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

# The T-50 Boron (Ag) Structure

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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 Bi(j) represents the ith atom on the jth 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.

• Prototype: Boron
• Pearson Symbol: tP50
• Strukturbericht Designation: Ag
• 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: 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).