Crystal Lattice Structures:	Creation Date: 25 Mar 1998
	Last Modified: 21 Oct 2004

Tetrahedrally Bonded Carbon with Three Member Rings

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.
• visualize the structure (Uses the JMOL Applet)

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• 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 .
• The distance between atoms on the three fold rings is related to x by
  

  d = (3 x - 1) a

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• Prototype: C (hypothetical 3 member ring structure)
• Pearson Symbol: hP6
• Space Group: P6₃/mmc (Cartesian and lattice coordinate listings available)
• Number: 194
• Reference: P. Schultz et al., Phys. Rev. B 59, 733-741 (1999)
• Primitive Vectors:

  A1	=	½ a X - ½ 3½ a Y
  A2	=	½ a X + ½ 3½ a Y
  A3	=	c Z

• Basis Vectors:

  B1	=	+ x A1 + 2 x A2 + ¼ A3	=	+ 3/2 x a X + 3½/2 x a Y + ¼ c Z	(C)	(6h)
  B2	=	- 2 x A1 - x A2 + ¼ A3	=	- 3/2 x a X + 3½/2 x a Y + ¼ c Z	(C)	(6h)
  B3	=	+ x A1 - x A2 + ¼ A3	=	- 3½ x a Y + ¼ c Z	(C)	(6h)
  B4	=	- x A1 - 2 x A2 + ¾ A3	=	- 3/2 x a X - 3½/2 x a Y + ¾ c Z	(C)	(6h)
  B5	=	+ 2 x A1 + x A2 + ¾ A3	=	+ 3/2 x a X - 3½/2 x a Y + ¾ c Z	(C)	(6h)
  B6	=	- x A1 + x A2 + ¾ A3	=	+ 3½ x a Y + ¾ c Z	(C)	(6h)

See these vectors LaTeX output format.

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