# Re: [SIESTA-L] [*] Re: [SIESTA-L] question about elastic constant

```Respected Sir,
Sorry for so many queries.

In the paper of S Q Wang et al. J Phys. Cond. Matter 15 (2003) 5307,
He uses three types of strains```
```
1. Tri-axial shear strain to calculate C44
2. volume conservative orthorombic strain to calculate shear modulus C`
and
3. Hydrostatic pressure to calculate Bulk modulus.

In my calculations, on applying the 3rd strain, I am getting different volumes
(Volume non-conserve) and 1st & 2nd type volume remain conserve.

Because in order to calculate 3 elastic constants (C11, C12 and C44) we require
3 equations, so do I have to use the above three equations, both type (volume
conservative and non-conservative) to calculate a single set of elastic
constants?

Bipul Rakshit

PhD in Physics

Computational Research Lab.

Barkatullah University,

Bhopal 462 026, India

Mob.: +919713445650

--- On Wed, 15/7/09, Sushil Auluck <saul...@iitk.ac.in> wrote:

From: Sushil Auluck <saul...@iitk.ac.in>
Subject: Re: [*]  Re: [SIESTA-L] question about elastic constant
To: "bipul rakshit" <bipu...@yahoo.co.in>
Date: Wednesday, 15 July, 2009, 8:56 PM

bipul,
you can have 2 kinds of strains...volume conserving
and volume non conserving...each gives different
elastic constants.....
s.auluck

> Dear Sir,
> I have one more doubt, that, if I calculate the set of lattice vector,
> applying the following strains
> Â Â  e = (Î´, Î´, (1 + Î´)^ (âˆ’2)Â  âˆ’ 1, 0, 0, 0)
>
> as given in the paper attached with this mail,
>
> then the cell volume was not remain constant for all the lattice vectors.
> Means for different lattice vectors, the cell volume changes.
>
> But for other two set of strains
> e = (0, 0, 0, Î´, Î´, Î´)
> and e =(Î´, Î´, Î´, 0, 0, 0)
> the cell volume doesnt change for all the lattice vector.
>
> So is it the correct method I am applying? Or there should be no change of
> cell volume?
>
> Â delta E/VÂ  = 6*C*Î´^2 + O(Î´^3
> ).Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  (7)
> V
>
>
> Bipul Rakshit
>
> PhD in Physics
>
> Computational Research Lab.
>
> Barkatullah University,
>
> Bhopal 462 026, India
>
> Mob.: +919713445650
>
> --- On Wed, 15/7/09, Sushil Auluck <saul...@iitk.ac.in> wrote:
>
> From: Sushil Auluck <saul...@iitk.ac.in>
> Subject: Re: [*]  Re: [SIESTA-L] question about elastic constant
> To: bipu...@yahoo.co.in
> Date: Wednesday, 15 July, 2009, 7:01 PM
>
> bipul,
> if you look at the derivation you will find terms like (1+d)**(1/2)
> or (1+d)**(1/3)....d is delta.....so when you expand using binomial
> theorem you will terms linear in d, quadratic in d, and cubic in d...
> in this context the series is terminated after the quadratic and so
> the remaining terms ( these are niglected) are order d**3.....
> s.auluck
>
>> Respected Sushil Auluck,
>> Thanks for your kind reply. As you said that the term means of order
>> delta
>> cube.
>> But I just want to know the equation of that term. Means how that order
>> delta cube, mathematically looks like. I asked this because, using that
>> equation, I have to find the elastic constants.
>> regards
>>
>> Bipul Rakshit
>>
>> PhD in Physics
>>
>> Computational Research Lab.
>>
>> Barkatullah University,
>>
>> Bhopal 462 026, India
>>
>> Mob.: +919713445650
>>
>> --- On Mon, 13/7/09, Sushil Auluck <saul...@iitk.ac.in> wrote:
>>
>> From: Sushil Auluck <saul...@iitk.ac.in>
>> Subject: Re: [SIESTA-L] question about elastic constant
>> To: SIESTA-L@listserv.uam.es
>> Date: Monday, 13 July, 2009, 9:48 PM
>>
>> hi,
>> that means terms of order delta cubed (delta**3)......
>> s.auluck
>>
>>> DearÃ‚Â  Siesta Users,
>>> I have read the paper
>>> "S. Q. Wang, H. Q. Ye, J. Phys.: Condens. Matter 15 (2003) p. 5307."
>>> Ã‚Â
>>> Most of the thing is clear to me, except in Equation (7) what is
>>> "O(ÃŽÂ´^3)"
>>> ? What does 'O' here.
>>>
>>>
>>> Please guide me for the same.
>>>
>>>
>>> Bipul Rakshit
>>>
>>> PhD in Physics
>>>
>>> Computational Research Lab.
>>>
>>> Barkatullah University,
>>>
>>> Bhopal 462 026, India
>>>
>>> Mob.: +919713445650
>>>
>>>
>>>Â  Â  Â Â Â See the Web's breaking stories, chosen by people like you..
>>> Check
>>> out Yahoo! Buzz. http://in.buzz.yahoo.com/
>>
>>
>> ........................................................................
>> Prof. Sushil AuluckÂ  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â
>> Phone:+91-512-6797092/6148
>> Department of PhysicsÂ  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â
>> +91-512-6798177(Home)
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>> E-mail:saul...@iitk.ac.inÂ  Â  Â  Â
>> Â
>> Â Â Â ................................................:saul...@gmail.com
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>> ........................................................................
>> ~
>>
>>
>>
>>Â  Â  Â Â Â See the Web's breaking stories, chosen by people like you.
>> Check
>> out Yahoo! Buzz. http://in.buzz.yahoo.com/
>
>
> ........................................................................
> Prof. Sushil AuluckÂ  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â
> Phone:+91-512-6797092/6148
> Department of PhysicsÂ  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â
> +91-512-6798177(Home)
> Indian Institute of TechnologyÂ  Â  Â  Â  Â Â Â Cell :+91-9305548667
> Kanpur 208016 (UP)Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â Â Â FaxÂ
> :+91-512-6790914
> IndiaÂ  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â
> E-mail:saul...@iitk..ac.inÂ  Â  Â  Â
> Â  Â Â Â ................................................:saul...@gmail.com
> http://www.iitk.ac.in/phy/People/phy_facvis.html
> http://www.iitk.ac.in/phy/New01/profile_SA.html
> ........................................................................
> ~
>
>
>
>       See the Web's breaking stories, chosen by people like you. Check
> out Yahoo! Buzz. http://in.buzz.yahoo.com/

........................................................................
Prof. Sushil Auluck                      Phone:+91-512-6797092/6148
Department of Physics                          +91-512-6798177(Home)
Indian Institute of Technology           Cell :+91-9305548667
Kanpur 208016 (UP)                       Fax  :+91-512-6790914
India                                    E-mail:saul...@iitk..ac.in
...............................................:saul...@gmail.com
http://www.iitk.ac.in/phy/People/phy_facvis.html
http://www.iitk.ac.in/phy/New01/profile_SA.html
........................................................................
~

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