Crystal Lattice Structures: Reference Date:  5 April 2001 Last Modified: 21 Oct 2004

# The PdAl Structure

You can now

• I've put this into the Hexagonal Close Packed Section because it looks close packed, and it looks as though the stacking is ABAB. At the very least, the (6f) atoms are reasonably close-packed.
• To avoid too much confusion with Pearson's Handbook, these Rhombohedral primitive vectors are written in terms of the Hexagonal lattice constants.
• On the other hand, it is rather inconvenient to use the Pearson's Handbook definitions for the lattice coordinates of the particles. Therefore we use the following conversions: if the lattice coordinates of an atom are (xhex,yhex,zhex) in the hexagonal lattice (a la Pearson), and (xrhomb,yrhomb,zrhomb) in the rhombohedral lattice (above), then

 xrhomb = -xhex + yhex zhex yrhomb = -yhex + zhex zrhomb = +xhex + zhex
• In the first incarnation of this file we made a mistake in listing the X coordinates of the (6f) atoms.

• Prototype: PdAl
• Pearson Symbol: hR26
• Space Group: R3 (Cartesian and lattice coordinate listings available)
• Number: 148
• Primitive Vectors:  A1 = 3-½ a Y + 1/3 c Z A2 = - ½ a X - ½ 3-½ a Y + 1/3 c Z A3 = + ½ a X - ½ 3-½ a Y + 1/3 c Z
• Basis Vectors:  B 1 = 0 (Al-I) (1a) B 2 = ½ (A1 + A2 + A3) = ½ c Z (Pd-I) (1b) B 3 = + x1 A1 + y1 A2 + z1 A3 = + ½ (z1 - y1) a X + 3-½ (2 x1 - y1 - z1) a Y + 1/3 (x1 + y1 + z1) a Z (Al-II) (6f) B 4 = + z1 A1 + x1 A2 + y1 A3 = + ½ (y1 - x1) a X + 3-½ (2 z1 - x1 - y1) a Y + 1/3 (x1 + y1 + z1) a Z (Al-II) (6f) B 5 = + y1 A1 + z1 A2 + x1 A3 = + ½ (x1 - z1) a X + 3-½ (2 y1 - z1 - x1) a Y + 1/3 (x1 + y1 + z1) a Z (Al-II) (6f) B 6 = - x1 A1 - y1 A2 - z1 A3 = + ½ (y1 - z1) a X - 3-½ (2 x1 - y1 - z1) a Y - 1/3 (x1 + y1 + z1) a Z (Al-II) (6f) B 7 = - z1 A1 - x1 A2 - y1 A3 = + ½ (x1 - y1) a X - 3-½ (2 z1 - x1 - y1) a Y - 1/3 (x1 + y1 + z1) a Z (Al-II) (6f) B 8 = - y1 A1 - z1 A2 - x1 A3 = + ½ (z1 - x1) a X - 3-½ (2 y1 - z1 - x1) a Y - 1/3 (x1 + y1 + z1) a Z (Al-II) (6f) B 9 = + x2 A1 + y2 A2 + z2 A3 = + ½ (z2 - y2) a X + 3-½ (2 x2 - y2 - z2) a Y + 1/3 (x2 + y2 + z2) a Z (Pd-II) (6f) B10 = + z2 A1 + x2 A2 + y2 A3 = + ½ (y2 - x2) a X + 3-½ (2 z2 - x2 - y2) a Y + 1/3 (x2 + y2 + z2) a Z (Pd-II) (6f) B11 = + y2 A1 + z2 A2 + x2 A3 = + ½ (x2 - z2) a X + 3-½ (2 y2 - z2 - x2) a Y + 1/3 (x2 + y2 + z2) a Z (Pd-II) (6f) B12 = - x2 A1 - y2 A2 - z2 A3 = + ½ (y2 - z2) a X - 3-½ (2 x2 - y2 - z2) a Y - 1/3 (x2 + y2 + z2) a Z (Pd-II) (6f) B13 = - z2 A1 - x2 A2 - y2 A3 = + ½ (x2 - y2) a X - 3-½ (2 z2 - x2 - y2) a Y - 1/3 (x2 + y2 + z2) a Z (Pd-II) (6f) B14 = - y2 A1 - z2 A2 - x2 A3 = + ½ (z2 - x2) a X - 3-½ (2 y2 - z2 - x2) a Y - 1/3 (x2 + y2 + z2) a Z (Pd-II) (6f) B15 = + x3 A1 + y3 A2 + z3 A3 = + ½ (z3 - y3) a X + 3-½ (2 x3 - y3 - z3) a Y + 1/3 (x3 + y3 + z3) a Z (Al-III) (6f) B16 = + z3 A1 + x3 A2 + y3 A3 = + ½ (y3 - x3) a X + 3-½ (2 z3 - x3 - y3) a Y + 1/3 (x3 + y3 + z3) a Z (Al-III) (6f) B17 = + y3 A1 + z3 A2 + x3 A3 = + ½ (x3 - z3) a X + 3-½ (2 y3 - z3 - x3) a Y + 1/3 (x3 + y3 + z3) a Z (Al-III) (6f) B18 = - x3 A1 - y3 A2 - z3 A3 = + ½ (y3 - z3) a X - 3-½ (2 x3 - y3 - z3) a Y - 1/3 (x3 + y3 + z3) a Z (Al-III) (6f) B19 = - z3 A1 - x3 A2 - y3 A3 = + ½ (x3 - y3) a X - 3-½ (2 z3 - x3 - y3) a Y - 1/3 (x3 + y3 + z3) a Z (Al-III) (6f) B20 = - y3 A1 - z3 A2 - x3 A3 = + ½ (z3 - x3) a X - 3-½ (2 y3 - z3 - x3) a Y - 1/3 (x3 + y3 + z3) a Z (Al-III) (6f) B21 = + x4 A1 + y4 A2 + z4 A3 = + ½ (z4 - y4) a X + 3-½ (2 x4 - y4 - z4) a Y + 1/3 (x4 + y4 + z4) a Z (Pd-III) (6f) B22 = + z4 A1 + x4 A2 + y4 A3 = + ½ (y4 - x4) a X + 3-½ (2 z4 - x4 - y4) a Y + 1/3 (x4 + y4 + z4) a Z (Pd-III) (6f) B23 = + y4 A1 + z4 A2 + x4 A3 = + ½ (x4 - z4) a X + 3-½ (2 y4 - z4 - x4) a Y + 1/3 (x4 + y4 + z4) a Z (Pd-III) (6f) B24 = - x4 A1 - y4 A2 - z4 A3 = + ½ (y4 - z4) a X - 3-½ (2 x4 - y4 - z4) a Y - 1/3 (x4 + y4 + z4) a Z (Pd-III) (6f) B25 = - z4 A1 - x4 A2 - y4 A3 = + ½ (x4 - y4) a X - 3-½ (2 z4 - x4 - y4) a Y - 1/3 (x4 + y4 + z4) a Z (Pd-III) (6f) B26 = - y4 A1 - z4 A2 - x4 A3 = + ½ (z4 - x4) a X - 3-½ (2 y4 - z4 - x4) a Y - 1/3 (x4 + y4 + z4) a Z (Pd-III) (6f)

Go back to the hexagonal close packed structures page.

Go back to Crystal Lattice Structure page.

 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).