1. What is this database?

2. How the diffraction patterns are calculated?

3. How to use the database?

4. Data format.

2. How the diffraction patterns are calculated?

3. How to use the database?

4. Data format.

This database contains simulated x-ray and neutron powder diffraction patterns of the nano-sized model samples of the materials from the Crystallography Open Database (COD). For each crystalline material, the size of model sample varies in the range from 6 to 30 nm with step 3 nm allowing to identify the dependency of the powder diffraction pattern on the crystalline size. The database was obtained using volunteer computing powered by BOINC.

The powder diffraction patterns were calculated using open-source software XaNSoNS (X-ray and Neutron Scattering on Nanoscale Structures). The data from the Periodictable package for Python were used for x-ray atomic form factors and neutron scattering lengths.

XaNSoNS implements Monte-Carlo approach to handle fractional site occupancy numbers and non-zero atomic displacement parameters. Note that only isotropic atomic displacement parameters are considered (all the anisotropic atomic displacement parameters are ignored).

The site occupancy number of the atom (_atom_site_occupancy CIF field) is interpreted as a probability that atom of this type will occupy this site.

The position of each atom in each cell is shifted to a random
direction on the randomized but normally distributed distance
according to the value of the isotropic atomic displacement parameter
(_atom_site_U_iso_or_equiv CIF field), which is interpreted as a σ^{2}
of this normal distribution.

X-ray and neutron powder diffraction patterns are calculated for two different types of model samples:

spherical crystalline*isolated*of a given size (diameter),*particle**D*;crystalline*solid*with long-range order broken on the distances greater than a given value,*material**D*.

In the case of ** isolated particle** (model sample of type "a"),
the x-ray powder diffraction pattern is calculated using the following equation:

$\begin{array}{cc}\phantom{\rule{1.0em}{0ex}}& S\left(q\right)=\genfrac{}{}{0.1ex}{}{1}{N}{\displaystyle \sum _{e{l}_{i}=1}^{{N}_{el}}}({({f}_{e{l}_{i}}(q))}^{2}{N}_{e{l}_{i}}^{"at"}+2{\displaystyle \sum _{e{l}_{j}=e{l}_{i}}^{{N}_{el}}}{f}_{e{l}_{i}}(q){f}_{e{l}_{j}}(q){\displaystyle \sum _{k=0}^{{N}_{bin}-1}}{\left[{H}_{e{l}_{i},e{l}_{j}}\right]}_{k}\genfrac{}{}{0.1ex}{}{\mathrm{sin}\left(q\right(k+0.5\left){\Delta}_{bin}\right)}{q(k+0.5){\Delta}_{bin}})\hfill \end{array}$

where $q=4\pi \mathrm{sin}(\theta /\lambda )$ is the scattering vector magnitude (2θ is the scattering angle and λ is a wavelength of the source),
In the case of ** solid material** (model sample of type "b"),
the x-ray powder diffraction pattern is calculated using the modified equation:

$\begin{array}{cc}\phantom{\rule{1.0em}{0ex}}& S\left(q\right)=4\pi \rho {\left({R}_{cut}\right)}^{3}{({f}_{av}(q))}^{2}\genfrac{}{}{0.1ex}{}{\mathrm{sin}\left(q{R}_{cut}\right)}{q{R}_{cut}({\left(q{R}_{cut}\right)}^{2}-{\pi}^{2})}+\genfrac{}{}{0.1ex}{}{1}{{N}_{BS}}{\displaystyle \sum _{e{l}_{i}=1}^{{N}_{el}}}({({f}_{e{l}_{i}}(q))}^{2}{N}_{e{l}_{i}}^{"at"}+2{\displaystyle \sum _{e{l}_{j}=e{l}_{i}}^{{N}_{el}}}{f}_{e{l}_{i}}(q){f}_{e{l}_{j}}(q){\displaystyle \sum _{k=0}^{{N}_{bin}-1}}{\left[{H}_{e{l}_{i},e{l}_{j}}\right]}_{k}\genfrac{}{}{0.1ex}{}{\mathrm{sin}(\pi {r}_{k}/{R}_{cut})}{\pi {r}_{k}/{R}_{cut}}\genfrac{}{}{0.1ex}{}{\mathrm{sin}\left(q{r}_{k}\right)}{q{r}_{k}})\hfill \end{array}$

where ρ is the average atomic density of the model sample,
Note that Lorentz-polarization factor is omitted to make the diffraction patterns
dependable only on *q* and not on scattering angle and source wavelength. One should
apply Lorentz-polarization correction to the x-ray powder diffraction patterns before use.

Neutron diffraction patterns are calculated by the same formulas with the only
difference that x-ray atomic form factors are replaced by neutron scattering lengths
that do not depend on *q*.

Note that multiple scattering, inelastic scattering and absorption are not considered.

Since the COD contains all necessary information about the structures, there is no need to duplicate it in this database. If you need to search the structure by its parameters, use the advanced search in the COD website. In this database, just enter the COD ID of the structure of interest in the search field to get to the structure’s page. Alternatively, just add the COD ID to the address field after slash, e.g., http://database.xansons4cod.com/1514018.

The structure's webpage contains interactive charts showing simulated powder diffraction patterns, links to the data files (txt) with these diffraction patterns and the list of volunteers who contributed to this page by donating their computing power.

You can show/hide the curves by clicking on the respective entries
in the legend. By default, only the diffraction patterns for solid materials
for 6, 12, 18, 24 and 30 nm samples are shown. Zoom the diffraction patterns
in or out with ←→ and →← buttons. Move zoomed area right
or left with → or ← buttons.
Note that the limits of y-axis are set in such a way as to show the main
features of diffraction pattern, therefore for the single particles the
large sinusoid at small values of *q* is cropped.

You can download the data files with simulated powder diffraction patterns by clicking the links below the charts. The filename contains COD ID, type of the source (x-ray or neutron) and type of the model sample (single particle or solid material).

The first 4 lines of the file start with # symbol.

The 1^{st} line contains the information on the volunteers (ids and usernames) who
contributed to this file.

Example: `# Volunteers [id|"name"]: 34|"Conan" 13|"McShane of TSBT" 57|"gaballus"
122|"Coleslaw" 91|"PDW" 29|"fzs600"`

The 2^{nd} line is a list of the chemical elements contained in the structure.

Example: `# Elements: Sr F Al Na`

The 3^{rd} line contains the range of scattering vector magnitude,
*q*, in Å^{-1} as well as the resolution of the diffraction patterns.
For all the diffraction patterns in the database, *q _{min}* = 0.1 Å

Example: `# q in 1/A [min max N]: 0.1 8.15 4096`

The 4^{th} line is an ordered list of the sizes of the model sample in Å.

Example: `# Sizes in A: 60 90 120 150 180 210 240 270 300`

Each column of the data is a powder diffraction pattern for the respective size of the
model sample from the list of the 4^{th} line.