containing SiO2, CaO, Na2O and Al2O3 as a function of temperature and composition. The compositions of the oxide melts were chosen to correspond to those of ladle slags in secondary metallurgy and to casting powders in continuous casting of steel. The first model uses Butler's equation to calculate the surface tensions of the multicomponent melts and is based on Tanaka et al.'s consideration of the ionic radii of the components as well as surface tensions and molar volumes of pure components. In the second model the same ionic radii dependent contribution is applied as activity coefficients to a constrained free energy model where the surface layer is considered as a separate phase in the system. In the model, the constrained interfacial area is analogous with a component mass balance in a traditional computation of a multiphase chemical equilibrium and surface energy with the corresponding chemical potential. Based on the results it is concluded that the effect of temperature on the surface tensions of the considered oxide melts is insignificant when compared to the effect of chemical composition. According to the validation the results agree well with published surface tension data. The multi‐component surface tension approach provides a practical method for evaluation of e.g. functioning of various casting powders in industrial steel casting practice.

Thermophysical Properties of Ag and Ag–Cu Liquid Alloys at 1098K to 1573K

The surface tension and density of liquid Ag and Ag–Cu alloys were measured with the sessile drop method. The sessile drop tests were carried out at temperatures from 1098K to 1573 K, on cooling (temperature decreasing stepwise) under a protective atmosphere of high purity Ar (6N). The density of liquid Ag and Ag–Cu alloys decreases linearly with increasing temperature, and an increase in concentration of copper results in a lower density. The surface tension dependence on temperature can be described by linear equations, and the surface tension increases with increasing Cu content. The results of the measurements show good agreement with existing literature data and with thermodynamic calculations made using the Butler equation.

Thermophysical Properties of Liquid AlTi-Based Alloys

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.

Modified Tafel Equation for Electroless Metal Deposition

The concept of the Dynamic Electrical Double Layer (DEDL) is the physicochemical basis for electrochemical processes that proceed without an external source of current (electroless processes). The most characteristic feature of such processes is that they proceed only in an oscillation regime, with the anodic processes of electrode charging and the cathodic processes of its discharging alternating periodically at maximum values of the stationary electrode potential (the phenomenon of overpotential).The DEDL model enables full account to be taken of this specific feature (adsorption and a heterogeneous chemical reaction at the anodic stage of the process and subsequent deposition of the metal in the cathodic stage) and the process to be described from a unified standpoint. In the framework of the DEDL model, the autocatalytic process of metal coating deposition depending on process conditions is described by modified Nernst or Tafel equations, which enable direct computation of both the values of the oscillating stationary electrode potential and of the characteristics of metal deposition (thickness and weight of the coating) by the kinetic dependence of “electrode potential vs time”.It is demonstrated that both the modified Tafel equation for exchange current density (oscillation regime of the stationary electrode potential in electroless processes) and its classical interpretation for systems with constant values of the stationary electrode potential are particular cases of the Volmer – Butler equation.

Behavior of Nitrogen During AOD Process

A computational model based on mass transfer and thermodynamic data as well as kinetic information from the industrial AOD process has been created in order to simulate the nitrogen content of the stainless steel melt as a function of blowing time. The model uses Butler's equation to calculate the reaction area available for nitrogen transfer between the steel and gas bubbles. Thermodynamic driving force is calculated as a function of temperature as well as stainless steel melt and gas compositions. According to the study effective surface area for nitrogen transfer achieved its maximum as well as thermodynamic driving force is also high during the 1st stage (absorption). During desorption effective reaction surface area is only approximately 7–9%. Typical initial nitrogen contents were about 400 ppm whereas the maximum values of 1000–1500 ppm were achieved before nitrogen argon switch-point. Simulations showed that desorption rate of nitrogen is low and final nitrogen contents below 400 ppm's are very difficult to be achieved economically. According to the simulations model predicts final nitrogen content of stainless steel melt after AOD process with 50 ppm accuracy.

Surface Tension of Molten Ag-Sn and Au-Cu Alloys at Different Oxygen Partial Pressures

A semi-empirical method to estimate the surface tension of molten alloys at different oxygen partial pressures is suggested in this study. The surface tension of molten Ag-Sn and Ag-Cu alloys were calculated using the Butler equation with the surface tension value of pure substance at a given oxygen partial pressure. The oxygen partial pressure ranges were <TEX>$2.86{\times}10^{-12}$</TEX>－<TEX>$1.24{\times}10^{-9}$</TEX> Pa for the Ag-Sn system and <TEX>$2.27{\times}10^{-11}$</TEX>－<TEX>$5.68{\times}10^{-4}$</TEX> Pa for the Ag-Cu system. In this calculation, the interactions of the adsorbed oxygen with other metallic constituents were ignored. The calculated results of the Ag-Sn alloys were in reasonable accordance with the experimental data within a difference of 8%. For the Ag-Cu alloy system at a higher oxygen partial pressure, the surface tension initially decreased but showed a minimum at <TEX>$X_{Ag}$</TEX> = 0.05 to increase as the silver content increased. This behavior appears to be related to the oxygen adsorption and the corresponding surface segregation of the constituent with a lower surface tension. Nevertheless, the calculated results of the Ag-Cu alloys with the present model were in good agreement with the experimental data within a difference of 10%.

