The Basics of Crystallography and Diffraction

Abstract

This book provides an introduction to crystallography, light, X-ray, and electron diffraction. The book also shows, by historical and biographical references, how the subject has developed from the work and insights of successive generations of crystallographers and scientists. The book shows how an understanding of crystal structures, both inorganic and organic may be built up from simple ideas of atomic and molecular packing. Beginning with (two-dimensional) examples of patterns and tilings, the concepts of lattices, symmetry point, and space groups are developed. ‘Penrose’ tilings and quasiperiodic structures are also included. The reciprocal lattice and its importance in understanding the geometry of light, X-ray, and electron diffraction patterns is explained in simple terms, leading to Fourier analysis in diffraction, crystal structure determination, image formation, and the diffraction-limited resolution in these techniques. Practical X-ray and electron diffraction techniques and their applications are described. A recurring theme is the common principles: the techniques are not treated in isolation.

Rosetas e concrescências cristalinas silicificadas em Piper (Piperaceae): registros inéditos de macropadrões

“…As birrefringências mostradas pelos cristais das três espécies de Piper são características anisotrópicas de cristais com os padrões químicos composicionais verificados (Hammond 2009). Cristais de composição química mista são referidos como não birrefringentes (He et al 2012), devido a serem analisados sem rotação do polarizador analisador, impossibilitando, assim, avaliar os diferentes índices de refração que possuem, pois apresentam alterações de propriedades ópticas em relação aos cristais puros (Hammond 2009).…”

“…Cristais de composição química mista são referidos como não birrefringentes (He et al 2012), devido a serem analisados sem rotação do polarizador analisador, impossibilitando, assim, avaliar os diferentes índices de refração que possuem, pois apresentam alterações de propriedades ópticas em relação aos cristais puros (Hammond 2009). …”

Electron Diffraction Re-Explained (The Intense Magnetic Fields Interactions within Crystals)

“…A single crystals diffraction is shown in Fig.1-A, with a fixed orientation, the produced dots pattern rotates by the same angle as the crystal; if the number of the crystals are superimposed to four as in Fig.1-B, it gives four different groups of dots, each represents specific orientation, while using 40 randomly oriented crystals powder in Fig.1-C, it produced visible rings [19]; and since it is necessary to rotate the crystal in the xray or neutron beam in order to generate the complete diffraction pattern [20], hence the crystal powder gives effects of many layers; but this diffraction is envisaged from the geometrical analogy between light and electron diffraction, based on the smallness of wavelengths of light and electrons compared with the spacing of the diffracted objects [21], as carried by Bragg and based on Huygen's idea [22], although the whole pattern is due to the cathode rays, thought to have been deflected by the film [15]; but G. P. Thomson questioned the nature of this wave? And the relation it has with electrons associated with it [23], and as repeatedly mentioned the only wave produced by an accelerated electron [1], is the Circular Magnetic Field (CMF) [24,25,26], the magnitude of which is given by…”

“…The x-ray crystallography work of W. and L. Bragg in 1913 confirmed the microscopic regularity of crystalline matter [28], although the spatial characteristics of crystal lattices, was investigated and became known, but the forces holding these units in position are still not completely understood, [6], it is stated that, in inorganic crystals, the dominant bonding forces are ionic or heteropolar bonds and covalent or homopolar bonds, with lesser contributions from van der Waals and hydrogen bonds, and the ionic bond is non-directional, this is shares with the metallic bond which is the dominant cohesive force in metals with high conductivity [21], while the attractive electrostatic interaction between electrons and the nuclei is entirely thought responsible for the cohesion of solids, and magnetic forces is thought to have weak effect [27], but to what extend does that have?…”

Mapping of axial plastic zone for roller bearing overloads using neutron transmission imaging

“…X-ray diffraction application to quantify plastic strain is limited however [19]. In X-ray diffraction, lattice spacings for specific hkl planes (hkl being the miller indices [20]), represented as Bragg peaks are measured. The change in spacing is associated with elastic strain, calculated by measuring the shifts in these interplanar spacings [21].…”