# Define ligancy and critical radius ratio. Calculate critical radius radio for ligancy 6. - Applied Physics 1

Short Note

#### Solution

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.
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 rC /rA . Here rC and rA 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 , < BOC = 90°, BC = 2r , OB = rC + rA and <BCO =45°,

Hence, ( BO)/(BC) = cos45°

Or, ( r_C +r _A)/(2r_A) = 1/(√2)

The critical radius ratio here is,

(r_C)/(r_A)=0.414

Concept: Study of characteristics of unit cell of Diamond, ZnS, NaCl and HCP;
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