SPINEL STRUCTURE :

(1) Structure of FeO, Fe₂O₃, and Fe₃O₄  :

(1) FeO: This oxide is non-stoichiometric and has a composition FexO (Generally ‘x’ varying from0.92 to 0.97). The oxide ions form a cubic close packing. The octahedral voids are occupied by Fe2+ but a small number of Fe²⁺ is replaced by Fe³⁺ ions. Three Fe²⁺will be replaced by two Fe³⁺ to maintain electrical neutrality but then what we obtain is an iron-deficient crystal.

(2) Fe₂O₃: If all Fe2+ are replaced by Fe3+, the ratio between Fe:O will be 2 : 3 (since 3 Fe²⁺ are replaced by 2Fe³⁺⁾ and not 1 : 1. As such, we obtain Fe₂O₃.

(3) Fe₃O₄: This is obtained by replacing exactly two thirds of Fe²⁺ by Fe³⁺ (in FeO structure).The remaining Fe²⁺ ions and 50% of Fe³⁺ ions occupy the octahedral voids. The remaining Fe³⁺ ions occupy tetrahedral voids. If in the structure of Fe₃O₄, the Fe²⁺ ions are replaced by divalent cations such as Mg^2+, Zn^2+, etc., the compounds obtained are called ferrites. In ferrites, divalent cations occupy tetrahedral voids and trivalent cations occupy octahedral voids. This structure is called spinel structure.

(2) NORMAL SPINEL (AB₂O₄ ) STRUCTURE:

Example of Spinel is a MgAl₂O₄.( mineral) In it oxide ions (O^-2) are arranged in ccp with Mg⁺² ions occupying tetrahedral voids and Al⁺³ ions in a set of octahedral voids.

Many ferrites (such as ZnFe₂O₄) also possess spinel structure. These are very important magnetic materials and are used in telephone and memory loops in computers.

(3) INVERSE SPINEL STRUCTURE (Fe₃O₄-Magnetite):

In Fe₃O₄, Fe⁺² and Fe⁺³ ions are present in the ratio 2:1. it may be considered as having composition FeO.Fe₂O₃. In Fe₃O₄ Oxide arranged in ccp. Fe⁺² ions occupy octahedral voids while Fe⁺³ ions are equally distributed between octahedral and tetrahedral voids

MgFe₂O₄ also has structure similar to magnetite. In this Mg⁺² ions are present in place of Fe⁺² ion in Fe₃O₄. Magnetite has inverse spinet structure.

ANTIFLUORITE STRUCTURE (REVERE OF FLUORITE) Na2O:

The compound having A₂B formula are compounds having anti fluorite structure :

Anti fluorite structure is having arrangement of cations and anions opposite to the fluorite structure Li₂O has an anti fluorite structure.

(1)  In the crystal structure of Li₂O, the O^-2 ions constitute a cubic close packed lattice (fcc structure) and the Li⁺ ions occupy all the tetrahedral voids

(2)  Each oxide ion, O^-2 ion is in contact with 8 Li⁺ ions and each Li⁺ ions having contact with 4 oxide ion. Therefore, Li₂O has 4:8 coordination
(3) Stoichiometric ratio  of Na₂O is 2:1
(4)  radius ratio , Packing efficiency, density and void %:

 Other Examples: – Na₂O, K₂O, K₂S, Na₂S, Rb₂O, Rb₂S

Note: Metals like Al, Ag, Au, Cu, Ni, and Pt have ccp structure and Be, Mg, Co and Zn have a hcp structure. And Noble gases (except He has a hcp structure) have ccp structure.

CALCIUM FLORIDE (FLORITE) STRUCTURE:

The salient features of fluorite structure are:

(1)  The Ca⁺² ions are arranged in ccp arrangement, i.e. these ions occupy all the corners and the centres of each face of the cube

(2)  The F^– ions occupy all the tetrahedral holes.

(3)  Since there are two tetrahedral holes for each Ca⁺² ion and F^- ions occupy all the tetrahedral holes, there will be two F^- ions for each Ca⁺² ions, thus the stoichiometry of the compound is 1:2.

