Crystal Lattice Structures: Creation Date: 18 Sep 2000 Last Modified: 21 Oct 2004

# The αBoron (R12) Structure

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• This is a metastable phase of Boron, and the simplest known phase (the ground state, beta-Boron, has 105 or 320 atoms in the unit cell). Pearson's Handbook gives the lattice constants and positions in terms of the hexagonal unit cell. I've translated everything into the primitive rhombohedral unit cell.
• Note the relationship between the icosahedra in this structure, in T50 Boron, and in βBoron.
• There are two types of atoms, B-I and B-II, both of which occupy (6h) sites. Note that there is nothing special about xI,II = 0 or xI,II = ¼.

• Prototype: αB
• Pearson Symbol: hR12
• Space Group: R3m (Cartesian and lattice coordinate listings available)
• Number: 166
• Primitive Vectors:  A1 = + ½ 31/2 a X - ½ a Y + c Z A2 = a Y + c Z A3 = - ½ 31/2 a X - ½ a Y + c Z
• Basis Vectors:  B1 = + xI A1 + xI A2 + zI A3 = + ½ 31/2 (xI - zI) a X + ½ (xI - zI) a Y + (2 xI + zI) c Z (B-I) (6h) B2 = + xI A1 + zI A2 + xI A3 = - (xI - zI) a Y + (2 xI + zI) c Z (B-I) (6h) B3 = + zI A1 + xI A2 + xI A3 = - ½ 31/2 (xI - zI) a X + ½ (xI - zI) a Y + (2 xI + zI) c Z (B-I) (6h) B4 = - xI A1 - xI A2 - zI A3 = - ½ 31/2 (xI - zI) a X - ½ (xI - zI) a Y - (2 xI + zI) c Z (B-I) (6h) B5 = - xI A1 - zI A2 - xI A3 = + (xI - zI) a Y - (2 xI + zI) c Z (B-I) (6h) B6 = - zI A1 - xI A2 - xI A3 = + ½ 31/2 (xI - zI) a X - ½ (xI - zI) a Y - (2 xI + zI) c Z (B-I) (6h) B7 = + xII A1 + xII A2 + zII A3 = + ½ 31/2 (xII - zII) a X + ½ (xII - zII) a Y + (2 xII + zII) c Z (B-II) (6h) B8 = + xII A1 + zII A2 + xII A3 = - (xII - zII) a Y + (2 xII + zII) c Z (B-II) (6h) B9 = + zII A1 + xII A2 + xII A3 = - ½ 31/2 (xII - zII) a X + ½ (xII - zII) a Y + (2 xII + zII) c Z (B-II) (6h) B10 = - xII A1 - xII A2 - zII A3 = - ½ 31/2 (xII - zII) a X - ½ (xII - zII) a Y - (2 xII + zII) c Z (B-II) (6h) B11 = - xII A1 - zII A2 - xII A3 = + (xII - zII) a Y - (2 xII + zII) c Z (B-II) (6h) B12 = - zII A1 - xII A2 - xII A3 = + ½ 31/2 (xII - zII) a X - ½ (xII - zII) a Y - (2 xII + zII) c Z (B-II) (6h)

### See these vectors in LaTeX output format.

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 Structures indexed by: This is a mirror of an old page created at theNaval Research LaboratoryCenter for Computational Materials ScienceThe 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).