George Kaptay

Grain boundaries (GBs) are crucial microstructural components that significantly influence material properties. Establishing an interfacial thermodynamic model to calculate GB phase diagrams is essential for predicting GB complexion transformations and structural stability. In this work, the CALPHAD (CALculation of PHAse Diagrams) method was combined with an interfacial thermodynamic model to calculate GB phase diagrams of the Cu-Ag and Cu-Cr systems for predicting GB disorder. To verify the calculations, GB thicknesses in Cu–Ag and Cu–Cr alloys were measured using transmission electron microscopy, showing good agreement with calculated values. The relationship between Cu alloy densification and Ag doping during isothermal sintering, as well as alloy density variation with Ag content, was investigated to elucidate GB disordering trends. The constructed GB phase diagrams effectively predict the relationship between composition, temperature, and GB structure. This work provides a theoretical foundation for designing new copper alloys via GB structure engineering.

The Butler equation claims the equality of surface tension of a solution and the partial surface tensions of all its components. In this paper this equation is proven in a general way for the first time to be in agreement for binary and ternary solutions with the general requirement of thermodynamic equilibrium: the total Gibbs energy of a phase (taking into account its bulk and also its surface region) should have a minimum value. Note that the same was proven for a special binary case with constant (not concentration-dependent) partial molar surface areas of the components before [Colloids Surf A: Physicochem Eng Asp 2017;533:296–301]. In the current general derivation the constancy of the partial molarsurfaces areas is not supposed; the general derivation is succeeded here by applying our recent surface Gibbs-Duhem equations [Langmuir 2022;38:4906–12]. In this paper also a previous equation of Santos and Reis [J Alloy Compd 2023;939:168791] is corrected on the equality of surface tension to the weighed partial surface tensions of the components. It is further shown that the Butler equation is only the necessary, but not a sufficient condition for surface equilibrium: the sufficient condition is also derived here and it is demonstrated how to apply it to find real surface equilibrium using some binary and ternary solutions as examples. It is shown that when the Butler equation has a single mathematical solution, then it corresponds to real surface equilibrium. However, when the Butler equation has more than one mathematical solutions, only one of them (with the lowest surface tension) corresponds to the global surface equilibrium except the case of “surface phase transition” corresponding to two different surface equilibria (with two equal and lowest surface tensions).

Equations for the integral molar Gibbs energy of nanophases and the partial molar Gibbs energy of components dissolved in nanophases have been derived here by extending the classical thermodynamics of Gibbs to nanosizes in three different ways, found in the literature: according to Kelvin, the nanoeffect is proportional to the curvature of the phase; according to Searcy, the nanoeffect is proportional to dA/dV (where A and V are the surface area and the volume of the nanophase, respectively); and according to the previous papers of the present author, the nanoeffect is proportional to the specific surface area of the nanophase defined as A/V. It has been shown in many experiments that for all possible shapes of all nanophases, their molar Gibbs energies are inversely proportional to their characteristic sizes, such as to the radius of a nanosphere, to the side length of a nanocube, or to the thickness of a thin film. It is shown that the approaches due to Kelvin (curvature) and Searcy (dA/dV) lead to some controversial results versus experimental evidence, so they are excluded here. Moreover, they both contradict the nucleation theory of Gibbs, providing the same equations for the equilibrium size of a spherical nanophase and for the critical size of the spherical nucleus, being the second reason to exclude these equations. Moreover, the model by Searcy contradicts the nucleation theory of Gibbs, providing the same equation for the equilibrium size of a cubic nanophase and for the critical size of the cubic nucleus, being the third reason to exclude this equation. It is also shown that the previous approach by the author (A/V) is free of such contradictions; therefore, it is suggested for further use here.

Herein, the impregnation dynamics of the space between rectangular, polymer‐coated copper hairpins in electric motors, using polyester‐based and epoxy‐based liquid resins, are described both experimentally and theoretically. The rectangular capillary is formed along its sides by two copper hairpins coated with a polymer, with paper along its bottom and air along its top. The following properties of the two test liquid resins are measured from 25 to 80 °C: their contact angles on the hairpin and on the paper, their dynamic viscosities, densities, and surface tension. Dynamic viscosity is modeled by the Vogel–Fulcher–Tammann model, while surface tension is modeled by the Eötvös model, used also to estimate the molar masses of the resins. Penetration times of the test liquids are measured into the capillaries for ten penetration lengths. A model is derived for the penetration length as a function of time for a liquid penetrating into horizontal, rectangular, and thin capillaries. The resulting model is similar to that of the Lucas–Washburn but the geometrical parameters differ. The temperature dependence of the penetration rate is modeled by the extended Vogel–Fulcher–Tamman model.