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.

ZINCE BLENDE (ZnS) TYPE STRUCTURE (SPHELERITE):

The zinc sulphide crystals are composed of equal number of Zn⁺² and S^2- ions. The radii of the two ions (Zn⁺² = 74 pm and S^-2 = 184 pm) led to the radius r⁺/r^- as 0.40 which suggests a tetrahedral arrangement.

The salient features of this structure are as follows:

(1)The Sulphide ions are arranged in ccp arrangement, i.e. sulphide ions are present at the corners and the centres of each face of the cube  

(2)  Zinc ions occupy tetrahedral hole. Only half (50 %) of the tetrahedral holes are occupied by Zn⁺² so that the formula of the zinc sulphide is ZnS i.e. the stoichiometry of the compound is 1:1 (Only alternate tetrahedral holes are occupied by Zn⁺²)

(3)  Since the void is tetrahedral, each zinc ion is surrounded by four sulphide ions and each sulphide ion is surrounded tetrahedrally by four zinc ions. Thus zinc sulphide has [4:4] Coordination.

(4)  For exact fitting of Zn⁺² in the tetrahedral holes, formed by close packing of S^-2 ions, the ratio Zn⁺²/S^-2 should be 0.225. Actually this ratio is slightly large (0.40)

(5)  There are four Zn⁺² ions and four S^-2 ions per unit cell as calculated below:

      No. of S^-2 ions = 8(at corners)´1/8 + 6(at face centres)´1/2 = 4

      No. of Zn⁺² ions = 4 (within the body)´1 = 4

(6) Density, Packing efficiency (PE) and Void % ;

Examples: Thus, the number of ZnS units per unit cell is equal to 4. Some more examples of ionic solids having Zinc blende structures are CuCl, CuBr, CuI, AgI, BeS (beryllium sulphide).

ILLUSTRATIVE EXAMPLE:       If silver iodide crystallizes in a zinc blende structure with I^- ions forming the lattice then calculate fraction of the tetrahedral voids occupied by Ag⁺ ions.

SOLUTION:      In AgI, if there are nI^- ions, there will be nAg⁺ ions. As I^- ions form the lattice, number of tetrahedral voids = 2n. As there are nAg⁺ ions to occupy these voids, therefore fraction of tetrahedral voids occupied by Ag⁺ ions = n/2n = ½ = 50%.