The Al₃Zn (D0₂₃) Structure

Last modified 5 April 2001

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.

A lattice with tetragonal symmetry. The atoms are on the sites of a face centered cubic lattice when c = 4 a, z₁ = 3/8 and z₂ = 1/8. This phase can also be described as a set of alternating L1₂ and D0₂₂ lattices.

Note: I've changed the representation of the basis just a little bit, in order to make it easier to see the relationship between the atomic positions and the Wyckoff notation.

• Prototype: Al₃Zn
• Pearson Symbol: tI16
• Strukturbericht Designation: D0₂₃
• Space Group: I4/mmm (Cartesian and lattice coordinate listings available)
• Number: 139
• Other Compounds with this Structure: Al₃Zr, Al₃Hf
• Primitive Vectors:
  • A₁ = a X
  • A₂ = a Y
  • A₃ = ½ a X + ½ a Y + ½ c Z
• Basis Vectors (when drawing the pictures above, we took z₁ = 3/8 and z₂ = 1/8):

  B1	=	½ A2	=	½ a Y	(4c)	(Al-I)
  B2	=	½ A1	=	½ a X	(4c)	(Al-I)
  B3	=	- ¼ A1 + ¼ A2 + ½ A3	=	½ a Y + ¼ c Z	(4d)	(Al-II)
  B4	=	+ ¼ A1 - ¼ A2 + ½ A3	=	½ a X + ¼ c Z	(4d)	(Al-II)
  B5	=	- z1 A1 - z1 A2 + 2 z1 A3	=	+ z1 c Z	(4e)	(Al-III)
  B6	=	+ z1 A1 + z1 A2 - 2 z1 A3	=	- z1 c Z	(4e)	(Al-III)
  B7	=	- z2 A2 - z2 A2 + 2 z1 A3	=	+ z2 c Z	(4e)	(Zn)
  B8	=	+ z2 A1 + z2 A2 - 2 z2 A3	=	- z2 c Z	(4e)	(Zn)

See these vectors in a better notation.

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