Gibbs citations and interpretations in the theory of surface tension of solids: A conceptual approach

Josiah Willard Gibbs is definitely the most respectable and citable author in the surface tension of solids, however there are many incorrect citations of concepts and notions ascribed to Gibbs, but completely alien to his scientific heritage. Unfortunately, they became decidedly important for development of the contemporary theory of the surface tension of solids. For example, the erroneous notion of the ??reversible cleavage??, as the conceptual background of this theory, appeared half a century after the most recent Gibbs?? works. Here we discuss not just formal linguistic, but conceptual matters using the advanced statistical method to identify wrong concepts ascribed to Gibbs. They existed in the theory of surface tension of solids for long decades and were accepted and used by most experts in this field. Today, we should formally recognize the high status of the current theory of surface tension of solids since it is supported by the scientific majority. It is based on the Shuttleworth equation, the vague concept of ??reversible cleavage?? and incorrect citations and interpretations of Gibbs thermodynamics. Up till now, neither this equation nor the theory as a whole had any experimental confirmations; moreover, they were shown to contradict all available experimental data. In connection with incorrect citations and interpretations of Gibbs works, we underline some pseudo-concepts and terms that Gibbs never used (like ??reversible cleavage?? or just ??cleavage??), and contrarily, the important notions that Gibbs introduced for the first time, but almost nobody heard about them, for example -??actual and possible components?? and the principal absence of ??pure phases?? in equilibrium of multiphase systems. We have also considered in detail the key difference between citation (as a possible free and often incorrect interpretation of the original text) and quotation (as an exact part of the original). Semantically citations and quotations are usually regarded as synonyms, but in practice it is not always correct and the sequences of their proposed equivalence might be critical for development of new concepts and theories.     

Concept of reversible cleavage in surface tension of solids

“Wholly plastic (as in cleavage)” surface area changing is the widely accepted concept formally allowing the application of Gibbs thermodynamics to surface tension of solids considered as a reversible process of partly plastic and partly elastic deformation as recommended by the IUPAC. However, this concept contains some internal contradictions that are serious enough to raise doubts about its correctness and, consequently in validity of the thermodynamic analysis of surface tension of solid electrodes based on this concept. This analysis leads to the generalized Lippmann equation and eventually approves using the classical Lippman equation for solids. The latter is shown to be erroneous since it is based on the misleading concept of “reversible cleavage” and contradicts all available in situ experimental data.     

Surface tension of liquid Au-Bi-Sn alloys

The surface tension of a promising lead-free solder Au-Bi-Sn alloys was investigated both by the sessile-drop method and calculation. Experimental measurements were carried out for two cross-sections with the constant gold to bismuth ration of 1:1 and 1:2. For all the investigated compositions, decrease of the surface tension is observed with increasing temperature. Meanwhile, the surface tension values were also calculated based on Butler's equation, with using the newest research on thermodynamics data of...     

CO2气体保护焊表面张力过渡

CO2气体保护焊采用短路过渡,飞溅大、成形差.在研究CO2气保焊短路过渡理论基础上,深入研究了表面张力过渡各个阶段参数与送丝速度的关系、焊接电压与液桥缩径状态的检测方法.研究表明,在表面张力过渡区内存在一段失控区,增加了表面张力过渡的不确定性.随着送丝速度的变化,熔滴过渡各阶段时间影响液桥分断时的表面张力过渡.依据表面张力过渡对电源特性的要求,提出了两种实现方案,逆变环节控制和输出斩波控制,并指出仅采用逆变环节实现表面张力控制的局限性,研究还表明改变表面张力过渡区的电流值可改善过渡的稳定性.研究方案在实际中得到了验证.     

Surface tension and thermodynamic properties of liquid Ag-Bi solutions

With the maximum bubble pressure method, the density and surface tension were measured for five Ag-Bi liquid alloys (X _Bi=0.05, 0.15, 0.25, 0.5, and 0.75), as well as for pure silver. The experiments were performed in the temperature range 544–1443 K. Linear dependences of both density and surface tension versus temperature were observed, and therefore the experimental data were described by linear equations. The density dependence on concentration and temperature was derived using the polynomial method. A similar dependence of surface tension on temperature and concentration is presented. Next, the Gibbs energy of formation of solid Bi₂O₃, as well as activities of Bi in liquid Ag-Bi alloys, were determined by a solid-state electromotive force (emf) technique using the following galvanic cells: Ni, NiO, Pt/O ⁻²/W, Ag _X Bi _(1−X), Bi ₂ O _3(s). The Gibbs energy of formation of solid Bi₂O₃ from pure elements was derived: =−598 148 + 309.27T [J · mol⁻¹] and =−548 008 + 258.94T [J · mol⁻¹]; the temperature and the heat of the α → δ transformation for this solid oxide were calculated as 996 K and 50.14 J · mol⁻¹. Activities of Bi in the liquid alloys were determined in the temperature range from 860–1075 K, for five Ag-Bi alloys (X _Ag=0.2, 0.35, 0.5, 0.65, 0.8), and a Redlich-Kister polynomial expansion was used to describe the thermodynamic properties of the liquid phase. Using Thermo-Calc software, the Ag-Bi phase diagram was calculated. Finally, thermodynamic data were used to predict surface tension behavior in the Ag-Bi binary system.     

