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

The αBoron (R12) Structure

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.
• visualize the structure (Uses the JMOL Applet)

---

• 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 x_I,II = 0 or x_I,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.

---

Go back to the IIIb-VIIb elements structures page.

Go back to Crystal Lattice Structure page.

Structures indexed by: Strukturbericht Symbol Pearson Symbol Space Group Prototype

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).