Question

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.

Answer 1

`4\ R=\sqrt 3\ a`

Step-by-step 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

`AB^2=AD^2+BD^2`

`AB^2=a^2+a^2`

`AB=\sqrt 2\ a`

In triangle ABC

`AC^2=AB^2+BC^2`

AC=4R

BC=a

`AB=\sqrt 2\ a`

So

`16R^2=2a^2+a^2`

`4\ R=\sqrt 3\ a`

So the relationship between lattice constant and radius of unit cell

`4\ R=\sqrt 3\ a`