Crystal Lattice Structures:	Creation Date: 26 Jan 2001
	Last Modified: 21 Oct 2004

The T-50 Boron (A_g) 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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• This is apparently the most common form of Boron. At least, it's listed first in Donohue.
• Note that the basic building block is a slightly distorted icosahedron, just as it is in αBoron (R12) and βBoron (R105).
• The fifty Boron atoms in the primitive cell occupy five symmetry sites in the P4₂/nnm space group. We'll number the types by the index j, and basis vector B_i(j) represents the i^th atom on the j^th symmetry site. To summarize the sites first:

  Index	Wyckoff Notation	Internal Parameters
  j = 1	(2b)	None
  j = 2	(8m)	[x2,z2]
  j = 3	(8m)	[x3,z3]
  j = 4	(16n)	[x4,y4,z4]
  j = 5	(16n)	[x5,y5,z5]

  
  
  
• Note that we will use the second setting of space group #134, so that the origin is at an inversion site. This is not the definition used by Donohue or Pearson's Handbook. These references place one of the (2a) atoms on the inversion site.
• Also note that we only list the Cartesian coordinates of the atoms in the basis, leaving the transformation to lattice coordinates as an exercise for the reader.

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• Prototype: Boron
• Pearson Symbol: tP50
• Strukturbericht Designation: A_g
• Space Group: P4₂/nnm (Cartesian and lattice coordinate listings available)
• Number: 134
• Reference: Donohue, Structures of the Elements, pp. 48-56.
• Primitive Vectors:

  A1	=	a X
  A2	=	a Y
  A3	=	c Z

• Basis Vectors:

  j = 1							(2b)
  	B1(1)	=	+ ¾ a X	+ ¼ a Y	+ ¼ c Z
  	B2(1)	=	+ ¼ a X	+ ¾ a Y	+ ¾ c Z
  j = 2 and j = 3							(8m)
  	B1(j)	=	+ xj a X	- xj a Y	+ zj c Z
  	B2(j)	=	- xj a X	+ xj a Y	- zj c Z
  	B3(j)	=	- xj a X	+ (½ - xj) a Y	+ (½ + zj) c Z
  	B4(j)	=	+ xj a X	+ (½ + xj) a Y	+ (½ - zj) c Z
  	B5(j)	=	+ (½ + xj) a X	+ xj a Y	+ (½ + zj) c Z
  	B6(j)	=	+ (½ - xj) a X	- xj a Y	+ (½ - zj) c Z
  	B7(j)	=	+ (½ - xj) a X	+ (½ + xj) a Y	+ zj c Z
  	B8(j)	=	+ (½ + xj) a X	+ (½ - xj) a Y	- zj c Z
  j = 4 and j = 5							(16n)
  	B1(j)	=	+ xj a X	+ yj a Y	+ zj c Z
  	B2(j)	=	- xj a X	- yj a Y	- zj c Z
  	B3(j)	=	+ (½ + yj) a X	+ (½ + xj) a Y	+ zj c Z
  	B4(j)	=	+ (½ - yj) a X	+ (½ - xj) a Y	- zj c Z
  	B5(j)	=	- xj a X	+ (½ + yj) a Y	+ (½ + zj) c Z
  	B6(j)	=	+ xj a X	+ (½ - xj) a Y	+ (½ - zj) c Z
  	B7(j)	=	(½ - yj) a X	+ xj a Y	+ (½ + zj) c Z
  	B8(j)	=	(½ + yj) a X	- xj a Y	+ (½ - zj) c Z
  	B9(j)	=	(½ + xj) a X	- yj a Y	+ (½ + zj) c Z
  	B10(j)	=	(½ - xj) a X	+ yj a Y	+ (½ - zj) c Z
  	B11(j)	=	+ yj a X	+ (½ - xj) a Y	+ (½ + zj) c Z
  	B12(j)	=	- yj a X	+ (½ + xj) a Y	+ (½ - zj) c Z
  	B13(j)	=	+ (½ - xj) a X	+ (½ - yj) a Y	+ zj c Z
  	B14(j)	=	+ (½ + xj) a X	+ (½ + yj) a Y	- zj c Z
  	B15(j)	=	- yj a X	- x j a Y	+ zj c Z
  	B16(j)	=	+ yj a X	+ x j a Y	- zj c Z

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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).