Crystalline Electron

Several research approaches are pursued in the quest for more efficient and active photocatalysts for water splitting (i) to find new single-phase materials, (ii) to tune the band-gap energy of TJV-active photocatalysts (band-gap engineering), and (iii) to modify the surface of photocatalysts by deposition of cocatalysts to reduce the activation energy for gas evolution. Obviously, the previous strategies must be combined with the control of the s)mthesis of materials to customize the crystallinity, electronic structure, and morphology of materials at nanometric scale, as these properties have a major impact on photoactivity. 

A New Model. The results of the studies on anodic oxide films (see section 5.9 and chapter 3 on passive film and anodic oxides) show that anodic oxide properties (oxidation state, degree of hydration, 0/Si ratio, degree of crystallinity, electronic and ionic conductivities, and etch rate) are a function of the formation field (the applied potential). Also, they vary from the surface to the oxide/silicon interface, which means that they change with time as the layer of oxide near the oxide/silicon interface moves to the surface during the formation and dissolution process. The oxide near the silicon/oxide interface is more disordered in composition and structure than that in the bulk of the oxide film. Also, the degree of disorder depends on the formation field which is a function of thickness and potential. The range of disorder in the oxide stmcture is thus responsible for the variation in the etch rate of the oxide formed at different times during a period of the oscillation. The etch rate of silicon oxides is very sensitive to the stmcture and composition (see Chapter 4). 

The phase stability of crystalline electron phases or Hume-Rothery (HR) phases has been explained by the afore-mentioned band-structure effects. For this purpose, the k- as well as r-space representation have been used successfully [5.45,46]. Crystalline HR-phases are well documented and excellent text books or reviews exist in this field [5.13,14, 35]. In the present section, only a few facts are mentioned in order to show how glassy metals belong to this class of phases. 

When the surfaces of the samples are crystalline, electron backscatter diffraction (EBSD) patterns, called Kikuchi lines, generated from reflected electrons, are observed. EBSD patterns provide knowledge concerning crystal stmctures and orientations. Thus, the combination of SEM and EBSD is one of the powerful tools, which can tell us the microstmctures of the sample surfaces and the orientations of the grains on the sample surfaces. 

Linear scaling (so-called 0 N)) algorithms for calculation of crystalline electronic structure are based on the concept of WFs [50]. 

While the original atomic functions describing the valence electrons, of course, no longer are eigenstates of the problem, their characteristics can be used as a good approximate set of basis states to describe the crystalline electrons. For most semiconductor materials of interest, the atomic functions required to describe the outermost electrons are s, px, py, and pz types, as shown by O Table 23-1. A common approach of choosing the above n) at the F point is to foUow Kane (1957) and define a set of eight states, that is, t(r) in O Eq. 23.1 at fc = 0, S t), X t), y t)> 2 t). S i)>l 1), where the arrows indicate spin up and down. X,Y,Z)... 

Now we can summarize previous considerations In the case of the break down of the B-O approximation the electron-roton and electron-translon parts of the extended Born-Handy formula play the role of the trigger inducing a structural instability in the system. These parts are a direct consequence of the introduction of centre-of-mass problem into focus. They are responsible for the formation of molecular and crystallic structure. On the other hand, the electron-phonon part plays the role of a stabilizer of a new equilibrium position corresponding with new nuclear displacements. Therefore it is responsible for the formation of molecular and crystalline electronic structure. 

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