Crystal Lattice Structures:	Creation Date: 18 Sep 2001
	Last Modified: 21 Oct 2004

The AlN₃Ti₄ Structure

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• 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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• This is one of the MAX phases discovered by Barsoum and others. The structural data for AlN₃Ti₄ was taken from the paper Thermal Properties of Ti₄AlN₃, M. W. Barsoum et al., Journal of Applied Physics 87, 8407-8414 (2000).
• All of the atoms sit on close packed <0001> planes. The stacking sequence may be written
  
  

  Atom

  Ti-II

  N-II

  Ti-I

  N-I

  Ti-I

  N-I

  Ti-II

  Al

  Ti-II

  N-II

  Ti-I

  N-I

  Ti-I

  N-II

  Ti-II

  Al

  Position

  A

  C

  B

  A

  C

  B

  A

  C

  A

  B

  C

  A

  B

  C

  A

  B

  
  Thus the all of the Ti and N atoms are always in an fcc-like local environment, while the Al atoms are in an hcp-like local environment.
• According to the above paper, the (2a) sites are only 86% occupied.
• The paper lists the reference N-II atom position as (2/3,1/3,0.1050). We have converted this to the standard reference position for a (4f) site, (1/3,2/3,0.6050).

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• Prototype: AlN₃Ti₄
• Pearson Symbol: hP16
• Space Group: P6₃/mmc (Cartesian and lattice coordinate listings available)
• Number: 194
• Reference: Barsoum et al., Journal of Applied Physics 87, 8407-8414 (2000).
• Primitive Vectors:

  A1	=	½ a X - ½ 31/2 a Y
  A2	=	½ a X + ½ 31/2 a Y
  A3	=	c Z

• Basis Vectors:

  B1  =			0			(N-I)	(2a)
  B2  =	½ A3		=	½ c Z		(N-I)	(2a)
  B3  =	1/3 a A1  + 2/3 a A1  +	¼ A3	=	½ a X - ½ 3-1/2 a Y +	¼   c Z	(Al)	(2c)
  B4  =	2/3 a A1  + 1/3 a A1  +	¾ A3	=	½ a X + ½ 3-1/2 a Y +	¾   c Z	(Al)	(2c)
  B5  =	2/3 a A1  + 1/3 a A1  -	zTi-I A3	=	½ a X + ½ 3-1/2 a Y -	zTi-I   c Z	(Ti-I)	(4f)
  B6  =	1/3 a A1  + 2/3 a A1  +	zTi-I A3	=	½ a X - ½ 3-1/2 a Y +	zTi-I   c Z	(Ti-I)	(4f)
  B7  =	1/3 a A1  + 2/3 a A1  +	(½ - zTi-I) A3	=	½ a X + ½ 3-1/2 a Y +	(½ - zTi-I) c Z	(Ti-I)	(4f)
  B8  =	2/3 a A1  + 1/3 a A1  +	(½ + zTi-I) A3	=	½ a X - ½ 3-1/2 a Y +	(½ + zTi-I) c Z	(Ti-I)	(4f)
  B9  =	zTi-II A3		=	zTi-II c Z		(Ti-II)	(4e)
  B10  =	- zTi-II A3		=	- zTi-II c Z		(Ti-II)	(4e)
  B11  =	(½ + zTi-II) A3		=	(½ + zTi-II) c Z		(Ti-II)	(4e)
  B12  =	(½ - zTi-II) A3		=	(½ - zTi-II) c Z		(Ti-II)	(4e)
  B13  =	2/3 a A1  + 1/3 a A1  -	zN A3	=	½ a X + ½ 3-1/2 a Y -	zN  c Z	(N-II)	(4f)
  B14  =	1/3 a A1  + 2/3 a A1  +	zN A3	=	½ a X - ½ 3-1/2 a Y +	zN   c Z	(N-II)	(4f)
  B15  =	1/3 a A1  + 2/3 a A1  +	(½ - zN) A3	=	½ a X + ½ 3-1/2 a Y +	(½ - zN) c Z	(N-II)	(4f)
  B16  =	2/3 a A1  + 1/3 a A1  +	(½ + zN) A3	=	½ a X - ½ 3-1/2 a Y +	(½ + zN) c Z	(N-II)	(4f)

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