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Enumeration of symmetrically unique derivative superstructures of crystals.

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This code is used to enumerate all the derivative structures of a system within a crystalographic system within specified concentration and cell size ranges. The code uses a newly developed group theoretic approach that is extremely efficient and can include the enumeration of displacement directions, or arrow directions, within a system.

Full API Documentation available at: github pages.

Installing the code

To install the code use the following command in the phonon-enumeration directory:

pip intsall phenum

Alternatively you can clone this repository and use:

python install

from within the phonon-enumeration directory.

Running the code

Complete enumeration of a system.

If you want to enumerate every possible structure specified in your ‘’ file, a sample of which can be found in the input folder, then use the commend:

enumeration-py -enum

Enumerating a subset

If the total number of arrangements in your system is huge you may not want to enumerate them all. In that case it is possible to enumerate a subset of the system as follows. Examples of all input files can be found in the input folder. First have the code find the polya distribution for the system described in your file: -polya

Next we need to build an file. You may either build this by hand or have the code build it for you using the -distribution option which takes two arguments, the type of distribution and the number of structures we want in the results. -distribution all all -distribution all 100

If any option other than ‘all’ is passed into the first argument then the code will not produce an file that will be useful for the actual enumeration. The options of ‘HNF’, ‘shape’, and ‘conc’ are simply for the user’s viewing purposes.

Once an file has been constructed we can enumerate the entire set of unique configurations: -enum

This will make an enum.out file listing the unique configurations.


Phenum contains a second executable for making POSCARS. To make a POSCAR first select a structure number, or range of structures, for the POSCARs to be constructed for from the enum.out file. Then run: 10

This would make the POSCAR for the 10th structure. For a range of structures use: 20 30

To make POSCARs for the 20th to 30th structures. The POSCARS are saved as vasp.* files. To have the code calculate the lattice parameter as well use: 10 -species Al Ni

Where the Al and Ni are replaced with the elements in the system being modeled.


At times it is useful to construct the distribution based off the shapes of the supercells. For the non-expert user an option has been added to the code to make pictures of the supercells. To do this first we need to make a distribution of only the supercells: -distribution shape all -savedist

This created an file that lists only the supercells and the number of unique arrangements within each supercell. We can now visualize each of the supercells: -visualize -shape

This creates a pdf file for each of the supercells. The -shape option forces the code to include the lines that define the cell in the pdfs.

Python Packages Used

The code require the following python packages to run:

  • numpy

  • pyparsing

  • termcolor

  • matplotlib

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