Shape analysis¶

This notebook shows how to perform shape analysis using GEMDAT.

This uses a generalized algorithm that for all symmetrically equivalent cluster centers, finds nearest atoms from trajectory, and transforms them back to the asymmetric unit. This helps the statistics for performing shape analysis and making plots.

As input you will need:

symmetrized crystal or material structure
- contains unique sites to act as cluster centers (asymmetic unit)
- provides symmetry operations
- Gemdat uses SpacegroupAnalyzer to find symmetry in P1 structures
trajectory
- typically P1
- maybe a supercell of the structure in #1
- lattice can be triclinic (non-constrained in simulation)

The ShapeAnalyzer algorithm works as follows:

reduce supercell of trajectory to match clusters
- assert trajectory and cluster lattices are similar
for every unique center:
- for every symmetry operation:
  - apply symmetry operation to center coordinates
  - find all trajectory points within X distance of transformed coordinates (wrap around pbc)
  - copy and map points back to asymmetric unit (reverse symmetry op)
  - subtract center coords
- concatenate all coords and convert to Cartesian coordinate system

The result is a set of trajectory positions centered on the input sites. These can be used to perform shape analysis: plots, fits, heat maps, msd, etc.

See: https://github.com/GEMDAT-repos/GEMDAT/pull/166

Loading data¶

Loading trajectory for argyrodite and cif file with 3 unique sites as cluster centers.

In [1]:

Copied!

from pathlib import Path
from IPython.display import Image

from gemdat import Trajectory, load_known_material, read_cif

from gemdat.utils import VASPRUN

# Use your own data:
#VASPRUN = '/home/simone/shape_analysis/vasprun.xml'

trajectory = Trajectory.from_vasprun(VASPRUN)
diff_trajectory = trajectory.filter('Li')

workdir = Path('/home/simone/shape_analysis')
structure = read_cif(workdir / 'argyrodite_48h48h16e.cif')
from pathlib import Path
from IPython.display import Image

from gemdat import Trajectory, load_known_material, read_cif

from gemdat.utils import VASPRUN

# Use your own data:
#VASPRUN = '/home/simone/shape_analysis/vasprun.xml'

trajectory = Trajectory.from_vasprun(VASPRUN)
diff_trajectory = trajectory.filter('Li')

workdir = Path('/home/simone/shape_analysis')
structure = read_cif(workdir / 'argyrodite_48h48h16e.cif')

/home/simone/.virtualenvs/GEMDAT/lib/python3.10/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html
  from .autonotebook import tqdm as notebook_tqdm

Set up shape analyzer¶

Note that the we use the .from_structure constructor. This symmetrizes the input structure.

In [2]:

Copied!

from gemdat.shape import ShapeAnalyzer

sa = ShapeAnalyzer.from_structure(structure)
sa
from gemdat.shape import ShapeAnalyzer

sa = ShapeAnalyzer.from_structure(structure)
sa

Out[2]:

ShapeAnalyzer
    Spacegroup
        F-43m (216)
    Lattice
        abc   :   9.924000   9.924000   9.924000
        angles:  90.000000  90.000000  90.000000
    Unique sites (3)
        PeriodicSite: 48h (Li) (1.816, 1.816, 0.2382) [0.183, 0.183, 0.024]
        PeriodicSite: 48h2 (Li) (0.7939, 0.7939, 1.816) [0.08, 0.08, 0.183]
        PeriodicSite: 16e (Li) (8.535, 8.535, 8.535) [0.86, 0.86, 0.86]

Clustering¶

The next cell shows how to run the shape analysis. The radius in Ångström is used to determine if an atom belongs to a cluster.

The supercell is used to fold the trajectory coordinates to the same lattice as the input sites. A warning will be raised if the lattices are not close.

Alternatively, you can pass any numpy array with fractional coordinates to sa.analyze_positions()

In [3]:

Copied!





supercell = (2, 1, 1)
radius = 1.5  # Å

shapes = sa.analyze_trajectory(
    trajectory=diff_trajectory,
    supercell=supercell,
    radius=radius,
)

shapes[0]
supercell = (2, 1, 1)
radius = 1.5  # Å

shapes = sa.analyze_trajectory(
    trajectory=diff_trajectory,
    supercell=supercell,
    radius=radius,
)

shapes[0]

Out[3]:

ShapeData(site=PeriodicSite: 48h (Li) (1.816, 1.816, 0.2382) [0.183, 0.183, 0.024], coords=array([[-0.11849693, -0.18059447, -0.13624759],
       [-0.11845465, -0.18054009, -0.13623201],
       [-0.11408353, -0.17492211, -0.13461787],
       ...,
       [ 0.14599772, -0.3845679 ,  0.33624656],
       [ 0.09911793, -0.08174161,  0.16656819],
       [ 0.15608983, -0.3903394 ,  0.32736338]]), radius=1.5)

Plot shapes¶

Shape data can be plotted using the plots module. This shows each set of shape coordinates from all three directions.

