Cubic unit cells, 421 table

Mallinson et al. (1988) have performed an analysis of a set of static theoretical structure factors based on a wave function of the octahedral, high-spin hexa-aquairon(II) ion by Newton and coworkers (Jafri et al. 1980, Logan et al. 1984). To simulate the crystal field, the occupancy of the orbitals was modified to represent a low-spin complex with preferential occupancy of the t2g orbitals, rather than the more even distribution found in the high-spin complex. The complex ion (Fig. 10.14) was centered at the corners of a cubic unit cell with a = 10.000 A and space group Pm3. Refinement of the 1375 static structure factors (sin 8/X < 1.2 A 1) gave an agreement factor of R = 4.35% for the spherical-atom model with variable positional parameters (Table 10.12). Addition of three anharmonic thermal... 

When these four types of lattice are combined with the 7 possible unit cell shapes, 14 permissible Bravais lattices (Table 1.3) are produced. (It is not possible to combine some of the shapes and lattice types and retain the symmetry requirements listed in Table 1.2. For instance, it is not possible to have an A-centred, cubic, unit cell if only two of the six faces are centred, the unit cell necessarily loses its cubic symmetry.)... 

There are two polymorphic structures of ZnS, zinc blende (or sphalerite) (3 2PT) and wurtzite (2 2PT). In zinc blende there is a ccp arrangement of S atoms with Zn atoms filling one of the two T layers as shown in Figure 6.1. The diamond has the same structure, with the sites of P and one T layer filled by C atoms (Section 4.3.3). The structure of zinc blende has six (3 2) layers in the repeating unit. This structure is encountered for many binary compounds with significant covalent character as shown in Table 6.1. The space group for zinc blende is T%, F43m, and a0 = 5.4093 A, for the cubic unit cell. ... 

The X-ray spectra of the heated samples (Figures 1 and 2 and Tables I and II) show different results depending on R. For samples with R < 0.05, the spectrum contains the characteristic lines of the NaY zeolite and no additional lines. In particular, no lines characteristic of V2C>5 are observed. The cubic-unit-cell parameter rises from 2.4639 0.0005 nm for NaY zeolite to 2.4673 0.0015 nm for the sample with R = 0.05. 

The cubic unit-cell dimensions (a) of NaCl and NaBr crystals are 563 and 597 pm, respectively (Table 10.1.4). As shown in Fig.1.5.2, the side (denoted as l below) of the three-dimensional box for an electron occupying a color center can at most be the body diagonal of the unit cell minus twice the cationic radius (the true value should be somewhat less) ... 

Table 10.1.4. Compounds with the NaCl structure and parameters of their cubic unit cells...

Silver iodide, Agl, exists in several polymorphic forms. In the a-Agl crystal, the 1 ions adopt the bcp structure, and the Ag+ cations are distributed statistically among the 6(b), 12(d), and 24(h) sites of space group — Im3m, as listed in Table 10.3.1, and also partially populate the passageways between these positions. The cubic unit cell, with a — 504 pm, provides 42 possible positions for two Ag+ cations, and the Ag+ I- distances are listed below ... 

XRD patterns of dealuminated samples D-l and D-2 agree well with previous work (15). The samples are highly crystalline and the (cubic) unit cell parameter is reduced (Table n) by the dealumination of the framework. The Si/Al ratios of samples D-l and D-2 were 3.10 and 4.91, respectively, which confirms that the degree of dealumination increases with the duration of hydrothermal treatment. 

The fluorite structure has been described in terms of a face-centered-cubic unit cell containing four units of M02. Table I lists the lattice parameters for these substances. 

It is only in structures in which small proportions of the two types of hole are occupied that the nearest neighbours of an atom in a tetrahedral (octahedral) hole are only the nearest 4 (6) c.p. atoms. This is true, for example, in the spinel and olivine structures (Table 4.8). The CogSg structure is closely related to the spinel structure, which has 32 c.p. 0 atoms in the cubic unit cell. In CogSg there are 32 c.p. S atoms with 4 Co in octahedral and 32 Co in tetrahedral holes compare C03S4 with a slightly distorted spinel structure, also with 32 S in the cubic unit cell, but 16 Co in octahedral and 8 Co in tetrahedral holes. The spinel structure is discussed in detail on p.490 for the olivine structure see p. 811. An expanded version of part of Table 4.8 will be found on p. 619, where the structures of a number... 

The observed values of sin 0 for the first 16 lines are listed in Table 10-5, together with the visually estimated relative line intensities. This pattern can be indexed on the basis of a cubic unit cell, and the indices of the observed lines are given in the table. The lattice parameter, calculated from the sin 6 value for the highest-angle line, is 6.46 A. 

Not all types of lattice are allowable within each crystal system, because the symmetrical relationships between cell parameters mean a smaller cell could be drawn in another crystal system. For example a C-centred cubic unit cell can be redrawn as a body-centred tetragonal cell. The fourteen allowable combinations for the lattices are given in Table 1.4. These lattices are called the Bravais lattices. 

Table 3. Lattice constants of Prttssian blue analogs M M (CN)i l H O. Z = number of formula units per cell a = edge of the cubic unit cell (A) / dm, dc —measured and calculated densities, respectively (gcmr )...

There are seven crystal systems, listed in Table 1, that result from the possible symmetry of the crystal lattice (24). For example, if the crystal lattice describes a cubic unit cell, rotations of 90° or 120° or 180° about appropriate directions will give a lattice indistinguishable from the original this can be verified by examination ofa cube. The unit cell conditions (a = b = c, a=P=y=90°) follow from the lattice symmetry. If, however, a = b=t c and neither a nor P nor y= 90°, then the symmetry of the crystal lattice is low (triclinic). 

The spinel structure is found among a very large number of oxides AB2X and also in a limited number of sulphides, selenides, fluorides and cyanides of the same composition, some of which are recorded in table 8.09. The cubic unit cell of this structure is shown in fig. 8.21 and contains 32 X ions. Each A ion is tetrahedrally co-ordinated by four and each B ion is octahedrally co-ordinated by six X neighbours, and each X ion is bound to one A and to three B ions. The co-ordination may therefore be summarized thus ... 

The cubic unit cell constants, a, of a number of P-A zeolites were determined over a range of phosphorus content (0 to 10 wt % P2O5). The unit cell dimension decreases with increase in phosphorus content (Table IV, Figure 7). This reduction in unit cell constant is consistent with the substitution of phosphorus in the zeolite framework by the mechanism discussed later, and is attributed to the smaller tetrahedral P—O bond distance of 1.54 A, compared to the tetrahedral Si—O bond distance of 1.61 A and A1—O bond distance of 1.75 A. Unit cell compositions for P-A zeolites calculated on the basis of the pseudo cubic unit cell of Type A zeolite, a <—12 A, are included in Table V. Measured densities for the sodium forms and calcium-exchanged forms of zeolite A and zeolite P-A are given in Table VI. 

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