# Primitive Translation Vectors from Lattice Vectors (with varying Space Groups) [closed]

I am looking at some raw POSCAR data of some Primitive Cells, and I wonder how I can get a simplified directional representation of the lattice vectors. I have two examples:

Example 1:

unknown system
1.00000000000000
3.891768    0.000000    2.246913
1.297256    3.669194    2.246913
0.000000    0.000000    4.493827
A   B
2     1
Direct
0.750000  0.750000  0.750000
0.250000  0.250000  0.250000
0.000000  0.000000  0.000000


Example 2:

unknown system
1.00000000000000
-2.015017    2.015017    2.856697
2.015017   -2.015017    2.856697
2.015017    2.015017   -2.856697
P   Q   R
2     1     1
Direct
-0.000000  0.000000  0.000000
0.250000  0.750000  0.500000
0.500000  0.500000 -0.000000
0.750000  0.250000  0.500000


Now here's the question: For Example 1 I know that the lattice can be represented by the following primitive translation vector representation:

     0.5    0.5    0.0
0.0    0.5    0.5
0.5    0.0    0.5


I know the above is correct because it is a basic FCC primitive cell. (Spacegroup: 225/Fm-3m | Lattice Angles: (60,60,60)).

Now I wonder what would be the relevant primitive lattice vector representation for Example 2? I just have one extra info about Example 2: It is an FCC Primitive Cell (Spacegroup: 216/F-43m | Lattice Angles: (120,120,90)).

• second example is not 216, it is 119/I-4m2. To change above into primitive unit cell. Type phonopy -c POSCAR --symmetry. It will generate PPOSCAR Commented Jan 24, 2023 at 9:23
• @Pranavkumar I strongly believe that example 2 is cubic. If you compute the lattice parameters from the aforesaid lattice vectors. You will find that a=b=c. Commented Jan 24, 2023 at 19:05
• Why don't you try spglib or phonopy(based on spglib) which detects symmetry based on all rotational symmetry. If you check symmetry with phonopy, it will also generate primitive unit cell in a file name PPOSCAR. Commented Jan 25, 2023 at 1:47
• Thanks for your suggestion, but that does not answer my question. Also what is a PPOSCAR? Commented Jan 27, 2023 at 1:51
• PPOSCAR is primitive unit cell of any given POSCAR. Phonopy create a POSCAR file name PPOSCAR based on underlying point symmetry. Commented Jan 27, 2023 at 3:36