In [4]:

Copied!





import matplotlib.pyplot as plt
import numpy as np

bins = np.linspace(-radius, radius, 50)

# [Optional] To save space in the notebook, we convert the interactive figures to a images. 
# You can use fig.show() as shown above to get the interactive figure instead 
for shape in shapes:
    fig = shape.plot(bins=bins)
    img_bytes = fig.to_image(format="png")
    display(Image(img_bytes))
    
import matplotlib.pyplot as plt
import numpy as np

bins = np.linspace(-radius, radius, 50)

# [Optional] To save space in the notebook, we convert the interactive figures to a images. 
# You can use fig.show() as shown above to get the interactive figure instead 
for shape in shapes:
    fig = shape.plot(bins=bins)
    img_bytes = fig.to_image(format="png")
    display(Image(img_bytes))
    

No description has been provided for this image

Plot nearby sites¶

You can supply a nearby sites to display them on the plot.

In [5]:

Copied!

shape = shapes[0]

sites = structure.get_sites_in_sphere(pt=shape.origin, r=radius)

fig = shape.plot(bins=bins, sites=sites);

# [Optional] To save space in the notebook, we convert the interactive figures to a images. 
# You can use fig.show() as shown above to get the interactive figure instead 
img_bytes = fig.to_image(format="png")
Image(img_bytes)
shape = shapes[0]

sites = structure.get_sites_in_sphere(pt=shape.origin, r=radius)

fig = shape.plot(bins=bins, sites=sites);

# [Optional] To save space in the notebook, we convert the interactive figures to a images. 
# You can use fig.show() as shown above to get the interactive figure instead 
img_bytes = fig.to_image(format="png")
Image(img_bytes)

Out[5]:

Optimize sites¶

You can optimize the site positions using the ShapeAnalyzer.optimize_sites() method. This uses the centroid of the shapes to shift the sites.

In [6]:

Copied!

sa_shifted = sa.optimize_sites(shapes=shapes)
sa_shifted
sa_shifted = sa.optimize_sites(shapes=shapes)
sa_shifted

Out[6]:

ShapeAnalyzer
    Spacegroup
        F-43m (216)
    Lattice
        abc   :   9.924000   9.924000   9.924000
        angles:  90.000000  90.000000  90.000000
    Unique sites (3)
        PeriodicSite: 48h (Li) (1.889, 1.889, 0.3047) [0.1903, 0.1903, 0.0307]
        PeriodicSite: 48h2 (Li) (0.9555, 0.9555, 1.861) [0.09629, 0.09629, 0.1875]
        PeriodicSite: 16e (Li) (8.658, 8.658, 8.658) [0.8725, 0.8725, 0.8725]

In [7]:

Copied!





shapes = sa_shifted.analyze_trajectory(
    trajectory=diff_trajectory,
    supercell=supercell,
    radius=radius,
)

for shape in shapes:
    fig = shape.plot(bins=bins)
    # [Optional] To save space in the notebook, we convert the interactive figures to a images. 
    # You can use fig.show() as shown above to get the interactive figure instead 
    img_bytes = fig.to_image(format="png")
    display(Image(img_bytes))
    
shapes = sa_shifted.analyze_trajectory(
    trajectory=diff_trajectory,
    supercell=supercell,
    radius=radius,
)

for shape in shapes:
    fig = shape.plot(bins=bins)
    # [Optional] To save space in the notebook, we convert the interactive figures to a images. 
    # You can use fig.show() as shown above to get the interactive figure instead 
    img_bytes = fig.to_image(format="png")
    display(Image(img_bytes))
    

Custom shifts¶

You can also use your own vectors to shift the sites:

In [8]:

Copied!





vectors = (
    [1, 0, 0],
    [2, 0, 0],
    [3, 0, 0],
)

sa_shifted = sa.shift_sites(vectors=vectors)
sa_shifted
vectors = (
    [1, 0, 0],
    [2, 0, 0],
    [3, 0, 0],
)

sa_shifted = sa.shift_sites(vectors=vectors)
sa_shifted

Out[8]:

ShapeAnalyzer
    Spacegroup
        F-43m (216)
    Lattice
        abc   :   9.924000   9.924000   9.924000
        angles:  90.000000  90.000000  90.000000
    Unique sites (3)
        PeriodicSite: 48h (Li) (2.816, 1.816, 0.2382) [0.2838, 0.183, 0.024]
        PeriodicSite: 48h2 (Li) (2.794, 0.7939, 1.816) [0.2815, 0.08, 0.183]
        PeriodicSite: 16e (Li) (11.53, 8.535, 8.535) [1.162, 0.86, 0.86]

Get structure¶

Use ShapeAnalyzer.get_structure() to retrieve a pymatgen Structure object back:

In [9]:

Copied!

