Lattice:Hexagonal diamond

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The hexagonal diamond lattice is an arrangement of tetrahedrally-bonded elements, within a hexagonal unit cell. Whereas conventional diamond (a.k.a. cubic diamond) exists within a cubic unit cell, hexagonal diamond exists within a hexagonal unit cell. In both cases, elements are bonded tetrahdrally. However, in cubic diamond, the six-membered rings are all in the chair conformation, whereas in hexagonal diamond, some six-membered rings are in the boat conformation.

The four distinct positions in the unit cell are each given a different color. From: "Structural and vibrational properties of the 6H diamond: First-principles study" doi: 10.1016/j.diamond.2006.03.013


Canonical Hexagonal Diamond

A canonical hexagonal diamond lattice (single atom/particle type arranged as shown above) has symmetry Fd3m.

Symmetry

  • Crystal Family: Hexagonal
  • Crystal System: Hexagonal
  • Bravais Lattice: hexagonal
  • Crystal class: Hexoctahedral
  • Space Group: P63/mmc
  • Particles per unit cell:
  • Volume of unit cell:
  • Dimensionality:

Structure

TBD

Particle Positions

There are 14 positions. In total there are 4 particles in the unit cell.

Fractional

Positions are given in terms of fractional coordinates relative to the unit-cell edge-vectors:

Absolute

Distances

For a particle-particle bond-length of :

Absolute (in terms of particle-particle distance)

Examples

Atomics

  • Lonsdaleite form of carbon (C), also known as hexagonal diamond, 2H diamond, or 'sp3 diamond' (a = 2.51 Å, c = 4.12 Å)

Alternating Hexagonal Diamond

This is the Wurtzite crystal structure, a hexagonal unit cell with alternating species.

Examples

Atomics

  • Wurtzite (Zn,Fe)S (a = b = 3.82 Å, c = 6.26 Å)

Along Connections

This lattice can be thought of as the hexagonal-dimaond analog of the cubic-diamond cristobalite. Here, a four-bonded species occupies all the sites of the canonical hexagonal diamond lattice, and a two-bonded species sits along each of the connections between these tetrahedral sites.

Particle Positions

Particle Type A (bond tetrahedrally)

These are the same positions as the canonical hexagonal diamond.

Particle Type B (two-fold bonded)

There are 11 positions. In total there are 8 particles of this type in the unit cell.

Fractional

Positions are given in terms of fractional coordinates relative to the unit-cell edge-vectors:

See Also