Crystal Lattice Structures:	Creation Date: 22 Jan 2001
	Last Modified: 11 Jan 2006

The αSulfur (A16) 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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• Sulfur forms eight-atom molecular rings. If you don't see them in the pictures above, here are two of them.
• Note the coordinates used in the pictures above are adjusted so that the origin is on an inversion site. Pearson chooses the alternative setting for the Fddd space group.
• If we take the special parameters:

  a = 8½ a0				b = 4  a0				c = 32½ a0
  x(1)	=	0		y(1)	=	1/16		z(1)	=	1/16
  x(2)	=	1/4		y(2)	=	1/16		z(2)	=	-1/16
  x(3)	=	1/2		y(3)	=	1/16		z(3)	=	1/16
  x(4)	=	1/4		y(4)	=	3/16		z(4)	=	-3/16

  The atoms are on the sites of a bcc (A2) lattice with cubic lattice constant a₀.

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• Prototype: αS
• Pearson Symbol: oF128
• Strukturbericht Designation: A16
• Space Group: Fddd (Cartesian and lattice coordinate listings available)
• Number: 70
• Reference: Villars and Calvert, Pearson's Handbook, vol. IV, 5117.
• Primitive Vectors:

  A1	=	½ b Y + ½ c Z
  A2	=	½ a X + ½ c Z
  A3	=	½ a X + ½ b Y

• Basis Vectors:
  
  All of the sulfur atoms sit on (32h) sites, each having eight atoms in the primitive unit cell. Rather than repeat all of the basis vectors four times, we'll denote the basis vectors as B_i(j), meaning the i^th atom (i = [1-8]) in the j^th group (j = 1,2,3,4). Each group j is specified by three coordinates, (x(j),y(j),z(j)), as noted below:
  
  

  B1(j)	=	+  [y(j)+z(j)-x(j)]  A1 +  [z(j)+x(j)-y(j)]  A2 +  [x(j)+y(j)-z(j)]  A3	=	+ x(j) a X + y(j) b Y + z(j) c Z	[S(j)]	(32h)
  B2(j)	=	-  [y(j)+z(j)-x(j)]  A1 -  [z(j)+x(j)-y(j)]  A2 -  [x(j)+y(j)-z(j)]  A3	=	- x(j) a X - y(j) b Y - z(j) c Z	[S(j)]	(32h)
  B3(j)	=	+  [½-x(j)-y(j)-z(j)]  A1 +  [x(j)+y(j)-z(j)]  A2 +  [z(j)+x(j)-y(j)]  A3	=	+ x(j) a X +  [¼ - y(j)]  b Y +  [¼-z(j)]  c Z	[S(j)]	(32h)
  B4(j)	=	+  [½+x(j)+y(j)+z(j)]  A1 -  [x(j)+y(j)-z(j)]  A2 -  [z(j)+x(j)-y(j)]  A3	=	- x(j) a X +  [¼ + y(j)]  b Y +  [¼+z(j)]  c Z	[S(j)]	(32h)
  B5(j)	=	+  [x(j)+y(j)-z(j)]  A1 +  [½-x(j)-y(j)-z(j)]  A2 +  [y(j)+z(j)-x(j)]  A3	=	+  [¼-x(j)]  a X + y(j) b Y +  [¼-z(j)]  c Z	[S(j)]	(32h)
  B6(j)	=	-  [x(j)+y(j)-z(j)]  A1 +  [½+x(j)+y(j)+z(j)]  A2 -  [y(j)+z(j)-x(j)]  A3	=	+  [¼+x(j)]  a X - y(j) b Y +  [¼+z(j)]  c Z	[S(j)]	(32h)
  B7(j)	=	+  [z(j)+x(j)-y(j)]  A1 +  [y(j)+z(j)-x(j)]  A2 +  [½-x(j)-y(j)-z(j)]  A3	=	+  [¼-x(j)]  a X +  [¼-y(j)]  b Y + z(j) c Z	[S(j)]	(32h)
  B8(j)	=	-  [z(j)+x(j)-y(j)]  A1 -  [y(j)+z(j)-x(j)]  A2 +  [½+x(j)+y(j)+z(j)]  A3	=	+  [¼+x(j)]  a X +  [¼+y(j)]  b Y - z(j) c Z	[S(j)]	(32h)

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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).