sa_shifted = sa_shifted.to_structure()
sa_shifted
sa_shifted = sa_shifted.to_structure()
sa_shifted

Out[9]:

Structure Summary
Lattice
    abc : 9.924 9.924 9.924
 angles : 90.0 90.0 90.0
 volume : 977.3728410239999
      A : 9.924 0.0 6.076697417369166e-16
      B : 1.5959009175390938e-15 9.924 6.076697417369166e-16
      C : 0.0 0.0 9.924
    pbc : True True True
PeriodicSite: 48h (Li) (7.108, 5.2, 3.146) [0.7162, 0.524, 0.317]
PeriodicSite: 48h (Li) (0.2382, 2.146, 3.146) [0.024, 0.2162, 0.317]
PeriodicSite: 48h (Li) (7.108, 4.724, 6.778) [0.7162, 0.476, 0.683]
PeriodicSite: 48h (Li) (9.686, 7.778, 3.146) [0.976, 0.7838, 0.317]
PeriodicSite: 48h (Li) (2.816, 5.2, 6.778) [0.2838, 0.524, 0.683]
PeriodicSite: 48h (Li) (1.816, 5.2, 7.778) [0.183, 0.524, 0.7838]
PeriodicSite: 48h (Li) (1.816, 4.724, 2.146) [0.183, 0.476, 0.2162]
PeriodicSite: 48h (Li) (9.686, 7.108, 1.816) [0.976, 0.7162, 0.183]
PeriodicSite: 48h (Li) (7.108, 0.2382, 8.108) [0.7162, 0.024, 0.817]
PeriodicSite: 48h (Li) (0.2382, 7.108, 8.108) [0.024, 0.7162, 0.817]
PeriodicSite: 48h (Li) (8.108, 2.816, 9.686) [0.817, 0.2838, 0.976]
PeriodicSite: 48h (Li) (2.816, 8.108, 9.686) [0.2838, 0.817, 0.976]
PeriodicSite: 48h (Li) (1.816, 7.108, 9.686) [0.183, 0.7162, 0.976]
PeriodicSite: 48h (Li) (7.108, 8.108, 0.2382) [0.7162, 0.817, 0.024]
PeriodicSite: 48h (Li) (2.816, 1.816, 0.2382) [0.2838, 0.183, 0.024]
PeriodicSite: 48h (Li) (8.108, 7.108, 0.2382) [0.817, 0.7162, 0.024]
PeriodicSite: 48h (Li) (7.108, 1.816, 9.686) [0.7162, 0.183, 0.976]
PeriodicSite: 48h (Li) (7.108, 6.778, 4.724) [0.7162, 0.683, 0.476]
PeriodicSite: 48h (Li) (1.816, 7.778, 5.2) [0.183, 0.7838, 0.524]
PeriodicSite: 48h (Li) (0.2382, 7.778, 6.778) [0.024, 0.7838, 0.683]
PeriodicSite: 48h (Li) (8.108, 7.778, 4.724) [0.817, 0.7838, 0.476]
PeriodicSite: 48h (Li) (2.816, 3.146, 4.724) [0.2838, 0.317, 0.476]
PeriodicSite: 48h (Li) (8.108, 2.146, 5.2) [0.817, 0.2162, 0.524]
PeriodicSite: 48h (Li) (3.146, 7.108, 5.2) [0.317, 0.7162, 0.524]
PeriodicSite: 48h (Li) (2.146, 1.816, 4.724) [0.2162, 0.183, 0.476]
PeriodicSite: 48h (Li) (6.778, 2.816, 5.2) [0.683, 0.2838, 0.524]
PeriodicSite: 48h (Li) (5.2, 2.816, 6.778) [0.524, 0.2838, 0.683]
PeriodicSite: 48h (Li) (7.778, 9.686, 3.146) [0.7838, 0.976, 0.317]
PeriodicSite: 48h (Li) (4.724, 7.108, 6.778) [0.476, 0.7162, 0.683]
PeriodicSite: 48h (Li) (2.146, 0.2382, 3.146) [0.2162, 0.024, 0.317]
PeriodicSite: 48h (Li) (5.2, 7.108, 3.146) [0.524, 0.7162, 0.317]
PeriodicSite: 48h (Li) (2.146, 9.686, 6.778) [0.2162, 0.976, 0.683]
PeriodicSite: 48h (Li) (4.724, 2.816, 3.146) [0.476, 0.2838, 0.317]
PeriodicSite: 48h (Li) (7.778, 0.2382, 6.778) [0.7838, 0.024, 0.683]
PeriodicSite: 48h (Li) (6.778, 0.2382, 7.778) [0.683, 0.024, 0.7838]
