[Wien] tutorial 2 berrypi

[Oleg Rubel]

Dear Kadda,

the description for this tutorial is a bit outdated and refers to the 
output from the very first version of BerryPI. Here is what you can get 
for two cases with the newest version (Wien2k v17.1, BerryPI v1.3.4, 
Python v2.7.1, Numpy v1.12.0):

lambda1:

> CALCULATION OF ELECTRONIC POLARIZATION
> =======================================================================================
> Value                           |  spin   |    dir(1)    |    dir(2)    |    dir(3)
> ---------------------------------------------------------------------------------------
> ...
> Berry phase (rad) [-pi ... +pi]    up+dn  [ 4.296544e-09, -8.103055e-09, -1.078847e+00]
> ...
> =======================================================================================
> 
> CALCULATION OF IONIC POLARIZATION
> =======================================================================================
> Elem.|  Fractional coord.  |  spin | Zion |    dir(1)    |    dir(2)    |    dir(3)
> ---------------------------------------------------------------------------------------
> ...
> Total ionic phase wrap. (rad) sp(1)       [ 0.000000e+00,  4.464472e-14,  9.424778e-01]
> ...
> =======================================================================================

You need to add ionic and electronic phases for Z component to get the 
total phase:
-1.078847e+00 + 9.424778e-01 = -0.1363692 rad


lambda2:

> CALCULATION OF ELECTRONIC POLARIZATION
> =======================================================================================
> Value                           |  spin   |    dir(1)    |    dir(2)    |    dir(3)
> ---------------------------------------------------------------------------------------
> ...
> Berry phase (rad) [-pi ... +pi]    up+dn  [-4.134427e-10, -1.956464e-10,  1.078808e+00]
> ...
> =======================================================================================
> 
> CALCULATION OF IONIC POLARIZATION
> =======================================================================================
> Elem.|  Fractional coord.  |  spin | Zion |    dir(1)    |    dir(2)    |    dir(3)
> ---------------------------------------------------------------------------------------
> ...
> Total ionic phase wrap. (rad) sp(1)       [ 0.000000e+00,  4.464472e-14, -9.424778e-01]
> ...
> =======================================================================================

The total phase along Z axis:
1.078808e+00+(-9.424778e-01) = 0.1363302 rad

Change in the total phase between lambda1 and lambda2 cases:
0.1363302 - (-0.1363692) = 0.2726994 rad

The effective change:
Z*_zz=(1/(2*pi))*d_phi/d_rho = (1/(2*pi))*0.2726994/(0.01-(-0.01)) = +2.17

The positive change means that the atom "donates" electrons, which makes 
sense for Ga in GaAs.

Please note that the Born effective change is a 2nd rank tensor in 
general. Sometimes it shows a strong anisotropy depending on whether the 
displacement is along the chemical bond direction or perpendicular to 
that (e.g., perovskites). In this case I would take the charge obtained 
by a displacement perpendicular to the bond as a "true" ionic charge.


I hope this will help.

Oleg

--
Oleg Rubel (PhD, PEng)
Department of Materials Science and Engineering
McMaster University
JHE 359, 1280 Main Street West, Hamilton, Ontario L8S 4L8, Canada
Email: rubelo at mcmaster.ca
Tel: +1-905-525-9140, ext. 24094
Web: http://olegrubel.mcmaster.ca

On 2018-07-03 12:41, kadda AMARA wrote:
> *Dear WIEN2k users,
> I'm attempting an berrypi Version 1.3.4 calculation with the tutorial 2
> *
> *it is mentioned :*
> 
> 1.5 Once the calculation is completed the result will be printed like 
> this ---PHASES/2*PI IN [0 to 2]RANGE--- TOTAL PHASE/(2*PI): 
> [0.99999999991459032, 1.0000000091132539, 0.97814709926563959] 
> ---PHASES/2*PI IN [-1 to +1]RANGE--- TOTAL PHASE/(2*PI): 
> [0.99999999991459032, -0.99999999088674607, 0.97814709926563959]
> 
> *Where this result will be printed?
> *
> *
> 
> 
> Best regards
> *
> *Kadda Amara*
> 
> 
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