freud.locality.PeriodicBuffer: Unit Cell RDF¶
PeriodicBuffer class is meant to replicate points beyond a single image while respecting box periodicity. This example demonstrates how we can use this to compute the radial distribution function from a sample crystal’s unit cell.
%matplotlib inline import freud import numpy as np import matplotlib.pyplot as plt
Here, we create a box to represent the unit cell and put two points inside. We plot the box and points below.
box = freud.box.Box(Lx=2, Ly=2, xy=np.sqrt(1/3), is2D=True) points = np.array([[-0.5, -0.5, 0], [0.5, 0.5, 0]]) system = freud.AABBQuery(box, points) system.plot(ax=plt.gca()) plt.show()
Next, we create a
PeriodicBuffer instance and have it compute the “buffer” points that lie outside the first periodicity. These positions are stored in the
buffer_points attribute. The corresponding
buffer_ids array gives a mapping from the index of the buffer particle to the index of the particle it was replicated from, in the original array of
points. Finally, the
buffer_box attribute returns a larger box, expanded from the original box to contain the replicated points.
pbuff = freud.locality.PeriodicBuffer() pbuff.compute(system=(box, points), buffer=6, images=True) print(pbuff.buffer_points[:10], '...')
[[ 0.65470022 1.5 0. ] [ 1.80940032 3.5 0. ] [ 2.96410179 5.5 0. ] [-3.96410131 -6.5 0. ] [-2.80940104 -4.49999952 0. ] [-1.65470016 -2.50000048 0. ] [ 1.50000024 -0.5 0. ] [ 2.65470076 1.5 0. ] [ 3.80940032 3.5 0. ] [ 4.96410179 5.5 0. ]] ...
Below, we plot the original unit cell and the replicated buffer points and buffer box.
system.plot(ax=plt.gca()) plt.scatter(pbuff.buffer_points[:, 0], pbuff.buffer_points[:, 1]) pbuff.buffer_box.plot(ax=plt.gca(), linestyle='dashed', color='gray') plt.show()
Finally, we can plot the radial distribution function (RDF) of this replicated system, using a value of
r_max that is larger than the size of the original box. This allows us to see the interaction of the original points with their replicated neighbors from the buffer.
rdf = freud.density.RDF(bins=250, r_max=5) rdf.compute(system=(pbuff.buffer_box, pbuff.buffer_points), query_points=points) rdf.plot(ax=plt.gca()) plt.show()