In most papers, X atoms occupies the tetrahedral sites {Wyckoff position (0,0,0) and (1/2,1/2,1/2) while the Y&Z elements are at (1/4,1/4,1/4) and (3/4,3/4,3/4) Wyckoff positions}. However, there are again papers that presents the position of the X atoms to be at the octahedral sites {Wyckoff position (1/4,1/4,1/4) & (3/4,3/4,3/4)} and that of Y&Z to be at Wyckoff position (0,0,0) and (1/2,1/2,1/2).
I need to generate POSCAR file and so I need to know the actual position of the atoms on the different lattice sites.
Hi, Abegail
In fact, (0 0 0) and (1/2 1/2 1/2) sites are equivalent to (1/4 1/4 1/4) and (3/4 3/4 3/4) if you traslate the lattice in direction. Thus, you can describe the lattice using both styles and the choice that you wrote is question of taste for L2_1 structure.
Moreover, if you wish to describe in Wycoff positions, you need to describe only three atoms. X atom is located in 8c (1/4 1/4 1/4) and Y and Z atoms are locate in 4a ( 0 0 0 ) and 4b (1/2 1/2 1/2), respectively.
I hope this answer helps you.
Best wishes
Alejandro Alés I am a little confused here. X is described to have occupied the tetrahedral sites, while Y &Z, the octahedral sites of the unit cell. If (0,0,0) and (1/2,1/2,1/2) are equivalent to (1/4,1/41,/4) and (3/4,3/4,3/4), then does it mean these sites are also interchangeable and choice of origin deppendent?
Hi, Abegail Yimchunger
The most elegant way to describe the lattice for Cu_2AlMn (Heusler prototype) is
Basis Vectors:
B1 = 0 (Al) (4a)
B2 = -½ A1 + ½ A2 + ½ A3 = ½ a X (Mn) (4b)
B3 = - ¼ A1 - ¼ A2 - ¼ A3 = - ¼ a X - ¼ a Y - ¼ a Z (Cu) (8c)
B4 = + ¼ A1 + ¼ A2 + ¼ A3 = + ¼ a X + ¼ a Y + ¼ a Z (Cu) (8c)
Where
Primitive Vectors:
A1 = ½ a Y + ½ a Z
A2 = ½ a X + ½ a Z
A3 = ½ a X + ½ a Y
Therefore, atom X, which has duplicity, occupies the octahedral sites.
If the Wycoff scheme is used for the fm3m symmetry, it is enough to describe it only once in site 8c (with duplicity).
However, it is possible, using the given primitive vectors, to shift the lattice in the direction described in the previous answer. It is technically correct and is the most common when you want to represent the majority atom X occupying the external sites (those corresponding to position 0 0 0 and similar) in the graphs.
This, of course, does not change the observed physics and is just a matter of taste and comfort.
If you feel more confident performing the calculations, you can use the POSCAR files from https://github.com/ksyang2013/Heusler. Please cite the author if you use it.
Although I have no experience using VASP software because I have used another free package, feel free to ask me about these types of structures that I have worked with.
Basis and Primitive Vectores are extracted from https://www.atomic-scale-physics.de/lattice/struk/l2_1.html#:~:text=The%20Heusler%20(L21)%20Structure&text=All%20of%20the%20atoms%20are,crystallographically%20equivalent%20D03%20lattice.
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