Tetrahedrally Bonded Carbon with Three Member Rings

Last modified 5 April 2001

You can now

• see the structure from several perspectives;
• examine the structure with an external viewer; or
• download the coordinates of the atoms in these pictures in XYZ format.

This structure was proposed by Peter Schultz of Sandia Albuquerque, to show that three-member rings could exist in amorphous carbon. See his 1998 APS talk. The published reference is Peter A. Schultz, Kevin Leung, and E. B. Stechel, Phys. Rev. B 59, 733-741 (1999), available on-line at PRB .

• Prototype: C
• Pearson Symbol: hP6
• Space Group: P6₃/mmc (Cartesian and lattice coordinate listings available)
• Number: 194
• Primitive Vectors:
  • A₁ = ½ a X - ½ 3^½ a Y
  • A₂ = ½ a X + ½ 3^½ a Y
  • A₃ = c Z
• Basis Vectors [All atoms sit on the (6h) sites of the P6₃/mmc space group]. The distance between atoms on the three fold rings is related to x by

  ---

  d = (3 x - 1) a

  ---

  • B₁ = + x A₁ + 2 x A₂ + ¼ A₃ = + 3/2 x a X + 3^½/2 x a Y + ¼ c Z
  • B₂ = - 2 x A₁ - x A₂ + ¼ A₃ = - 3/2 x a X + 3^½/2 x a Y + ¼ c Z
  • B₃ = + x A₁ - x A₂ + ¼ A₃ = - 3^½ x a Y + ¼ c Z
  • B₄ = - x A₁ - 2 x A₂ + ¾ A₃ = - 3/2 x a X - 3^½/2 x a Y + ¾ c Z
  • B₅ = + 2 x A₁ + x A₂ + ¾ A₃ = + 3/2 x a X - 3^½/2 x a Y + ¾ c Z
  • B₆ = - x A₁ + x A₂ + ¾ A₃ = + 3^½ x a Y + ¾ c Z

See these vectors in a better notation.

Go back to The Carbon Structures page.

Go back to The Crystal Lattice Structure page.

Structures indexed by:

• Strukturbericht Designation
• Pearson Symbol
• Space Group
• Prototype