[Wien] Query regarding elastic constants of SnSe2

[Fecher, Gerhard]

This means,
2nd order  a0 + a1 x + a2 x^2, 3rd order a0 + a1 x + a2 x^2 + a3x^3 and 4th order polynomials a0 + a1 x + a2 x^2 + a3x^3 +a4 x^4  are fitted to the strain data to find the coefficients cij or combinations of cij's.

Note: a 4th order polynomial fit to data with the 5 standard used strains (+2% ... -2%) does not make much sense, as the number of fit parameters (a_i, i=0,4) equals the number of available data n=5.
such a fit will look perfect (the curve will go through all points)  but the uncertainty will be infinite.
A correct determination of accuracy of the parameters, standard deviation, and skewness of the curves will indeed need more distortions than 5 (I guess at least 9 or 11), also the maximum size (+-2%) needs to be checked.
Anyway, one needs to check which order of the polynomial describes the functional dependence well. (Procedures are well described in textbooks on statistics and non linear curve fitting)

If you know about non-linear curve fitting procedures and model functions then you know what those outputs mean and which output to consider.

In all SYMM cases, one calculation is for hydrostatic pressure (not volume-conserving), in that case I would prefer a Birch Murnaghan (or other) equation of state fit instead o a simple polynomial.
(It also will result in more reliable values for the bulk modulus, directly)

I checked the scripts and found that the set_elast script finds the correct space group for compounds with C6 (CdI2) structures from which it should use "symm=R", however it takes the H lattice type from the structure file instead of interpreting 
the space group with trigonal crystal system correctly. Therefore, it calculates only 5 instead of 6 coefficients (see textbook of J.F. Nye Physical Properties Of Crystals).
(Note that "crystal system" and "lattice type" are not the same, in general)

Ciao
Gerhard

DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:
"I think the problem, to be quite honest with you,
is that you have never actually known what the question is."

====================================
Dr. Gerhard H. Fecher
Institut of Physics
Johannes Gutenberg - University
55099 Mainz
________________________________________
Von: Wien [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von shamik chakrabarti [shamik15041981 at gmail.com]
Gesendet: Mittwoch, 7. August 2024 03:48
An: A Mailing list for WIEN2k users
Betreff: Re: [Wien] Query regarding elastic constants of SnSe2

Dear Sir,

               In the output-order file there are 3 types of outputs. One is for order of fit 2, another is order of fit 3 and the last one is order of fit is 4. My query which output among those three should be considered?

with regards,

On Tue, 6 Aug 2024 at 13:37, Fecher, Gerhard <fecher at uni-mainz.de<mailto:fecher at uni-mainz.de>> wrote:
Why runsp_lapw, isn't SnSe2 a semiconductor without magnetic order and a non-spinpolarized calculation is just fine ?

According to Pearsons Crystal Database from 2022, SnSe2 should crystallize in P -3m1 (no. 164),
in its crystal class -3m (also for 3m, 32) one has 6 independent elastic constants (11 12 13 14 33 44)
(dependent are 22=11, 55=44, 23=13, 24=-14, 56=14,  c66 =( c11-c12)/2))

If you use a hexagonal structure, you will have only 5 independent constants (11 12 13 33 44)
in both cases hexagonal and trigonal (also crystal classes 3, -3 with seven independent constants) you have c66 =( c11-c12)/2 which is NOT independent

As Morteza mentions, Se on 2d has a free z-parameter and thus the position needs to be optimized.
Moreover, when the lattice is distorted, some atoms may occupy sites with free parameters even though the original didn't have.
Therefore you need to minimize the forces and optimize all free positions that appear in all structures during the determination of the elastic constants.
Usually one compares the elastic properties with fixed and relaxed positions. The differences in the equation of state p-V-E curves can be attributed to something like an intenal pressure as in real gases cpmpared to ideal ones.

Did you use the correct structure and space group ?
On the materials explorer project webpage you will find the matrix with 6 independent values for the stiffness or compliance tensors.

Everything one needs to know is provided in textbooks !

Ciao
Gerhard

DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:
"I think the problem, to be quite honest with you,
is that you have never actually known what the question is."

====================================
Dr. Gerhard H. Fecher
Institut of Physics
Johannes Gutenberg - University
55099 Mainz
________________________________________
Von: Wien [wien-bounces at zeus.theochem.tuwien.ac.at<mailto:wien-bounces at zeus.theochem.tuwien.ac.at>] im Auftrag von morteza jamal via Wien [wien at zeus.theochem.tuwien.ac.at<mailto:wien at zeus.theochem.tuwien.ac.at>]
Gesendet: Montag, 5. August 2024 20:24
An: shamik15041981 at gmail.com<mailto:shamik15041981 at gmail.com>; wien at zeus.theochem.tuwien.ac.at<mailto:wien at zeus.theochem.tuwien.ac.at>
Cc: morteza jamal
Betreff: Re: [Wien] Query regarding elastic constants of SnSe2

Dear  Shamik,
As i checked your scf files for C33 calculation, I saw there are forces on your atoms (atom 2) and you must relax your stuct files ( runsp_lapw  -min .....  or  min_lapw " runsp_lapw ....".

Try to converge  "Energy,  Charge and force"
runsp_lapw  -min ..... -ec 0.0001 -cc ... -fc ...


With best,
Morteza
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--
Dr. Shamik Chakrabarti
Research Fellow
Department of Physics
Indian Institute of Technology Patna
Bihta-801103
Patna
Bihar, India