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

# The αSulfur (A16) Structure

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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.

• 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 Bi(j), meaning the ith atom (i = [1-8]) in the jth 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: 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).