[Wien] amorphous binary rare-earth transition metal alloys

[Gavin Abo]

*Short answer*

The WIEN2k webpage has the sentence [1]:

/The linearized augmented plane wave (LAPW) method is among the most 
accurate methods for performing electronic *structure calculations for 
crystals*./

Amorphous is defined in [2] as non-crystalline and in [3] it means 
"shapeless" and defined an arrangement of particles that do not form 
crystals.  Thus, a strict definition of *amorphous is not a crystal*.

Under this strict definition the calculation would not be possible.  
WIEN2k requires you to provide a crystal structure with a periodic 
arrangement using lattice parameters and atomic positions (e.g. 
StructGen).  A completely amorphous material would be a non-periodic 
arrangement with randomly positioned atomic positions such that there 
would no lattice parameters.

*Long answer*

Directly quoting [4] that uses a less strict definition of amorphous 
which states:

/It is often said that amorphous materials have no structure. This is 
not strictly true.../

As described by [5], amorphous is not all the way random and has some order.

With WIEN2k, multiple supercell calculations and averaging can be used 
for an amorphous solid but it can be expected to be computational 
expensive.  Thus, it is only be possible if you have the computational 
resources for the computation.  This is paraphrased from the following 
cited references which you can look to for more information:

At [6], it has ... /average over all inequivalent occupations of the 
sites but this may need large number of calculations for large 
supercells/...

Link [7] has ... /you can also make an averaging over few calculations 
of few different unit cells/ ....

Per [8], ... /An alloy is DISORDERED and you need to simulate that by 
some random distribution of the atoms in a supercell which should be as 
large as possible./

Within section I. INTRODUCTION in [9] there is: /... the WIEN2k code is 
an example of the latter. We represent the solid by a unit cell, which 
is repeated in all three directions, corresponding to periodic boundary 
conditions. This assumes that the solid is perfect, ordered, and 
infinite; however, a real crystal differs from this ideal situation, 
since it is finite, may contain defects or impurities, and may deviate 
from its ideal stoichiometry. For these important aspects and how to 
handle them using supercells, see Chap. 8.2 of Ref. 4./

While [10] has: /One needs to use larger supercells and either a 
"quasi-random structure" or at least test a couple of arrangements of 
your impurities (more nearest-neigbors or far away, ...)/

A reference for quasi-random structure is [11].

There is other literature that may be of interest to you such as 
[12,13], "Monte Carlo study of magnetic structures in rare-earth 
amorphous alloys/"/ by A. Bondarev et. al. [14], "Recent Developments in 
Computer Modeling of Amorphous Materials" by D. A. Brabold et. al. [15], 
and "Materials modeling by design: applications to amorphous solids" by 
P. Biswas et. al. [16].

[1] http://susi.theochem.tuwien.ac.at/lapw/index.html
[2] Slide 9: 
https://www.feis.unesp.br/Home/departamentos/engenhariamecanica/maprotec/5aula_cme.pdf
[3] https://www.ck12.org/chemistry/solid/lesson/Solids-MS-PS/
       - Of note, "amorphous" is Greek for "without shape": 
https://en.wikipedia.org/wiki/Amorphous_solid
[4] http://pd.chem.ucl.ac.uk/pdnn/diff1/recip.htm
[5] https://www.doitpoms.ac.uk/tlplib/atomic-scale-structure/intro.php
[6] 
https://www.mail-archive.com/wien%40zeus.theochem.tuwien.ac.at/msg05007.html
[7] 
https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg12106.html
[8] 
https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg09398.html
[9] https://doi.org/10.1063/1.5143061
[10] 
https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg19766.html
[11] https://doi.org/10.1103/PhysRevLett.65.353
[12] https://doi.org/10.5402/2012/736341
[13] https://arxiv.org/pdf/2201.06986v1.pdf
[14] https://doi.org/10.1051/epjconf/201818504017
[15] https://arxiv.org/ftp/cond-mat/papers/0312/0312607.pdf
[16] https://doi.org/10.1088/0953-8984/21/8/084207

Kind Regards,

Gavin
WIEN2 user

On 1/19/2022 8:56 AM, sherif Yehia wrote:
> Dear Wien2k experts and users
>
> I would like to ask your kind help to clarify the following question 
> to me.
>
> We are interested in calculating some physical properties of amorphous 
> binary rare-earth transition metal alloys e.g.  GdxCo1-x  , for 
> example Gd0.16Co 0.84 using Wien2k code. Is there a possibility to 
> calculate the magnetic moment, DOS and/or other magnetic properties of 
> amorphous materials in general and for the above-mentioned alloys in 
> particular? Any comment or advice is appreciated.
>
> Thanks all for your help and guidance
>
> Sherif Yehia
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