Surface tension of liquid binary alloys – theory versus experiment

Abstract In the present study, we compare available experimental surface tension data with two theoretical concepts: the Butler equation and a multilayer model in which the surface is described as a stacking of atomic layers. The experimental data were measured systematically over a wide temperature and concentration range using electromagnetic levitation and the oscillating drop technique. Three classes of alloys are studied: alloys with rather weak or no segregation, alloys with strong segregation, and associate forming alloys.

Study of surface tension and surface properties of binary alcohol/ n-alkyl acetate mixtures

The Butler equation is employed to describe quantitatively the nature, properties, and compositions of surface layers in binary liquid mixtures. Bulk mole fraction, surface molar area, and surface tension of pure components are necessary inputs for this equation. In addition, the UNIFAC group contribution method is applied to account for the nonideality of the bulk liquid as well as that of the surface layer. The average relative error obtained from the comparison of experimental and calculated surface tension values for 12 binary systems is less than 1%. Therefore, the model has good accuracy in comparison with other predictive equations. In addition to finding more information about the surface structure of binary mixtures, surface mole fraction was calculated using relative Gibbs adsorption values and an extended Langmuir model (EL). The obtained results show a good consistency between two models employed, i.e., the Gibbs adsorption model and EL model, based on the UNIFAC method.

Surface tension of molten Ni-(Cr, Co, W) alloys and segregation of elements

Surface tension of molten Ni-(Cr, Co, W) alloys was measured at the temperature of 1 773–1 873 K in an Ar+3%H 2 atmosphere using an improved sessile drop method. The segregation of Cr, Co and W in alloy was calculated and analyzed using Butler's equation. The results show a good agreement between measured and calculated data. The surface tension of molten Ni-(Cr, Co, W) alloys decreases with increasing temperature. In Ni-(Cr, Co, W) alloys, the element with lower surface tension tends to segregate on the surface of molten alloy while that with higher surface tension tends to segregate inside of the molten alloy. The larger the differences in surface tension, atom radius and electron configuration between solvent and solute are, the more significant the segregation is. As a result, Ni segregates onto the surface and Co and W segregate inside the alloys.

Surface tension of liquid ternary Fe–Cu–Mo alloys measured by electromagnetic levitation oscillating drop method

For the liquid Fe-Cu-Mo ternary system, the surface tensions of three selected alloys, i.e., three typical monotectic alloys, were measured by the electromagnetic levitation oscillating drop method over a broad temperature range, including both superheated and undercooled states. The maximum undercooling attained is up to 173 K. The experimental results show a good linear correlation between the surface tension and the temperature. By applying on the Butler equation, the surface tensions were also calculated and they are in good agreement with the measured ones, except that in the undercooled state, the calculated value is slightly larger than the measured results. Interestingly, both the measured and calculated results indicate that the enriched element on the droplet surface is much more conspicuous than other elements in influencing the surface tension. Besides, the viscosity and the density of the liquid Fe-Cu-Mo ternary alloys are also derived on the grounds of the experimentally measured surface tensions.

Surface Tension of Molten Nickel-Tungsten Alloy

Abstract Surface tension of molten Ni-(5-10)W (mass fraction, %) alloys was measured in the temperature range of 1773-1873 K with an alumina substrate in an Ar+3%H2 atmosphere using an improved sessile drop method. The surface tension of molten Ni-W alloys decreases with increasing of temperature. On the basis of experimental data, the surface tension of molten Ni-W alloys was also theoretically deduced as functions of concentration and temperature using a model of Butler's equation. The surface segregation in Ni-W system was calculated. The measured results agree well with a model for the surface tension. The surface concentration of tungsten is lower than that in bulk.

The surface tension of liquid aluminium-based alloys

In a systematic study, the surface tensions of the binary alloys Al–Fe and Al–Ni were investigated over a wide temperature and concentration range using electromagnetic levitation and the oscillating drop technique. Surface tensions were derived from the oscillation frequencies applying the formalism of Cummings and Blackburn. Temperature was measured by single-color pyrometry. Of particular interest in these alloys are melts corresponding to compositions of intermetallic phases, because potential ordering phenomena may influence all thermophysical properties. In both systems, an increase of the surface tension is observed at such concentrations. On the basis of partial excess Gibbs enthalpies, surface tensions can be calculated via the Butler equation and compared with experimental results. The agreement with our experimental data depends crucially on the quality of the thermodynamic potentials used. In addition, phenomenological models are also discussed, which describe the general trend correctly.