PeriodicSite: 48h (Li) (6.778, 9.686, 2.146) [0.683, 0.976, 0.2162]
PeriodicSite: 48h (Li) (4.724, 8.108, 7.778) [0.476, 0.817, 0.7838]
PeriodicSite: 48h (Li) (3.146, 0.2382, 2.146) [0.317, 0.024, 0.2162]
PeriodicSite: 48h (Li) (5.2, 1.816, 7.778) [0.524, 0.183, 0.7838]
PeriodicSite: 48h (Li) (3.146, 9.686, 7.778) [0.317, 0.976, 0.7838]
PeriodicSite: 48h (Li) (4.724, 1.816, 2.146) [0.476, 0.183, 0.2162]
PeriodicSite: 48h (Li) (5.2, 8.108, 2.146) [0.524, 0.817, 0.2162]
PeriodicSite: 48h (Li) (6.778, 2.146, 9.686) [0.683, 0.2162, 0.976]
PeriodicSite: 48h (Li) (2.146, 3.146, 0.2382) [0.2162, 0.317, 0.024]
PeriodicSite: 48h (Li) (3.146, 7.778, 9.686) [0.317, 0.7838, 0.976]
PeriodicSite: 48h (Li) (7.778, 3.146, 9.686) [0.7838, 0.317, 0.976]
PeriodicSite: 48h (Li) (2.146, 8.108, 5.2) [0.2162, 0.817, 0.524]
PeriodicSite: 48h (Li) (3.146, 2.816, 4.724) [0.317, 0.2838, 0.476]
PeriodicSite: 48h (Li) (7.778, 8.108, 4.724) [0.7838, 0.817, 0.476]
PeriodicSite: 48h (Li) (0.2382, 3.146, 2.146) [0.024, 0.317, 0.2162]
PeriodicSite: 48h (Li) (7.778, 1.816, 5.2) [0.7838, 0.183, 0.524]
PeriodicSite: 48h (Li) (6.778, 7.108, 4.724) [0.683, 0.7162, 0.476]
PeriodicSite: 48h (Li) (9.686, 3.146, 7.778) [0.976, 0.317, 0.7838]
PeriodicSite: 48h (Li) (8.108, 5.2, 2.146) [0.817, 0.524, 0.2162]
PeriodicSite: 48h (Li) (0.2382, 6.778, 7.778) [0.024, 0.683, 0.7838]
PeriodicSite: 48h (Li) (8.108, 4.724, 7.778) [0.817, 0.476, 0.7838]
PeriodicSite: 48h (Li) (7.778, 6.778, 0.2382) [0.7838, 0.683, 0.024]
PeriodicSite: 48h (Li) (3.146, 2.146, 0.2382) [0.317, 0.2162, 0.024]
PeriodicSite: 48h (Li) (2.146, 6.778, 9.686) [0.2162, 0.683, 0.976]
PeriodicSite: 48h (Li) (6.778, 7.778, 0.2382) [0.683, 0.7838, 0.024]
PeriodicSite: 48h (Li) (5.2, 7.778, 1.816) [0.524, 0.7838, 0.183]
PeriodicSite: 48h (Li) (7.778, 4.724, 8.108) [0.7838, 0.476, 0.817]
PeriodicSite: 48h (Li) (4.724, 2.146, 1.816) [0.476, 0.2162, 0.183]
PeriodicSite: 48h (Li) (2.146, 5.2, 8.108) [0.2162, 0.524, 0.817]
PeriodicSite: 48h (Li) (5.2, 2.146, 8.108) [0.524, 0.2162, 0.817]
PeriodicSite: 48h (Li) (2.146, 4.724, 1.816) [0.2162, 0.476, 0.183]
PeriodicSite: 48h (Li) (9.686, 6.778, 2.146) [0.976, 0.683, 0.2162]
PeriodicSite: 48h (Li) (1.816, 2.816, 0.2382) [0.183, 0.2838, 0.024]
PeriodicSite: 48h (Li) (0.2382, 2.816, 1.816) [0.024, 0.2838, 0.183]
PeriodicSite: 48h (Li) (2.816, 9.686, 8.108) [0.2838, 0.976, 0.817]
PeriodicSite: 48h (Li) (7.108, 9.686, 1.816) [0.7162, 0.976, 0.183]
PeriodicSite: 48h (Li) (9.686, 2.816, 8.108) [0.976, 0.2838, 0.817]
PeriodicSite: 48h (Li) (2.816, 0.2382, 1.816) [0.2838, 0.024, 0.183]
PeriodicSite: 48h (Li) (1.816, 0.2382, 2.816) [0.183, 0.024, 0.2838]
PeriodicSite: 48h (Li) (1.816, 9.686, 7.108) [0.183, 0.976, 0.7162]
PeriodicSite: 48h (Li) (9.686, 8.108, 2.816) [0.976, 0.817, 0.2838]
