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

The PdAl 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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• 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 (x_hex,y_hex,z_hex) in the hexagonal lattice (a la Pearson), and (x_rhomb,y_rhomb,z_rhomb) 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.

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• 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)

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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).