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RADIUS RATIO RULES IN IONIC SOLIDS:

The structure of many ionic solids can be accounted by considering the relative sizes of the cation and anion, and their relative numbers. By simple calculations, we can work out as how
Many ions of a given size can be in contact with a smaller ion. Thus, we can predict the coordination number from the relative size of the ions.
Following conditions must be satisfied simultaneously during the stacking of ions of different sizes in an ionic crystal:
(1) An anion and a cation are assumed to be hard spheres always touching each other.
(2) Anions generally will not touch but may be close enough to be in contact with one another in a limiting situation.
(3) A cation should surround itself with as many anions as possible. Each ion tends to surround itself with as many ions of opposite sign as possible to reduce the potential energy. This tendency promotes the formation of close-packed structures.
(4)The ratio of the cation to that of the anion is called RADIUS RATIO.
(5) Eventually greater is the radius , the larger is the size of cation and hence greater is it's coordination number.
(6)The relationship between the radius and coordination number and structural arrangement are called radius ratio rule and are given as table below.
RADIUS RATIO AND COORDINATION NUMBER:
ILLUSTRATIVE EXAMPLE (1): The two ions A+ and B- have radii 88 and 200 pm respectively. In the close packed crystal of compound AB, predict the coordination number of A+.
SOLUTION:

                        It lies in the range of 0.414 – 0.732
                        Hence, the coordination number of A+ = 6
ILLUSTRATIVE EXAMPLE(2): Br- ion forms a close packed structure. If the radius of Br- ions is 195 pm. Calculate the radius of the cation that just fits into the tetrahedral hole. Can a cation A+ having a radius of 82 pm be slipped into the octahedral hole of the crystal A+ Br-?
SOLUTION: (1)  Radius of the cations just filling into the tetrahedral hole
                              = Radius of the tetrahedral hole = 0.225´195
                              = 43.875 pm
                        (2)  For cation A+ with radius = 82 pm
As it lies in the range 0.414 – 0.732, hence the cation A+ can be slipped into the octahedral hole of the crystal A+ Br-.

ILLUSTRATIVE EXAMPLE(3):  Why is co-ordination number of 12 not found in ionic crystals?
SOLUTION:  Maximum radius ratio in ionic crystals lies in the range 0.732 – 1 which corresponds to a coordination number of 8. Hence coordination number greater than 8 is not possible in ionic crystals.

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