Crystal structure unit cells

A) The c and b vectors indicate the directions of the chains relative to the cell axes of the crystal structure unit cell axes. The double tetrahedral chain of composition [(Si,A1)40,i]n is formed from corner-linked SiO or AIO4 tetrahedra (T). 

Consistently reliable approaches for the de novo prediction of a material s crystal structure (unit cell shape, size, and space group), morphology (external symmetry), microstructure, as well as its physical properties, remain elusive for... 

Fe-C composition (crystal structure) Unit cell parameters (A)... 

The detailed behavior of an individual grain boundary depends on its geometry, see Fig. 14.2, and the presence of doping elements. Epitaxial growth where the crystal structure unit cell of the deposited material has a fixed orientation relationship with respect to the unit cell of the substrate is most often desired when depositing thin films where a high Jc is required. 

Fig. 46. Crystal structure (unit cell) and muon location for NaCl-type compounds MX. Solid circles, M atoms open circles, X atoms.

Crystal structure Unit cell dimensions Atomic positions Positions of the crystalline reflections Positions and the intensities of the crystalline reflections... 

In the 1960s, Hassel8 studied the structures of many mixed crystals whose unit cells correspond to noncovalently linked donor-acceptor complexes, such as the... 

The structure amplitude, F. In an ammonium chloride crystal the unit cell is a cube containing one NH4 and one Cl ion. If the centre of a chlorine ion is taken as the corner of the unit cell, then the ammonium ion lies in the centre of the cell (Fig. 110). 

Phase 0 U ratio Structure Crystal class Unit cell dimensions (A) Ref. 

The atom-atom potential fitted to the ab initio data gives fairly re stic results for the equilibrium structure (unit cell parameters and molecular oriratations in the cell), the cohesion energy and the phonon frequencies of the molecular crystal. The latter have been obtained via both a harmonic and a self-consistent phonon lattice dynamics calculation and they were compared with and Raman spectra. About some of the aninncal hydrocarbon atom-atom potentials which are fitted to the crystal data, we can say that they correspond reasonably well with the ab initio results (see figs. 6, 7, 8), their main defect being an underestimate of the electrostatic multipole-multipolc interactions. 

It is important to note that no motion having a period in excess of L/v can be reproduced in the simulations, where L is the length of the simulation box and is a velocity of sound in the medium.In addition, use of periodic boundary conditions together with a single structural unit cell as the simulation box restricts the calculation of spectral quantities to those at the center of the Brillouin zone the periodic boundary conditions force atoms in all images of the simulation box to vibrate in-phase, that is, the definition of a motion at the center of Brillouin zone. When comparing results of the calculations with the experimental spectra, one must also bear in mind that the model used in the calculations implies a perfect crystal structure, whereas experiments are usually done with microcrystals having defects. 

Sometimes different compounds give apparently identical crystals. Isomorphism is the similarity of crystal shape, unit cell dimensions, and structure between substances of nearly, but not completely, identical chemical composition. It is derived from the Greek words - isos meaning equal and morphe for form or shape. The arrangements of atoms in the isomorphous crystals are identical, but the identity of one or more atoms in this arrangement has been changed. For example, sulfur in a sulfate may often be replaced by selenium, to give an isomorphous selenate. Ideally, isomorphous compounds are so closely similar in composition that... 

Isomorphism Similarity of crystal shape, unit cell dimensions, and structure between substances of similar chemical composition. Generally only the identity of one atom in the chemical formula is changed. Ideally, the substances are so closely similar that they may form a continuous series of solid solutions. 

Another classification is based on the presence or absence of translation in a symmetry element or operation. Symmetry elements containing a translational component, such as a simple translation, screw axis or glide plane, produce infinite numbers of symmetrically equivalent objects, and therefore, these are called infinite symmetry elements. For example, the lattice is infinite because of the presence of translations. All other symmetry elements that do not contain translations always produce a finite number of objects and they are called finite symmetry elements. Center of inversion, mirror plane, rotation and roto-inversion axes are all finite symmetry elements. Finite symmetry elements and operations are used to describe the symmetry of finite objects, e.g. molecules, clusters, polyhedra, crystal forms, unit cell shape, and any non-crystallographic finite objects, for example, the human body. Both finite and infinite symmetry elements are necessary to describe the symmetry of infinite or continuous structures, such as a crystal structure, two-dimensional wall patterns, and others. We will begin the detailed analysis of crystallographic symmetry from simpler finite symmetry elements, followed by the consideration of more complex infinite symmetry elements. 

Internal structure (unit cell) can be different in crystals that are chemically identical. This is called polymorphism. Polymorphs can vary substantially in physical and chemical properties such as bioavailability and solubility. They can be identified by analytical techniques such as X-ray diffraction, infrared, Raman spectro, and microscopic techniques. For the same internal structure, very small amounts of foreign substances will often completely change the crystal habit. The selective adsorption of dyes by different faces of a crystal or the change from an alkaline to an acidic environment will often produce pronounced changes in the crystal habit. The presence of other soluble anions and cations often has a similar influence. In the crystallization of ammonium sulfate, the reduction in soluble iron to below 50 ppm of ferric ion is sufficient to cause significant change in the habit of an ammonium sulfate costal from a long, narrow form to a relatively chunky and compact form. Additional information is available in the patent literature and Table 18-4 lists some of the better-known additives and their influences. 

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