[Wien] Born effective charge in GaN

Oleg Rubel orubel at lakeheadu.ca
Mon Nov 4 23:13:38 CET 2013 

Dear Shahrbano,

I was able to obtain the effective charge of Z(Ga) = 2.76

Here is the approach:

1) Take the structure files enclosed (I assume they are not different 
from yours).

2) create directories 'lambda1' and 'lambda2'. In both cases I displace 
the Ga atom by +0.01 and -0.01 along z-axis. There is nothing specific 
about the choice of displacements. In fact 0.005 should work too. I 
encourage you to test the convergence and plot Z as a function of 
displacement. I do not recommend to go for displacements larger than 0.01

3) initialize both using 'init_lapw -b -vxc 13 -ecut -6 -numk 230'

4) rum wien2k 'run_lapw'

5) run berrypi 'berrypi -p$(pwd) -k6:6:4'. You should obtain the output 
as shown below.

6) Z = (1.7626777806241982 - 1.7075447765644145)/(0.01+0.01) = 2.76
(see Eq. 14 in 
http://www.tbrri.com/~orubel/publications/2013/Ahmed_CPC_184_2013.pdf)

The result really close to Vanderbilt. Good sign :)

In order to address the spontaneous polarization, we need two cases:
(a) the initial reference structure and
(b) your relaxed structure.
The spontaneous polarization is the difference between them. Please, 
look in the literature what is used as a reference structure. The choice 
of structure (a) for GaN is not obvious to me. Once you determine that, 
I can help you to move on.


Thank you
Oleg



+++++++++++++++++++++++++++++++++++
                                   ---PHASES/2*PI IN [0 to 2]RANGE---

       IONIC PHASE/(2*PI):         [6.010209219198259e-08, 
1.9999999400510458, 0.8898641300788697]

ELECTRONIC PHASE/(2*PI):         [2.000035665164408, 
-3.5664951224354753e-05, 0.87281365054532878]

       TOTAL PHASE/(2*PI):         [3.572526650019725e-05, 
1.9999642750998212, 1.7626777806241982]


                           ---POLARIZATION IN C/m^2 FOR [0 to 2] 
PHASE/2PI RANGE---

       IONIC POLARIZATION:        [6.734131068339737e-08, 
2.2408973201721545, 1.6229398446248238]

ELECTRONIC POLARIZATION:        [2.2409373483287527, 
-3.9960748009166113e-05, 1.5918430719045986]

       TOTAL POLARIZATION:        [4.0028328181192241e-05, 
2.2408573594241452, 3.2147829165294222]


                                   ---PHASES/2*PI IN [-1 to +1]RANGE---

       IONIC PHASE/(2*PI):        [6.010209219198259e-08, 
-5.994895424521474e-08, 0.8898641300788697]

ELECTRONIC PHASE/(2*PI):        [3.5665164408005268e-05, 
-3.5664951224312347e-05, 0.87281365054532878]

       TOTAL PHASE/(2*PI):        [3.572526650019725e-05, 
-3.5724900178779606e-05, -0.23732221937580178]


                           ---POLARIZATION IN C/m^2 FOR [-1 to +1] 
PHASE/2PI RANGE---

       IONIC POLARIZATION:        [6.734131068339736e-08, 
-6.716972747098987e-08, 1.6229398446248238]

ELECTRONIC POLARIZATION:        [3.9960986870508846e-05, 
-3.9960748009118604e-05, 1.5918430719045986]

       TOTAL POLARIZATION:        [4.0028328181192241e-05, 
-4.0027917736838375e-05, -0.432829768973433]

+++++++++++++++++++++++++
                                   ---PHASES/2*PI IN [0 to 2]RANGE---

       IONIC PHASE/(2*PI):         [6.010209219198259e-08, 
1.9999999400510458, 0.6298641300758288]

ELECTRONIC PHASE/(2*PI):         [-2.9599378548340341e-05, 
2.0000295996358957, 1.0776806464885857]

       TOTAL PHASE/(2*PI):         [1.9999704607235438, 
2.9539686940971421e-05, 1.7075447765644145]


                           ---POLARIZATION IN C/m^2 FOR [0 to 2] 
PHASE/2PI RANGE---

       IONIC POLARIZATION:        [6.734131068339737e-08, 
2.2408973201721545, 1.1487501955039068]

ELECTRONIC POLARIZATION:        [-3.3164585027959612e-05, 
2.2409305522152549, 1.9654807985263416]

       TOTAL POLARIZATION:        [2.2408642900981648, 
3.3097703644459985e-05, 3.1142309940302484]


                                   ---PHASES/2*PI IN [-1 to +1]RANGE---

       IONIC PHASE/(2*PI):        [6.010209219198259e-08, 
-5.994895424521474e-08, 0.6298641300758288]

ELECTRONIC PHASE/(2*PI):        [-2.9599378548406108e-05, 
2.9599635895660725e-05, -0.92231935351141425]

       TOTAL PHASE/(2*PI):        [-2.9539276456214125e-05, 
2.9539686940971421e-05, -0.2924552234355855]