(4) Each Ca⁺² ion is surrounded by 8F^- ions and each F^- ions is surrounded by 4Ca⁺² ions. The Coordination number of Ca⁺² ion is eight and that of F^- ion is four, this is called 8:4 Coordination.

 (5) Each unit cell has 4 calcium ions and 8 fluoride ions so formula of unit cell is Ca₄F₈ which is explained as  below

      No. of Ca⁺² ions = 8(at corners)´1/8 + 6 (at face centres)´1/2

      No. of F ions = 8 (within the body)´1 = 8

      Thus the number of CaF₂ units per unit cell is 4.

(6) Radius Ratio, packing efficiency ,void % and density:

Other examples: of structure are SrF₂, BaCl₂, BaF₂, PbF₂, CdF₂, HgF₂, CuF₂, SrCl₂, etc.

CAESIUM CHLORIDE (CsCl) STRUCTURE:

The caesium chloride crystal is composed of equal number of caesium (Cs⁺) and Chloride Cl^- ions. The radii of two ions (Cs⁺ = 169 pm and Cl^- = 181 pm) led to radius ratio of Cs+ to Cl- as 0.93 which suggest a body centred cubic structure having a cubic hole

The salient features of this structure are as follows:

(1)  The chloride ion form the simple cubic arrangement and the caesium ions occupy the cubic interstitial holes. In other words Cl^- ions are at the corners of a cube whereas Cs⁺ ion is at the centre of the cube or vice versa

(2)  Each Cs⁺ ion is surrounded by 8 Cl^- ions and each Cl^- ion in surrounded by 8 Cs⁺ ions. Thus the Co – ordination number of each ion is eight. 

(3)  For exact fitting of Cs⁺ ions in the cubic voids the ratio r Cs⁺/rCl^-  should be equal to 0.732. However, actually the ratio is slightly larger (0.93). Therefore packing of Cl^- ions slightly open up to accommodate Cs⁺ ions.

(4)  The unit cell of caesium chloride has one Cs⁺ ion and one Cl^- ion as calculated below

      No. of Cl^- ion = 8(at corners) ´1/8 = 1

      No. of Cs⁺ ion = 1(at body centre)´1=1

      Thus, number of CsCl units per unit cell is 1

(5)  Relation between radius of cation and anion and edge length of the cube,

Effect of temperature on crystal structure:

Increase of temperature decreases the coordination of number, e.g. upon heating to
760 K, the CsCl type crystal structure having coordination 8:8 changed to NaCl type crystal structures having coordination 6:6.

Effect of pressure on crystal structure:

Increase of pressure increases the Co – ordination number during crystallization e.g. by applying pressure, the NaCl type crystal structure having 6:6 coordination number changes to CsCl type crystal having coordination number 8:8

Other common examples  of this type of structure are CsBr, CsI, TlCl, TlBr, TlI and TlCN

      Higher coordination number in CsCl(8:8) suggest that the caesium chloride lattice is more stable than the sodium chloride lattice in which Co – ordination number is 6:6. Actually the caesium chloride lattice is found to be 1% more stable than the sodium chloride lattice. Then the question arises why NaCl and other similar compounds do not have CsCl type
lattice – This is due to their smaller radius ratio. Any attempt to pack 8 anions around the relatively small cation (Li⁺, Na⁺, K⁺, Rb⁺) will produce a state in which negative ions will touch each other, sooner they approach a positive ion. This causes unstability to the lattice.   

THE WURTIZE STRUCTURES (ZnS):

It is an alternate form in which ZnS occurs in nature. The main features of this structure are

                                    A unit cell representation of wurtzite structure

(1) Sulphide ions have HCP arrangement and zinc ions occupy tetrahedral voids.

(2)  Only half the alternate tetrahedral voids are occupied by Zn⁺² ions.

(3)  Coordinate no. of Zn⁺² ions as well as S^-2 ions is 4. Thus, this structure has 4 : 4 coordination.

(4)  No. of Zn⁺² ions per unit cell: 

                                 = 4(within the unit cell) ´1 + 6(at edge centres) ´1/3  = 6

(5) No. of S^-2 ions per unit cell =

                                 = 12(at corners) ´1/6 +2 (at face centres) ½ +3 (within the unit cell)1=6

                            Thus, there are 6 formula units per unit cell.