Mean free path interatomic distances

As is to be expected, inherent disorder has an effect on electronic and optical properties of amorphous semiconductors providing for distinct differences between them and the crystalline semiconductors. The inherent disorder provides for localized as well as nonlocalized states within the same band such that a critical energy, can be defined by distinguishing the two types of states (4). At E = E, the mean free path of the electron is on the order of the interatomic distance and the wave function fluctuates randomly such that the quantum number, k, is no longer vaHd. For E < E the wave functions are localized and for E > E they are nonlocalized. For E > E the motion of the electron is diffusive and the extended state mobiHty is approximately 10 cm /sV. For U <, conduction takes place by hopping from one localized site to the next. Hence, at U =, )J. goes through a... 

Characterization techniques become surface sensitive if the particles or radiation to be detected come from the outer layers of the sample. Low energy electrons, ions and neutrals can only travel over distances between one and ten interatomic spacings in the solid state, implying that such particles coming off a catalyst reveal surface-specific information. The inherent disadvantage of the small mean free path is that measurements need to be carried out in vacuum, which conflicts with the wish to investigate catalysts under reaction conditions. 

Amorphous materials have no long-range structural order, so there is no continuous lattice in which atoms can vibrate in concert in order for phonons to propagate. As a result, phonon mean free paths are restricted to distances corresponding to interatomic spacing, and the (effective) thermal conductivity of (oxide) glasses remains low and increases only with photon conduction (Figure 8.2). 

In 1958, Anderson [9] showed that localization of electronic wavefunctions occurs if the random component of the disorder potential is large with respect to the bandwidth of the system, as shown in the schematic diagram in Fig. 3.1. The mean free path ( ) in a system with bandwidth B, random potential Vo, and interatomic distance a is given by... 

Strongly localized, l a l — Mean free path a — Interatomic distance... 

The periodicity of this modulation of the absorption will be dependent upon the inteiatomic distance between the absorbing and back-scat tei i ng atoms, R, and the phase shifts, 5. , encountered when the photoelect i on expeiiences the potentials at these centres. Its intensity will be governed by the number of back-scatterers, Nj and their back-scattering amplitudes, F (k). Finally the amplitude is dampened by disorder (thermal and static), a in the interatomic distance and any inelastic piocesses (related to the mean free path of the election, j)- The recognition of the stiuctural information intrinsic to this phenomenon and the derivation of a tractable formula for the estimation of interatomic distances was the result of the work of Sayers, Lytle and... 

Allen (1980) points out that the maximum resistivity for d-band compounds and alloys is of the order of 150 A cm. He suggests that this value is reasonable from a theoretical point of view since it is related to the lower limit of the mean free path, i.e. the interatomic distance. However, certain alloys, such as Y6(Fe, Mn)23 and Y(Fe, 0)2 have resistivities which saturate above 220p,ncm (see section 4 for details). This may well be due to resonance scattering effects for the d-electrons in disordered pseudobinaries (Harris et al., 1978). 

The electrical conductivity is mainly determined by the carrier density, n, relaxation time, T, and effective mass, m, of the carrier (electrical conductivity, electron charge). According to the loffe-Regel criterion, the interatomic distance is considered as the lower limit for the mean free path, A, in a metallic system. Hence, for a metallic system kpX is greater than 1, where kpA. = [h(37f) ] / kp is the Fermi... 

Quantum mechanics show that the mean free path of the electrons in a metal cannot be smaller than the interatomic distance. For many concentrated alloys of transition metals this limit is approached. Near this hmit the resistivity becomes insensitive to a further increase of lattice disorder, and thus the TCR becomes low. It turns out that for these alloys the TCR is approximately zero when the resistivity is around 150 /U.S2 cm, positive when it is lower and negative when it is higher. Their low TCR makes these alloys useful for fixed resistors. 

Langmuir and Dushman(ii9) proposed a semi-empirical equation for diffusion in cubic lattices, which has proved a useful guide to the behaviour of diffusion processes in ionic and metallic lattices (Tables 66 and 67). It was derived by considering the lattice as composed of layers of atoms in planes a distance d apart, where d denotes the interionic or interatomic distance. It wrs assumed that d was also the mean free path of a diffusing ion or atom. The number of atoms per unit area is then and the chance that an atom will leave this... 

Fig. 2.9. Electronic wave function (r) for the case (a) when the mean free path A is much larger than the mean interatomic distance a and (b) when A is comparable with a (after Mott, 1974).

The scattering kernel is a fundamental quantity summarizing the basic information on the gas-surface interaction. It is indirectly contained in the velocity distribution function of the atomic flux departing from the surface (Eq. (2.158)). Therefore, the atoms "remember" how they have been scattered by the surface as long as interatomic collisions in the gas do not destroy this information. This destruction happens at distances of the order of the mean free path from the surface. The corresponding gas slab nearby the surface is called the Knudsen layer. 

Glass structure being amorphous, the mean free path of the phonons is limited to interatomic distances. Hence, conductivity is limited as compared to crystalline materials. 

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