Common crystal-chemical formulae. Unit cell volumes and interatomic distances

3 Common crystal-chemical formulae. Unit cell volumes and interatomic distances. In the analysis and description of a structure some calculation may be useful. A few common formulae are collected here. 

1 Volume of the unit cell (VcM). This may be calculated from the unit cell constants by using the following formulae. From this the density (/ ) of the compound may be obtained p = Mcc /FccM, where MceH is the mass of the matter in the unit cell, that is the sum of the masses of all the atoms contained. The mass of an individual atom is calculated in grams by the ratio of the atomic molar mass and the Avogadro number. 

2 Examples of alternative descriptions of the unit cell In a number of cases, in order for instance, to compare a given atomic distribution and arrangement with several others, it may be useful to use different descriptions of the same structure (to refer to different, but obviously equivalent, unit cells). The transformations (of the unit cell constants and, consequently, of the coordinates of the atomic positions) are described, for the general case, for instance, in the International Tables (Hahn 2002). A few, frequently used, transformation formulae of the unit cell constants are reported here. 

Description of a rhombohedral unit cell in terms of the equivalent, triple-primitive, hexagonal cell (see Fig. 3.9). 

A detailed example of the alternative descriptions of a given compound, both in terms of its hexagonal unit cell and of the corresponding rhombohedral primitive cell is presented in Chapter 4 the rhombohedral compound Mo6PbSx (the prototype of the family of the so-called Chevrel phases) is described and unit cell constants and atomic positions are listed for its conventional hexagonal cell and for the rhombohedral primitive cell. 

---