George Kaptay

On the Tendency of Solutions to Tend Toward Ideal Solutions at High Temperatures

The rule of Lupis and Elliott (LE rule) proposed for the first time in 1966 is reformulated in this article as, “Real solid, liquid and gaseous solutions (and pure gases) gradually approach the state of an ideal solution (perfect gas) as temperature increases at any fixed pressure and composition.” This rule is rationalized through the heat expansion of phases and loss of any interaction with increased separation between the atoms. It is shown that the rule is valid only if the standard state is selected properly, i.e., if mixing does not involve any hidden phase changes, such as melting. It is shown that the necessary and sufficient practical conditions to obey the LE rule is the equality of signs of the heat of mixing and excess entropy of mixing and the nonequality of signs of heat of mixing and excess heat capacity of mixing of the same solution. It is shown that these two conditions are fulfilled for most of the experimentally measured high-temperature solutions. The LE rule is compared with the existing laws of thermodynamics. It is shown that the LE rule can be considered as a potential fourth law of materials thermodynamics.

Partial surface tension of components of a solution.

First, extending the boundaries of the thermodynamic framework of Gibbs, a definition of the partial surface tension of a component of a solution is provided. Second, a formal thermodynamic relationship is established between the partial surface tensions of different components of a solution and the surface tension of the same solution. Third, the partial surface tension of a component is derived as a function of bulk and surface concentrations of the given component, using general equations for the thermodynamics of solutions. The above equations are derived without an initial knowledge of the Gibbs adsorption equation and without imposing any restrictions on the thickness or structure of the surface region of the solution. Only surface tension and the composition of the surface region are used as independent thermodynamic parameters, similar to Gibbs, who used only the surface tension of the solution and the relative surface excesses of the components. The final result formally coincides with the historical Butler equation (1932), but without its theoretical restrictions. (Butler used too many unnecessary model restrictions during his work: he started from the Gibbs adsorption equation, and he assumed the existence of a surface monolayer.) Thus, the renovated Butler equation has gained general validity in this article. It was applied to derive both the Langmuir equation and the Gibbs adsorption equation, but the latter two equations do not follow from each other. Thus, it is shown that logically (not historically) the renovated Butler equation is a root equation for surface tension and the adsorption of solutions. It can be used to perform calculations for specific systems if the corresponding specific experimental data/models are loaded into it. In this case, both surface tension and surface composition can be calculated from the renovated Butler equation, which cannot be done using the Gibbs adsorption equation alone.

Theoretical Analysis of Melting Point Depression of Pure Metals in Different Initial Configurations

Abstract A general equation is derived for melting point depression (MPD) of pure metals, consisting of three terms: MPD due to high gas pressure, MPD due to high strain energy, and MPD due to small size of the metal. Particular equations are derived for different configurations of the solid metal, including grains embedded within a matrix. The equations obtained in this paper can be used to design nano-joining structures with improved MPD.

Interfacial Design for Joining Technologies: An Historical Perspective

This paper gives an historic perspective of the concept of “Interfacial Design” in joined (e.g. soldered, brazed, diffusion bonded) assemblies. During the course of history, the awareness grew that the interface in a material joint can be perceived at different length scales. With the continuing development of joining materials and technologies, it became evident that the performance of assemblies is critically dependent on the structure and composition of the multiple internal interfaces in the material joints. Resulting trends in the microstructural design of soldering, brazing, and other bonding materials by smart engineering of internal interfaces, as driven by increasingly complex technological requirements, are briefly addressed.

Interfacial Forces in Dispersion Science and Technology

Interfacial forces determine many phenomena in dispersion science and technology. Eight types of interfacial forces are classified in this article. A general equation for all of them is derived here, with particular equation for each of them (being valid for simplified geometries, such as spheres, cylinders, etc.). As a new element, an interfacial anti-stretching force is introduced in this article, being equivalent to the definition of the interfacial energy in terms of tension as understood by Young. The differences and similarities between the interfacial gradient force and the interfacial spreading force (the Marangoni force) are shown. The well-known case of the liquid bridge induced interfacial force is supplemented by its less known version of a gaseous bridge induced interfacial force.

A new theoretical equation for temperature dependent self-diffusion coefficients of pure liquid metals

Abstract A unified equation on the viscosity of pure liquid metals (published recently by the author) is combined with the well-known Sutherland – Einstein equation to obtain a new equation for the temperature dependence of the self-diffusion coefficients of pure liquid metals. The equation does not contain new adjustable parameters. It reproduces perfectly the experimental values, measured under micro-gravity conditions for liquid Sn, Pb, In and Sb. The experimental data, obtained under normal gravity conditions appear to be equal or somewhat higher than those calculated from the present model. This is explained by the effect of gravity induced convection in the liquid.

Enthalpy Effect of Adding Cobalt to Liquid Sn-3.8Ag-0.7Cu Lead-Free Solder Alloy: Difference between Bulk and Nanosized Cobalt

Heat effects for the addition of Co in bulk and nanosized forms into the liquid Sn-3.8Ag-0.7Cu alloy were studied using drop calorimetry at four temperatures between 673 and 1173 K. Significant differences in the heat effects between nano and bulk Co additions were observed. The considerably more exothermic values of the measured enthalpy for nano Co additions are connected with the loss of the surface enthalpy of the nanoparticles due to the elimination of the surface of the nanoparticles upon their dissolution in the liquid alloy. This effect is shown to be independent of the calorimeter temperature (it depends only on the dropping temperature through the temperature dependence of the surface energy of the nanoparticles). Integral and partial enthalpies of mixing for Co in the liquid SAC-alloy were evaluated from the experimental data.

