Unit cell standard choice

Figure Bl.21.4. Direct lattices (at left) and reciprocal lattices (middle) for the five two-dimensional Bravais lattices. The reciprocal lattice corresponds directly to the diffraction pattern observed on a standard LEED display. Note that other choices of unit cells are possible e.g., for hexagonal lattices, one often chooses vectors a and b that are subtended by an angle y of 120° rather than 60°. Then the reciprocal unit cell vectors also change in the hexagonal case, the angle between a and b becomes 60° rather than 120°.

Without adopting certain conventions, different unit cell dimensions might and most definitely would be assigned to the same material based on preferences of different researchers. Therefore, long ago the following rules Table 1.12) were established to designate a standard choice of the unit cell, dependent on the crystal system. This set of rules explains both the unit cell shape and relationships between the unit cell parameters listed in Table 1.11 (i.e. rule number one), and can be considered as rule number two in the proper selection of the unit cell. 

Crystal family Standard unit cell choice Alternative unit cell choice... 

Applying the rules established in Table 1.12 to two of the four unit cells shown on top of Figure 1.21, the cell based on vectors aj and bi is the standard choice. The unit cell based on vectors aj and b2 has the angle between the vectors much farther from 90 than the first one. The remaining... 

The first two reduction rules are normally employed only during the indexing. They usually do not produce a standard choice of the unit cell since at this stage the space group symmetry, and often even the lattice type, are not involved. For example, in the orthorhombic space group symmetry Pnma (a standard setting) the condition a< b< c is not necessarily obeyed. 

The idealised or aristotype perovskite stmcture is cubic and is adopted by SrTiOj at room temperature (but not at all temperatures). There are two general ways of listing the atoms in the cubic unit cell. The standard crystallographic description places the choice of origin at the Sr atom ... 

In addition to the tools described for specific searches of the CSD, one of the major requirements for crystal engineering is a capability to compare sets of crystal structures in order to identify degrees of similarity and difference. It is obvious that this task has formed the very basis of the development of crystal engineering, [40] but consistent with the general contemporary trend there is a move towards automated procedures for large-scale structure comparison. The key concept that is required for automation is some unique representation of a crystal structure. Standard items in a CSD entry can cause problems in this respect for example, unit-cell parameters may differ on account of thermal expansion the space group may be influenced by a particular choice of origin... 

For the first example of fiilly ab initio periodic SCF study of a molecular crystal see Dovesi, R. Causa, M. Orlando, R. Roetti, C. Saunders, V.R. Ab initio approach to molecular crystals a periodic Hartree-Fock study of crystalline urea, J. Chem. Phys. 1990,92,7402-7411. The unit cell contains sixteen atoms and the basis set employed is 6-21G. The band structure, density of states, and deformation electronic densities are obtained. The lattice energy is -117 kJ mol without, and 67 kJmol with basis set superposition error correction [8]. The latter value reflects the absence of dispersion contributions in the HF approach (experimental heat of sublimation 88 kJ mol ). Such a study would now be comfortably feasible on any standard PC, but clearly the computational load of a periodic crystal calculation increases with the increasing number of atoms in the unit cell and size of the atomic orbital basis set. A good critical entry point to the literature is Spackman, M.A. Mitchell, A.S. Basis set choice and basis set superposition error (BSSE) in periodic Hartree-Fock calculations on molecular crystals, Phys. Chem. Chem. Phys. 2001,3,1518-1523. 

The level of enzyme needed can influence the choice of preparation used for the study. Microsomal preparations from cell cultures allow the use of higher concentrations of active enzyme per unit volume than use of whole cells or cell lysates. The use of whole, viable cells allows the use of longer incubation times but at a lower enzyme concentration per unit volume. In addition, adequate oxygen transfer and nutrient concentrations are needed to maintain culture viability. These requirements impose limitations on cell concentration. In addition, microsomes cannot be efficiently prepared from all cultured cell types. We have found that standard microsome preparation procedures as used for human or rodent liver were unsuitable for isolating active enzymes from human lymphoblasts, and this appears to be a general property of cultured cell lines. Specific catalytic activities in microsomes were lower than for whole cell lysates. This loss of activity appears to happen in other mammalian cell systems which has led to the common use of whole cell lysates.With human lymphoblasts, shortening the length of... 

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