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Quasicrystals were known well before 2015. The recent developments is in showing that such crystals exist naturally, rather than just in synthesized samples. The first (nowadays generally accepted) clear demonstration of an aperiodic crystal was published in 1984. Examples of such crystals remain very rare compared to periodic crystals, however. So rare in ...
18
You can see it with VESTA software. For example, we can see the different lattice planes of NaCl crystal.
[001] plane of NaCl:
[101] plane of NaCl:
[111] plane of NaCl:
13
Assuming you have an atoms object, all you need to do is call the "write" function.
from ase import Atoms
supercell = Atoms()
supercell.write("supercell.xyz")
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Assuming a generic chemistry background I wouldn't assume that knowledge of crystal structure would be too in depth at an undergraduate level. It is definitely encountered, but depending on the type of chemistry you want to go into, you probably never deal with solid state chemistry. I would first explain briefly how crystals are described by periodic ...
12
I think the naming conventions are standardized and people computing band structures employ them directly. I will break down the high-symmetry points for a 2-D brillouin zone and post very good references for you to explore 3-D BZs.
Take a rectangular Brillouin zone as the one depicted below:
The center of the brillouin zone is unequivocally marked as $\...
9
If you haven't figured it out yet here is what I would've done using mercury to get the xyz file of the dimer. There is some disorder in the crystal structure which I think means that there are partial occupations of molecules/atoms at different positions so you need to delete them to get only one of set of the dimers in the xyz file.
9
The $\Sigma$ values represent the volume of the Coincident Site Lattice (CSL) of the grain boundary in terms of the volume of the unit cell of the crystal. In general, grain boundaries with higher symmetry have lower $\Sigma$ values.
Note that CSL boundaries are special grain boundaries. So, they do not represent all grain boundaries comprehensively. But, ...
9
Yes, nematic order is an alignment of rotational degrees of freedom without spatial structure.
One good example of a nematic phase occurs in a liquid crystal composed of elongated molecules. The molecules can align their long axes (breaking the rotational symmetry) without forming any lattice or long-range correlations in their spatial positions. If you were ...
9
From that reference, what we got is the bond length from the atomic positions.
One easy way is to look for a CIF file with the crystal information.
From the CIF49801 bellow, we get the following info:
(label type_symbol symmetry_multiplicity Wyckoff_symbol fract_x fract_y fract_z B_iso_or_equiv occupancy)
Mo1 Mo4+ 2 c 0.3333 0.6667 0.25 . 1.
S1 ...
8
If you know which atoms correspond to each other in the two structures,
you can use a structural superposition method.
Least-squares superposition methods find the rotation matrix and translation that minimizes the RMSD between given points.
There are a few well-established methods.
Recently, I had to use one and I picked QCP
(because it comes with BSD-...
8
As Thomas mentioned, there are tools from Materials Project that we use for structure similarity. See for example this paper, with code available in pymatgen. This works by creating local environment "fingerprints" (e.g. octahedral, tetrahedral sites, etc.) and creating a distance between structures based on this.
Other that this, one method I'm ...
7
As far as I understand, this warning can be safely ignored. While parsing a cif structure, the get_spacegroup() function in the cif parser of ASE, checks whether the space group evaluated by ASE is consistent with the cell symmetry mentioned in the cif file. The relevant part of the function is shown below:
if setting_name:
no = Spacegroup(...
7
Cut a surface with ASE:
from ase.io import read,write
from ase.build import surface
A=read('Input_Your_Strcuture.cif',format='cif') ### format can be vasp.
B=surface(A,(-1,0,1),1,vacuum=15)
write('Output_Your_Surface.vasp',ou_struct,format='vasp')
Reference: https://wiki.fysik.dtu.dk/ase/ase/build/surface.html
Reconstruct your surface with ...
7
I understand that you are trying to implement cell lists. For orthogonal unit cell (or even better - cubic) the cells that subdivide the unit cell are nicely aligned with the unit cell. Wikipedia has this illustration:
For a non-orthogonal unit cell the calculations are more complex, but you can still use a rectangular box divided into cells. Here is an ...
7
Not sure what your input files are, but there's a technique based on spherical harmonics that is relevant described here: High Throughput Profiling of Molecular Shapes in Crystals https://doi.org/10.1038/srep22204
The spherical harmonics approximate the shape of the electron distribution. They are then made rotationally invariant, and result in a descriptor ...
