Question

express the relationship between atomic radious and edge length in bcc and fcc. unit.cell

Answer 1

1. For a Primitive unit cell:
Atoms located at corners are in contact with adjacent atoms.

i.e.

a  = 2r
Face of cube



2. For FCC unit cell:
Atoms on face diagonal are in contact

Length of face diagonal = r + 2r + r = 4r

In triangle ABC,


i.e. 4r = √2 a
(i) a = 
(ii) d = 2r. (Here d = distance between two nearest atoms)



3. For BCC unit cell: Atoms on body diagonal are in contact with each other

i. e.
Length of body diagonal = r + 2r + r = 4r
Also, body diagonal = 
 4r = √3 a

(i) a = 
(ii) d = 2r (distance between centers of two closest atoms)

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