Chapters / Chapter 1 · Solid state / Topic 8 of 14

Diamond cubic

Chapter 1 · Solid state and crystal structures

Diamond cubic unit cell

Diamond is a special type of fcc lattice. Four additional atoms are present within the face-centred cube, distributed symmetrically so that each one has an identical environment. They sit at the centres of alternating small cubes within the fcc cell, that is, at 4 of the 8 alternative tetrahedral holes. In this arrangement every atom is tetrahedrally surrounded.

Total lattice points per diamond cubic unit cell:

n = 1/8 × Nc + 1/2 × Nf + Ni = 1/8 × 8 + 1/2 × 6 + 4 = 1 + 3 + 4 = 8

The four internal lattice points lie along the four body diagonals of the fcc unit cell, each one a quarter of the way along a body diagonal from a corner. Taking a corner atom and the nearest atom along the body diagonal:

2r = 1/4 × √3 a
a = 8r / √3

Percentage of space actually occupied:

[8 × (4/3)πr³ × 100] / [(8/√3 r)³] = 34%

Space occupied 34%, space unoccupied 66%, 8 atoms per unit cell, coordination number 4.

Compare fcc metals at 74%: diamond is much more open, because every atom is held in a directional tetrahedral network rather than in close packing.