The halite structure

It is important to note that in the halite-structure materials the displacement sequence is along a close-packed direction enabling momentum transfer to occur such that the interstitial becomes separated from the vacancy by several atomic positions. In the fluorite-structure compounds and in crystalline SiC however, such a displacement sequence is not possible since the STE is not aligned along a close-packed direction. As a result stable, well-separated interstitials and vacancies are very unlikely in these materials at all but the very lowest temperatures. Transient defect formation only is observed (9,16). 

A third series of perovskite related intergrowths has a general formula A B 03 +2, where A is a large cation, and B a medium sized cation, typified by the (Na,Ca) Nb 03 +2 series. The oxides are intergrowths of slabs of perovskite stracture with the halite structure. They differ from the Ruddleston-Popper series in that the (idealized) perovskite slabs are sliced along 110 rather than 100. ... 

The misfit layer compounds are typified by materials with a formula MS +fiTS2)m, in which T is a transition metal atom, Ti, V, Cr, Nb, or Ta, and M is a large atom such as Sn, Pb, Bi, with stereochemically active electron lone pairs, or a lanthanide. The structures are built from S-T-S layers, in which the metal T takes trigonal-prismatic coordination. These layers are interleaved with layers of the halite structure, usually two or three atom layers in thickness, with composition MSx. This leads to a chemical formula of [MSx]n(71S 2)m, where n varies from approximately 1.08-1.24, and m takes values of 1-3, depending upon the nature of T and M. A typical example is the compound [(Lni/3Sr2/3S)i.5]i.i5 NbS2. In all of the misfit layer compounds, the lattice parameter of the interpolated halite layers fit one lattice parameter of the rS2 layer but not the other, so that in this direction, the... 

FCj O or wiistite has probably the most studied defect structure. The hypothetical compound where x = 0 would crystallize with a perfect version of the halite structure where iron lies in an octahedral site surrounded by oxygen atoms. Removal of some of the iron should just give iron vacancies with the remaining irons remaining in an octahedral environment. 

A The halite structure consists of a cubic close-packed lattice where all octahedral holes are filled. However, the tetrahedral holes which are generated by a cubic close-packed array of spheres (Chapter 1) will be empty. There are a number of available holes, for example... 

VOj, jc = 0.1, has an oxygen-deficient lattice based on the halite structure. The distribution of vacancies is random at very high temperature, but they cluster together, along certain directions, as the temperature falls. 

TiO, where 0.7 < x < 1.25, crystallizes with the sodium chloride structure. By consideration of the incorporation of vacancies into the halite structure, describe how defects could be incorporated to give the formulae at the extremes of the values of x. 

Defects are incorporated into the halite structure by formation of vacancies on the normal lattice sites. When x = 0.7, there are simply vacancies in the oxide sublattice. When x = 1.25, which can be rewritten by dividing the formula by 1.25 as Ti gO, the vacancies are on the cation sublattice. 

Sodium chloride forms crystals with cubic symmetry. In these, the larger chloride ions are arranged in a cubic close-packing, while the smaller sodium ions fdl the octahedral gaps between them. Each ion is surrounded by six of the other kind. This same basic structure is found in many other minerals, and is known as the halite structure. 

The general formula of crystals with the halite structure is MX. The mineral halite, which names the group, is sodium chloride, NaCl, also called rock salt. 

There are four sodium and four chlorine atoms in the unit cell. For all materials with the halite structure, Z = 4. In this structure, each atom is surrounded by six atoms of the opposite type at the comers of a regular octahedron (see Chapter 7). A perspective view of the halite structure is shown in Figure 1.10a, and a projection, down the c-axis, in Figure 1.10b. 

The unit cell of the halite structure contains 4 sodium (Na) and 4 chlorine (Cl) atoms. The mass of the unit cell, m, is then given by ... 

The number of atoms in the unit cell of the halite structure is ... 

Systematic absences arise from symmetry considerations and always have F(hkl) equal to zero. They are quite different from structural absences, which arise because the scattering factors of the atoms combine so as to give a value of F(hkl) = zero for other reasons. For example, the (100) diffraction spots in NaCl and KC1 are systematically absent, as the crystals adopt the halite structure, which is derived from an all-face centred (F) lattice, (see Table 6.4). On the other hand, the (111) reflection is present in NaCl, but is (virtually) absent in KC1 for structural reasons - the atomic scattering factor for K+ is virtually equal to that of Cl-, as the number of electrons on both ions is 18. 

A small particle of CrN, which has the halite structure (see Chapter 1) with a = 0.4140 nm, gives a reflection from the (200) planes at an angle of 33.60°. The angular range over which the reflection occurs is approximately 1.55°. (a) Calculate the wavelength of the radiation used, (b) Estimate the size of the particle in a direction normal to the (200) planes. 

Should the anions adopt hexagonal close-packing and all of the octahedral sites contain a cation, the hexagonal analogue of the halite structure is produced. In this case, the formula of the crystal is again MX. The structure is the nicolite, (NiAs), structure, and is adopted by a number of alloys and metallic sulphides, including NiAs, CoS, VS, FeS and TiS. 

Model A Assume that the iron atoms in the crystal are in a perfect array, identical to the metal atoms in the halite structure and an excess of oxygen is due to interstitial oxygen atoms over and above those on the normal anion positions. The ideal unit cell of the structure contains 4 Fe and 4 O, and so, in this model, the unit cell must contain 4 atoms of Fe and 4(1+x) atoms of oxygen. The unit cell contents are Fc404+4a and the composition is FeOi.059-... 

Model B Assume that the oxygen array is perfect and identical to the non-metal atom array in the halite structure and that the unit cell contains some vacancies on the iron positions. In this case, one unit cell will contain 4 atoms of oxygen and (4-4x) atoms of iron. The unit cell contents are Fc4 4a04 and the composition is Fei/i.058O1.0 or Feo.9440. 

Data are presented in five tables. Table 1 lists the main crystallographic and semiconducting properties of a large number of semiconducting materials in three main categories Tetrahedral Semiconductors in which every atom is tetrahedraUy coordinated to four nearest neighbor atoms (or atomic sites) as for example in the diamond structure Octahedral Semiconductors in which every atom is octahedrally coordinated to six nearest neighbor atoms—as for example the halite structure and Other Semiconductors. ... 

Consider the structures that arise from a cubic close-packed array of X anions. If every octahedral position contains an M cation there are equal numbers of cations and anions in the structure. The formula of the compounds with this structure is MX, and the structure corresponds to the halite (NaCl, Bl) structure. In the case of halide anions, X, to maintain charge balance, each cation must have a charge of +1, and the alkali halide, MX, structure results. Should oxygen anions, 0, form the anion array, the cations must necessarily have a charge of 2- -, to ensure that the charges balance, and the oxides will have a formula MO, but still retain the halite structure. This structure is possessed by a number of oxides, including MgO, CaO, SrO, BaO, MnO, FeO, CoO, NiO and CoO. 

The unit cell size of CaO is 0.48105 nm, and that of SrO is 0.51602 nm. Both adopt the halite structure type. Estimate the composition of a crystal of formula Ca cSri cO, which was found to have a unit cell of 0.5003 nm. 

Although ionic solids themselves cannot form closest-packed structures, that does not prevent them from trying. Many ionic solids can be represented as closest-packed arrays of one type of ion with the other type of ion occupying vacancies (or holes) in this lattice. Thus, for example, the halite structure, shown in Figure 12.1, consists of a face-centered cube of chloride ions with the smaller sodium ions distributed in one type of vacancy that exists within the lattice. 

---