Relationship Between Atomic Radius (R) And Edge Length (A)

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)
		Body diagonal plane of a cube

Property	Primitive	FCC	BCC
Diagonal	Facial  r	Facial 4r	Body Diagonal 4r
Edge length, a	a = 2r	a =	a =
Volume of unit cell	a3 = 8r3	a3 = (2√2 r)3	a3 =
Volume occupied by atoms per unit cell	1 x   r3	4 x   r3	2 x   r3
Packing Fraction =	= 0.524	= 0.74	= 0.68
% Free space per unit cell	47.6%	26%	32%