Crystal Lattice Structures:	Creation Date:  8 Feb 2003
	Last Modified: 21 Oct 2004

The AlF₃ (D0₁₄) 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)

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• Prototype: AlF₃
• Pearson Symbol: hR8
• Strukturbericht Designation: D0₁₄
• Space Group: R32 (Cartesian and lattice coordinate listings available)
• Number: 155
• Other Compounds with this Structure: FeF₃
• Primitive Vectors:

  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

  a_hex = 2 a sin(½ θ)

  c_hex = 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

• Basis Vectors:

  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: Strukturbericht Symbol Pearson Symbol Space Group Prototype

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