PeriodicSite: 48h (Li) (4.724, 7.778, 8.108) [0.476, 0.7838, 0.817]
PeriodicSite: 48h (Li) (7.778, 5.2, 1.816) [0.7838, 0.524, 0.183]
PeriodicSite: 48h (Li) (6.778, 5.2, 2.816) [0.683, 0.524, 0.2838]
PeriodicSite: 48h (Li) (8.108, 0.2382, 7.108) [0.817, 0.024, 0.7162]
PeriodicSite: 48h (Li) (2.816, 4.724, 3.146) [0.2838, 0.476, 0.317]
PeriodicSite: 48h (Li) (9.686, 2.146, 6.778) [0.976, 0.2162, 0.683]
PeriodicSite: 48h (Li) (0.2382, 1.816, 2.816) [0.024, 0.183, 0.2838]
PeriodicSite: 48h (Li) (8.108, 9.686, 2.816) [0.817, 0.976, 0.2838]
PeriodicSite: 48h (Li) (9.686, 1.816, 7.108) [0.976, 0.183, 0.7162]
PeriodicSite: 48h (Li) (0.2382, 8.108, 7.108) [0.024, 0.817, 0.7162]
PeriodicSite: 48h (Li) (2.816, 6.778, 5.2) [0.2838, 0.683, 0.524]
PeriodicSite: 48h (Li) (1.816, 2.146, 4.724) [0.183, 0.2162, 0.476]
PeriodicSite: 48h (Li) (7.108, 3.146, 5.2) [0.7162, 0.317, 0.524]
PeriodicSite: 48h (Li) (6.778, 4.724, 7.108) [0.683, 0.476, 0.7162]
PeriodicSite: 48h (Li) (4.724, 3.146, 2.816) [0.476, 0.317, 0.2838]
PeriodicSite: 48h (Li) (3.146, 5.2, 7.108) [0.317, 0.524, 0.7162]
PeriodicSite: 48h (Li) (5.2, 6.778, 2.816) [0.524, 0.683, 0.2838]
PeriodicSite: 48h (Li) (3.146, 4.724, 2.816) [0.317, 0.476, 0.2838]
PeriodicSite: 48h (Li) (4.724, 6.778, 7.108) [0.476, 0.683, 0.7162]
PeriodicSite: 48h (Li) (5.2, 3.146, 7.108) [0.524, 0.317, 0.7162]
PeriodicSite: 48h2 (Li) (7.13, 6.778, 4.168) [0.7185, 0.683, 0.42]
PeriodicSite: 48h2 (Li) (1.816, 2.168, 4.168) [0.183, 0.2185, 0.42]
PeriodicSite: 48h2 (Li) (7.13, 3.146, 5.756) [0.7185, 0.317, 0.58]
PeriodicSite: 48h2 (Li) (8.108, 7.756, 4.168) [0.817, 0.7815, 0.42]
PeriodicSite: 48h2 (Li) (2.794, 6.778, 5.756) [0.2815, 0.683, 0.58]
PeriodicSite: 48h2 (Li) (0.7939, 6.778, 7.756) [0.08, 0.683, 0.7815]
PeriodicSite: 48h2 (Li) (0.7939, 3.146, 2.168) [0.08, 0.317, 0.2185]
PeriodicSite: 48h2 (Li) (8.108, 7.13, 0.7939) [0.817, 0.7185, 0.08]
PeriodicSite: 48h2 (Li) (7.13, 1.816, 9.13) [0.7185, 0.183, 0.92]
PeriodicSite: 48h2 (Li) (1.816, 7.13, 9.13) [0.183, 0.7185, 0.92]
PeriodicSite: 48h2 (Li) (9.13, 2.794, 8.108) [0.92, 0.2815, 0.817]
PeriodicSite: 48h2 (Li) (2.794, 9.13, 8.108) [0.2815, 0.92, 0.817]
PeriodicSite: 48h2 (Li) (0.7939, 7.13, 8.108) [0.08, 0.7185, 0.817]
PeriodicSite: 48h2 (Li) (7.13, 9.13, 1.816) [0.7185, 0.92, 0.183]
PeriodicSite: 48h2 (Li) (2.794, 0.7939, 1.816) [0.2815, 0.08, 0.183]
PeriodicSite: 48h2 (Li) (9.13, 7.13, 1.816) [0.92, 0.7185, 0.183]
PeriodicSite: 48h2 (Li) (7.13, 0.7939, 8.108) [0.7185, 0.08, 0.817]
PeriodicSite: 48h2 (Li) (7.13, 5.756, 3.146) [0.7185, 0.58, 0.317]
PeriodicSite: 48h2 (Li) (0.7939, 7.756, 6.778) [0.08, 0.7815, 0.683]
PeriodicSite: 48h2 (Li) (1.816, 7.756, 5.756) [0.183, 0.7815, 0.58]
PeriodicSite: 48h2 (Li) (9.13, 7.756, 3.146) [0.92, 0.7815, 0.317]
