From WolfWikis

Halite: The sodium chloride structure type

The sodium chloride crystal structure is formed by sodium cations filling all of the octahedral holes in a lattice of cubic closest packed chloride anions. In addition it is observed that each chloride anion is surrounded by an octahedron of sodium cations. This packing geometry provides the best cancellation of charge for ions with a coordination number of six, and thus is the structure adopted for highly ionic compounds.

While the sodium chloride structure-type is commonly described as an example of cubic closest packing of anions, the right image of Figure 1 clearly shows that size of the sodium cations is too large for the octahedral holes created by the closest packing. Thus the chloride sub-lattice is expanded such that about 0.5 Å of free space exists between adjacent chloride anions.

Figure 1. Unit cell drawings of the Sodium Chloride crystal structure (left) emphasizing the octahedral coordination geometry of both sodium (purple) and chlorine (orange), and (right) a view showing the space filling representation of the ions.

Many different compounds are known to adopt this basic structure type as highlighted in Table 1. One must consider both the composition, and the relative size of the ions making up the compound to understand the range of compounds that can adopt this structure type. Compositionally, it is clear that a 1:1 stoichiometry is required since in this structure type there are an equal number of octahedral holes as spheres packing.

Table 1. Compounds and their lattice constants (Å) that adopt a halite crystal structure. (Data taken from West: Solid State Chemistry and its Applications (1984) p235)

EUTACTIC STRUCTURES

Using basic trigonometry one can recognize that in the closest packed limit, the edge of the cubic unit cell must be equal to 2r+ + 2r- (where r+ is the radius of the cation and r- is the anion radius). Similarly the face diagonal of such a cube must be equal to 4r-. Therefore, r+ = 0.414 r-. As a result for a compound to adopt the sodium chloride crystal structure the cation must be greater than or equal to 0.414 times the size of the anion. A smaller cation would result in increased anion-anion repulsion which is energetically unfavorable. By contrast, larger cations can result in an expansion of the anion sublattice until the inverse ratio (where r- = 0.414 r+) is achieved. Such structures, in which the arrangement of ions is the same as a close packed array, but in which the ions are not necessarily contacting are known as eutactic structures.

For example, in the case of alkali metal halides shown in Figure 2, it is observed that only LiI comes close to adopting a truly close packed crystalline structure. Nevertheless all of the possible alkali halides can adopt the halite crystal structure since their relative ratio’s fall between the range 0.414  r+/r-  2.414. In the case of CsF which contains the largest alkali metal cation and smallest halide anion, it is best to describe this material as adopting the anti-halite structure type. The anti-type being the structure obtained by the reversal of the anion and cation positions.

Figure 2. Eutactic structures of the alkaki metal halides.

NaCl vs. CsCl

CsCl with a radius ratio of approximately 1, can under certain conditions be made to adopt a halite structure-type. However, from the perspective of the packing of hard spheres, one observes a simple cubic packing of the anions and cations, which is very inefficient with respect to filling space (only 52% packing efficiency). A higher packing efficiency can be achieved by compression along a body diagonal such that two additional anions that capped octahedral faces are moved into the cations coordination sphere resulting in cubic coordination. In this body-centered cubic type packing in which each cation is surrounded by a cube of anions (and each anion is surrounded by a cube of cations) a 68% packing efficiency for equal sized cations and anions is achieved, as shown in Figure 3. This crystalline structure is known as the CsCl structure type. The CsCl structure-type is possible for ions whose radius ratio is intermediate between 0.73 and 1.37.

Figure 3. Comparison of the NaCl and CsCl structure types, and table of the radius ratios of alkali metal halides. All compounds can adopt the NaCl structure type. However only those compounds highlighted in blue can adopt the CsCl structure-type.

DISTORTIONS TO THE HALITE STRUCTURE-TYPE

Cations with Lone Pairs.

As described above, the sodium chloride structure type is the ideal structure for ionic compounds with the ions radius ratio’s that favor a coordination number of six. However, elements of this structure-type can also be observed in compounds for which lone pairs on the cation distort it from a spherical geometry. The Tl+ cations in TlI have one lone pair that requires distortion from the NaCl structure to minimize repulsion between the Tl lone pair and I- anions. As a result, instead of six equivalent Tl-I contacts, a square based pyramidal geometry with one Tl-I contact of 3.36Å and four at 3.49Å make up a double layer NaCl-type structure, as shown on the left in Figure 4. These NaCl-type sheets are diagonally displaced such that the lone-pair is in-between two I anions in the layer above or below with Tl-I contacts of 3.87Å. This also provides for two Tl-lone pair to Tl cation contacts of 3.83Å.

Figure 4. (left) representation of the TlI crystal structure showing the square-based pyramidal coordination of Tl (purple) as well as the double-layer type distortion of the NaCl-type lattice. (right) representation of the PbO type structure. The Pb cations (blue) exhibit a square pyramidal coordination, with the lone pairs requiring a single-layer type distortion of the NaCl-type lattice.

Pb2+ also has one lone pair that occupies a finite volume in the red-PbO crystal structure. Unlike Tl, in the example above, Pb2+ and O2- are nearly the same size. To accommodate both the relative size of the ions, and the lone-pair of the cations, the metal cation is distorted out of the plane of the oxygens resulting is a square pyramidal coordination of the lead cations. In any given layer, the arrangement of the lead and oxygen atoms is equivalent to the face-centered network of the NaCl structure type, albeit with the cations distorted alternately above and below the oxygen anion plane. However, to accommodate the cation’s large size and lone pair, every other layer of a NaCl-structure type is vacant in this PbO structure-type.

Metal-Metal Bonding

Figure 5. Unit cell of the structure of NbO. O atoms are red, Nb atoms yellow, and the Nb-Nb bonding forming an octahedral cluster is shown in blue.

Additional structural distortions are possible when the cation contains valence electrons that can form additional chemical bonds, as opposed to being stable as a non-bonding lone pair. Consider, for example the compound NbO. In a 2+ oxidation state (after forming the Nb-O bonds), the Nb cations have three electrons that are available to form metal-metal bonds. Interestingly NbO and NaCl exhibit essentially the identical cation/anion radius ratio of 0.69. As shown in Figure 5, this is accomplished by removing one quarter of the cation and anion sites found in the basic NaCl unit cell. Metal-metal bonds are then formed between Nb cations forming an octahedral cluster around the site from which an anion was removed. It is further important to recognize that each Nb participates in forming an octahedral cluster in the neighboring unit cell as well, such that in NbO one observes a network of corner-shared octahedral niobium clusters.

NaCl Structure-type with multiple metal cations

Not surprisingly, the halite structure type can be observed for materials in which the octahedral holes are filled with different types of cations. Most simply, there may be a completely random distribution of two different cations as observed for LiFeO2 and Li2TiO3. This generally will require cations that are reasonably similar in size. By contrast when multiple metal cations are of different size, or exhibit distinct bonding characteristics, super-structures of the NaCl-structure are observed. The example of LiNiO2, shown in Figure 6, shows a rhombohedral distortion of the cubic-close packed arrangement of oxide anions. Li and Ni cations fill the octahedral holes between oxide layers in alternating layers. Such structural arrangements are critical to the materials properties, for example giving rise to low dimensional magnetism and both electronic and ionic conductivity.

Figure 6. Structure of LiNiO2 which exhibits an ordering of the Li and Ni cations into distinct layers exhibiting a rhombohedral superstructure of the NaCl structure-type.