Surface energy simple metals

Metals A and B form an alloy or solid solution. To take a hypothetical case, suppose that the structure is simple cubic, so that each interior atom has six nearest neighbors and each surface atom has five. A particular alloy has a bulk mole fraction XA = 0.50, the side of the unit cell is 4.0 A, and the energies of vaporization Ea and Eb are 30 and 35 kcal/mol for the respective pure metals. The A—A bond energy is aa and the B—B bond energy is bb assume that ab = j( aa + bb)- Calculate the surface energy as a function of surface composition. What should the surface composition be at 0 K In what direction should it change on heaf)pg, and why ... 

A particularly simple example would be the energy of a sample of aluminum metal in air. The surface of the metal is covered with a continuous layer of aluminum oxide which may be less than 20 angstroms in thickness in a dry atmosphere but will be much thicker in moist air or after contact with hot water. Consequently, the... 

Another example of the interaction of water with a relatively simple metal oxide surface is provided by the water vapor/a-Al203(0001) system (Figure 7.9(a)). Oxygen Is synchrotron radiation photoemission results indicate that significant dissociative chemisorption of water molecules does not occur below 1 torr p(H20) [149]. However, following exposure of the alumina (0001) surface to water vapor above this threshold p(H20) , a low kinetic energy feature in the Is spectrum grows quickly,... 

A numerical evaluation of the Fermi energy lor a simple metal having one or two conduction electrons per atom yields a value of approximately ID-11 erg. or a few electron volts. The equivalent temperature. E,/b. is several lens of thousands of degrees Kelvin. Thus, except in extraordinary circumstances, when dealing with metals. bT -SC ( i.e.. the energy range or partially filled states is small, and the Fermi surface is well defined by the foregoing statement. It must be noted, however, that this is not necessarily true for semiconductors where the number of free electrons per unit volume may be very much smaller. 

Heterogeneous catalysis provides many important examples of those intermediate cases [26]. Accurate numerical study of the interaction of very simple molecules with the clean, atomically flat surfaces of pure metals has only very recently become feasible [27-34]. For example, the full six-dimensional energy surfaces of H2 on clean [33] and sulfur-poisoned [34] Pd(100) surfaces have been calculated. The energy surfaces which result from these computations have... 

The central problem of the atomic theory of metal surfaces is the proper determination of the surface energy of ideally flat and atomically smooth faces of a simple metal crystal. The methods of quantum mechanics permit the computation of energies with much less effort than is needed for a description in terms of correct wave functions and, of course, the construction of a successful theory of surface energy must touch on most other aspects of the atomic nature of surfaces, such as the potential in the surface region and its associated double layer, or the atomic arrangement and the change in electronic configuration in the surface. 

It is immediately apparent from Fig. 20-1 that along the one symmetry line in the Brillouin Zone shown, there are two or three bands crossing the Fermi energy for each metal and therefore quite a complex set of Fermi surfaces. These have been thoroughly studied, using the techniques discussed in connection with simple metals. It would, however, be quite inappropriate here to attempt any complete discussion of this problem, Instead, the Fermi surface of a single system, chromium, will be discussed. It is perhaps the most interesting case, and it illustrates the principal effects that enter considerations of the other systems. We shall then turn to the density of states, which dominates many of the electronic properties. 

Our restriction to simple fluids was meant to emphasize general laws and phenomena. For this reason, we did not discuss theories of the surface tension of solids, for which a variety of models have been elaborated. One of the considerations for omitting these was that such tensions cannot be measured, so that a check of the quality is edso impossible. We also consciously excluded the surface tensions of liquid metals, liquid crystals, molten crystals and polymer melts. However, spread and adsorbed polymer layers will be considered in chapter 3 and 4, respectively. For similar reasons, and because most practical applications involve ambient temperatures, we did not extensively discuss critical phenomena, notwithstanding their Intrinsic Interest. Under critical conditions the surface energy - surface entropy balance differs considerably from that at lower temperatures, emphasized in this chapter. 

---