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Structures of Alloys Generation And Recognition

Project description

This is a (P)ure python implementation of algorithm to determin Niggli cell. The library supports both 2D and 3D niggli transformations.

Rows of list or rows of numpy.ndarray correspond basis vectors, a, b, c or a, b They are input to niggli_reduce as a row with three colum matrices, same as most DFT softwares’ lattice inputs.

In the implementation details, since the lattice is represented by a row vector, the transformation operation on the lattice is left-multiplied, such as:

import numpy as np

# TMatrix is the transform matrix
new_Lattice = np.matmul(TMatrix, old_Lattice)

For details of the algorithm, see [[Niggli for 2d and 3d]](http://)


$ pip install pniggli


from pniggli import niggli_reduce, niggli_check

lattice_3D = [4.912, 0.000, 0.000,
            -2.456, 4.254, 0.000,
            0.000, 0.000, 0.000]
niggli_lattice = niggli_reduce(lattice_3D)
# Out:
# array([[ 4.912,  0.   ,  0.   ],
#        [-2.456,  4.254,  0.   ],
#        [ 0.   ,  0.   , 16.   ]])
print(niggli_check(niggli_lattice)) # True

lattice_2D = [2.4560000896, 0.0000000000,
            11.0520002567, 2.1269502021]
niggli_lattice = niggli_reduce(lattice_2D)
# Out[6]:
# array([[-1.2279999 , -2.1269502 ],
#        [-1.22800019,  2.1269502 ]])

The 2D example is a triangle motif.



  • 2D and 3D niggli reduce support

  • niggli_check for 3D lattice


  • 3D niggli reduce support

  • niggli_check for 3D lattice

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