Question

Calculate the % empty space in a body centered lattice (BCC), and show that it does not depend on the edge length of the unit cell or on the size fo the atoms in the unit cell.

   - The edge length in terms of the radii of the atoms in the unit cell

   - The total volume of the unit cell in terms of the edge length

   - The filled volume from the total volume

   - % empty space

Please help... I keep getting the wrong answer, and I don't know how to fix it

Answer 1

For body-centered cubic system there are 2 spheres per unit cell and one should use the relationship:

4r = (3)^1/2a since the atoms touch each other along the body diagonal.

Fraction of space occupied = Volume of one sphere / Volume of one cube

Fraction of space occupied = (4/3)r³/a³

Fraction of space occupied = 2(4/3)r³/a³     a = 4r / (3)^1/2

                                             = 0.6802

Fraction of empty space = 0.3198 or 31.98 %