Evaporation from plane surfaces

ESDU 534, 566 Evans, F. L. 524, 566 Evaporation from plane surfaces 650... 

It may be shown that the vapour pressure exerted by a convex surface is greater than that exerted by a plane surface (Starling, 1935). This effect of the curvature of the surface is referred to as the Kelvin effect, and is of importance in considering the stability of small liquid droplets. If a very small droplet occurs in an atmosphere in which the vapour pressure is the maximum associated with a plane surface (SVP), evaporation from the surface of the droplet will still occur as a result of the vapour pressure exerted by the droplet surface exceeding the SVP. As the droplet becomes smaller, so the curvature of the surface increases and evaporation continues. This effect in part explains the observation that a dust-free vapour does not form droplets at a temperature below the normal temperature of condensation (the dew point). The Kelvin effect must be taken into account when considering the stability of small liquid aerosol droplets in the airways. 

Equation [7.35] is one form of an equation known as Kelvin s equation. In the example of Fig. 7.6(a), r is negative so that p < po, i.e. evaporation from a surface convex to the liquid is more difficult than from a plane surface. 

In several important processes, one component in a gaseous mixture will be transported relative to a fixed plane, such as a liquid interface, for example, and the other will undergo no net movement. In gas absorption a soluble gas A is transferred to the liquid surface where it dissolves, whereas the insoluble gas B undergoes no net movement with respect to the interface. Similarly, in evaporation from a free surface, the vapour moves away from the surface but the air has no net movement. The mass transfer process therefore differs from that described in Section 10.2.2. 

Powia i. R.W. and Griffiths. F.. Trans. Inst. Client. Eng. 13 (1935) 175. The evaporation of water from plane and cylindrical surfaces. 

If pi differs from p0, as in Eq. (63), then the rate of evaporation of a small droplet should be different from that from a plane surface of equal extent. This reasoning was extended133 to the vaporization of minute silver crystals (e.g.,... 

It has previously been indicated that charges have comparatively little direct effect on the vapor pressure of a material until the particle diameter is substantially less than 1 micron and their effect is toward keeping the vapor pressure closer to that from a plane surface. Consequently, it may be concluded that charge will not significantly affect evaporation rate of a given droplet. 

Evaporation from drops of liquid is generally much faster than from a plane surface, on account of the geometry of the system aiding the concentration to fall steeply away from the surface, and so making the concentration gradient steep. 

It is found that for metals, low temperature field evaporation almost always produces surfaces with the (1 x 1) structure, or the structure corresponding to the truncation of a solid. A few such surfaces have already been shown in Fig. 2.32. That this should be so can be easily understood. For metals, field penetration depth is usually less than 0.5 A,1 or much smaller than both the atomic size and the step height of the closely packed planes. Low temperature field evaporation proceeds from plane edges of these closely packed planes where the step height is largest and atoms are also much more exposed to the applied field. Atoms in the middle of the planes are well shielded from the applied field by the itinerant electronic charges which will form a smooth surface to lower the surface free energy, and these atoms will not be field evaporated. Therefore the surfaces produced by low temperature field evaporation should have the same structures as the bulk, or the (lxl) structures, and indeed with a few exceptions most of the surfaces produced by low temperature field evaporation exhibit the (1 x 1) structures. 

Fig. 5.16 Mapping of misplaced Pt atoms, which are Pt atoms occupying Co sites, in a 110 plane of partially ordered Pt3Co alloy by slow field evaporation of a surface layer. From the work of Berg etal.9S...

Hondros and Moore (22) also found that heating under vacuum or in nitrogen did not lead to the formation of facets. The latter produced smooth surfaces, and the former led to pit formation. From these data and the studies of earlier workers, the authors concluded that the mechanism of silver etching is the preferential evaporation of silver oxide from certain surface planes. 

After fracturing, platinum was evaporated from a carbon crucible at an angle of 45° onto the surface of the exposed plane to form a thin him (1.5 to 2.0 nm thick). Mechanically, this him was not very stable, so a further layer of carbon was evaporated onto the platinum perpendicular to the fracture surface, as a thick layer (15 to 20 nm), to give support to the metal him. After this procedure the rivets were removed from the apparatus and the original sample was dissolved off the platinum... 

Toei et al. (T5, T6) believe that when the moisture content on the surface becomes less than the critical moisture content, the first falling-rate period starts and the evaporation occurs at the interior of the solid. The second falling-rate period starts when the moisture content at the surface reaches the equilibrium value. The evaporating plane retreats into the solid and dried-up zone begins to grow from the surface into the solid. The dried zone retains the equilibrium moisture content. 

These thermodynamical considerations are due in the main to Lord Kelvin. He also was the first to recognise the fact that the vapour pressure of a liquid is dependent on the magnitude and shape of the sruface. Let us calculate the work dtv which can be obtained by allowing the mass dm of a liquid whose surface tension is y, and whose density is s, to evaporate from a sphere of radius r. to a plane siuface. The mass m of the sphere is -jTrr s and its surface a is 4 7rr. When the mass of the small sphere of liquid is diminished... 

Results are presented for stepped surfaces with terrace orientations (100) and (111) on Pt and (001) on Ru. In fact, these planes, together with various others, form the surface of a field emitter tip which can be regarded as a catalyst particle with a diameter of about 20 to 200 nm. Although our probe hole measurements sample only a few atomic sites (up to about 200) the detailed crystallography of the probed area, i.e. terrace widths and step site symmetries, is not known because the concomitant removal of substrate atoms by field evaporation (from kink site positions) during the measurements causes continuous alterations of the morphology. 

Sakurai et al. [218] have used the atom probe field ion microscope [219] to make a direct study of hydride phases on silicon. Continuous field evaporation from 111 and 110 Si planes in the presence of hydrogen produced Si+, SiH+ and SiHj. Some Si atoms evaporate without forming hydrides to give Si+ SiH+ derives simply from the monohydride phase and SiHj from the dihydride. However, this latter comes from the 111 surface, whereas UPS data consistent with the presence of a dihydride came from 100 lxl. This apparent difference can be reconciled by the fact that some kink site atoms on 111 planes have two dangling orbitals per Si atom (as on 100 surfaces) and field evaporation occurs primarily at kink sites. 

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