PeriodicSite: 48h2 (Li) (2.794, 4.168, 3.146) [0.2815, 0.42, 0.317]
PeriodicSite: 48h2 (Li) (9.13, 2.168, 6.778) [0.92, 0.2185, 0.683]
PeriodicSite: 48h2 (Li) (4.168, 7.13, 6.778) [0.42, 0.7185, 0.683]
PeriodicSite: 48h2 (Li) (2.168, 0.7939, 3.146) [0.2185, 0.08, 0.317]
PeriodicSite: 48h2 (Li) (5.756, 2.794, 6.778) [0.58, 0.2815, 0.683]
PeriodicSite: 48h2 (Li) (6.778, 2.794, 5.756) [0.683, 0.2815, 0.58]
PeriodicSite: 48h2 (Li) (7.756, 8.108, 4.168) [0.7815, 0.817, 0.42]
PeriodicSite: 48h2 (Li) (3.146, 7.13, 5.756) [0.317, 0.7185, 0.58]
PeriodicSite: 48h2 (Li) (2.168, 1.816, 4.168) [0.2185, 0.183, 0.42]
PeriodicSite: 48h2 (Li) (6.778, 7.13, 4.168) [0.683, 0.7185, 0.42]
PeriodicSite: 48h2 (Li) (2.168, 8.108, 5.756) [0.2185, 0.817, 0.58]
PeriodicSite: 48h2 (Li) (3.146, 2.794, 4.168) [0.317, 0.2815, 0.42]
PeriodicSite: 48h2 (Li) (7.756, 1.816, 5.756) [0.7815, 0.183, 0.58]
PeriodicSite: 48h2 (Li) (5.756, 1.816, 7.756) [0.58, 0.183, 0.7815]
PeriodicSite: 48h2 (Li) (5.756, 8.108, 2.168) [0.58, 0.817, 0.2185]
PeriodicSite: 48h2 (Li) (3.146, 9.13, 7.756) [0.317, 0.92, 0.7815]
PeriodicSite: 48h2 (Li) (4.168, 1.816, 2.168) [0.42, 0.183, 0.2185]
PeriodicSite: 48h2 (Li) (6.778, 0.7939, 7.756) [0.683, 0.08, 0.7815]
PeriodicSite: 48h2 (Li) (4.168, 8.108, 7.756) [0.42, 0.817, 0.7815]
PeriodicSite: 48h2 (Li) (3.146, 0.7939, 2.168) [0.317, 0.08, 0.2185]
PeriodicSite: 48h2 (Li) (6.778, 9.13, 2.168) [0.683, 0.92, 0.2185]
PeriodicSite: 48h2 (Li) (5.756, 2.168, 8.108) [0.58, 0.2185, 0.817]
PeriodicSite: 48h2 (Li) (2.168, 4.168, 1.816) [0.2185, 0.42, 0.183]
PeriodicSite: 48h2 (Li) (4.168, 7.756, 8.108) [0.42, 0.7815, 0.817]
PeriodicSite: 48h2 (Li) (7.756, 4.168, 8.108) [0.7815, 0.42, 0.817]
PeriodicSite: 48h2 (Li) (2.168, 9.13, 6.778) [0.2185, 0.92, 0.683]
PeriodicSite: 48h2 (Li) (4.168, 2.794, 3.146) [0.42, 0.2815, 0.317]
PeriodicSite: 48h2 (Li) (7.756, 9.13, 3.146) [0.7815, 0.92, 0.317]
PeriodicSite: 48h2 (Li) (1.816, 4.168, 2.168) [0.183, 0.42, 0.2185]
PeriodicSite: 48h2 (Li) (7.756, 0.7939, 6.778) [0.7815, 0.08, 0.683]
PeriodicSite: 48h2 (Li) (5.756, 7.13, 3.146) [0.58, 0.7185, 0.317]
PeriodicSite: 48h2 (Li) (8.108, 4.168, 7.756) [0.817, 0.42, 0.7815]
PeriodicSite: 48h2 (Li) (9.13, 6.778, 2.168) [0.92, 0.683, 0.2185]
PeriodicSite: 48h2 (Li) (1.816, 5.756, 7.756) [0.183, 0.58, 0.7815]
PeriodicSite: 48h2 (Li) (9.13, 3.146, 7.756) [0.92, 0.317, 0.7815]
PeriodicSite: 48h2 (Li) (7.756, 5.756, 1.816) [0.7815, 0.58, 0.183]
PeriodicSite: 48h2 (Li) (4.168, 2.168, 1.816) [0.42, 0.2185, 0.183]
PeriodicSite: 48h2 (Li) (2.168, 5.756, 8.108) [0.2185, 0.58, 0.817]
PeriodicSite: 48h2 (Li) (5.756, 7.756, 1.816) [0.58, 0.7815, 0.183]
PeriodicSite: 48h2 (Li) (6.778, 7.756, 0.7939) [0.683, 0.7815, 0.08]
