LIGANCY:-

In an ionic solid the cation and anion are positioned at alternate lattice points. Generally cations are smaller than anions in size. In a given crystal the number of anions surrounding a cation is called the ligancy i.e., the coordination number of an ionic crystal.

RADIUS RATIO:-

If the surrounding anions touch each other as well as touch the central cations the condition is called critical. In this case the cation-anion radius ratio is called the critical radius ratio $r_C/r_A$. Here $r_C$ and$ r_A$ are the cation and anion radii respectively.

OCTAHEDRAL CONFIGURATION:

The octahedral configuration of neighbouring anions is found in NaCl structure. Here four anions A, B ,C and D are arranged at the corners of a square with the cation O at the centre of the square. Two more anions are situated in front and at the back of the cation. The centres of all six anions form an octahedron.

Here in $∆ BOC , \lt BOC = 90°, BC = 2r_A , OB = r_C+r_A and \lt BCO =45°,$

Hence, BO/BC=cos45°

Or, $(r_C+r_A)/(2r_A ) = 1/(√2)$