`ST12' Structure of
Silicon
Last modified 5 July
2001
You can now
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.
- Prototype: Si
- Pearson Symbol: tP12
- Space Group: P43212 (Cartesian and lattice coordinate listings
available)
- Number: 96
- Primitive Vectors:
- A1 = a X
- A2 = a Y
- A3 = c Z
- Basis Vectors
- B1 = + x1 A1 +
x1 A2 = + x1 a X +
x1 a Y (4a)
- B2 = - x1 A1 -
x1 A2 + ½ A3 = -
x1 a X - x1 a Y + ½ c
Z (4a)
- B3 = (½ - x1)
A1 + (½ + x1) A2
+ ¾ A3 = (½ - x1) a X
+ (½ + x1) a Y + ¾ c Z
(4a)
- B4 = (½ + x1)
A1 + (½ - x1) A2
+ ¼ A3 = (½ + x1) a X
+ (½ - x1) a Y + ¼ c Z
(4a)
- B5 = + x2 A1 +
y2 A2 + z2
A3 = + x2 a X + y2 a
Y + z2 c Z (8b)
- B6 = - x2 A1 -
y2 A2 + (½ + z2)
A3 = - x2 a X - y2 a
Y + (½ + z2) c Z (8b)
- B7 = (½ - y2)
A1 + (½ + x2) A2
+ (¾ + z2) A3 = (½ -
y2) a X + (½ + x2) a Y +
(¾ + z2) c Z (8b)
- B8 = (½ + y2)
A1 + (½ - x2) A2
+ (¼ + z2) A3 = (½ +
y2) a X + (½ - x2) a Y +
(¼ + z2) c Z (8b)
- B9 = + y2 A1 +
x2 A2 - z2
A3 = + y2 a X + x2 a
Y - z2 c Z (8b)
- B10 = - y2 A1 -
x2 A2 + (½ - z2)
A3 = - y2 a X - x2 a
Y + (½ - z2) c Z (8b)
- B11 = (½ - x2)
A1 + (½ + y2) A2
+ (¾ - z2) A3 = (½ -
x2) a X + (½ + y2) a Y +
(¾ - z2) c Z (8b)
- B12 = (½ + x2)
A1 + (½ - y2) A2
+ (¼ - z2) A3 = (½ +
x2) a X + (½ - y2) a Y +
(¼ - z2) c Z (8b)
Go back to The Carbon Structures page.
Go back to The Crystal Lattice Structure
page.
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