PeriodicSite: 48h2 (Li) (7.756, 3.146, 9.13) [0.7815, 0.317, 0.92]
PeriodicSite: 48h2 (Li) (3.146, 2.168, 0.7939) [0.317, 0.2185, 0.08]
PeriodicSite: 48h2 (Li) (2.168, 6.778, 9.13) [0.2185, 0.683, 0.92]
PeriodicSite: 48h2 (Li) (6.778, 2.168, 9.13) [0.683, 0.2185, 0.92]
PeriodicSite: 48h2 (Li) (2.168, 3.146, 0.7939) [0.2185, 0.317, 0.08]
PeriodicSite: 48h2 (Li) (8.108, 5.756, 2.168) [0.817, 0.58, 0.2185]
PeriodicSite: 48h2 (Li) (0.7939, 2.794, 1.816) [0.08, 0.2815, 0.183]
PeriodicSite: 48h2 (Li) (1.816, 2.794, 0.7939) [0.183, 0.2815, 0.08]
PeriodicSite: 48h2 (Li) (2.794, 8.108, 9.13) [0.2815, 0.817, 0.92]
PeriodicSite: 48h2 (Li) (7.13, 8.108, 0.7939) [0.7185, 0.817, 0.08]
PeriodicSite: 48h2 (Li) (8.108, 2.794, 9.13) [0.817, 0.2815, 0.92]
PeriodicSite: 48h2 (Li) (2.794, 1.816, 0.7939) [0.2815, 0.183, 0.08]
PeriodicSite: 48h2 (Li) (0.7939, 1.816, 2.794) [0.08, 0.183, 0.2815]
PeriodicSite: 48h2 (Li) (0.7939, 8.108, 7.13) [0.08, 0.817, 0.7185]
PeriodicSite: 48h2 (Li) (8.108, 9.13, 2.794) [0.817, 0.92, 0.2815]
PeriodicSite: 48h2 (Li) (3.146, 7.756, 9.13) [0.317, 0.7815, 0.92]
PeriodicSite: 48h2 (Li) (7.756, 6.778, 0.7939) [0.7815, 0.683, 0.08]
PeriodicSite: 48h2 (Li) (5.756, 6.778, 2.794) [0.58, 0.683, 0.2815]
PeriodicSite: 48h2 (Li) (9.13, 1.816, 7.13) [0.92, 0.183, 0.7185]
PeriodicSite: 48h2 (Li) (2.794, 3.146, 4.168) [0.2815, 0.317, 0.42]
PeriodicSite: 48h2 (Li) (8.108, 2.168, 5.756) [0.817, 0.2185, 0.58]
PeriodicSite: 48h2 (Li) (1.816, 0.7939, 2.794) [0.183, 0.08, 0.2815]
PeriodicSite: 48h2 (Li) (9.13, 8.108, 2.794) [0.92, 0.817, 0.2815]
PeriodicSite: 48h2 (Li) (8.108, 0.7939, 7.13) [0.817, 0.08, 0.7185]
PeriodicSite: 48h2 (Li) (1.816, 9.13, 7.13) [0.183, 0.92, 0.7185]
PeriodicSite: 48h2 (Li) (2.794, 5.756, 6.778) [0.2815, 0.58, 0.683]
PeriodicSite: 48h2 (Li) (0.7939, 2.168, 3.146) [0.08, 0.2185, 0.317]
PeriodicSite: 48h2 (Li) (7.13, 4.168, 6.778) [0.7185, 0.42, 0.683]
PeriodicSite: 48h2 (Li) (5.756, 3.146, 7.13) [0.58, 0.317, 0.7185]
PeriodicSite: 48h2 (Li) (3.146, 4.168, 2.794) [0.317, 0.42, 0.2815]
PeriodicSite: 48h2 (Li) (4.168, 6.778, 7.13) [0.42, 0.683, 0.7185]
PeriodicSite: 48h2 (Li) (6.778, 5.756, 2.794) [0.683, 0.58, 0.2815]
PeriodicSite: 48h2 (Li) (4.168, 3.146, 2.794) [0.42, 0.317, 0.2815]
PeriodicSite: 48h2 (Li) (3.146, 5.756, 7.13) [0.317, 0.58, 0.7185]
PeriodicSite: 48h2 (Li) (6.778, 4.168, 7.13) [0.683, 0.42, 0.7185]
PeriodicSite: 16e (Li) (8.313, 3.573, 6.351) [0.8377, 0.36, 0.64]
PeriodicSite: 16e (Li) (8.535, 3.351, 6.351) [0.86, 0.3377, 0.64]
PeriodicSite: 16e (Li) (8.313, 6.351, 3.573) [0.8377, 0.64, 0.36]
PeriodicSite: 16e (Li) (1.389, 6.573, 6.351) [0.14, 0.6623, 0.64]
PeriodicSite: 16e (Li) (1.611, 3.573, 3.573) [0.1623, 0.36, 0.36]
PeriodicSite: 16e (Li) (8.535, 3.573, 6.573) [0.86, 0.36, 0.6623]