                           ---POLARIZATION IN C/m^2 FOR [-1 to +1] 
PHASE/2PI RANGE---

       IONIC POLARIZATION:        [6.734131068339736e-08, 
-6.716972747098987e-08, 1.1487501955039066]

ELECTRONIC POLARIZATION:        [-3.3164585028033304e-05, 
3.3164873372428553e-05, -1.6821318869765136]

       TOTAL POLARIZATION:        [-3.3097243717349902e-05, 
3.3097703644459985e-05, -0.53338169147260672]
+++++++++++++++++++++++++++++++++++

On 04/11/2013 3:35 AM, Shahrbano Raheme wrote:
> Dear Prof Oleg Rubel,______
> I went trough tutorials 1 and 2 of the BerryPI, and could reproduce the
> results without any problems.
> But, now I would like to calculate the spontaneous polarization for  the
> GaN __
> structure. For sure, GaN.struct is pasted at the end of this e-mail. I
> have done these steps;____
> 1.I relaxed the system____
> 2.init_lapw____
> 3.run_lapw____
> 4.Run BerryPI using python____
> __ __
> I found the following values:____
> ·__________________________________________________________Total phase
> in z directionbetween [0 - 2] range ..... 0.4468____
> ·Total polarization in z direction between [0 - 2] range......0.8204____
> ·Total phase in z direction between [-1 - +1] range...... 0.4498____
> ·Total polarization in z direction between [-1 - +1] range.....__
> ______0.8204____
> __ __
> But the value of polarization in “arXiv:1201.4294v3 [cond-mat.mar-sci] 6
> Aug 2012 “ is__ reported to be ______– 0.02.____
> So, would you help me, how I can improve my result.____
> My another question is about Born effective charge. Idisplaced the
> second Ga atom along the z-axisin relaxed struct file.”ATOM-2:
> X=0.66666667 Y=0.33333333 Z=0.50004893”____
> __ ____ __
> Displacement____
> 	
> Total phase in z directionbetween [0 - 2] range____
> 	
> Total polarization in z direction between [0 - 2] range____
> 	
> Total phase in z direction between [-1 - +1] range____
> 	
> Total polarization in z direction between [-1 - +1] range____
> +0.01____
> 	
> 0.4122____
> 	
> 0.7518____
> 	
> 0.4122____
> 	
> 0.7518____
> -0.01____
> 	
> 0.0523____
> 	
> 0.0955____
> 	
> 0.0523____
> 	
> 0.0955____
>
> __ __
> Iobtainedthese values according the readme of tuturial2. When I
> calculate the born effective charge, my result is far from -2.72 which
> is reported in “D. Vanderbilt, J. Phys. Chem. Solids 61 (2000) 147.”____
> Please help me to improve my results.____
>
> Do the results depend on the displacement? If they do, which
> displacement should we select? In the tutorials of BerryPI, 0.01 and
> -0.01 are selected for the displacements? But, it is not clear for me
> why these displacements are selected? For example, we did a test by
> -0.002 and 0.002 displacements and found completely different results.
> Should we try by changing the displacements to reproduce the
> experimental results.
>
> GaN
> H4186_P63mc
> RELA
> 6.0206706.0206709.800124 90.000000 90.000000 60.000000
> ATOM-1: X=0.00000000 Y=0.00000000 Z=0.00004872
> MULT= 1ISPLIT= 4
> Ga1NPT=781R0=0.00005000 RMT=1.9600Z:31.00000
> LOCAL ROT MATRIX:1.0000000 0.0000000 0.0000000
> 0.0000000 1.0000000 0.0000000
> 0.0000000 0.0000000 1.0000000
> ATOM-2: X=0.66666667 Y=0.33333333 Z=0.50004893
> MULT= 1ISPLIT= 4
> Ga2NPT=781R0=0.00005000 RMT=1.9600Z:31.00000
> LOCAL ROT MATRIX:1.0000000 0.0000000 0.0000000
> 0.0000000 1.0000000 0.0000000
> 0.0000000 0.0000000 1.0000000
> ATOM-3: X=0.00000000 Y=0.00000000 Z=0.37603484
> MULT= 1ISPLIT= 4
> N 1NPT=781R0=0.00010000 RMT=1.6900Z:7.00000
> LOCAL ROT MATRIX:1.0000000 0.0000000 0.0000000
> 0.0000000 1.0000000 0.0000000
> 0.0000000 0.0000000 1.0000000
> ATOM-4: X=0.66666667 Y=0.33333333 Z=0.87603488
> MULT= 1ISPLIT= 4
> N 2NPT=781R0=0.00010000 RMT=1.6900Z:7.00000
> LOCAL ROT MATRIX:1.0000000 0.0000000 0.0000000
> 0.0000000 1.0000000 0.0000000
> 0.0000000 0.0000000 1.0000000
> 6NUMBER OF SYMMETRY OPERATIONS
>
> Your comments will be appreciated.
>
> Best wishes,
> SH. Rahimi