Surface tension and thermodynamic properties of liquid Ag-Bi solutions

With the maximum bubble pressure method, the density and surface tension were measured for five Ag-Bi liquid alloys (X _Bi=0.05, 0.15, 0.25, 0.5, and 0.75), as well as for pure silver. The experiments were performed in the temperature range 544–1443 K. Linear dependences of both density and surface tension versus temperature were observed, and therefore the experimental data were described by linear equations. The density dependence on concentration and temperature was derived using the polynomial method. A similar dependence of surface tension on temperature and concentration is presented. Next, the Gibbs energy of formation of solid Bi₂O₃, as well as activities of Bi in liquid Ag-Bi alloys, were determined by a solid-state electromotive force (emf) technique using the following galvanic cells: Ni, NiO, Pt/O ⁻²/W, Ag _X Bi _(1−X), Bi ₂ O _3(s). The Gibbs energy of formation of solid Bi₂O₃ from pure elements was derived: =−598 148 + 309.27T [J · mol⁻¹] and =−548 008 + 258.94T [J · mol⁻¹]; the temperature and the heat of the α → δ transformation for this solid oxide were calculated as 996 K and 50.14 J · mol⁻¹. Activities of Bi in the liquid alloys were determined in the temperature range from 860–1075 K, for five Ag-Bi alloys (X _Ag=0.2, 0.35, 0.5, 0.65, 0.8), and a Redlich-Kister polynomial expansion was used to describe the thermodynamic properties of the liquid phase. Using Thermo-Calc software, the Ag-Bi phase diagram was calculated. Finally, thermodynamic data were used to predict surface tension behavior in the Ag-Bi binary system.     

Surface tension of liquid Ag-Sn alloys: Experiment versus modeling

The maximum bubble pressure method has been used to measure the surface tension of pure tin and seven binary alloys with concentrations of 15, 30, 40, 60, 75, 87.8, and 96.2 at.% Sn. Measurements were performed at the temperature range from 500 to about 1400 K depending on the composition of the investigated alloy. Densities of the Ag-Sn alloys were measured dilatometrically. The linear dependencies of densities and surface tensions on temperature were observed, and they are described by a straight-line equation. Experimental data of the surface tensions were compared with calculations using Butler’s model, which assumes an equilibrium between the bulk phase and the monolayer surface phase. Excess Gibbs energies of silver and tin necessary in calculations were taken from the optimized thermodynamic parameters reported recently from Tohoku University. It is shown that the calculated surface tension data from the optimized thermodynamic parameters of the liquid phase of the Ag-Sn are in good agreement with the experimental results.     

拉伸弯曲矫直机破鳞功能的研究

总结了拉矫机破鳞理论,研究了拉矫机工艺参数与破鳞效果之间的关系,提出了酸洗拉矫机工艺参数优化的准则及拉矫机破鳞方面的新看法。     

Surface tension of liquid Ag-Sn alloys: Experiment versus modeling

The maximum bubble pressure method has been used to measure the surface tension of pure tin and seven binary alloys with concentrations of 15, 30, 40, 60, 75, 87.8, and 96.2 at.% Sn. Measurements were performed at the temperature range from 500 to about 1400 K depending on the composition of the investigated alloy. Densities of the Ag-Sn alloys were measured dilatometrically. The linear dependencies of densities and surface tensions on temperature were observed, and they are described by a straight-line equation. Experimental data of the surface tensions were compared with calculations using Butler’s model, which assumes an equilibrium between the bulk phase and the monolayer surface phase. Excess Gibbs energies of silver and tin necessary in calculations were taken from the optimized thermodynamic parameters reported recently from Tohoku University. It is shown that the calculated surface tension data from the optimized thermodynamic parameters of the liquid phase of the Ag-Sn are in good agreement with the experimental results.     

Surface tension of molten tin investigated with sessile drop method

1INTRODUCTIONSurface tension is one of the most i mportantthermophysical parameters of molten metals,which greatly influences the processes of crystalli-zation,phase transition and crystal growth of mol-ten metals,and plays a key roleinthe processes ofmetallurgy,casting and welding.Measurement ofsurface tension and its temperature coefficient isi mportant to the research of metal thermophysicalproperties[13].Tin andits alloys are applied widelyin the solder industries and the manufacture o…     

Current state and problems in surface tension of solids,logical and experimental analysis of basic equations

Of the four basic thermodynamic equations for the surface tension of solids: the generalized and classical Lippmann equations, and the Shuttleworth and Gokhshtein equations, only the Gokhshtein equation has been confirmed experimentally. The generalized Lippmann equation is generally considered to be more universal, since three other equations could be derived from it. This fact has been widely accepted, but recently it was reevaluated in two opposite ways. In the first approach, the experimental verification of the Gokhshtein equation should support the correctness of the generalized Lippmann and Shuttleworth equations. In the second approach, the incompatibility of the Shuttleworth equation with Hermann’s mathematical structure of thermodynamics raises doubts upon all its corollaries, including the generalized Lippmann and Gokhshtein equations. Both these logical approaches are shown to be erroneous, since the Gokhshtein equation cannot be correctly derived from any of the above-mentioned equations, and the opposite is also true: neither the generalized Lippmann nor Shuttleworth equations could be derived from the Gokhshtein equation. The high sensitivity of the contact electric resistance method to negative adsorbate charge allows detail investigation of the kinetics of the charge transfer during anion adsorption. For the fist time, this permits a tentative approach to quantify the potential dependence of the partial charge transfer during halide ions adsorption on IB metals.     

