Theoretical calculation of the temperature coefficient of surface excess entropy of pure liquid metals

The temperature coefficient of surface excess entropy dS_s/dT of pure liquid metals (Al, Ga and Bi) has been calculated in the framework of Skapski's nearest-neighbor interaction-broken-bond model. It is found that this coefficient varies by 47.2%, 69% and 85% for pure liquids Al, Bi and Ga, respectively, in the temperature range between the melting temperature T_m and T_m + 400 K. The value of the coefficient for pure liquid Ga is an order of magnitude larger than that of Al and Bi. The largest increase in dS_S/dT with temperature occurs in the first 100 K away from T_m, being the largest for liquid Ga which is about 43%. This variation is experimentally inaccessible and therefore lacking in the literature and has never been reported.     

Investigation of surface entropy for liquid less simple metals

We have derived an efficient expression in closed form for the surface entropy of liquid metals from the statistical mechanical theory of zeroth order involving hard sphere model interaction. Using this expression we have investigated the surface entropy for liquid less simple metals namely Zn, Cd, In, Sn, Pb, Sb, Tl and Bi selfconsistently. The effective hard sphere diameters are obtained from the thermodynamic perturbation theory called the LWCA. The prediction of the selfconsistent calculation improves significantly for all concerned systems except for Zn and Cd. The underlying cause of discrepancy for Zn and Cd is also discussed.     

Surface energies of metals in both liquid and solid states

Although during the last years one has seen a number of systematic studies of the surface energies of metals, the aim and the scientific meaning of this research is to establish a simple and a straightforward theoretical model to calculate accurately the mechanical and the thermodynamic properties of metal surfaces due to their important application in materials processes and in the understanding of a wide range of surface phenomena. Through extensive theoretical calculations of the surface tension of most of the liquid metals, we found that the fraction of broken bonds in liquid metals (f) is constant which is equal to 0.287. Using our estimated f value, the surface tension (γ_m), surface energy (γ_SV), surface excess entropy (−dγ/dT), surface excess enthalpy (H_s), coefficient of thermal expansion (α_m and α_b), sound velocity (c_m) and its temperature coefficient (−dc/dT) have been calculated for more than sixty metals. The results of the calculated quantities agree well with available experimental data.     

A surface tension study of liquid threads

According to symmetry of liquid threads, definitions of surface tension in axial direction and angular direction are given. The formulas of surface tension in axial direction γ_z and surface tension in angular direction γ_θ are derived. A scheme to calculate Δγ = γ_z − γ_θ is designed. We investigate seven different systems (the numbers of molecules N are 1600, 2240, 2880,3360,4000,4800 and 5280) by molecular dynamics simulations. For liquid threads, Δγ increases with the decreasing radius of dividing surface. It shows that there exists surface tension anisotropy for liquid threads. The results obtained by molecular dynamics simulations support that surface tension is dependent on the dividing surface curvature.     

Surface relaxation and surface stress of 4d transition metals

Using the density functional theory formulated within the framework of the exact muffin-tin orbitals method, we present a systematic study of the top layer relaxation and surface stress of 4d transition metals. Our calculations predict layer contractions for most surfaces. We also find that the relaxations of the close packed surfaces decrease with increasing atomic number through the 4d series. We propose that the relaxation is mainly due to the reduction of the number of sp electrons in the surface layer relative to bulk. The surface stress is found to be very sensitive to the relaxation and, therefore, an accurate determination of the layer relaxation is necessary for obtaining reliable values for the surface stress. Comparing the top layer relaxations for the close packed surfaces, we see essential deviations between data derived in different ab initio calculations. At the same time, the overall trend for the present surface stress of 4d metals is in reasonable agreement with recent full-potential data.     

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.     

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.     

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.     

Structure of some liquid transition metals using integral equation theory

We present the results of calculations of the structure factorS(q) of some liquid 3d transition metals using the self consistent hybridized mean spherical approximation (HMSA) integral equation. The local pseudopotential used is composed of the empty core model and a part that takes care of s-d mixing through an inverse scattering approach to model the interionic pair potential. The results presented are in very good agreement with experiment for most of the systems investigated near freezing, as well as for the noble metals Cu, Ag and Au, thus, confirming the reliability of the pseudopotential in the present integral equation scheme.     

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.     

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.     

Surface properties of 3d transition metals

Using the projector augmented wave method within density functional theory, we present a systematic study of the layer relaxation, surface energy and surface stress of 3d transition metals. Comparing the calculated trends for the surface energy and stress with those obtained for 4d and 5d metals we find that magnetism has a significant effect on the surface properties. Enhanced surface magnetic moments decrease the size of the surface relaxation, lower the surface energy and surface stress, leading to compressive stress in Cr and Mn.     

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.     

Surface tension of liquid Cu-Ti binary alloys measured by electromagnetic levitation and thermodynamic modelling

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 1275-2050 K. 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.     

Convexity properties of the surface tension and equilibrium crystals

We study the thermodynamic limit of the orientation-dependent surface tension. Under general conditions, which we show to hold true for a large class of lattice systems, we prove that the limit exists and that it satisfies some convexity properties related to the pyramidal inequality introduced by R. L. Dobrushin and S. B. Shlosman⁽¹⁾. We discuss some consequences of these results for the equilibrium crystal shape.     

探讨测量液体表面张力系数的优化方法

针对用拉脱法测液体表面张力系数的系统误差较大的系列问题,提出了自动降拉双π丝补偿法.用自动化降拉代替手动提拉,提高了操作过程的稳定性;用双π丝代替π丝,消除了拉膜丝的不光滑点;用突变初态和补偿态作为测量状态,有效地排除了浮力、膜重以及侧丝上的表面张力对实验结果的影响.自动降拉双π丝补偿法得到的实验结果,其精度比拉脱法提高3%.     

Adsorbate interactions and surface excess entropy

Using the Gibbs definition of surface excess properties and classical statistics of the adsorbed molecules, it is shown that interactions between these molecules can in some cases increase the surface excess entropy. This is in contradistinction to the classical result for a field-free bulk phase gas, but similar to effects which are possible for quantum gases.Research supported by National Science Foundation Grant No. GP33535X.     

Surface free energies of solid metals: Estimation from liquid surface tension measurements

An equation is derived on semi-theoretical grounds which expresses the solid-vapour surface free energy as a function of the liquid surface tension and the solid-liquid interfacial free energy. A means of calculating reliable values for the solid-liquid energy is presented, which then allows an accurate estimate of solid surface energy at the melting temperature, T_m, to be made for the large number of elements for which dependable liquid surface tension data exist. A method of estimating surface entropy is presented, and has been used to calculate the energies typical of “average”, high-index surfaces at temperatures ranging from 0 K to T_m. It is felt that this paper describes the most accurate method presently available for the calculation of the surface energy of solids in the absence of direct experimental measurement.