A crystal structure is formed by connecting atoms, groups of atoms, or molecules. The intrinsic nature of the constituent particles generates symmetric patterns, which results in this structure. The unit cell of a structure is a tiny group of repeating patterns of the atomic structure. 

The fluorite structure is a popular solid-state chemistry motif for molecules with the formula MX2. The eight tetrahedral interstitial sites are occupied by X ions, while M ions occupy the regular sites of an FCC (face-centered cubic) structure. This structure is adopted by several compounds, including the common mineral fluorite (CaF2). Some essential points of fluorite structure are:

  • In comparison to other structures, the cations are slightly larger.
  • Coordination numbers are eight cations, four anions, and FCC lattice.
  • The cations create a big void in the centre of the unit cell in this structure.
  • Because of these empty gaps, oxides become effective ionic conductors, which is important in energy storage applications like batteries.

Unit Cell

The unit cells are building blocks of a crystal, which is the smallest repeating unit in the crystal lattice. The edges, principal axes, length, and angle between the unit cells are lattice constants (lattice parameters). A unit cell can be either BCC (body-centred cubic), FCC (face-centred cubic), or primitive cubic.

Body-centred cubic unit cell (BCC)

  • Every corner of a BCC unit cell has atoms.
  • At the centre of the structure, there is only one atom.
  • The total number of atoms present per unit cell = 2 atoms. 

[1/8 per corner atom × 8 corners = 1/8 × 8 = 1 atom

1 body centre atom = 1 × 1 = 1 atom]

Face-centred cubic unit cell (FCC)

  • Atoms are present in all four corners of the crystal lattice in FCC unit cells.
  • In addition, every cube’s face has an atom at its centre.
  • This face-centre atom is shared by two unit cells next to it.
  • A unit cell is made up of only 12 atoms.

Primitive cubic unit cell

  • Atoms are only present in the corners of the primitive cubic unit cell. 
  • Every atom in the corner is shared by eight unit cells next to it. 
  • Four unit cells are in the same layer, and four are in the upper or lower layer.
  • As a result, each unit cell contains only 1/8th of an atom.

Allotropes of Carbon

Carbon is an example of an element that exhibits allotropy. Carbon allotropes can be amorphous or crystalline. Dimond, graphene, Q-carbon, Fullerene, Graphite are allotropes of carbon.

  • Diamond is a clear, tough substance composed of carbon atoms organised in a tetrahedral lattice. This carbon allotrope has low electrical conductivity but high heat conductivity.
  • Hexagonal diamonds are also known as Lonsdaleite.
  • Other allotropes, charcoal, nanotubes, and fullerenes contain graphene as a structural constituent.
  • Graphite is a black, flaky, soft material that is a moderate conductor of electricity. The carbon atoms are linked together in flat hexagonal lattices subsequently stacked into sheets.
  • Allotropes of carbon with a cylindrical nanostructure are known as carbon nanotubes.