Calculate atomic lattice plane densities in arbitrary crystal structures (CIF input) for arbitrary lattice planes (HKL indices).

For the paper, please refer to https://doi.org/10.1107/S1600576722001492.

• MaXrd package

The following instructions are adapted from https://mathematica.stackexchange.com/a/672/61736.

1. Open LatticePlane.m in Mathematica
2. Choose File --> Install...
3. Choose Type --> Package, Source --> (the open notebook), Install Name --> LatticePlane
4. Load the package by evaluating (including the <<):

<<LatticePlane`

Ensure the name is not mispelled (including capitalization).

The Install... menu item will put the package into FileNameJoin[{$UserBaseDirectory, "Applications"}] which on Windows is %AppData%\Mathematica\Applications.

To test that it has installed correctly, open the documentation via:

?LatticePlane

CIF files are loaded using a slightly modified version of MaXrd ImportCrystalData[] named ImportCrystalData2[]. The first argument to ImportCrystalData2 is the path to the CIF file (without the .cif extension), and the second argument is a key that will be used to access data relating to the compound.

The primary functionality of LatticePlane is contained in DensityHKL[], which can be used as follows:

{Aoutn, AoutCt, hkl, Afulln, AfullCt, hklFull, elem}=DensityHKL[mpid,n,hklMax,radiusFactorIn];

where mpid is the Materials Project ID or other key for a CIF file assigned via ImportCrystalData2, n is the supercell size, hklMax is the maximum HKL index to consider, and radiusFactorIn is the maximum distance between the HKL plane of interest and each atom in the compound that is allowed for an atom to be considered in the intersection scheme. Aoutn contains the area of each element in a particular plane normalized by the radius of that atom for the unique HKL planes. AoutCt contains the total number of atoms (fractional values OK) of an element within a plane for the unique HKL planes. hkl is a list of the unique HKL planes. Afulln, AfullCt, and hklFull consider the degenerate HKL planes as well. Finally, elem is the list of unique elements.

To reproduce the plots from the paper such as the following (annotations added manually), see PlotSymmetrizedFullHKL[] which uses several of the outputs from DensityHKl[].

Please refer to LatticePlane-example.nb. A high-throughput calculation workflow and machine learning application is given in ml-test.nb.