Brownian Motion Effects on Particle Pushing and Engulfment During Solidification in Metal-Matrix Composites

Particle pushing and/or engulfment by the moving solidification front (SF) is important for the uniform distribution of reinforcement particles in metal-matrix composites (MMCs) synthesized from solidification processing, which can lead to a substantial increase in the strength of the composite materials. Previous theoretical models describing the interactions between particle and moving SF predict that large particles will be engulfed by SF while smaller particles including nanoparticles (NPs) will be pushed by it. However, there is evidence from metal-matrix nanocomposites (MMNCs) that NPs can sometimes be engulfed and distributed throughout the material rather than pushed and concentrated in the last regions to solidify. To address this disparity, in this work, an analytical model has been developed to account for Brownian motion effects. Computer simulations employing this model over a range of the SF geometries and time steps demonstrate that NPs are often engulfed rather than pushed. Based on our results, two distinct capture mechanisms were identified: (i) when a high random velocity is imparted to the particle by Brownian motion, large jumps allow the particle to overcome the repulsion of the SF, and (ii) when the net force acting on the particle is insufficient, the particle is not accelerated to a velocity high enough to outrun the advancing SF. This manuscript will quantitatively show the effect of particle size on the steady state or critical velocity of the SF when Brownian motion are taken into consideration. The statistical results incorporating the effects of Brownian motion based on the Al/Al2O3 MMNC system clearly show that ultrafine particles can be captured by the moving SF, which cannot be predicted by any of classical deterministic treatments.

A new paradigm on the chemical potentials of components in multi-component nano-phases within multi-phase systems

The chemical potentials of components in nano-phases determine the equilibrium of nano-materials. In this paper the difference between the equilibrium of a nano-phase and the equilibrium of an analogous macro-phase under the same constraints is called a “nano-effect”. Historically the first paper to describe the nano-effect was published by Kelvin (1871), claiming that it is due to the increased curvature of the nano-phase. This approach forms the basis of the Kelvin paradigm, still widely used in chemistry, biology and materials science (but not in physics). The Kelvin paradigm is the basis of the Kelvin equation, the Gibbs–Thomson equation and the Ostwald–Freundlich equation for the vapor pressure, melting point and solubility of nano-phases, respectively. The Kelvin paradigm is also successful in the interpretation of more complex phenomena, such as capillary condensation. However, the Kelvin paradigm predicts no nano-effect for not curved nano-phases, such as crystals and thin films, contradicting experimental facts. Moreover, it wrongly predicts that a cubic (or any other crystal-shaped) nano-droplet is more stable than a spherical nano-droplet of the same volume (this contradiction is shown here for the first time). In addition to its positive features, these and other shortcomings of the Kelvin paradigm call for a paradigm shift. A new paradigm is presented in this paper, claiming that the nano-effect is due to the increased specific surface area of the nano-phase. Chemical potentials of components in multi-component phases are derived in this paper within this new paradigm. These equations are extended for nano-phases in multi-phase situations, such as liquids confined within nano-capillaries, or nano-sized sessile drops attached to flat solid substrates. The new paradigm leads to similar results compared to the Kelvin paradigm for the case of capillary condensation into capillaries (this is because the specific surface area of a cylindrical wall is the same as the curvature of the spherical phase: 2/r). However, the new paradigm is able to provide meaningful solutions also for problems, not tractable by the Kelvin equation, such as the case of crystals and thin films having no curvature.

On the solid/liquid interfacial energies of metals and alloys

The solid/liquid interfacial energies of pure metals and metallic alloys are modelled in this paper. A simple model is offered for pure metals, showing that their solid/liquid interfacial energy (sigma) slightly increases with temperature. Sigma for metallic alloys is considered for the interface between solid and liquid solutions being in thermodynamic equilibrium, calculated by the CALPHAD method. The Butler equation is extended to find the equilibrium composition of the solid/liquid interfacial region and the solid/liquid interfacial energy at fixed temperatures. This method takes into account the segregation of low-interfacial energy components to the solid/liquid interfacial region. It is shown how the new method can be extended to multi-component alloys. The method is applied to calculate the solid/liquid interfacial energy of Al-rich solid solutions in equilibrium with eutectic liquid alloys of Al–Cu, Al–Ni, Al–Ag and Al–Ag–Cu systems. Good agreement was found with experimental values. For the Al–Ag–Cu system, the modelled value allows to select the more probable experimental value from the two contradicting experimental values published in the literature. The solid/liquid interfacial energy is calculated for the eutectic Ag–Cu system as function of liquidus composition (which determines both the equilibrium solidus composition and the equilibrium temperature). Finally it is claimed that using solely bulk thermodynamic data (melting enthalpy and molar volumes of pure components and molar excess Gibbs energies of equilibrium solid and liquid solutions) it is possible to provide meaningful values for the temperature and concentration dependence of solid/liquid interfacial energies of alloys. The method can be applied for simulation of solid/liquid phase transformation and also to solid/liquid equilibrium calculations of nano-alloys.