Electrons traveling through solids

Oxygen anions travel from the source side through the solid electrolyte to the sink side (anode) under the combination of the influence of an applied dc electric field and an oxygen chemical potential gradient. At the sink side (the anode of the SOFC), the oxygen anions react electrochemically with both zirconium and yttrium reactants from the sink vapor phase to form the desired product, yttria doped zirconia, and release electrons to the metallic anode. Electrons travel through the external electrical circuit back to the source side for further cathodic reaction. 

Therefore, the catalyst is characterized by the surface area of platinum by mass of carbon support. The electrochemical half-cell reactions can only occur, where all the necessary reactants have access to the catalyst surface. This means that the carbon particles have to be mixed with some electrolyte material in order to ensure that the hydrogen protons can migrate towards the catalyst surface. This "coating" of electrolyte must be sufficiently thin to allow the reactant gases to dissolve and diffuse towards the catalyst surface (Figure 1.8). Since the electrons travel through the solid matrix of the electrodes, these have to be connected to the catalyst material, i.e. an isolated carbon particle with platinum surrounded by electrolyte material will not contribute to the chemical reaction. 

A fuel cell electrode is essentially a thin catalyst layer pressed between the ionomer membrane and porous, electrically conductive substrate. It is the layer where the electrochemical reactions take place. More precisely, the electrochemical reactions take place on the catalyst surface. Because there are three kinds of species that participate in the electrochemical reactions, namely gases, electrons and protons, the reactions can take place on a portion of the catalyst surface where all three species have access. Electrons travel through electrically conductive solids, including the catalyst itself, but it is important that the catalyst particles are somehow electrically connected to the substrate. Protons travel through ionomer therefore the catalyst must be in intimate contact with the ionomer. And finally, the reactant gases travel only through voids therefore the electrode must be porous to allow gases to travel to... 

At the anode, the lithium loses electrons forming lithium ions (Li+). The ions travel through the solid electrolyte layer and the electrons travel through the external load lo reach the cathode. At the cathode, the lithium ions react with the composite cathode material and the incoming electrons to form the discharge products. The discharge reactions can be expressed by the following equations ... 

Although most of the results described in this review are aimed towards an understanding of the electronic structure of the bulk solid, the most widespread applications of XPS exploit its surface sensitivity, as a result of the numerous interactions that an ejected photoelectron undergoes as it travels through the surface layers [2]. The photoelectron collides with other electrons, either elastically so that its trajectory changes, or inelastically so that its KE decreases (by 10-40 eV per collision) [2,19,20]. The distance travelled between inelastic collisions is called the... 

A technique becomes surface sensitive if the radiation or particles to be detected travel no more than a few atomic distances through the solid. Figure 3.1 shows that the mean free path, A, of electrons in elemental solids depends on the kinetic energy, but is limited to less than 1-2 nm for kinetic energies in the range 15-1000 eV [16]. 

The second term in (6-9) expresses that nearest and next nearest neighbors dominate scattering contributions to the EXAFS signal, while contributions from distant shells are weak. The dependence of the amplitude on 1/r2 reflects that the outgoing electron is a spherical wave, the intensity of which decreases with the distance squared. The term exp(-2r/X) represents the exponential attenuation of the electron when it travels through the solid, as in the electron spectroscopies of Chapter 3. The factor 2 is there because the electron has to make a round trip between the emitting and the scattering atom in order to cause interference. 

The theory assumes that the nuclei stay fixed on their lattice sites surrounded by the inner or core electrons whilst the outer or valence electrons travel freely through the solid. If we ignore the cores then the quantum mechanical description of the outer electrons becomes very simple. Taking just one of these electrons the problem becomes the well-known one of the particle in a box. We start by considering an electron in a one-dimensional solid. 

In a semiconductor, an empty conduction band lies close in energy to a full valence band. As a result, as the solid is warmed, electrons can be excited from the valence band into the conduction band where they can travel through the solid. So the resistance of a semiconductor decreases as its temperature is raised. 

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