Crystal Lattice Structures: | Creation Date: 8 Feb 2003 |
Last Modified: 21 Oct 2004 |
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The rhombohedral lattice can be specified by the length of the primitive vectors, a, and the angle between them, θ, or by the lattice constants of the equivalent hexagonal lattice. In terms of a and θ we have
ahex = 2 a sin(½ θ)
chex = a {3 [1 + 2 cos(θ)]}½
In rhombohedral form:
A1 | = | + ½ ahex X - 12-½ ahex Y + 1/3 chex Z |
A2 | = | + 3-½ ahex Y + 1/3 chex Z |
A3 | = | - ½ ahex X - 12-½ ahex Y + 1/3 chex Z |
B1 | = | + z A1 + z A2 + z A3 | = | + z c Z | (F) | (2c) |
B2 | = | - z A1 - z A2 - z A3 | = | - z c Z | (F) | (2c) |
B3 | = | + y1 A2 - y1 A3 | = | ½ y1 a X + ½ 3½ y1 a Y | (F-I) | (3d) |
B4 | = | - y1 A1 + y1 A3 | = | - y1 a X | (F-I) | (3d) |
B5 | = | + y1 A1 - y1 A2 | = | ½ y1 a X - ½ 3½ y1 a Y | (F-I) | (3d) |
B6 | = | ½ A1 + y2 A2 - y2 A3 | = | ¼ (2 y2 + 1) a X + 48-½ (6 y2 - 1) a Y + 1/6 c Z | (F-II) | (3e) |
B7 | = | - y2 A1 + ½ A2 + y2 A3 | = | - y2 a X + 12-½ a Y + 1/6 c Z | (F-II) | (3e) |
B8 | = | + y2 A1 - y2 A2 + ½ A3 | = | ¼ (2 y2 - 1) a X - 48-½ (6 y2 + 1) a Y + 1/6 c Z | (F-II) | (3e) |
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Structures indexed by: | 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). |