The rock salt NaCl structure type

The complete NaCl stmcture is built up by placing unit cells next to one another so that ions residing in the comer, edge or face sites (Fig. 6.16b) are shared heisf/een adjacent unit cells. Bearing this in mind, Fig. 6.16b shows that each Na and CU ion is 6-coordinate in the crystal lattice, while within a single unit cell, the octahedral environment is defined completely only for the central Na ion. 

Among the many compounds that crystallize with the NaCl stmcture type are NaF, NaBr, Nal, NaH, halides of 

Worked example 6.3 Compound stoichiometry from a unit cell 

Show that the structure of the unit cell for sodium chloride (Fig. 6.16h) is consistent with the formula NaCl. 

In Fig. 6.16b, 14 Q ions and 13 Na ions are shown. However, all but one of the irais are shared between two or more unit cells. 

In salts of formula MX, the coordination numbers of M and X must be equal. 

The method of X-ray diffraction is widely used for the determination of the structures of molecular soUds (i.e. solids composed of discrete molecules) and of non-molecular solids (e.g. ionic materials). As the technique has been developed, its range of applications has expanded to include polymers, proteins and other macromolecules. The reason that X-rays are chosen for these experiments is that the wavelength (p lO m) is of the same order of magnitude as the internuclear distances in molecules or non-molecular solids. As a consequence of this, diffraction is observed when X-rays interact with an array of atoms in a soUd (see below). 

X-rays are scattered by electrons surrounding the nuclei. Because the scattering power of an atom depends on the number of electrons, it is difficult (often impossible) to locate H atoms in the presence of heavy atoms. 

In the diagram opposite, an ordered array of atoms is represented simply by black dots. Consider the two waves of incident radiation (angle of incidence = 0) to be in-phase. Let one wave be reflected from an atom in the first lattice plane and the second wave be reflected by an atom in the second lattice plane as shown in the diagram. The two scattered waves will only be in-phase if the additional distance travelled by the second wave is equal to a multiple of the wavelength, i.e. n. If the lattice spacing (i.e. the distance between the planes of atoms in the crystal) is d, then by simple trigonometry, we can see from the diagram opposite that  

For the two waves (originally in-phase) to remain in-phase as they are scattered  

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