Unit cells crystal systems

Minerals Composition Polytype" Crystal System Unit Cell Dimension ... 

Crystal system Unit cell Lattice Fundamental translations Point groups... 

Formula Name Crystal system" Unit cell parameters (nm) a b c Space group Z D. (kgm-" ) Ref. 

Crystal system Unit cell vector lengths Unit cell vector angles... 

The crystal systems unit cells and characteristic symmetry... 

The unit cell determination gives a unit cell with parameters a= 13.3674 A, b = 5.7367A, c = 14.4758A, a = 90°, /] = 105.485° y = 90° and V = 1069.78AA Thus, compound 1 crystallizes in a monoclinic crystal system (unit cell), we can now estimate WAu with various Z values and the diffraction power by calculating dp. Since the compound 1 contains one heavier element (chlorine), let s make an... 

Crystal System Unit Cell Symmetry Bravais Latt... 

Crystal system Unit cell parameters d-spacing Low-order reflections... 

Angles between two edges a (between edges b and c) p (between a and c) y (between a and b) Seven crystal systems (unit cell shapes)... 

For powder photographs, the use of the charts described on p. 143 and in Appendix 3 will show whether the substance is cubic, tetragonal, or hexagonal if it is not, the numerical methods of indexing the patterns of crystals of low symmetry may be tried or, if it is. possible to pick out single crystals, or if the specimen can be recrystallized to give suitable crystals, the unit cell dimensions may be determined by the methods described earlier. A search may then be made in the tables of Donnay and Nowacki (1954), in which, for each crystal system, the species are arranged in order of the axial ratios. 

The next step is for a protein crystallographer to mount a small perfect crystal in a closed silica capillary tube and to use an X-ray camera to record diffraction patterns such as that in Fig. 3-20. These patterns indicate how perfectly the crystal is formed and how well it diffracts X-rays. The patterns are also used to calculate the dimensions of the unit cell and to assign the crystal to one of the seven crystal systems and one of the 65 enantiomorphic space groups. This provides important information about the relationship of one molecule to another within the unit cell of the crystal. The unit cell (Fig. 3-21) is a parallelopiped... 

System Crystal classes Unit cell Standard axes... 

In the above, ijk denote the Cartesian coordinates of a molecule, IJK those of a crystal (a unit cell), 7Vt is the number of molecules in a unit volume occupying each particular inequivalent site in the unit cell,/ is the number of inequivalent positions of a molecule in a unit cell, and Ng is the number of equivalent positions in a unit cell. The directional cosines are used to transform each of the molecular 0 components to those of the new coordinate system (bUK) and the contributions are summed. 

Boughton system isotopic naming, 259 chemical constants, 149, 151 chirality symbols and symmetry site terms, 262-263 crystal lattice unit cells, 262 element symbols in chemical names, 232 for emphasis, 92 for genus and species, 92-93 for indicated hydrogen, 232 for newly defined terms, 92 for periodicals, books, and newspaper titles, 92... 

Crystal System Unit Space group cell... 

When atoms, molecules, or molecular fragments adsorb onto a single-crystal surface, they often arrange themselves into an ordered pattern. Generally, the size of the adsorbate-induced two-dimensional surface unit cell is larger than that of the clean surface. The same nomenclature is used to describe the surface unit cell of an adsorbate system as is used to describe a reconstructed surface, i.e. the synmietry is given with respect to the bulk tenninated (unreconstructed) two-dimensional surface unit cell. 

The otiier type of noncrystalline solid was discovered in the 1980s in certain rapidly cooled alloy systems. D Shechtman and coworkers [15] observed electron diffraction patterns with sharp spots with fivefold rotational synnnetry, a syimnetry that had been, until that time, assumed to be impossible. It is easy to show that it is impossible to fill two- or tliree-dimensional space with identical objects that have rotational symmetries of orders other than two, tliree, four or six, and it had been assumed that the long-range periodicity necessary to produce a diffraction pattern with sharp spots could only exist in materials made by the stacking of identical unit cells. The materials that produced these diffraction patterns, but clearly could not be crystals, became known as quasicrystals. 

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