Formula units per unit cell

Calculate the number of cations, anions, and formula units per unit cell in each of the following solids (a) the cesium chloride unit cell shown in Fig. 5.41 (b) the rutile (Ti02) unit... 

Specification of the lattice parameters and the positions of all atoms contained in the unit cell is sufficient to characterize all essential aspects of a crystal structure. A unit cell can only contain an integral number of atoms. When stating the contents of the cell one refers to the chemical formula, i. e. the number of formula units per unit cell is given this number is usually termed Z. How the atoms are to be counted is shown in Fig. 2.7. 

Give the number of formula units per unit cell for ... 

Thus, there are four formula units per unit cell of MgO. 

Silica has 22 polymorphs, although only some of them are of geochemical interest—namely, the crystalline polymorphs quartz, tridymite, cristobahte, coesite, and stishovite (in their structural modifications of low and high T, usually designated, respectively, as a and jS forms) and the amorphous phases chalcedony and opal (hydrated amorphous silica). The crystalline polymorphs of silica are tectosilicates (dimensionality = 3). Table 5.68 reports their structural properties, after the synthesis of Smyth and Bish (1988). Note that the number of formula units per unit cell varies conspicuously from phase to phase. Also noteworthy is the high density of the stishovite polymorph. 

A positive evidence for a true cr-bonded organolanthanide complex is presented by Cotton et at. (32) in a crystal structure analysis of the anionic complex [Lu(III)-tetrakis-2,6-dimethylphenyl] . This anion crystaJUizes as [Li(I)-tetrakis-tetra-hydrofuran]+ salt, [Li(C4HgO)4]+ [Lu(C8H9)4] , in orthorhombic space group (P2i2i2i) with a = 15.093, 6 = 15.265 and c = 19.959 A and four formula units per unit cell. 

It is interesting that tris-acetylacetonato-Yb(III)-monohydrate tends to retain solvent molecules. Thus if Yb(acac)3 3HaO is recrystaUized from acetone or benzene, one molecule of the solvent is present for two molecules of Yb(acac)3 H2O. The hemibenzene solvated Yb(acac)3 of composition [Yb(acac)3 H2O O.bCeHs] also crystallizes in triclinic space group PT, hke the unsolvated complex, with a =8.728, 6 = 8.435, c = 15.623 A, and a = 95.95°, /S = 107.72° and y =96.18° but with two formula units per unit cell (84). 

Akaganeite (named after the Akagane mine in Japan) is isostructural with hollan-dite. Compounds with this structure have a tetragonal or monoclinic unit cell. Bernal et al. (1959) and Keller (1970) both concluded that the unit cell of akaganeite was tetragonal with a = 1.000 nm and c = 0.3023 nm. The structural refinement of a natural sample using XRD and Rietveld analysis indicated, however, that the unit cell is monoclinic with a = 1.060 nm, b = 0.3039 nm, c = 1.0513 nm and p = 90.24° (Post Buchwald, 1991). There are eight formula units per unit cell. 

FeOOH is isostructural with Fe(OH)2. It has a hexagonal unit cell with a = 0.294 nm and c = 0.449 nm. A related compound exists in nature under the mineral name feroxyhyte (named by F.V. Chukhrov see Chukhrov et al., 1976), also termed 5 -FeOOH. Feroxyhyte has a hexagonal unit cell with a = 0.294nm and c = 0.456 nm. It contains two formula units per unit cell, whereas the unit cell of the synthetic material contains only one formula unit. 

The unit cell parameters given by Towe and Bradley (1967) for 6-line ferrihydrite are a = 0.508 nm and c = 0.94 nm. There are four formula units per unit cell. A con-... 

Stephens et al. determined the lattice structure of powdered TDAE-C60 to be monoclinic C2/m with one formula unit per unit cell [84]. However, a structural analysis performed on single crystals [85] showed the room temperature structure to be monoclinic with unit cell dimensions a=15.858(2) A, b=12.998(2) A, c=l9.987(2) A, (3=93 37° and four formula units per unit cell. The correct space group was found to be C2/c and not C2/m as originally reported from the powder data. The unit cell in fact consists of two subcells, which are stacked along the c-direction so that the unit cell size in the c-direction is doubled (Fig. 13). In one of the subcells the TDAE ion is shifted by about 0.02 A along... 

AIN exists in two types the hexagonal (wurtzite structure) and the cubic (zincblende structure). The former is more stable, and has been investigated in more detail. The wurtzitic AIN has two formula units per unit cell (4 atoms per cell) and 9 optical branches to the phonon dispersion curves [1] ... 

Salt Melting point Dimensions of unit cell Vol. Meas. density g/cc at 5 °C 0.005 Hydration number (chemical) Hydration number (crystal) Number of formula units per unit cell... 

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