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Exploiting superspace to enable DFT calculations of modulated structures with disordered sites using the example of mullite
* 1 , 2 , 1
1  Dpto de Física de la Materia Condensada, Facultad de Ciencia y Tecnología, Universidad del País Vasco UPV/EHU
2  Dpto de Física Aplicada II, Facultad de Ciencia y Tecnología, Universidad del País Vasco UPV/EHU


Modulated structures with a harmonic occupational modulation are not suitable for force field methods (including molecular dynamics) or density functional theory (DFT) calculations because fully occupied sites are required. Instead of assuming a random distribution with some constraints, which is a common approach, the harmonic occupational modulation function from a refinement in superspace can be replaced by a block wave function resulting in a model, that represents the hypothetical completely ordered structure with fully occupied sites. If the modulation wave vector corresponds to a commensurate modulation, the corresponding model in physical space can be used for DFT calculations, otherwise a commensurate approximation is needed. As an example, the present approach is applied to the modulated structure of mullite to determine the ideal Al/Si ordering for different compositions and supercell sizes. For the analyzed composition, the calculations yield consistently the same Al/Si ordering pattern. The results are also in qualitative agreement with the refinement of the not fully ordered structure, i.e. the volumes of tetrahedra with Al/Si disorder follow the trend of the Al/Si ordering pattern from the DFT calculations. The example shows that the approach allows to determine structural parameters, that are very difficult or even impossible to access experimentally.

Keywords: disorder; DFT; superspace; mullite; Al/Si ordering;
Comments on this paper
Paul Klar
Download button leads you to the poster.
Please click on the download button to the see poster that explains graphically this abstract.

Alberto Girlando
Poster is good to catch the eye, but you can prepare a paper where the details can be better explained.

I remember some cases in the field of organic metals (for instance, Tetrathiafulvalene-Tetracyanoquinodimethane, TTF-TCNQ) where the incommensuration is between the electronic density (or Charge Density Wave) and the positions of the ions (molecules in this case). Can your method be applied to there cases also ?
Paul Klar
In principal this method is applicable to any modulated structure. The main limitation (nowadays) is the number of atoms in the supercell that represents the commensurate approximation. The largest structure I worked with has 594 atoms and is a 38-fold supercell of mullite. Although the DFT calculation took months (!), the result is in agrrement with the other calculations of smaller supercells with different compositions.
If I am right, your example has two modulation wave vectors. It depends on these modulation wave vectors if a commensurate approximation of appropriate size is available or not. With improving computing power, larger and larger systems can be investigated in the future and the size limitation will become less relevant.