Re: [Phonopy-users] definition of q-vector

[Atz T. <atz...@gm...>]

Hi,

Lattice vectors in reciprocal space are calculated from lattice
vectors in real space in usual manner. Q-vector in phonopy input and
output is represented in fractional value, where the periodic unit
corresponds to 1. The following is a small code  that I used for this
test.

import numpy as np

a = np.array( [[ 0.5, 0.5, 0.0 ],
              [ 0.0, 0.5, 0.5 ],
              [ 0.5, 0.0, 0.5 ]] )

b = np.linalg.inv( a ).T

print a
print b

print 0.5 * ( b[1] + b[2] )


b is calculated same as you, where the definition is without 2pi. Then
Si[001] is, if I understand correctly, the direction has to be along a
Cartesian axis in reciprocal space, because Si[001] is defined for
conventional unit cell, but not for primitive cell (am I correct?).
Therefore, the vector in reciprocal space has to be also along a
Cartesian axis. I think that this is not a specific definition of
phonopy.

Cheers,

Togo

2010/7/23 Xiaoliang Zhang <zha...@ie...>:
> Hi, Togo,
> Could you please help me with the definition of q-vector? thanks, I just
> don't understand.
>
> For Si diamond crystal structure, I want to get the phonon dispersion of
> Si[001] direction.
> Before, I tried to use
> QI = 0.0 0.0 0.0
> QF = 0.0 0.0 1.0
> You said that it's wrong, and the q-points should be like this:
> QI = 0.0 0.0 0.0
> QF = 0.0 0.5 0.5
>
> I just don't exactly understand what you said above.
>
> I know that for diamond crystal, the primitive lattice vector is(as in
> POSCAR):
> a1 = 0.5 0.5 0.0
> a2 = 0.0 0.5 0.5
> a3 = 0.5 0.0 0.5
> so the reciprocal lattice vector should be
> b1 = 1.0 1.0 -1.0
> b2 = -1.0 1.0 1.0
> b3 = 1.0 -1.0 1.0
> Am I right?
>
> Then why QF should be [0.0 0.5 0.5] for Si[001] direction? Thanks.
>
>
>
>
>
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-- 
Atsushi Togo
http://atztogo.users.sourceforge.net/
atz...@gm...