Crystalline solids electron diffraction

Atomic X-rays are emitted during electronic transitions to the inner shells of atoms. These X-rays have characteristic energies related to the atomic number, and each element therefore has a characteristic X-ray spectrum. Crystalline solids will diffract X-rays and the diffraction patterns can be used to derive bond distances and bond angles in a molecular structure. X-ray diffraction can also be used to study ionic substances and forms the basis of X-ray crystallography. 

To answer this question we need to consider the kind of physical techniques that are used to study the solid state. The main ones are based on diffraction, which may be of electrons, neutrons or X-rays (Moore, 1972 Franks, 1983). In all cases exposure of a crystalline solid to a beam of the particular type gives rise to a well-defined diffraction pattern, which by appropriate mathematical techniques can be interpreted to give information about the structure of the solid. When a liquid such as water is exposed to X-rays, electrons or neutrons, diffraction patterns are produced, though they have much less regularity and detail it is also more difficult to interpret them than for solids. Such results are taken to show that liquids do, in fact, have some kind of long-range order which can justifiably be referred to as a structure . 

Cowley, J.M. (1992) Scattering factors for the diffraction of electrons by crystalline solids, In International Tables for Crystallography, Wilson, A.J.C. (Ed.), Volume C. Kluwer Academic Publishers, Dordrecht/Boston/London. 

Schel, S. A. etal., J. Mol. Struct., 1986, 147(3 -4), 203 -215 Although it is highly explosive, like other polyunsaturated azides, it was possible to record spectral data under the following conditions gaseous electron diffraction IR spectra of matrix-isolated species in argon at 15°K of amorphous and crystalline solids at 90°K and Raman spectra of the liquid at 240°K. 

Experimental structural data are available for two crystalline derivatives of c/s,cis-cyclo-octadiene-1,5 (86). The distorted-boat form occurs in both crystals (observed C—CH2—CH2—C torsion angles 65 and 74°, respectively). Hedberg and Hedberg have performed a gas-electron diffraction study and found that the distorted boat conformation predominates also in the gas-phase (87). For the dibenzo derivative, however, there are crystallographic indications that in the solid state the eight-membered ring has the chair conformation (88). 

Another characteristic point is the special attention that in intermetallic science, as in several fields of chemistry, needs to be dedicated to the structural aspects and to the description of the phases. The structure of intermetallic alloys in their different states, liquid, amorphous (glassy), quasi-crystalline and fully, three-dimensionally (3D) periodic crystalline are closely related to the different properties shown by these substances. Two chapters are therefore dedicated to selected aspects of intermetallic structural chemistry. Particular attention is dedicated to the solid state, in which a very large variety of properties and structures can be found. Solid intermetallic phases, generally non-molecular by nature, are characterized by their 3D crystal (or quasicrystal) structure. A great many crystal structures (often complex or very complex) have been elucidated, and intermetallic crystallochemistry is a fundamental topic of reference. A great number of papers have been published containing results obtained by powder and single crystal X-ray diffractometry and by neutron and electron diffraction methods. A characteristic nomenclature and several symbols and representations have been developed for the description, classification and identification of these phases. 

Investigation of structure and properties of crystal is one of the most important problems in solid state physics and chemistry. Thus study of the features of electron diffraction (ED) and their relation to the inner crystalline field and establishment of their link to physical properties is one of the major requests of modem stmcture analysis (SA). 

The detailed data from He-scattering experiments provide information about the electron density distribution on crystalline solid surfaces. Especially, it provides direct information on the corrugation amplitude of the surface charge density at the classical turning point of the incident He atom, as shown in Fig. 4.13. As a classical particle, an incident He atom can reach a point at the solid surface where its vertical kinetic energy equals the repulsive energy at that point. The corrugation amplitude of the surface electron density on that plane determines the intensity of the diffracted atomic beam. 

In the diffraction pattern from a crystalline solid, the positions of the diffraction maxima depend on the periodicity of the stmcmre (i.e. the dimensions of the unit cell), whereas the relative intensities of the diffraction maxima depend on the distribution of scattering matter (i.e. the atoms or molecules) within the unit cell. In the case of XRD, the scattering matter is the electron density within the unit cell. Each diffraction maximum is characterized by a unique set of integers h, k and I (Miller indices) and is defined by a scattering vector H in three-dimensional... 

The arrangement of helices in the solid and liquid crystalline states of poly(a-phenylethyl isocyanide) were determined by X-ray and electron diffraction. Well-defined diffraction patterns were obtained from oriented films using selected area electron diffraction. Intermolecular and intramolecular patterns were calculated from the five Debye-Scherrer rings. All the reflections were indexed in terms of a pseudo-hexagonal triclinic unit cell, with... 

An electron diffraction study of [Zn(acac)2] has recently been reported. The Zn—O distances of 1.942 0.006 A correlate reasonably well with those determined from an X-ray structural study of the crystalline solid (Zn—O, 1.999 A) and are shorter than those observed in the solid state structure of the monohydrate (Zn—O, 2.02 A).744... 

The classical theory for electronic conduction in solids was developed by Drude in 1900. This theory has since been reinterpreted to explain why all contributions to the conductivity are made by electrons which can be excited into unoccupied states (Pauli principle) and why electrons moving through a perfectly periodic lattice are not scattered (wave-particle duality in quantum mechanics). Because of the wavelike character of an electron in quantum mechanics, the electron is subject to diffraction by the periodic array, yielding diffraction maxima in certain crystalline directions and diffraction minima in other directions. Although the periodic lattice does not scattei the elections, it nevertheless modifies the mobility of the electrons. The cyclotron resonance technique is used in making detailed investigations in this field. 

These embrace X-ray diffraction, neutron diffraction and electron diffraction. The first two of these are almost entirely used in the study of crystalline solids, while electron diffraction is of most value (to inorganic chemists at least) for structure determinations of gaseous substances. X-ray diffraction has been used to obtain structural information for species in solution, and electron diffraction has applications in the... 

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