Liquid metal surface energy effect

Modern theories of electronic structure at a metal surface, which have proved their accuracy for bare metal surfaces, have now been applied to the calculation of electron density profiles in the presence of adsorbed species or other external sources of potential. The spillover of the negative (electronic) charge density from the positive (ionic) background and the overlap of the former with the electrolyte are the crucial effects. Self-consistent calculations, in which the electronic kinetic energy is correctly taken into account, may have to replace the simpler density-functional treatments which have been used most often. The situation for liquid metals, for which the density profile for the positive (ionic) charge density is required, is not as satisfactory as for solid metals, for which the crystal structure is known. 

Sessile drop experiments are also used to measure the effects of temperature on liquid surface energies. Because the temperature coefficient dliquid metals and oxides is usually a very small, negative, value (—0.05 to —0.5 mJ.m-2.K-1), a temperature rise of several hundred degrees is necessary to produce decreases in the surface energy that can be reliably detected by measurements of drop profiles. Even in this case, the error on the temperature coefficient lies between 30% and 100% (see Section 4.1.1). 

Rapid fluid flow cannot be achieved with active metal brazes because of the need to form solid wettable reaction product layers for their liquid fronts to advance. Equations (10.1) to (10.2) relating liquid flow rates to the opposed effects of surface energy imbalances and of viscous drag are not relevant. Actual penetration rates are so slow, usually of the order of 1 pm.s, that the usual practice is to place the active metal braze alloy within the joints rather than expecting it to fill them, and, as explained already, gap width is not the dominant consideration when designing ceramic-metal joints. 

Solid state physicists are familiar with the free- and nearly free-electron models of simple metals [9]. The essence of those models is the fact that the effective potential seen by the conduction electrons in metals like Na, K, etc., is nearly constant through the volume of the metal. This is so because (a) the ion cores occupy only a small fraction of the atomic volume, and (b) the effective ionic potential is weak. Under these circumstances, a constant potential in the interior of the metal is a good approximation—even better if the metal is liquid. However, electrons cannot escape from the metal spontaneously in fact, the energy needed to extract one electron through the surface is called the work function. This means that the potential rises abruptly at the surface of the metal. If the piece of metal has microscopic dimensions and we assume for simplicity its form to be spherical - like a classical liquid drop, then the effective potential confining the valence electrons will be spherically symmetric, with a form intermediate between an isotropic harmonic oscillator and a square well [10]. These simple model potentials can already give an idea of the reason for the magic numbers the formation of electronic shells. 

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