6
I recommend that you calculate directly. You can use a package like ASE to generate terminations of a given surface using the build module. For the treatment of surface energies I would refer you to this paper. If you find that an automated approach to surface terminations would be useful you may also want to look at CatKit.
Once you have surface energies,...
6
The 0001 facet area will be only dependent on the $a$ lattice constant. To solve for the area of that surface, you will just need to find the area of a rhombus with a $60^{\circ}$ angle.
To read the intended cell, start from the unit cell of the 0001 surface. Then multiply the surface vectors by the two values given, $\sqrt{3}$ and $\sqrt{3}$. Then you ...
6
It seems you are looking for a package to compute the irreducible representation of electronic states computed by VASP. This has been recently developed:
J. Gao J, Wu Q, Persson C, Z. Wang. Irvsp: to obtain irreducible representations of electronic states in the VASP. Comput. Phys. Comm. 261, 107760 (2021). https://doi.org/10.1016/j.cpc.2020.107760.
And the ...
6
tldr; Try one of the [nightly builds](https://nightly.link/OpenChemistry/avogadrolibs/workflows/build_cmake/master)
Avogadro uses Open Babel to read CIF files, and unfortunately, OB versions before v3 would break molecules such that all atoms fit within the unit cell. Typically, most people would rather have a contiguous molecule even if it goes through a ...
6
You can use ASE.
For your case, I assume you are using the Pd crystal structure with space group 225.
Cut the (111) surface with ASE:
from ase.io import read, write
from ase.build import surface
####================================================
A=read('Pd_mp-2_conventional_standard.cif',format='cif')
B=surface(A,(1,1,1),5,vacuum=10)
write('111.vasp',B,...
6
I don't know if this is exactly what you want to do, but pymatgen may be able to help (disclosure, I am a developer of this package).
See this example code below for your example input file:
from pymatgen.core.structure import Structure, Molecule
from pymatgen.analysis.graphs import StructureGraph
from pymatgen.analysis.local_env import JmolNN
# load the ...
5
I would propably explain that there are different planes within a crystal, show some of them in an animation or pyhsical prop and depending on the depth of the presentation just omit the numbering and details.
5
It is important to distinguish the origin of twinning, because it produces different features (and different kinds of what is commonly referred to as "twinning").
For example twinning can develop during the crystal growth as a special feature of the crystal morphology (contact or penetration twins). On the other hand, a single crystal undergoing a ...
4
This Physics Stack Exchange thread answers this question very well.
Apparently, the length scale of such "logarithmic divergence" is actually merely in the order of atomic distances even if the entire graphene sheet is as large as the solar system!
So practically, the results of the theorem is irrelevant to the real-world graphene, even though ...
4
Take care in the figure posted by Jack that the [hkl] notation actually represents the vector plane, that is the direction perpendicular to the plane. The plane are indexed as (hkl).
for example, the first figure should be read as (001) plane of NaCl, whereas [001] represents the direction along the c-axis.
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I have done computational fitting of LEED-IV in the past using an older code and, yes, you are correct. You can do these optimizations on a workstation now for small systems, although I don't recommend it. I ended up doing most of the calculations on a high-performance computer anyway (and you will do that as well for such a large system).
For the system ...
4
In Bragg's law, $n\lambda=2d\sin(\theta)$. Here, $n$ is the order of the reflection, and corresponds to the path length difference between X-rays diffracted from two different layers of atoms, in terms of the number of wavelengths. So if the path lengths differ by exactly one wavelength, it is a first order reflection.
By convention, we treat all reflections ...
4
If you're familiar with Python, this can be done using pymatgen fairly easily.
To illustrate, let's first define our problem:
from pymatgen.core.lattice import Lattice
from pymatgen.core.structure import Structure
malnac_lattice = Lattice.from_parameters(5.33, 5.14, 11.25, 102.7, 135.17, 85.17)
malnac02_lattice = Lattice.from_parameters(5.156, 5.341, 8.407, ...
4
There is a nice explanation here outlining the difficulties for the minimum image convention in triclinic cells.
It describes an exact approach, as well an approximate algorithm (referencing appendix C here and Tuckerman appendix B) used by many major molecular dynamics codes. This related discussion is also useful.
There is also this question from the ...
3
For an atom in the boundary, the distance with all other atoms of the molecule it is part of will be different based on whether we take into account minimum image convention (MIC) or not. Thus we can,
first identify the indices of all the molecules in the structure and
then exclude the molecules for which any of the distance is different if MIC is ...
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