多晶体钛拉伸变形表面褶皱的形成及晶粒变形

用原子力显微镜对多晶体钛拉伸塑性变形中表面褶皱的形成及单个晶粒的变形进行了连续观察和测量.结果表明,表面褶皱随着应变量的增加而增大,而凹凸的相对位置关系不随变形的进行而变化.从单个晶粒来看应变量在0.1附近时由于孪晶的形成产生了新的凹凸,但对整体的表面褶皱凹凸位置关系没有大的影响.表面平均粗糙度和表面最大高低差随应变量的增加近似呈直线性增大,应变量在0.1左右时由于孪晶的形成,使粗糙度有较明显的增大.     

Surface tension and wetting behaviour of molten Bi–Pb alloys

The present work represents an experimentally based investigation on the surface properties of molten Bi, Pb and Bi–Pb alloys. The surface tensions of the two pure elements and of seven alloys were measured by the sessile-drop method over the temperature range 623–773 K. In addition the wetting behaviour of the eutectic Bi–Pb alloy on AISI 316L substrate was also investigated in the same temperature range. The results obtained show general agreement with other reported measurements on pure elements and their alloys as well as with calculated surface tension values obtained by the application of the compound formation model (CFM).     

Surface tension and mass density of liquid Cu–Ge alloys

We report a study on the mass density and surface tension of liquid Cu–Ge alloys in the temperature range between the liquidus line and 1373 K. The experiments have been carried out by means of the sessile-drop method. The temperature dependences of both properties are given in terms of linear relations for all alloys under investigation. Both, density and surface tension show remarkable deviations from linear mixing: The density is increased, and the surface tension reduced due to Ge acting as surfactant. The composition dependence of the surface tension is discussed in terms of a simple compound formation model which is well able to relate the results to previous findings on the short-range order of the alloys under investigation.     

Optimization of the mechanical properties of virtual porous solids using a hybrid approach

A hybrid strategy based on artificial neural network/genetic algorithms is suggested to optimize the mechanical properties of cellular solids. Three-dimensional void structures are generated using a random sequential addition algorithm in which spherical void particles are positioned in a solid phase matrix with a control of their size distribution and overlapping. This allows us to create an open-cell structure with relative densities in the range 0.1–0.3. Finite element calculation is used to assess the effective Young’s modulus as a function of generation parameters. Relative Young’s moduli in the three main directions of the solid are isotropic with respect to the generation algorithm constraints and adhere qualitatively to the common theory on effective properties of open-cell structures. Moreover, the effective response is found to be correlated to the randomness of the void structure, which exhibits, in some cases, an ordered cell configuration. In order to quantitatively describe these correlations and to check the sensitivity of the mechanical response to the structural features in addition to sampling and discretization levels, the hybrid strategy described above is considered. The main motivation was to decrease the finite element simulation time by predicting, where possible, the correlations instead of calculating them. In addition, the use of the hybrid strategy informs about the optimal mesh with respect to the generation variables. This strategy proved to be an efficient technique in enhancing the predictions and complementary to the finite element methodology.     

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.     

Surface tension isotherms of a free surface and grain boundaries in the Cu-Sn system

Surface tension of pure copper and its alloys with Sn has been measured at 1000°C in a hydrogen atmosphere. Surface tension of a free surface equaled 1.81 N/m for pure copper, and 1.55, 1.38, and 1.28 N/m for the alloys with 0.05, 0.22, and 0.33 at % Sn, respectively; surface tension at grain boundaries equaled 0.5 N/m for pure copper, and 0.36, 0.3, and 0.23 N/m for the alloys, respectively. Based on these data, the concentration dependence of tin absorption at a free surface and grain boundaries has been calculated. Parameters of Sn absorption at grain boundaries and a free surface of copper have been compared with those of Sb and Bi.     

Surface free energy and surface stress as elastic components of the surface tension of condensed matter

The “surface free energy” and “surface stress” are basic notions in the current theory of the surface tension of solids; they were used online together or separately thousands times, but never “as elastic components of surface tension”. Most of experts highlight that these different notions cannot be mixed or confused since the first one is of the “plastic” and second is of “elastic” nature. Below these opinions are shown to be incorrect. Sufficient evidences, both theoretical and experimental, demonstrate the elastic nature of both the “surface energy” and “surface stress”. In this way, we considered the most convincible models of the metal surface based on the Coulomb interaction and purely elastic surface deformation. The reminiscent of the cantilever-beam-technique data and electrocapillary curves of mercury in combination with the specific adsorption data has logically led to the formulation of the “optimum surface electron density” notion (for the first time in the field of surface tension).