Metal free electron density

In the previous example, we have calculated the plasma frequency for metallic Na from the free electron density N. In Table 4.1, the measnred cutoff wavelengths, Xp, for different alkali metals are listed together with their free electron densities. The relatively good agreement between the experimental values of Xp and those calculated from Equation (4.20), within the ideal metal model, should be noted. It can also be observed that the N values range from abont 10 to about 10 cm leading to... 

These measurements cannot be used to quantify the electron transfer from the semiconductor to the metal deposit, but an estimate has been drawn from studies of oxygen photoadsorption on Pt/Ti(>2 samples in a pressure range such that nearly all of the free electrons are captured to form adsorbed 05 ion-radicals. Increasing Pt contents corresponded to decreasing amounts of photoadsorbed oxygen, which corroborates the effect of deposited Pt on the Ti(>2 free electron density. For Ti(>2 samples evacuated at 423 K and... 

The fact that LME can take place only when there is a good contact between the metal and the liquid metal — observation.4.1.5 - means free electrons must be free to move from solid metal to liquid metal and vice versa. This logically means the phenomenon of LME is due to the change in the free electron density in the solid metal under the influence of the free-electron density in liquid metal. Our task is to characterize a) the type of change, b) the type of mechanical effects (based on the theory proposed here) that can come from such a change and c) comparison between these theoretical intuitions against the experimental evidence to see how they fit together. 

In summary, LME in my view is due to the upsetting of the Ratio of covalent bond to metallic band and resulting in an increased difficulty in the creation of free radicals. This takes away the ductility and results in brittleness. In this context, one can venture to predict that if solid metal is coated with a liquid metal whose electron density is less than that in solid metal, solid metal may become free electrondeficient and may actually facilitate the creation of free radicals. In this case an enductilement may result in lieu of embrittlement. 

We consider a metallic phase of volume V, with N free electrons, and hence a free electron density n given by n = NjV. The charge of the core ions is smeared out and leads to a potential energy well keeping the free electrons in the metallic phase (Figure 3). Since in the Sommerfeld model the electrons do not interact with each other, we can describe the electron energy levels by one-electron wave functions. An independent electron can be described by a single-electron wave function ij/ x,y,z) which satisfies... 

The main differences between the kinetics of electron transfer at a metal and that at a semiconductor electrode originate in the difference in the density of free carriers. In a typical metal, the electrochemical potential or Fermi level, is located in a band. The free-electron density is huge, lO -lO cm . We discussed the metal/ solution interface in Section 4.5 it has a rather complicated structure with a double... 

The SMSI state of M/TiC catalysts have been examined from the electronic point of view in three different situations (i) chemisorpti-ve capacity, (ii) (CO + H ) interactions and (iii) CDIE photocata-lytic test. In all cases, the free electron density was involved. Without rejecting any influence of the decoration of the metal particles by suboxide species, the electronic effect can be considered as responsible - at least partially - for the SMSI state (11,21). ... 

The magnitude of Tg is quite high usually, T > 10 K. So, at common temperatures (T < 10 K), the free electron density of a metal is much smaller than in the case of the Maxwell-Boltzmann distribution. This allows us to explain why the experimental data on specific heat for metals are close to those for insulators. 

Various types of solid-state NO2 sensors have been proposed based on semiconducting metal oxides (including heterocontact materials) [42-50,58,59,234-238], solid electrolytes [1,239,240], metal phthalocyanine [241], and SAW devices [242]. Among these NO2 sensors, the semiconducting metal oxides and solid electrolytes appear to be the best. Specifically, semiconducting metal oxide gas sensors are most attractive because they are compact, sensitive, of low cost, and have low-power consumption. Their basic mechanism is that the NO2 gas is adsorbed on the surface of the material this decreases the free electron density into the space-charge layer and results in a resistance increase [243]. 

These predictions have been verified by experiments on low-energy helium atom scattering by metal surfaces [112]. The helium atom repels the Bloch electrons, because their wave function must become distorted to preserve orthogonality to the wave functions of the closed shells of helium. The repulsion potential appears in practise to be proportional to the local free electron density. Thus a helium atom scatters like a ping-pong ball from the electron cloud of the metal, and this allows to probe the distribution of electrons in the cloud, that is, the profile of the electronic tail and its lateral corrugation that usually follows the periodicity of the surface crystal plane [112]. 

Consider the effective potential of solvent acting on metal valence electrons, defined by Eq. (4.93) as the functional derivative of the solvation free energy with respect to the metal valence electron density, ne(r). Its derivation can be done similarly to the above expression for the excess chemical potential of solvation, A/Xsoiv, in the 3D-KH approximation. The variation of Eq. (4. A.9) is written as... 

The trends observed in the IR are confirmed by the transport measurements at 6.5 GHz. The high a- c observed as T — 0 in metallic PAN-CSA is accompanied by the presence of free electrons down to low temperature. In the samples where the free electron density freezes out at low temperature, ha much stronger insulating temperature dependence. 

In further developments, with Schmickler et al. (1984), two models of the solvent layer at the metal interface were considered. These self-consistent calculations of charge-induced electron relaxation predict in one form or another the well known hump in the compact-layer capacitance and introduce a dependence of the capacitance behavior on the properties of the metal electron system, that is, of course, not indicated in previous, purely molecular treatments of the metal/electrolyte interface. In general, metal-specific behavior (apart from that associated with specific orientation of solvent dipoles due to donor-acceptor interaction with the metal) is related to the free electron density of the metal. For further details, readers are referred to the review mentioned earlier (Feldman et al., 1986). 

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