PeriodicSite: 16e (Li) (8.535, 6.351, 3.351) [0.86, 0.64, 0.3377]
PeriodicSite: 16e (Li) (1.389, 8.313, 8.535) [0.14, 0.8377, 0.86]
PeriodicSite: 16e (Li) (8.313, 8.535, 1.389) [0.8377, 0.86, 0.14]
PeriodicSite: 16e (Li) (8.535, 8.313, 1.389) [0.86, 0.8377, 0.14]
PeriodicSite: 16e (Li) (1.389, 1.611, 1.389) [0.14, 0.1623, 0.14]
PeriodicSite: 16e (Li) (1.611, 1.389, 1.389) [0.1623, 0.14, 0.14]
PeriodicSite: 16e (Li) (8.313, 1.389, 8.535) [0.8377, 0.14, 0.86]
PeriodicSite: 16e (Li) (1.611, 8.535, 8.535) [0.1623, 0.86, 0.86]
PeriodicSite: 16e (Li) (8.535, 6.573, 3.573) [0.86, 0.6623, 0.36]
PeriodicSite: 16e (Li) (1.611, 6.351, 6.351) [0.1623, 0.64, 0.64]
PeriodicSite: 16e (Li) (1.389, 3.351, 3.573) [0.14, 0.3377, 0.36]
PeriodicSite: 16e (Li) (6.351, 8.313, 3.573) [0.64, 0.8377, 0.36]
PeriodicSite: 16e (Li) (3.351, 8.535, 6.351) [0.3377, 0.86, 0.64]
PeriodicSite: 16e (Li) (3.573, 1.611, 3.573) [0.36, 0.1623, 0.36]
PeriodicSite: 16e (Li) (6.573, 1.389, 6.351) [0.6623, 0.14, 0.64]
PeriodicSite: 16e (Li) (3.573, 8.313, 6.351) [0.36, 0.8377, 0.64]
PeriodicSite: 16e (Li) (3.351, 1.389, 3.573) [0.3377, 0.14, 0.36]
PeriodicSite: 16e (Li) (6.351, 1.611, 6.351) [0.64, 0.1623, 0.64]
PeriodicSite: 16e (Li) (6.573, 8.535, 3.573) [0.6623, 0.86, 0.36]
PeriodicSite: 16e (Li) (3.573, 8.535, 6.573) [0.36, 0.86, 0.6623]
PeriodicSite: 16e (Li) (3.573, 1.389, 3.351) [0.36, 0.14, 0.3377]
PeriodicSite: 16e (Li) (6.351, 1.389, 6.573) [0.64, 0.14, 0.6623]
PeriodicSite: 16e (Li) (6.351, 8.535, 3.351) [0.64, 0.86, 0.3377]
PeriodicSite: 16e (Li) (3.573, 3.351, 1.389) [0.36, 0.3377, 0.14]
PeriodicSite: 16e (Li) (3.351, 6.351, 8.535) [0.3377, 0.64, 0.86]
PeriodicSite: 16e (Li) (6.351, 6.573, 1.389) [0.64, 0.6623, 0.14]
PeriodicSite: 16e (Li) (6.573, 6.351, 1.389) [0.6623, 0.64, 0.14]
PeriodicSite: 16e (Li) (1.389, 6.351, 6.573) [0.14, 0.64, 0.6623]
PeriodicSite: 16e (Li) (1.389, 3.573, 3.351) [0.14, 0.36, 0.3377]
PeriodicSite: 16e (Li) (6.573, 3.573, 8.535) [0.6623, 0.36, 0.86]
PeriodicSite: 16e (Li) (6.351, 3.351, 8.535) [0.64, 0.3377, 0.86]
PeriodicSite: 16e (Li) (3.351, 3.573, 1.389) [0.3377, 0.36, 0.14]
PeriodicSite: 16e (Li) (3.573, 6.573, 8.535) [0.36, 0.6623, 0.86]
PeriodicSite: 16e (Li) (8.535, 1.611, 8.535) [0.86, 0.1623, 0.86]
PeriodicSite: 16e (Li) (8.535, 8.535, 1.611) [0.86, 0.86, 0.1623]
PeriodicSite: 16e (Li) (8.535, 1.389, 8.313) [0.86, 0.14, 0.8377]
PeriodicSite: 16e (Li) (1.389, 1.389, 1.611) [0.14, 0.14, 0.1623]
PeriodicSite: 16e (Li) (3.573, 3.573, 1.611) [0.36, 0.36, 0.1623]
PeriodicSite: 16e (Li) (1.389, 8.535, 8.313) [0.14, 0.86, 0.8377]
PeriodicSite: 16e (Li) (3.573, 6.351, 8.313) [0.36, 0.64, 0.8377]
PeriodicSite: 16e (Li) (6.351, 6.351, 1.611) [0.64, 0.64, 0.1623]
PeriodicSite: 16e (Li) (6.351, 3.573, 8.313) [0.64, 0.36, 0.8377]