Lets assume, a represents the edge length (lattice constant) of a bcc unit cell and r represents the radius of the atom in the unit cell. draw a bcc unit cell and show the atoms in the unit cell. derive the relationship between the a and r.

Explanation:

Given that

Lattice constant = a

Radius of unit cell cell =R

Atom is in BCC structure.

In BCC unit cell (Body centered cube)

1.Eight atoms at eight corner of cube which have 1/8 part in each cube.

2.One complete atom at the body center of the cube

So the total number of atoms in the BCC

 Z= 1/8 x 8 + 1 x 1

Z=2

In triangle ABD

In triangle ABC

AC=4R

BC=a

So

So the relationship between lattice constant and radius of unit cell

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