Chemical formula per unit cell

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. 

Synthetic Zeolites. Many new cry stalliue zeolites have been. synthesized and several fulfill important functions in the chemical and petroleum industries and in consumer products such as detergents. The structural formula of a zeolite is based on the crystal unit cell, the smallest unit of structure, represented by At, ((Alt), >, (SiO i t/ H 0. where n is the valence of cation M. ir is the number of water molecules per unit cell, v and r are. respectively, the number of AlOa and SiOj tetrahedra per unit cell, and y/v usually has values of 1-5. Examples of important synthetic zeolites are shown in Table I. 

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... 

Using the International Tables for Crystallography describe every atom in terms of the multiplicities and Wyckoff letters of their site positions and establish the content of the unit cell, the simplest chemical formula and the number of formula units (Z) per unit cell. 

The unit cell contains equal numbers of Na+ and CC ions, as required by its chemical formula. Alternatively, we could translate the unit cell by half its length in any axial direction within the lattice, and visualize the unit cell in which sodium and chloride ions have exchanged positions. Such an exchange is not always possible. You should confirm that this alternative description also gives four chloride ions and four sodium ions per unit cell. 

Materials. Four different samples with Al/Si ratios ranging from an extreme Y to an extreme X were supplied by the Linde Co., New York. As they constitute a complete substitutional series, the indications X and Y will not be used further but will be replaced by the symbol F followed by the name of the saturating ion and a figure indicating the number of ions per unit cell. In order to ensure complete saturation, the samples as received were treated with a IN NaCl solution and washed free from excess electrolyte. The chemical composition was determined and expressed in terms of unit cell formula, as follows ... 

The crystal structure of Zr(0H)2(N03)2(H20)4 has been determined (338). Chemically the structure may be considered as consisting of chains of [Zr(0H)2(N03)(0H2)2 ]M, which are joined by nitrate groups through hydrogen bonds. The zirconium atoms are joined by double bridges of hydroxide ions. The coordination number of the zirconium is 8 and the coordination polyhedron is a dodecahedron with triangular faces. There are two formula units per unit cell in the triclinic structure which has a =7.408 A, 6= 11.227 A, c = 6.741 A, with a = 60.91°, j3= 99.78°, and y= 99.78°. 

The nomenclature committee of the American Society for Testing Materials (1957) proposed a nomenclature which expresses the chemical formula followed by the number of atoms per unit cell and the Bravais lattice symbol. This notation was later developed by Schubert (1964) and by Pearson (1967). This symbology may be used for classification purposes and might help to find out if a particular structure type had been determined before, but it does not contain information on the geometry of the structure. 

Table 2.8 gives the highest filled and lowest unfilled energy bands, their widths, the fundamental gap, and the total energy per unit cell of these periodic polypeptides obtained from the ab initio calculations. The chemical formulas of the eight calculated polypeptides are given in Figure 2.6. 

The structural formula is usually reported on the basis of the half unit cell content, i.e. it is based on three octahedral sites. For example Nao.4(Ali.6Mgo.4n)Si40io(OH)2, where represents a vacancy in the octahedral sheet, is the chemical formula per half a unit cell of a synthetic montmoriUonite, a 2 1 dioctahedral phyllosilicate [205]. 

Garnets have the general chemical formula of C3 (A2](D3)Oi2, where O denotes the oxygen atom or ion, and C, A, and D denote cations. There are eight formula molecules per unit cell. Therefore, there are 96 fi-sites which are occupied by oxygens. The point symmetry of the fi-site is 1. The cation sites in the garnet structure are classified into three types of sites. They are ... 

When the composition of a crystal is defined by a distinct chemical formula e.g., Si02), it is known as a stoichiometric compound. If the composition of the crystal is altered upon doping or thermal treatment, the resulting solid may deviate from the original chemical formula, forming a nonstoichiometric solid. Nonstoichiometry and the existence of point defects in a solid are often closely related. For instance, the formation of x anion vacancies per each quartz unit cell will result in the nonstoichiometric compound Si02-x ... 

In the BaAl4 structure with crystal-chemical formula BaAl + Al there are two crystallographically different Al sites, i.e., four tetrahedral sites and four antiprismatic sites per tetragonal unit cell. In the BaAVtype derivatives the Al... 

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