Thermo-mechanical behavior of low-dimensional systems: The local bond average approach

Surface tension of liquid metals and alloys — Recent developments

There have been a large number of papers on the surface tensions of metals since Keene published his critical review in 1993. Consequently, current data for both the surface tensions of metals and their temperature dependencies have been critically assessed and recommended values are given. Experimental uncertainties can arise from two sources: systematic errors associated with the experimental methods (typically ±2%) and changes in surface tension arising from oxygen contamination of the specimen. Uncertainties arising from the latter can be variable.

Review of surface tension data for metallic elements and alloys: Part 1 – Pure metals

With the rapid improvement of computer performance, tremendous heat generation in the chip becomes a major serious concern for thermal management. Meanwhile, CPU chips are becoming smaller and smaller with almost no room for the heat to escape. The total power-dissipation levels now reside on the order of 100 W with a peak power density of 400–500 W/cm2, and are still steadily climbing. As a result, it is extremely hard to attain higher performance and reliability. Because the conventional conduction and forcedair convection techniques are becoming incapable in providing adequate cooling for sophisticated electronic systems, new solutions such as liquid cooling, thermoelectric cooling, heat pipes, vapor chambers, etc. are being studied. Recently, it was realized that using a liquid metal or its alloys with a low melting point as coolant could significantly lower the chip temperature. This new generation heat transfer enhancement method raised many important fundamentals and practical issues to be solved. To accommodate to the coming endeavor in this area, this paper is dedicated to presenting an overall review on chip cooling using liquid metals or their alloys as coolant. Much more attention will be paid to the thermal properties of liquid metals with low melting points or their alloys and their potential applications in the chip cooling. Meanwhile, principles of several typical pumping methods such as mechanical, electromagnetic or peristaltic pumps will be illustrated. Some new advancement in making a liquid metal cooling device will be discussed. The liquid metal cooling is expected to open a new world for computer chip cooling because of its evident merits over traditional coolant.

Liquid metal cooling in thermal management of computer chips

The abbreviation “nano-Calphad” stands for “Calculation of Phase Diagrams for nano-systems.” Nano-systems contain at least one phase or at least one interface layer (film, complexion) with at least one of its dimensions being below 100 nm. The essential task of nano-Calphad is to introduce correctly the surface term into the equation for the Gibbs energy. In view of the controversy between the Kelvin and Gibbs equations, even this task does not have an obvious solution (in the present paper, the Gibbs method is preferred). However, there are many further questions to be addressed when the Calphad method is converted into the nano-Calphad method. This paper attempts to give an as full as possible list of all those problems, such as: (i) the definition of a new, independent thermodynamic variable, (ii) the extended phase rule, (iii) the curvature dependence of the interfacial energies, (iv) the dependence of interfacial energies on the separation between interfaces (including the problem of surface melting), (v) the role of the shapes and relative arrangement of phases, (vi) the role of the substrate (if such exists), and (vii) the role of segregation, taking into account its effect on the mass balance within multi-component nano-phases and its surface phase transition and complexion. It is also shown that the well-known meaning of the tie line in binary two-phase fields is lost in nano-systems. The issues related to the size limits of materials thermodynamics and the need for a more complete databanks on molar volumes and interfacial energies are discussed.

/pdf/nano-calphad-extension-of-the-calphad-method-to-systems-with-3xfzxww1ks.pdf

Nano-Calphad: extension of the Calphad method to systems with nano-phases and complexions

The surface tension of liquid Sn-X (X=Ag, Cu) alloys was measured by the constrained drop method in the temperatures between 700 and 1500 K across whole composition range. Surface tension of the alloys increased with the content of Ag and Cu, and the temperature coefficient of the surface tension (d�= dT) had both positive and negative values. Experimental results were compared with the calculated results based on Butler’s model. The calculated results reasonably accorded with the measurements. The effect of thermo-physical parameters on the surface tension and the temperature coefficient were examined using the model. It was found that the temperature coefficient increases as the difference in the surface tension of component metals or the excess free energy increases in the high composition range of the component metal having higher surface tension, because of the surface enhancement of the other component metal.

/pdf/surface-tension-and-its-temperature-coefficient-of-liquid-sn-1ra0dvo1kt.pdf

Surface Tension and its Temperature Coefficient of Liquid Sn-X (X=Ag, Cu) Alloys

It is usually known that the surface tension of liquid metals and alloys decreases with increasing temperature, i.e., the temperature dependence of the surface tension is negative. We found, however, that some liquid alloys, which have large difference of the surface tension of pure components, show positive temperature dependence in certain composition ranges. Some Pb-free alloys, for which information on the surface tension is indispensable to be developed as environmental-friendly material, can be listed in this special category. The experimental results and the thermodynamic analysis of the temperature dependence of those alloys are discussed in the paper.

https://iopscience.iop.org/article/10.1088/0957-0233/16/2/015/pdf

Temperature dependence of surface tension of liquid Sn–Ag, In–Ag and In–Cu alloys

Temperature dependence of the surface tension of liquid Sn–Ag and Sn–Cu base lead-free solder alloys and oxygen partial pressure dependence of liquid Sn–Ag alloy were evaluated using the experimental data obtained, respectively, by the constrained drop method and the sessile drop method in the previous studies [1, 2]. The temperature dependences of the surface tension have maximum positive values when the mol fraction of Ag and Cu is about 0.7, while those for pure liquid Sn, Ag, and Cu have negative values. The calculated values based on Butler’s equations were found to be in reasonable agreement with those of the experimental data. The oxygen partial pressure dependences of the surface tension of liquid Sn–Ag alloys at 1253 K have a minimum value when the mol fraction of Ag is about 0.9 and the oxygen partial pressure is less than about 10−13 atm. From this, it is considered that the oxygen adsorption increased by adding Ag to Sn when the mol fraction of Ag is less than 0.9.

Wataru Shimoda

Papers

Surface Tension and its Temperature Coefficient of Liquid Sn-X (X=Ag, Cu) Alloys

Temperature dependence of surface tension of liquid Sn–Ag, In–Ag and In–Cu alloys

Temperature and Oxygen Partial Pressure Dependences of the Surface Tension of Liquid Sn–Ag and Sn–Cu Lead-free Solder Alloys