Crystal Lattice Structures:	Creation Date:  9 Oct 2000
	Last Modified: 21 Oct 2004

The `ST12' Structure of Silicon

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 is a tetragonally bonded structure which packs more efficiently than diamond. It is seen experimentally in some silicon and germanium samples an is a staple for testing silicon potentials and first-principles calculations. This page of Stewart Clark's thesis has more information, as does the paper
  
  J. Crain, S. J. Clark, G. J. Ackland, P. D. Hatton, B. J. Reid, M. C. Payne, and V. Milman, Phys. Rev. B 49, 5329 (1994).
  
  
• Note that this structure is similar to the BC8 structure of silicon.
  
  
• Also note that this structure differs from the cristobalite (SiO₂) structure only by the handedness of the screw axis.

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• Prototype: Si
• Pearson Symbol: tP12
• Space Group: P4₃2₁2 (Cartesian and lattice coordinate listings available)
• Number: 96
• Other elements with this structure: Ge (γ)
• Primitive Vectors:

  A1	=	a X
  A2	=	a Y
  A3	=	c Z

• Basis Vectors

  B1	=	+ x1 A1 + x1 A2	=	+ x1 a X + x1 a Y	(Si)	(4a)
  B2	=	- x1 A1 - x1 A2 + ½ A3	=	- x1 a X - x1 a Y + ½ c Z	(Si)	(4a)
  B3	=	(½ - x1) A1 + (½ + x1) A2 + ¾ A3	=	(½ - x1) a X + (½ + x1) a Y + ¾ c Z	(Si)	(4a)
  B4	=	(½ + x1) A1 + (½ - x1) A2 + ¼ A3	=	(½ + x1) a X + (½ - x1) a Y + ¼ c Z	(Si)	(4a)
  B5	=	+ x2 A1 + y2 A2 + z2 A3	=	+ x2 a X + y2 a Y + z2 c Z	(Si)	(8b)
  B6	=	- x2 A1 - y2 A2 + (½ + z2) A3	=	- x2 a X - y2 a Y + (½ + z2) c Z	(Si)	(8b)
  B7	=	(½ - y2) A1 + (½ + x2) A2 + (¾ + z2) A3	=	(½ - y2) a X + (½ + x2) a Y + (¾ + z2) c Z	(Si)	(8b)
  B8	=	(½ + y2) A1 + (½ - x2) A2 + (¼ + z2) A3	=	(½ + y2) a X + (½ - x2) a Y + (¼ + z2) c Z	(Si)	(8b)
  B9	=	+ y2 A1 + x2 A2 - z2 A3	=	+ y2 a X + x2 a Y - z2 c Z	(Si)	(8b)
  B10	=	- y2 A1 - x2 A2 + (½ - z2) A3	=	- y2 a X - x2 a Y + (½ - z2) c Z	(Si)	(8b)
  B11	=	(½ - x2) A1 + (½ + y2) A2 + (¾ - z2) A3	=	(½ - x2) a X + (½ + y2) a Y + (¾ - z2) c Z	(Si)	(8b)
  B12	=	(½ + x2) A1 + (½ - y2) A2 + (¼ - z2) A3	=	(½ + x2) a X + (½ - y2) a Y + (¼ - z2) c Z	(Si)	(8b)

See these vectors in LaTeX output.

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Structures indexed by: Strukturbericht Symbol Pearson Symbol Space Group Prototype

This is a mirror of an old page created at the Naval Research Laboratory Center for Computational Materials Science The 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).