Amorphous interatomic distance

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... 

EXAFS is a nondestructive, element-specific spectroscopic technique with application to all elements from lithium to uranium. It is employed as a direct probe of the atomic environment of an X-ray absorbing element and provides chemical bonding information. Although EXAFS is primarily used to determine the local structure of bulk solids (e.g., crystalline and amorphous materials), solid surfaces, and interfaces, its use is not limited to the solid state. As a structural tool, EXAFS complements the familiar X-ray diffraction technique, which is applicable only to crystalline solids. EXAFS provides an atomic-scale perspective about the X-ray absorbing element in terms of the numbers, types, and interatomic distances of neighboring atoms. 

In spite of the absence of periodicity, glasses exhibit, among other things, a specific volume, interatomic distances, coordination number, and local elastic modulus comparable to those of crystals. Therefore it has been considered natural to consider amorphous lattices as nearly periodic with the disorder treated as a perturbation, oftentimes in the form of defects, so such a study is not futile. This is indeed a sensible approach, as even the crystals themselves are rarely perfect, and many of their useful mechanical and other properties are determined by the existence and mobility of some sort of defects as well as by interaction between those defects. Nevertheless, a number of low-temperamre phenomena in glasses have persistently evaded a microscopic model-free description along those lines. A more radical revision of the concept of an elementary excitation on top of a unique ground state is necessary [3-5]. 

Table 8.53 shows the main features of XAS. The advantages of EXAFS over diffraction methods are that the technique does not depend on long-range order, hence it can always be used to study local environments in amorphous (and crystalline) solids and liquids it is atom specific and can be sensitive to low concentrations of the target atom (about 100 ppm). XAS provides information on interatomic distances, coordination numbers, atom types and structural disorder and oxidation state by inference. Accuracy is 1-2% for interatomic distances, and 10-25 % for coordination numbers. 

X-ray diffraction studies were carried out for cyclolinear copolymers and it was shown, that they are amorphous systems. Independently of the length of single-unit dimethylsiloxane chain, diffraction patterns display two amorphous halos. It is known that the first amorphous halo, d, characterizes the average interchain distance in amorphous polymer [52], whereas d2 is more complicated and corresponds to both intrachain and interchain or interatomic distances. 

The reduced RDF of a-Si H shown in Fig. 2.11 (Schulke 1981) has sharp structure at small interatomic distances, progressively less well-defined peaks at larger distances, and is featureless beyond about 10 A. This reflects the common property of all covalent amorphous semiconductors, that there is a high degree of short range order at the first and second neighbor distances, but then the spatial correlations decrease rapidly. 

EXAFS studies of A. vinelandii bacterioferritin have shown that there are fewer Fe-Fe contacts in the mineral core than occur with native horse ferritin, and those that do occur are at a greater interatomic distance. Moreover, the EXAFS data showed that the core iron of bacterioferritin had 5 to 6 phosphorus atoms no more than 3.17 A distant, thus supporting a model for the core of an amorphous Fe(III)-phosphate complex in which some of the phosphate bridges Fe(III) ions and some of it is nonbridging. 

Electron diffraction patterns of amorphous and nanocrystallme materials are analyzed to measure the radial distribution fimction (RDF) to provide interatomic distances and their distribution. The principle of RDF analysis using electron diffraction is similar to X ray diffraction with the... 

The amorphous material induces a broad hump or halo, in to the diffraction pattern. The width and the position of the halo indicate the distribution of interatomic distances in the structure of the material. The area under halo depends on the content of amorphous material, and therefore it is possible to semiquantitatively determine the content of amorphous material from the x-ray diffraction pattern, Mixtures of synthetic ash and common glass were used as calibration samples. 

Fig. 5.14 Side view of a slab model of the surface of amorphous silica [55]. The top surface consists only of Si and O atoms the bottom one is fully hydroxylated. Black, light grey and white spheres are silicon, oxygen and hydrogen atoms, respectively. The large spherical oxygen and all the silicon atoms are to scale with the interatomic distances.

The disordered nature of the amorphous phase has prevented the direct determination of the structural parameters by the usual structural techniques such as X-ray diffraction. Solid-state NMR can give us those parameters even for amorphous samples. Yannoni and Clark [14] applied nutation NMR spectroscopy, which is specifically designed to measure interatomic distances, to determine the bond lengths in both the cis- and tran -polyacetylenes. They used polyacetylene polymerized from a mixture of 4% doubly C-enriched acetylene and doubly depleted acetylene. In Fig. 7.6, the observed and simulated proton decoupled nutation spectra of the cis sample are shown. The sharp peak in the centre arises from the isolated nuclei in the sample. The remainder of the spectrum is a Pake-doublet arising from the dipolar coupling of adjacent nuclei in the polyacetylene. The best fit to the observed spectrum corresponds to a distribution of bond length with... 

When an X-ray beam falls on alums iwo processes may occur. The beam may be scaltcrcd or the beam may be absorbed with an ejection of electrons from an atom. In the case of a crystalline material the scattering of X-rays is used to determine the structure of the solid phase and the chemist applies this method to the proof of the structure of new compounds very often. But even when a regular crystalline arrangement does not exist, as in liquids or amorphous solids, scattering patterns are produced. I.ike in the crystalline solid phase the scattering of X-rays on disordered systems can be used to determine the probability of distribution of atoms in the environment of any reference atom, or in other words the frequency with which interatomic distances occur. 

The outgoing wave is spherical and is scattered by all species adjacent to the absorbing atom unlike X-ray diffraction, long-range order is not a prerequisite, so amorphous samples can be studied. The method does not directly identify the nature of the neighbours, which can only be inferred from the interatomic distances. 

The electrical properties of semiconductors depend on the perfection of the crystal structure and the nature of the impurities it contains. However, the decisive factor responsible for semiconductor properties is the short-range order. By this is meant the symmetry of the electron shells, the valence an es, the interatomic distances, etc., i.e., the nature of the forces of the chemical interaction between the atoms. This is indicated by the fact that the semiconducting properties of many crystalline semiconductors are retained after melting [1] and also by the existence of a large number of liquid, amorphous, and glassy semiconductors. 

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