Discussion:
[Wien] Formula to calculate Lattice Constant and angle of BiFeO3
2014-06-23 02:41:06 UTC
*Respected, Wien2K Community*
* I want to **calculate Lattice Constant and angle of BiFeO3 in space
group P1( Triclinic ). I have done volume optimization. I found a formula
[V = abc( 1-cos**2alpha -**cos**2beta**- **cos**2gamma**+2***cos alpha***cos
beta***cos gamma)**1/2]. I found only volume in volume optimization. How
can i found lattice parameters a, b , c and angles??? *
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delamora
2014-06-23 15:30:20 UTC
Yes, in the WIEN2k you find a, b and c optimization all set for you, but ti include the angles the number of structures would increase exponentially;

1 dimension n

2 dimensions n**2

3 dimensions n**3

4 dimensions n**4

5 dimensions n**5

6 dimensions n**6

4**6=4096

So you must do each optimization separately

First you optimize a, b, c

then you vary alpha and optimize, then beta and finally gamma

optimize a, b and c

until the changes in the cell parameters change little.

________________________________
De: wien-bounces at zeus.theochem.tuwien.ac.at <wien-bounces at zeus.theochem.tuwien.ac.at> en nombre de Mian Fayyaz Ahmad <fayyaz.pc at gmail.com>
Enviado: domingo, 22 de junio de 2014 09:41 p.m.
Para: Wien at zeus.theochem.tuwien.ac.at
Asunto: [Wien] Formula to calculate Lattice Constant and angle of BiFeO3

Respected, Wien2K Community
I want to calculate Lattice Constant and angle of BiFeO3 in space group P1( Triclinic ). I have done volume optimization. I found a formula [V = abc( 1?cos**2alpha ?cos**2beta? cos**2gamma+2*cos alpha*cos beta*cos gamma)**1/2]. I found only volume in volume optimization. How can i found lattice parameters a, b , c and angles???
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2014-06-24 03:51:59 UTC
Respected, "delamora at unam.mx"
Still i am confusing how to calculate . As you mentioned but still
confusion about concrete steps as you mentioned
( First you optimize a, b, c
then you vary alpha and optimize, then beta and finally gamma

optimize a, b and c

until the changes in the cell parameters change little.).

According to user guide at page #66 (listed from 1-6 ) in volume
optimization case.

Please guide me according to list in user guide step wise.

I would be very thankful to you.

On Tue, Jun 24, 2014 at 12:30 AM, delamora <delamora at unam.mx> wrote:

> Yes, in the WIEN2k you find a, b and c optimization all set for you, but
> ti include the angles the number of structures would increase exponentially;
>
> 1 dimension n
>
> 2 dimensions n**2
>
> 3 dimensions n**3
>
> 4 dimensions n**4
>
> 5 dimensions n**5
>
> 6 dimensions n**6
>
>
> 4**6=4096
>
>
> So you must do each optimization separately
>
> First you optimize a, b, c
>
> then you vary alpha and optimize, then beta and finally gamma
>
>
> then you return to the beginning;
>
> optimize a, b and c
>
> until the changes in the cell parameters change little.
>
>
> ------------------------------
> *De:* wien-bounces at zeus.theochem.tuwien.ac.at <
> wien-bounces at zeus.theochem.tuwien.ac.at> en nombre de Mian Fayyaz Ahmad <
> fayyaz.pc at gmail.com>
> *Enviado:* domingo, 22 de junio de 2014 09:41 p.m.
> *Para:* Wien at zeus.theochem.tuwien.ac.at
> *Asunto:* [Wien] Formula to calculate Lattice Constant and angle of BiFeO3
>
>
> *Respected, Wien2K Community*
> * I want to **calculate Lattice Constant and angle of BiFeO3 in space
> group P1( Triclinic ). I have done volume optimization. I found a formula
> [V = abc( 1-cos**2alpha -**cos**2beta**- **cos**2gamma**+2***cos alpha***cos
> beta***cos gamma)**1/2]. I found only volume in volume optimization. How
> can i found lattice parameters a, b , c and angles??? *
> *thanks in advance*
>
> _______________________________________________
> Wien mailing list
> Wien at zeus.theochem.tuwien.ac.at
> http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien
> SEARCH the MAILING-LIST at:
> http://www.mail-archive.com/wien at zeus.theochem.tuwien.ac.at/index.html
>
>
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delamora
2014-06-25 03:05:52 UTC
Dear Mian Fayyaz Ahmad,

BiFeO3 is a complex compound with many crystalline structures.

