The ABINIT Users Mailing List ( CLOSED )

["D. R. Hamann" <drhamann@mat-simresearch.com>]

Dear Jian,

Abinit calculates the elastic constants using density functional 
perturbation theory.  The strain distortions are treated analytically, 
not by actually using a strained structure for the calculations.  This 
is explained in detail in *Metric tensor formulation of strain in 
density-functional perturbation theory*, D. R. Hamann, X. Wu, K. M. 
Rabe, and D. Vanderbilt, /Phys. Rev. B/ *71*, 035117 (2005), which is in 
fact cited in the "Elastic properties" tutorial.

Best regards,
Don Hamann

Z.J. wrote:
> Dear Hamann,
>     Thank you very much for your help. I know abinit can calculate the 
> elastic tensor directly. But I want to know the calculating process of 
> elastic constants in abinit. Would you give me some instructions on 
> how to calculate the elastic constants by numerical differentiation? I 
> don't know how to obtain the input data of the distorted structure. 
> Please teach me to do this. Taking cubic structure as an example, the 
> tetragonal train and the rhombohedral one are applied to the original 
> cubic structure. Which vector of the original cubic structure, 
> primitive lattice vector or conventional lattice vector, should be 
> chosen to be multiplied by the train matrix? Comparing with the 
> cartesian coordinates and fractional coordinates of the original 
> structure, what will the cartesian coordinates and the fractional ones 
> of the distorted structure change to? To my knowledge, the fractional 
> coordinates do not change and only the cartesian coordinates do 
> change. Is this Right? I am looking forward to your reply. Thank you 
> very much for your help.
>     Best regards.
>                                                              Yours 
> sincerely,
>                                                              Jian Zhu
>
>  
> 2006/11/30, D. R. Hamann <drhamann@mat-simresearch.com 
> <mailto:drhamann@mat-simresearch.com>>:
>
>     Dear Jian,
>
>     Abinit can calculate the elastic tensor directly, giving the
>     results in
>     Cartesian coordinates and standard units (GPa).  Work through the
>     tutorial "elastic properties" and you should be able to apply these
>     methods to your problem.  (If you haven't done so, be sure to work
>     through the basic tutorials first.)
>
>     From your questions, it sounds as if you intended to calculate the
>     elastic constants by numerical differentiation.  This is very tricky,
>     and it is very difficult to get accurate results this way, especially
>     for any structure with internal degrees of freedom.
>
>     Don Hamann
>
>     Z.J. wrote:
>     > Hi, dear all users,
>     >       I am so sorry to disturb you. I have some problems
>     > about the elastic constants calculations to turn to you for your
>     > help.My problems are as follows:
>     >      (1) Must the strain matrix be multiplied with the vector of the
>     > primitive cell? If the strain matrix multiplies with the
>     conventional
>     > lattice vectors, could I obtain the right calculation results?
>     >      (2) Will both the Cartesian coordinates and the fractional
>     (x,y,z) of
>     > atoms in the distorted primitive cell change after distortation?
>     If they
>     > will change, how and what will they change?
>     >      (3) How to determine the space group of distorted primitive
>     cell?
>     >
>     >      In all, the key point of the problem is how to obtain the input
>     > data of
>     > distorted lattice of crystal.
>     >
>     >      Thank you for your valuable and informative advice very much.
>     >
>     >      Best regards.
>     >
>     >     Yours sincerely,
>     >
>     >                                                Jian Zhu
>
>     --
>     D. R. Hamann
>     Mat-Sim Research LLC    | Deptartment of Physics
>     P.O. Box 742            |  and Astronomy
>     Murray Hill, NJ 07974   | Rutgers University
>     phone: 908-370-8079     | 732-445-4381
>
>     email: drhamann@mat-simresearch.com
>     <mailto:drhamann@mat-simresearch.com>
>
>
>
>
>
> --
> School of Materials Science and Engineering
> Shanghai Jiao Tong University
> Kedy 

--
D. R. Hamann
Mat-Sim Research LLC    | Deptartment of Physics
P.O. Box 742            |  and Astronomy
Murray Hill, NJ 07974   | Rutgers University
phone: 908-370-8079     | 732-445-4381

email: drhamann@mat-simresearch.com