`SC16' Structure of III-V Semiconductors

Last modified 5 July 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 is a tetragonally bonded structure which packs more efficiently than diamond. This is structure is related to BC8 in the same way that Zincblende (B3) is related to diamond: we replace half of the atoms by another species, such that the four nearest neighbors of each atom are of the other species. 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 my choice of atom positions puts this system in the Pa(-3) (T_h⁶, #205) space group, while Clark states that the space group is P2₁3 (T⁴, #198). I'm not sure what the difference is between the two structures. However, not that in the P2₁3 space group we cannot specify the locations of 16 atoms using only two internal parameters, as the atoms must be located on (4a) sites. In the Pa(-3) space group both types of atoms sit on (8c) sites.

Also note the the positions given here are mirror images of those given in the BC8 page. If this bothers you, change to a left-handed coordinate system.

• Prototype: AlSb (Hypothetical)
• Pearson Symbol: cP16
• Space Group: Pa(-3) (Cartesian and lattice coordinate listings available)
• Number: 205
• Other compounds with this structure (all hypothetical, so far as I know): AlIn, GaAs, InP
• Primitive Vectors:
  • A₁ = a X
  • A₂ = a Y
  • A₃ = a Z
• Basis Vectors

  B1	=	+ x1 A1 + x1 A2 + x1 A3	=	+ x1 a X + x1 a Y + x1 a Z	(8c)	(Al)
  B2	=	(½ + x1) A1 + (½ - x1) A2 - x1 A3	=	(½ + x1) a X + (½ - x1) a Y - x1 a Z	(8c)	(Al)
  B3	=	- x1 A1 + (½ + x1) A2 + (½ - x1) A3	=	- x1 a X + (½ + x1) a Y + (½ - x1) a Z	(8c)	(Al)
  B4	=	(½ - x1) A1 - x1 A2 + (½ + x1) A3	=	+ (½ - x1) a X - x1 a Y + (½ + x1) a Z	(8c)	(Al)
  B5	=	- x1 A1 - x1 A2 - x1 A3	=	- x1 a X - x1 a Y - x1 a Z	(8c)	(Al)
  B6	=	(½ - x1) A1 + (½ + x1) A2 + x1 A3	=	(½ - x1) a X + (½ + x1) a Y + x1 a Z	(8c)	(Al)
  B7	=	+ x1 A1 + (½ - x1) A2 + (½ + x1) A3	=	+ x1 a X + (½ - x1) a Y + (½ + x1) a Z	(8c)	(Al)
  B8	=	(½ + x1) A1 + x1 A2 + (½ - x1) A3	=	+ (½ + x1) a X + x1 a Y + (½ - x1) a Z	(8c)	(Al)
  B9	=	+ x2 A1 + x2 A2 + x2 A3	=	+ x2 a X + x2 a Y + x2 a Z	(8c)	(Sb)
  B10	=	(½ + x2) A1 + (½ - x2) A2 - x2 A3	=	(½ + x2) a X + (½ - x2) a Y - x2 a Z	(8c)	(Sb)
  B11	=	- x2 A1 + (½ + x2) A2 + (½ - x2) A3	=	- x2 a X + (½ + x2) a Y + (½ - x2) a Z	(8c)	(Sb)
  B12	=	(½ - x2) A1 - x2 A2 + (½ + x2) A3	=	+ (½ - x2) a X - x2 a Y + (½ + x2) a Z	(8c)	(Sb)
  B13	=	- x2 A1 - x2 A2 - x2 A3	=	- x2 a X - x2 a Y - x2 a Z	(8c)	(Sb)
  B14	=	(½ - x2) A1 + (½ + x2) A2 + x2 A3	=	(½ - x2) a X + (½ + x2) a Y + x2 a Z	(8c)	(Sb)
  B15	=	+ x2 A1 + (½ - x2) A2 + (½ + x2) A3	=	+ x2 a X + (½ - x2) a Y + (½ + x2) a Z	(8c)	(Sb)
  B16	=	(½ + x2) A1 + x2 A2 + (½ - x2) A3	=	+ (½ + x2) a X + x2 a Y + (½ - x2) a Z	(8c)	(Sb)

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