phenum 1.5.3

Enumeration of symmetrically unique derivative superstructures of crystals.

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.

Prerequisites

The code currently requires a modified version of the previous enumeration code, available at https://github.com/msg-byu/enumlib, to run. To make this modified code do the following, get the symlib library:

git clone https://github.com/msg-byu/symlib.git
cd symlib/src/
make F90=(your compiler, gfortran or ifort)
cd ../../

Then get a copy of enumlib:

git clone https://github.com/msg-byu/enumlib.git

Now copy the Makefile, derivative_structure_generator.f90, and wrapper.f90 from the phonon-enumeration/support directory to the enumlib/src/ directory. Now we can make the enum.x executable and place it in our path:

cd enumlib/src/
make F90=(your compiler) enum.x
cp enum.x /bin/.

In order for enum.x to run you will need to have its input folder struct_enum.in, an example of which can be found in the input folder, for the system you desire to model. You may then choose to run enum.x yourself to generate the needed input files by typing:

enum.x

This will now generate a number of files titled cell_# where # is the cell size. These files contain the information needed to run the new enumeration code. If you do not run enum.x the enumeration.py code will execute it for you as long as its in your path. The input files are setup so that each HNF with it’s SNF and left transform (as described in http://msg.byu.edu/papers/multi.pdf and http://msg.byu.edu/papers/GLWHart_enumeration.pdf) are listed in a file titeled matrices:

#n    SNF        HNF                    left transform
 1  1  1  4    1  0  1  0  0  4      1    0    0    0    1    0    0    0    1
 1  1  1  4    1  0  1  0  1  4      1    0    0    0    1    0    0   -1    1

The first digit indicates which of the group.n files contains the symmetry group for that system. As can be seen only the diagonals of the SNF and lower traingular entries of the HNF should be included in this file. The group.n files contain the permutations of the sites on the lattice that constitute the symmtery group.

Installing the code

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

python setup.py install

Running the code

You now have everything you need to run the new enumeration code. You have two options for how to proceed. First the algorithm can use the burnside polya algorithm to predict the number of unique structures that exist for each HNF and symmetry group produced. This mode is run as follows:

enumeration.py -polya

and expects a file called lattice.in an example of which can be found in the input folder. This mode produces a file for each cell size that lists the number of unique configurations for each HNF at every possible concentration range for the cell size. This data can be very useful when modeling large systems as it will allow the user to select an appropriate distribution of structures to use given the number of each type available.

The second option is the actual enumeration of derivative structures. This mode is run using:

enumeration.py -enum

and expects a file called enum.in which can also be found in the input folder. The enum.in folder should contain a list of the desired HNFs, their concentration ranges, and the number of arrangements for the HNF concetrtaion range pair the user would like. For example:

# HNF                           Conc.       Number
  1 0 1 0 2 11                  8 3         2
  1 0 1 3 4 8                   4 4         1
  1 0 1 1 4 11                  6 5         3
  1 0 1 0 0 10                  6 4         2
  1 0 1 1 5 10                  8 2         1
  1 0 1 1 2 10                  7 3         1
  1 0 1 0 3 11                  7 4         3
  1 0 1 0 2 9                   5 4         2

Python Packages Used

The enumeration.py code require the following python packages to run:

• numpy

• pyparsing

• termcolor