-------------- next part --------------
GaN                                                                            
H   LATTICE,NONEQUIV.ATOMS:  4 156 P3m1                                        
MODE OF CALC=RELA unit=bohr                                                    
  6.020670  6.020670  9.800124 90.000000 90.000000120.000000                   
ATOM  -1: X=0.00000000 Y=0.00000000 Z=0.00000000
          MULT= 1          ISPLIT= 4
Ga1        NPT=  781  R0=0.00005000 RMT=   1.92      Z: 31.0                   
LOCAL ROT MATRIX:    1.0000000 0.0000000 0.0000000
                     0.0000000 1.0000000 0.0000000
                     0.0000000 0.0000000 1.0000000
ATOM  -2: X=0.66666667 Y=0.33333333 Z=0.49000021
          MULT= 1          ISPLIT= 4
Ga2        NPT=  781  R0=0.00005000 RMT=   1.92      Z: 31.0                   
LOCAL ROT MATRIX:    1.0000000 0.0000000 0.0000000
                     0.0000000 1.0000000 0.0000000
                     0.0000000 0.0000000 1.0000000
ATOM  -3: X=0.00000000 Y=0.00000000 Z=0.37598612
          MULT= 1          ISPLIT= 4
N 1        NPT=  781  R0=0.00010000 RMT=   1.65      Z:  7.0                   
LOCAL ROT MATRIX:    1.0000000 0.0000000 0.0000000
                     0.0000000 1.0000000 0.0000000
                     0.0000000 0.0000000 1.0000000
ATOM  -4: X=0.66666667 Y=0.33333333 Z=0.87598616
          MULT= 1          ISPLIT= 4
N 2        NPT=  781  R0=0.00010000 RMT=   1.65      Z:  7.0                   
LOCAL ROT MATRIX:    1.0000000 0.0000000 0.0000000
                     0.0000000 1.0000000 0.0000000
                     0.0000000 0.0000000 1.0000000
   6      NUMBER OF SYMMETRY OPERATIONS
 1 0 0 0.00000000
 0 1 0 0.00000000
 0 0 1 0.00000000
       1
 0-1 0 0.00000000
 1-1 0 0.00000000
 0 0 1 0.00000000
       2
-1 1 0 0.00000000
-1 0 0 0.00000000
 0 0 1 0.00000000
       3
 0-1 0 0.00000000
-1 0 0 0.00000000
 0 0 1 0.00000000
       4
-1 1 0 0.00000000
 0 1 0 0.00000000
 0 0 1 0.00000000
       5
 1 0 0 0.00000000
 1-1 0 0.00000000
 0 0 1 0.00000000
       6
-------------- next part --------------
GaN                                                                            
H   LATTICE,NONEQUIV.ATOMS:  4 156 P3m1                                        
MODE OF CALC=RELA unit=bohr                                                    
  6.020670  6.020670  9.800124 90.000000 90.000000120.000000                   
ATOM  -1: X=0.00000000 Y=0.00000000 Z=0.00000000
          MULT= 1          ISPLIT= 4
Ga1        NPT=  781  R0=0.00005000 RMT=   1.92      Z: 31.0                   
LOCAL ROT MATRIX:    1.0000000 0.0000000 0.0000000
                     0.0000000 1.0000000 0.0000000
                     0.0000000 0.0000000 1.0000000
ATOM  -2: X=0.66666667 Y=0.33333333 Z=0.51000021
          MULT= 1          ISPLIT= 4
Ga2        NPT=  781  R0=0.00005000 RMT=   1.92      Z: 31.0                   
LOCAL ROT MATRIX:    1.0000000 0.0000000 0.0000000
                     0.0000000 1.0000000 0.0000000
                     0.0000000 0.0000000 1.0000000
ATOM  -3: X=0.00000000 Y=0.00000000 Z=0.37598612
          MULT= 1          ISPLIT= 4
N 1        NPT=  781  R0=0.00010000 RMT=   1.65      Z:  7.0                   
LOCAL ROT MATRIX:    1.0000000 0.0000000 0.0000000
                     0.0000000 1.0000000 0.0000000
                     0.0000000 0.0000000 1.0000000
ATOM  -4: X=0.66666667 Y=0.33333333 Z=0.87598616
          MULT= 1          ISPLIT= 4
N 2        NPT=  781  R0=0.00010000 RMT=   1.65      Z:  7.0                   
LOCAL ROT MATRIX:    1.0000000 0.0000000 0.0000000
                     0.0000000 1.0000000 0.0000000
                     0.0000000 0.0000000 1.0000000
   6      NUMBER OF SYMMETRY OPERATIONS
 1 0 0 0.00000000
 0 1 0 0.00000000
 0 0 1 0.00000000
       1
 0-1 0 0.00000000
 1-1 0 0.00000000
 0 0 1 0.00000000
       2
-1 1 0 0.00000000
-1 0 0 0.00000000
 0 0 1 0.00000000
       3
 0-1 0 0.00000000
-1 0 0 0.00000000
 0 0 1 0.00000000
       4
-1 1 0 0.00000000
 0 1 0 0.00000000
 0 0 1 0.00000000
       5
 1 0 0 0.00000000
 1-1 0 0.00000000
 0 0 1 0.00000000
       6

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