The Hexagonal Diamond (Lonsdaleite) Structure
You can now
-
This is related to the hcp (A3)
lattice in the same way that
diamond (A4) is related to the
fcc lattice (A1). It can also be
obtained from Wurtzite (B4) by
replacing both the Zn and S atoms by Carbon. We've
shifted the origin compared to Wurtzite, so that the
inversion site is between one pair of Carbon atoms.
-
The ``ideal'' structure, where the nearest-neighbor
environment of each atom is the same as in diamond, is
achieved when we take c/a = (8/3)1/2
and u = 1/16. Alternatively, we can take
u = 3/16, in which case the origin is at the
center of a C-C bond aligned in the [0001] direction.
-
When u = 0 this structure becomes a set of
graphitic sheets, but not true graphite
(A9).
-
9 March 2003: Corrected the exponents in the
Cartesian expressions for the Basis Vectors (-1/3 ==>
½).
-
6 June 2006: corrected sign of
Y component of
B4.
-
10 October 2006: The text of the page previously
mislabeled the z coordinates of some of the
atoms. The coordinates used in generating the pictures
were correct. We have corrected the basis vectors and
reordered them so that they agree with the
coordinate file.
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Prototype: C (hexagonal diamond)
-
Pearson Symbol:
hP4
-
Space Group:
P63/mmc
(Cartesian and
lattice coordinate
listings available)
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Number: 194
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Other Compounds with this Structure: Si (Hexagonal)
-
Primitive Vectors:
|
A1
|
=
|
½ a X - ½
3½
a Y
|
|
A2
|
=
|
½ a X + ½
3½
a Y
|
|
A3
|
=
|
c Z
|
-
Basis Vectors:
|
B1
|
=
|
1/3 A1 + 2/3
A2 + z
A3
|
=
|
½ a X +
12-½ a Y + z c
Z
|
(C)
|
(4f)
|
|
B2
|
=
|
2/3 A1 + 1/3
A2 + (½ + z)
A3
|
=
|
½ a X -
12-½ a Y +
(½ + z) c
Z
|
(C)
|
(4f)
|
|
B3
|
=
|
1/3 A1 + 2/3
A2 + (½ - z)
A3
|
=
|
½ a X +
12-½ a Y +
(½ - z) c
Z
|
(C)
|
(4f)
|
|
B4
|
=
|
2/3 A1 + 1/3
A2 - z
A3
|
=
|
½ a X -
12-½ a Y - z c
Z
|
(C)
|
(4f)
|
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page.
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Structure page.
