The NaCl Structure

One above the chloride, one below the chloride, and four in the middle horizontal plane. 

Although aU of the ions surrounding any one sodium ion are not shown, how many chloride ions must surround each sodium ion  

There is a one-to-one ratio of sodium ions to chloride ions and therefore the coordination numbers of each must be the same. The coordination number of six for the sodium ion in NaCl should also be obvious because we know that the sodium ions are present in the octahedral holes of the closest packed chloride ions. 

How many sodium ions and chloride ions are in the unit cell  

There are four sodium ions and four chloride ions. The sodium ion on a particular comer is shared by eight cubes. This is shown below, where a sodium ion is at the center of eight cubes, each of which represents a unit cell. Thus, each of the comer sodium ions contributes one-eighth of an ion to the unit ceU. There are eight of these thus, 8x1/8 = 1. 

---

Titanium II) oxide, TiO. Has the NaCl structure but is non-stoicheiomeiric (Ti02 plus Ti). 

The lanthanoids also form metal-rich carbides of stoichiometry M3C in which individual C atoms occupy at random one-third of the octahedral Cl sites in a NaCl-like structure. Several of the actinoids (e.g. Th, U, Pu) form monocarbides, MC, in which all the octahedral Cl sites in the NaCl structure are occupied and this stoichiometry is also observed for several other carbides of the early transition elements, e.g. M = Ti, Zr, Hf V, Nb, Ta Mo, W. These... 

Monochalcogenides, LnZ (Z = S, Se, Te), have been prepared for all the lanthanides except Pm, mostly by direct combination.They are almost black and, like the monoxides, have the NaCl structure. However, with the exceptions of SmZ, EuZ, YbZ, TmSe and TmTe, they have metallic conductivity and evidently consist of Ln -t- Z ions with 1 electron from each cation delocalized in a conduction band. EuZ and YbZ, by contrast, are semiconductors or insulators with genuinely divalent cations, but SmZ seem to be intermediate and may involve the equilibrium ... 

Turning next to an ionic crystal, where the ions may be regarded as spheres, the total volume of the crystal is equal to the volumes of these spheres, together with the appropriate amount of void space between the spheres. To take the simplest case, it is convenient to discuss a set of substances, all of which have the same crystalline structure—for example, the 17 alkali halide crystals that have the NaCl structure. 

As expected from the similarity of ionic radii between Ag+ (1.15 A) and Na+ (1.01 A), one form has the NaCl structure (it is trimorphic) with other forms having the CsCl and inverse NiAs structures. Unlike the other silver(I) halides, it is very soluble in water (up to 14 M) and forms di- and tetra-hydrates it is decomposed by UV rather than visible light and melts unchanged at 435°C. 

TIO is cubic with the NaCl structure. A sample was annealed at 1300 °C. Density and X-ray measurements revealed that the intrinsic defects were Schottlqr in nature (Vxi + Vq) and that their concentration was 0.140. In... 

The structure of calcite (CaC03) can be derived from the NaCl structure by substituting the Cl- ions for CO2- ions. These are oriented perpendicular to one of the space diago-... 

Further examples where these rules are observed are as follows. Under pressure, some compounds with zinc blende structure, such as AlSb and GaSb, transform to modifications that correspond to the J3-Sn structure. Others, such as InAs, CdS, and CdSe, adopt the NaCl structure when compressed, and their atoms thus also attain coordination number 6. Graphite (c.n. 3, C-C distance 141.5 pm, density 2.26 gem-3) pr Te diamond (c.n. 4, C-C 154 pm, 3.51 gem-3). 

Whereas AgCl has the NaCl structure, Agl has the zinc blende structure. Could you imagine conditions under which both compounds would have the same structure ... 

Under pressure Agl could adopt the NaCl structure (it actually does). 

Figure 9.4 Mid-glide electrostatic faulting in the NaCl structure on the (100) planes.

The carbides with the NaCl structure may be considered to consist of alternating layers of metal atoms and layers of semiconductor atoms where the planes are octahedral ones of the cubic symmetry system. (Figure 10.1). In TiC, for example, the carbon atoms lie 3.06A apart which is about twice the covalent bond length of 1.54 A, so the carbon atoms are not covalently bonded, but they may transfer some charge to the metal layers, and they do increase the valence electron density. 