If you have a triclinic structure then you need to optimize 'a', 'b', 'c', 'alpha', 'beta' and 'gamma'. But you have to optimize the internal coordinates.

I will exemplify with a tetrahedral structure; you have a=b, c, angles=90.

The WIEN2k now does in one cycle, but 10 years ago was not the case.

Those days you would change the 'c' parameter by -6%, -3%, 0%, 3% and 6%, then after optimizing these 5 cases you would adjust a cubic curve, now it is a Murnaham curve, and find the minimum for 'c'.

Then you would optimize 'a' (=b)

And the last part of the first cycle would be an optimization of the internal coordinates;

min -j "run -ec 0.0001 -fc 5"

'-fc' is force convergence, and I find 5 to be good, even stronger than '-ec 0.0001'

Careful, if you do not put '-ec' it can happen that the force is optimized but the energy not, then you have problems.

Then you would return to the optimize the 'c' parameter and continue until the parameters change little.

For the case of a triclinic system then you have in each cycle to optimize (1) 'a', (2) 'b', (3) 'c', (4) 'alpha', (5) 'beta' and (6) 'gamma' and at the end (7) internal coordinates.

So it is a long process.

Now, the 'a', 'b' and 'c' parameters can be optimized in one step as you can see in the new WIEN2k. In this case you can choose a 3x3x3 or 4x4x4 or 5x5x5 mesh.

The same could be done for 'alpha', 'beta' and 'gamma', but you need to find the nxnxn mesh yourself.

I hope that this gives you a general guide.

Saludos

Pablo de la Mora

________________________________
De: wien-bounces at zeus.theochem.tuwien.ac.at <wien-bounces at zeus.theochem.tuwien.ac.at> en nombre de Mian Fayyaz Ahmad <fayyaz.pc at gmail.com>
Enviado: lunes, 23 de junio de 2014 10:51 p.m.
Para: A Mailing list for WIEN2k users
Asunto: Re: [Wien] Formula to calculate Lattice Constant and angle of BiFeO3

Respected, "delamora at unam.mx<mailto:delamora at unam.mx>"
Still i am confusing how to calculate . As you mentioned but still confusion about concrete steps as you mentioned
( First you optimize a, b, c
then you vary alpha and optimize, then beta and finally gamma

optimize a, b and c

until the changes in the cell parameters change little.).

According to user guide at page #66 (listed from 1-6 ) in volume optimization case.

Please guide me according to list in user guide step wise.

I would be very thankful to you.

On Tue, Jun 24, 2014 at 12:30 AM, delamora <delamora at unam.mx<mailto:delamora at unam.mx>> wrote:

Yes, in the WIEN2k you find a, b and c optimization all set for you, but ti include the angles the number of structures would increase exponentially;

1 dimension n

2 dimensions n**2

3 dimensions n**3

4 dimensions n**4

5 dimensions n**5

6 dimensions n**6

4**6=4096

So you must do each optimization separately

First you optimize a, b, c

then you vary alpha and optimize, then beta and finally gamma

optimize a, b and c

until the changes in the cell parameters change little.

________________________________
De: wien-bounces at zeus.theochem.tuwien.ac.at<mailto:wien-bounces at zeus.theochem.tuwien.ac.at> <wien-bounces at zeus.theochem.tuwien.ac.at<mailto:wien-bounces at zeus.theochem.tuwien.ac.at>> en nombre de Mian Fayyaz Ahmad <fayyaz.pc at gmail.com<mailto:fayyaz.pc at gmail.com>>
Enviado: domingo, 22 de junio de 2014 09:41 p.m.
Para: Wien at zeus.theochem.tuwien.ac.at<mailto:Wien at zeus.theochem.tuwien.ac.at>
Asunto: [Wien] Formula to calculate Lattice Constant and angle of BiFeO3

Respected, Wien2K Community
I want to calculate Lattice Constant and angle of BiFeO3 in space group P1( Triclinic ). I have done volume optimization. I found a formula [V = abc( 1?cos**2alpha ?cos**2beta? cos**2gamma+2*cos alpha*cos beta*cos gamma)**1/2]. I found only volume in volume optimization. How can i found lattice parameters a, b , c and angles???