Symmetrizing atoms in crytal
A key task is to symmetrize the atoms such that they transform like irreducible representations.
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Here we illustrate how to symmtrize displacements at a given q-point according to irreducible representations of the little group using the script pm-disp-qrep. Take the example of \(\bm{q}=(\frac{1}{2},\frac{1}{2},\frac{1}{2})\) in cubic SrTiO\(_3\). We will use pm-prototype-xtal to generate the crystal structure file.
$ pm-prototype-xtal --perovskite > xtal.yml
Printing out the irreducible representations, we have
$ pm-orbit-qrep -i xtal.yml --point-group Oh --qpoint 1/2,1/2,1/2 --print-irr-reps
Orbit Key: ('Sr', 0), Atom Index: [0]
A2u
Orbit Key: ('Ti', 0), Atom Index: [0]
A1g
Orbit Key: ('O', 0), Atom Index: [0, 1, 2]
T1u
We can also print out the irreducible representation vectors.
$ pm-orbit-qrep -i xtal.yml --point-group Oh --qpoint 1/2,1/2,1/2 --print-irr-vectors
irr-vectors
Orbit Key: ('Sr', 0), Atom Index: [0]
A2u
('A2u', 0)
[[1.]]
Orbit Key: ('Ti', 0), Atom Index: [0]
A1g
('A1g', 0)
[[1.]]
Orbit Key: ('O', 0), Atom Index: [0, 1, 2]
T1u
('T1u', 0)
[[1. 0. 0.]
[0. 1. 0.]
[0. 0. 1.]]
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