In all of these oxide phases it is possible that departures from the simple stoichiometric composition occur through variation of the charges of some of the cationic species. Furthermore, if a cation is raised to a higher oxidation state, by the addition of oxygen to the lattice, a corresponding number of vacant cation sites must be formed to compensate the structure. Thus in nickel oxide NiO, which at stoichiometric composition has only Ni2+ cations, oxidation leads to Ni3+ ion formation to counterbalance the addition of extra oxide ions. At the same time vacant sites must be added to the cation lattice to retain the NaCl structure. This balanced process can be described by a normal chemical equation thus... 

At all temperatures above 0°K Schottky, Frenkel, and antisite point defects are present in thermodynamic equilibrium, and it will not be possible to remove them by annealing or other thermal treatments. Unfortunately, it is not possible to predict, from knowledge of crystal structure alone, which defect type will be present in any crystal. However, it is possible to say that rather close-packed compounds, such as those with the NaCl structure, tend to contain Schottky defects. The important exceptions are the silver halides. More open structures, on the other hand, will be more receptive to the presence of Frenkel defects. Semiconductor crystals are more amenable to antisite defects. 

Burgers vector b, [101], is the shortest vector connecting two identical atoms in this structure. (.b) An edge dislocation in the NaCl structure, consisting of two extra half-planes of atoms. If these are ionic, the tip will bear a charge, depending upon the ions in the termination, and slip will occur on 110. ... 

When the structure is viewed down [111], the oxygen atoms can be seen to form close cubic packed layers, emphasizing the relationship with the NaCl structure. 

The reference to the structure type may be a simpler and more convenient way of describing the structure of the specific phase. The structure type is generally named after the formula of the first representative identified the prototype . Expressions such as KC1 has the NaCl structure type are frequently used. Trivial names and symbols may also be found in several cases. 

Figure 3.38. Experimental densities of titanium oxides (continuous lines). The upper dotted line gives the values computed for a 100% occupancy of the cation sites in the NaCl structure type (from Hyde and Andersson 1989).

Sulphides. The partially ionic alkali metal sulphides Me2S have the anti-fluorite-type structure (each Me surrounded by a tetrahedron of S, and each S atom surrounded by a cube of Me). The NaCl-structure type (6/6 coordination) is adopted by several mono-sulphides (alkaline earth, rare earth metals), whereas for instance the cubic ZnS-type structure (coordination 4/4) is observed in BeS, ZnS, CdS, HgS, etc. The hexagonal NiAs-type structure, the characteristics of which are described in 7.4.2.4.2, is observed in several mono-sulphides (and mono-selenides and tellurides) of the first-row transition metals the related Cdl2 (NiAs defect-derivative) type is formed by various di-chalcogenides. Pyrite (cP 12-FeS2 type see in 7.4.3.13 its description, and a comparison with the NaCl type) and marcasite oP6-FeS2 are structural types frequently observed in several sulphides containing the S2 unit. 

The comparison of the measured and calculated Vickers hardnesses is of acceptable quality. With this physical model of the hardness it should also be possible to compute the Vickers hardnesses of salts with a more complicated lattice structure than the NaCl-structure. This may be an approach for a description of the abrasion resistance of salts. Such a description of the abrasion resistance could be useful in calculating the secondary nucleation rates. 

In essence two types of carbonitride are formed in a Ti,Nb-hardened micro-alloyed steel. At high temperatures a predominantly TiN-rich carbonitride is formed. However, on cooling to lower temperatures a predominantly NbC-iich carbonitride also precipitates. Both caibonitrides are based on the NaCl structure and form part of a continuum usually described by a formula such as (TixNb. xXCzNi.2). This can be expanded to include elements such as V and Ta, so the formula becomes (TazTiyNb Vi.,. z)(CzNi.z). The formation of two types of carbonitride can be consisted due to phase separation and Fig. 10.54 shows a projected miscibility... 

---