A Calphad-compatible method to calculate liquid/liquid interfacial energies in immiscible metallic systems

For the calculation of liquid/liquid interfacial energies in monotectic metallic alloys only simplified models are known, which suppose the validity of the regular solution model for the liquid solution. In the present paper a Calphad-compatible method is developed to calculate the liquid/liquid interfacial energies in binary, ternary and multicomponent liquid monotectic alloys. The method can be considered as the extension of the Butler equation to the liquid/liquid interfaces. The first order interfacial phase transition has been predicted at a certain critical temperature, which is about 18% of the bulk critical temperature. Below this critical temperature the compositions of the two sides of the liquid/liquid interface are different, while above this critical temperature the compositions at the two sides of the interface are identical. The latter case is valid for the majority of liquid metallic systems above their monotectic temperatures. The method has been validated against the experimentally measured liquid/liquid interfacial energies in the Ga–Pb and Al–Bi systems. The method is found to be very sensitive to the correctness of the Calphad-assessment of the partial excess Gibbs energies of the components in the liquid solution. The excess Gibbs energy function of the liquid Al–Bi solution was reassessed using our recent exponential temperature dependence of the interaction energies.

Modeling Material Properties of Lead-Free Solder Alloys

A full set of physical and thermophysical properties for lead-free solder (LFS) alloys have been calculated, including liquidus/solidus temperatures, fraction solid, density, coefficient of thermal expansion, thermal conductivity, Young’s modulus, viscosity, and liquid surface tension, all as a function of composition and temperature (extending into the liquid state). The results have been extensively validated against data available in the literature. A detailed comparison of the properties of two LFS alloys Sn-20In-2.8Ag and Sn-5.5Zn-4.5In-3.5Bi with Sn-37Pb has been made to show the utility and need for calculations that cover a wide range of properties, including the need to consider the effect of nonequilibrium cooling. The modeling of many of these properties follows well-established procedures previously used in JMatPro software for a range of structural alloys. This paper describes an additional procedure for the calculation of the liquid surface tension for multicomponent systems, based on the Butler equation. Future software developments are reviewed, including the addition of mechanical properties, but the present calculations can already make a useful contribution to the selection of appropriate new LFS alloys.

Density and Surface Tension of Electromagnetically Levitated Cu–Co–Fe Alloys

The density and surface tension of Cu–Co–Fe alloys have been measured using the non-contact technique of electromagnetic levitation. At temperatures above and below the liquidus point, the density and surface tension are linear functions of temperature. The experimental density results can be predicted by means of the regular solution model from the binary phases alone, i.e., no assumption about ternary interactions needs to be made. The surface tension values are in good agreement with numerical solutions of the Butler equation if the known Gibbs excess energies are used. It is found that, for Cu–Co–Fe, it is possible to predict the surface tension from the binary systems as well. In addition to this, the surface tension is insensitive to substitution of the two transition metals, Co and Fe.

Chemical potentials and equation of state of surface layers for a model assuming two-dimensional compressibility of adsorbed molecules

Abstract Equations for the chemical potentials of surface layer components are derived by accounting for the two-dimensional compressibility ɛ of adsorbed molecules having a molecular area ω that depends linearly on the surface pressure Π . The modified equations for the chemical potentials representing a generalised Butler equation, are used to derive equations of state and adsorption isotherms of surface layers both in the framework of the real two-dimensional solution theory and in the framework of the Gibbs dividing surface model. Data of surface tension, adsorption and rheological characteristics of surface layers formed from solutions of C 12 DMPO agree well with the theoretical models based on the assumption of intrinsic compressibility of adsorbed molecules. A good description of experimental data by the theoretical models was achieved without the consideration of surface layer compressibility in the equations for the chemical potentials.

Determination of the Surface Tension of LiquidFe77.5Cu13Mo9.5 Ternary Monotectic Alloy

Thermophysical properties of undercooled liquid monotectic alloys areusually difficult to be determined because of the great difficulty inachieving large undercoolings. We measure the surface tension of liquidFe77.5Cu13Mo9.5 monotectic alloy by anelectromagnetic oscillating drop method over a wide temperature rangefrom 1577 to 1784 K, including both superheated and undercooled states.A good linear relationship exists between the surface tension andtemperature. The surface tension value is 1.588 N/m at themonotectic temperature of 1703 K, and its temperature coefficient is−3.7×10−4 Nm−1K−1. Based on the Butler equation, thesurface tension is also calculated theoretically. The experimental andcalculated results indicate that the effect of the enriched element ondroplet surface is much more conspicuous than the other elements todecrease the surface tension.