Hydrogen Fermi surface

Fig. 5 Donor packing and Fermi surface for BO compounds, (a) Face-to-face packing dotted lines indicate the CH---0 hydrogen bonds), (b) side-by-side contacts dotted lines indicate the short S---S atomic contacts), and calculated Fermi surfaces of (c) (BO)2Cl(H20)3. Calculated Fermi surface of (BO)2.4l3 is depicted in Fig. 3b...

Dowden and Reynolds (49,50) in further experimental work on the hydrogenation of benzene and styrene with nickel-copper alloys as catalysts, found a similar dependence. The specific activities of the nickel-copper alloy catalysts decreased with increasing copper content to a negligible value at 60% copper and 30-40% copper for benzene and styrene, respectively. Low-temperature specific heat data indicated a sharp fall (1) in the energy density of electron levels N(E) at the Fermi surface, where the d-band of nickel becomes filled at 60 % copper, and (2) from nickel to the binary alloy 80 nickel -)- 20 iron. Further work by these authors (50) on styrene hydrogenation with nickel-iron alloy... 

Figure 13.18b by the shaded square which is embedded in the band structure. Figure 13.18c shows an equivalent way to plot this two-dimensional system. Here, the contours are in units of and the dotted line corresponds to the situation for half-filling. The dotted line is then the boundary surface of (ka, kj,) values that separate the (k, k ) values leading to the unoccupied states from those leading to the occupied states. It Is called the Fermi surface and it is of vital concern for the transport properties of a material. For a compound, where there is a gap between the highest occupied and lowest unoccupied states, there is no Fermi surface. For our hydrogen square net problem, the Fermi surface can be drawn as in 13.51. The shaded area indicates that portion of k values which... 

For a 3D lattice of hydrogen atoms the simplest reasonable form of Fermi surface can be chosen as a sphere of radius kf, corresponding to the model of the homogeneous electron gas. The function 0(A ) can be represented as a multipole expansion with following coefficients... 

Similarly, for a 2D hydrogen lattice a circular Fermi surface can be considered with the following occupation distribution in A -space... 

Table 1 Delocalization indices from the DFT calculations and the analytical model as well as Cioslowski-Mixon bond orders for the shortest and next shortest contacts in the 2D hydrogen square lattice. The second line of the table head for the first three columns shows the number of /r-points being used in the DFT calculations. FS stays for the Fermi surface,...

Hydrogen forms three superstructures on Mo(llO) characterised by (2x1), (2x2) and (1x1) superstructures corresponding respectively to a coverage of 0.5 ML, 0.75 ML and 1 ML. The adsorbate resides always in the hollow sites. The surface phonon dispersion data are shown in Fig. 24 for HATOF and HREELS measurements. For lower coverage no anomalies are present, while at saturation a dip is observed both for the RW and for the L mode which is ascribed to a Kohn anomaly (see also the case of W(110) (1x1) H and the discussion in the introductory part). A further mode, whose frequency nearly vanishes at the critical wavevector, is observed only with HATOF. It corresponds either to the excitation of electron hole pairs [95Koh] or to a plasmon like motion of the H atoms [96Bun]. The dispersion of the H induced modes is reported in Fig. 25. The Kohn anomaly is due to the nesting of the Fermi surface contours... 

Figure 10.14 Angle-resolved photoelectron spectra of the clean C(lll)2xl surface scanning the surface Brillouin zone along a line through K. The resonance S corresponds to the surface state, K is reached for a polar angle of ft 45. The zero of the energy axis is the Fermi level. In the upper panel one spectrum for the hydrogen-terminated surface is shown to demonstrate the absence of S for that surface. (Data from Ref [57].)...

The Vacuum Reference The first reference in the double-reference method enables the surface potential of the metal slab to be related to the vacuum scale. This relationship is determined by calculating the workfunction of the model metal/water/adsorbate interface, including a few layers of water molecules. The workfunction, — < ermi. is then used to calibrate the system Fermi level to an electrochemical reference electrode. It is convenient to choose the normal hydrogen electrode (NHE), as it has been experimentally and theoretically determined that the NHE potential is —4.8 V with respect to the free electron in a vacuum [Wagner, 1993]. We therefore apply the relationship... 

Fig. 8. Reaction rate of hydrogen-deuterium exchange as a function of the position of the Fermi level at the surface of a crystal.

We shall limit our attention to the case where the Fermi level in an unilluminated specimen is situated fairly deeply below the D level, which can be brought about, for example, when the bands are sufficiently bent upward, as shown in Fig. 8b. This corresponds to the acceptor branch of the curve gfo = 0o ( s+), i.e., the hydrogen and deuterium atoms on the surface fulfill, in this case, the role of donors. Here we may suppose that (see Fig. 8a) i [Pg.184]

Let us now turn to a comparison of theory with experiment. Comparing (95), (84), and (68), we find that the dependence of the photocatalytic effect K on the position of the Fermi level at the surface s and in the bulk cv of an unexcited sample for the oxidation of water is the same as for the oxidation of CO or for the hydrogen-deuterium exchange reaction. For this reason, such factors as the introduction of impurities into a specimen, the adsorption of gases on the surface of the specimen, and the preliminary treatment of the specimen will exert the same influence on the photocatalytic effect in all the three reactions indicated above. The dependence of K on the intensity I of the exciting light must also be the same in all the three cases. 

The appearance on the surface of any acceptor particles resulting in the negative charging of the surface and hence in the lowering of the Fermi level at the surface (in an increase of es- at v = const) must lead, according to (95) or (98), to the weakening of the photocatalytic effect. This is what actually occurs in the photosynthesis of hydrogen peroxide [jsee references (65-67, 71-73, 77)]. 

---