cubic lattice

cubic_lattice.py

def generate_cubic_lattice(num_atoms, density):
  """
  Generate points on a cubic lattice using a desired final density.

  Parameters
  ----------
  num_atoms: int
    The number of atoms to place on the lattice.
  density: float
    The desired system density.

  Returns
  -------
  coords: list
    A nested list of generated coordinates.
  """

  # Calculate box length based on number of atoms and density.
  volume = num_atoms / density
  box_length = math.pow(volume, (1./3.))

  # Calculate the upper bound of cube size.
  # Our approach will be to place atoms until
  # we place all needed. For this, we need
  # to determine the maximum number of atoms on each
  # side.
  max_side = math.ceil(math.pow(num_atoms, (1./3.)))

  # Determine spacing based on number of atoms
  # and box length.
  spacing = box_length / max_side # units length / atom
  
  coordinates = []
  count = 0

  for i in range(max_side):
    for j in range(max_side):
      for k in range(max_side):
        coordinates.append([i*spacing, j*spacing, k*spacing])
        count += 1
        if count == num_atoms:
          return coordinates, box_length