Matters exist in solid state because of close packing of their constituent particles. There are two types of close packing found in solids. These are Cubic Close Packed (ccp) and Hexagonal Close Packed (hcp) lattice.
In this type of packing, the spheres of molecules are adjacent to each other that each row of spheres in a particular dimension is a repetition of the pervious row. The spheres of a particular row don’t fit in the depressions between two adjacent spheres of the previous row. This types of arrangement is called AAAA type arrangement. This is also known as face centered cubic (fcc). This type of close packing of constituent particles is found in metals like copper, silver, etc.
Lattice of this cubic close packed is simple cubic and its unit cell is primitive cubic unit cell.
In this type of packing, the spheres of molecules of a particular row in a particular dimension are in a position that they fit into depressions between adjacent spheres of the previous row. This type of arrangement is called ABAB type arrangement. This type of packed lattice is found in many metals such as magnesium, zinc, etc.
Coordination number: The number of adjacent particles of atoms is called coordination number.
In both ccp and hcp, each sphere is surrounded by 12 adjacent atoms, thus coordination number is equal to 12 in each case.
Empty space left after the packing is called void. Two types of voids are formed in ccp and hcp structures. These are tetrahedral voids and octahedral voids.
Tetrahedral voids are formed because of formation of tetrahedron between the layers of atoms. Thus, voids in the shape of tetrahedron are called tetrahedral voids.
Octahedral voids are formed because of formation of octahedron between the layers of atoms. Thus, voids in the shape of octahedron are called octahedral voids.
The number of formation of voids depends upon the number of close packed spheres. The number of tetrahedral voids is formed twice as the number of octahedral voids while close packing of atoms in ccp and hcp structures.
Thus, if number of close packed spheres is equal to ‘N’.
Therefore, number of octahedral voids formed = N
And, the number of tetrahedral voids formed = 2N
Formula of a compound and number of voids filled:
Bigger ions, usually anions, form close packed structure and smaller ions, usually cations occupy the voids in ionic solids. If cations are bigger in size, they occupy octahedral voids and if are smaller enough then they occupy tetrahedral voids.
The occupation of number of voids depends upon the chemical formula of compound. It may be possible to occupy all the voids or fraction of voids.
(a) If cation of an ionic solid occupies all the octahedral voids, then the formula of the compound can be obtained as follows:
Let ‘A’ are cations and ‘B’ are anions in the compound.
Since the number of close packed sphere is equal to the number of octahedral voids formed, thus the cations and anions must be in the ratio of 1:1.
Therefore, A and B will be combined in the ratio of A:B.
Thus the formula of the compound will be AB.
(b) If there are two ions A and B in an ionic compound and cations occupy all the tetrahedral voids formed because of close packing, then the formula of the compound can be obtained as follows:
Let A is the cation and B is the anion in given compound.
Since, number of tetrahedral voids formed = 2 X number of close packed spheres.
This means A and B will combined in the ratio of 1:2
Therefore, formula of the compound will be AB2
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