Crystal Lattice Structures: Reference Date:  8 Mar 1999 Last Modified:  10 Oct 2006

# The Hexagonal Diamond (Lonsdaleite) Structure

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• This is related to the hcp (A3) lattice in the same way that diamond (A4) is related to the fcc lattice (A1). It can also be obtained from Wurtzite (B4) by replacing both the Zn and S atoms by Carbon. We've shifted the origin compared to Wurtzite, so that the inversion site is between one pair of Carbon atoms.
• The ``ideal'' structure, where the nearest-neighbor environment of each atom is the same as in diamond, is achieved when we take c/a = (8/3)1/2 and u = 1/16. Alternatively, we can take u = 3/16, in which case the origin is at the center of a C-C bond aligned in the [0001] direction.
• When u = 0 this structure becomes a set of graphitic sheets, but not true graphite (A9).
• 9 March 2003: Corrected the exponents in the Cartesian expressions for the Basis Vectors (-1/3 ==> ½).
• 6 June 2006: corrected sign of Y component of B4.
• 10 October 2006: The text of the page previously mislabeled the z coordinates of some of the atoms. The coordinates used in generating the pictures were correct. We have corrected the basis vectors and reordered them so that they agree with the coordinate file.

• Prototype: C (hexagonal diamond)
• Pearson Symbol: hP4
• Space Group: P63/mmc (Cartesian and lattice coordinate listings available)
• Number: 194
• Other Compounds with this Structure: Si (Hexagonal)
• Primitive Vectors:  A1 = ½ a X - ½ 3½ a Y A2 = ½ a X + ½ 3½ a Y A3 = c Z
• Basis Vectors:  B1 = 1/3 A1 + 2/3 A2 + z A3 = ½ a X + 12-½ a Y + z c Z (C) (4f) B2 = 2/3 A1 + 1/3 A2 + (½ + z) A3 = ½ a X - 12-½ a Y + (½ + z) c Z (C) (4f) B3 = 1/3 A1 + 2/3 A2 + (½ - z) A3 = ½ a X + 12-½ a Y + (½ - z) c Z (C) (4f) B4 = 2/3 A1 + 1/3 A2 - z A3 = ½ a X - 12-½ a Y - z c Z (C) (4f)

 Structures indexed by: This is a mirror of an old page created at theNaval Research LaboratoryCenter for Computational Materials ScienceThe maintained successor is hosted at http://www.aflowlib.org/CrystalDatabase/ and published as M. Mehl et al., Comput. Mater. Sci. 136 (Supp.), S1-S828 (2017).