Edge density

Gomez R, Climent V, Feliu JM, Weaver MJ. 2000. Dependence of the potential of zero charge of stepped platinum (111) electrodes on the oriented step-edge density Electrochemical implications and comparison with work function behavior. J Phys Chem B 104 597-605. 

In the numerical simulation, we take a random graph of n = 1000 vertices with edge density varied accordingly to sparse graphs (p = 0.1), normal graphs... 

Structure 14 G) f(G) Edge Density Diameter Radius Petitjean Shape Index Zagreb index... 

Step-edge density 0.3-3.6 pm pm Average step edge coverage 1.8%... 

Step-edge density 0.5-2.3 pm pm" Average step edge coverage 0.8%... 

Figure 16.1.10 Nanowire diameter vs. (deposition time) for the growth of nanowires composed of four metals as indicated. Each series of experiments for a particular metal were performed using a single graphite crystal in order to limit the variation in the step edge density from experiment to experiment (see equation (16.1.1)). This crystal was cleaved before each experiment to expose a fresh, clean graphite surface. Error bars for each data point are twice the standard deviation for the mean particle diameter as measured from SEM images. Reprinted with permission of the American Chemical Society.

Table 3. Number of edges, density, and number of paths.

Table 5. Number of nodes, edges, density, estimated number of s-t paths and actual number of paths in (sub-) graphs.

Fig. 13.5 ZPS profiles foratheW(540)(0.16ML)andtheW(320)(0.28 ML) surfaces with respect to the W( 110) surface [24—27], b coordination-resolved valence LDOS of W(320) surface atoms [28], c Rh(l 11) vicinal (553) (0.26 ML) and (151,513) (0.07 ML) surfaces [29] and the missing-row type reconstructed Rh(lOO) surfaces. The reconstructed Rh(lOO) surfaces have the same edge density (0.5 ML) but slightly different atomic CNs [30]. ZPS profiles d of Rh atoms added on Rh(lOO) surface in different coverage [22]. Peaks above the bulk valley arise from the valence charge polarization that screens and splits the crystal potential and hence produces the T and P components. The valley at the bottom edge of the band represents the coupling effect of T and P...

Highly distorted and dangling bonds result in a continuum of states in the energy gap. These come primarily from the band edge density of states of the equivalent crystalline structure. 

---