Jump to: navigation, search

The diamond lattice, which consists of tetrahedrally-arranged atoms/particles, has simple cubic symmetry.


Along an appropriate axis, the lattice has six-fold symmetry (hexagonal).

Canonical Diamond

A canonical diamond lattice (single atom/particle type arranged as shown above) has symmetry Fd3m. The atoms occupy the positions (0,0,0;1/4,1/4,1/4)+face-centering.


  • Crystal Family: Cubic
  • Crystal System: Cubic
  • Bravais Lattice: F (fcc)
  • Crystal class: Hexoctahedral
  • Point Group: d3m
  • Space Group: Fd3m
  • Particles per unit cell:
  • Volume of unit cell:
  • Dimensionality:
  • Projected d-dimensional volume:
  • Solid angle:
  • Nearest-neighbor distance:
  • Assuming spherical particles of radius R:
    • Particle volume fraction:
    • Maximum volume fraction: when


The lattice may be thought of as two interpenetrating FCC lattices.

Particle Positions

There are 18 positions. In total there are 8 particles in the unit cell:



6. Carbon (C) (a = 3.567 Å)
14. Silicon (Si) (a = 5.431 Å)
32. Germanium (Ge) (a = 5.657 Å)
50. Gray Tin (Sn) (a = 6.491 Å)


  • TBD


Diamond-like Two-particle

Also known as zincblende. This is effectively




Double-filled Diamond-like Two-particle

The diamond lattice includes 8 "tetrahedral holes", with only 4 occupied in a 'normal' diamond structure. A two-particle lattice can be formed by filling all 8 internal holes with the 2nd particle-type, in which case the particles exist in a 1:2 ratio. This is often called a CaF2 lattice.

Double diamond01.png

Particle Positions

There are 22 positions. In total there are 12 particles in the unit cell:


There are 12 particles in the unit cell: 4 of type A, and 8 of type B. The type A particles each connect to 8 particles of type B. The type B particles each connect (tetrahedrally) to 4 particles of type A.

Double diamond03.png

The lattice may also be thought of as having cubes of type B with a connected type A particle at the center. However the extended lattice is not BCC-like, since only every second "BCC cube" has a central particle of type A.

Double diamond02.png



Double Inter-penetrating Diamond Two-Particle

This lattice is formed from two diamond lattices that inter-penetrate. It is often called the NaTl lattice.


Particle Positions

There are 36 positions. In total there are 16 particles in the unit cell, 8 of each type.

Particle Type A

Particle Type B



  • Sodium Thallium crystal (NaTl)



Cristobalite is a diamond-like lattice formed in silicon dioxide (SiO2). The Si atoms bond tetradrally, each to four O atoms. Each O atom is bonded to 2 Si atoms, effectively acting as a bridge.


Can be thought of as a diamond lattice, where the tetrahedral species sit on the positions of the canonical diamond sites, and the two-bonded species sites at the midway point of each bond.

Cristobalite01.png Cristobalite13.png Cristobalite35.png

The tetrahedral species sit on the 14 "FCC" sites, plus 4 "internal" diamond sites. The two-bonded species sit on the 16 internal bonds in the unit cell. The tetrahedral species sit at a distance from one another of:

  • Next-nearest-neighbor distance:

The different species thus have a distance of half that:

  • Nearest-neighbor distance:

Particle Positions

There are 34 positions (24 in unit cell)

Particle Type A (bond tetrahedrally)

There are 18 positions. In total there are 8 particles in the unit cell:

Particle Type B (two-fold bonded)

There are 16 positions (all 16 in the unit cell):



See Also