In face centred cubic (fcc) crystal lattice, edge length is 400 pm. Find the diameter of greatest sphere which can be fit into the interstitial void without distortion of lattice.
Answers
In face centered cubic (fcc) crystal lattice, edge length is 400 pm. Find the diameter of greatest sphere which can be fit into the interstitial void without distortion of lattice
Answer:
The diameter of greatest sphere is 117.16 pm.
Explanation:
Given data:
Type of crystal = face centred cubic (fcc) edge length = 400 pm
Radius of void sphere = R
Radius of lattice sphere = r
To Find:
the diameter of greatest sphere which can be fit into the interstitial void without distortion of lattice.
Solution
Fcc crystal has octahedral void as largest void.
Formula for octahedral void is given by
a = 2 (r + R)
Hence
Formula for r is given by
r = a/2√2
But a = 400
r = 400/2√2
= 141.44 pm.
Hence using above formula,
a = 2 (r + R)
R= a-2r/2
R= (400-2*141.44) /2
R= 117.12pm
Hence diameter if greatest sphere is 117.12pm