Bulk electron density

Here Es is the surface energy and the left side refers to the change of Es with change in bulk electron density. 

Here, a, = m,Z,/H where H, is the atomic weight. Strictly speaking, a, is proportional to each element s bulk electron density, which to a good approximation is proportional to the element s bulk density. The choice of the exponent value (=3.5) is empirical and other authors have presented similar formulas with somewhat different choices for the exponent. 

The density of electrons at a particular energy for surface and bulk atoms can be calculated according to the Mulliken procedure outlined in Section 11.B.1. The data in Fig. 13 show a different electron distribution on surface and bulk atoms. The bulk electron density is split-the maximum in surface electron density occurs at the minimum in bulk density. This behavior indicates that the bulk electron distribution is different from the surface electron distribution. 

When one thinks of a real surface, several difficulties present themselves which any theory of LEED must take into account. For example, presence of atomic steps on a surface makes understanding of experimental intensities more difficult than if the interface were prefectly plane (175). Owing to the abrupt termination of a solid at its surface, one can expect that electron distributions around the nuclei of surface atoms are not as symmetric as deep in the bulk. Electron density around surface atoms cannot be approximated so well by spherically symmetric... 

There are two general choices for modeling the fluid structure. The first is to use an error-function profile whose position and width are determined while the height of the error function is constrained to correspond to the bulk electron density of the fluid layer (pe- = 0.0333 e /A3 for water). Any specific adsorption to the mineral surface can be included by adding into the structure factor sum additional adsorbate atoms whose position and occupation are determined by the fitting procedure. A second approach is to use a layered water structure. (See section on the mica-water interface, below.)... 

Fig. 9 Surface electronic profile of a neutral and negatively charged jellium calculated for the bulk electron density of Hg.

Fig. 8 Schematic real-space model and normalized electron density profiles < p(z)>/pix> (where p is the bulk electron density of mercury) obtained from the fits of reflectivity data to a density-dependent model for n-octadecanethiol (bold line) and n-dodecanethiol (thin line). The upper and lower figures are aligned with each other. Vertical lines in the model mark the position of the three outermost surface layers of mercury, with the origin of z coinciding with the first mercury layer [89]. 

Here is the surface electron density (or hole, density for a p-type semiconductor), vIq is the bulk electron density, and A0sc is the potential drop in the semiconductor. The potential drop in the semiconductor is zero at the flatband potential so that Equation (3.59) can be written in terms of the electrode potential as... 

More recently, Lang and Kohn (1973) gave a detailed discussion of this problem, including the question of chemisorption, e.g., of alkali metal atoms on transition metal surfaces such as those of W, Ta, Re. The problem is approached first by considering the profiles of the charge induced by a uniform external electric field for metals of different bulk electron densities. At electrodes, it is to be noted, an additional factor is the potential-dependent surface electron density, q, given, in the case of liquid metals of surface tension y> by q = -(8y/9E),... 

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