# Interface¶

## Locating Particles on Interfacial Boundaries¶

The freud.interface module compares the distances between two sets of points to determine the interfacial particles.

[1]:

import freud
import numpy as np
import matplotlib.pyplot as plt


To make a pretend data set, we create a large number of blue (-1) particles on a square grid. Then we place grain centers on a larger grid and draw grain radii from a normal distribution. We color the particles red (+1) if their distance from a grain center is less than the grain radius.

[2]:

# Set up the system
box = freud.box.Box.square(L=10)
dx = 0.15
num_grains = 4
dg = box.Lx/num_grains
points = np.array([[i, j, 0]
for j in np.arange(-box.Ly/2, box.Ly/2, dx)
for i in np.arange(-box.Lx/2, box.Lx/2, dx)])
values = np.array([-1]*points.shape[0])
centroids = [[i*dg + 0.5*dg, j*dg + 0.5*dg, 0]
for i in range(num_grains) for j in range(num_grains)]
for i in lc.nlist.index_i:
values[i] = 1

blue_points = points[values < 0]
red_points = points[values > 0]

plt.figure(figsize=(8, 8))
plt.scatter(blue_points[:, 0],
blue_points[:, 1],
marker='o', color='blue', s=25)
plt.scatter(red_points[:, 0],
red_points[:, 1],
marker='o', color='red', s=25)
plt.show()


This system is phase-separated because the red particles are generally near one another, and so are the blue particles.

We can use freud.interface.InterfaceMeasure to label the particles on either side of the red-blue boundary. The class can tell us how many points are on either side of the interface:

[3]:

iface = freud.interface.InterfaceMeasure(r_cut=0.2)
iface.compute(box=box, ref_points=blue_points, points=red_points)

print('There are', iface.ref_point_count, 'reference (blue) points on the interface.')
print('There are', iface.point_count, '(red) points on the interface.')

There are 410 reference (blue) points on the interface.
There are 346 (red) points on the interface.


Now we can plot the particles on the interface. We color the outside of the interface cyan and the inside of the interface black.

[4]:

plt.figure(figsize=(8, 8))

plt.scatter(blue_points[:, 0],
blue_points[:, 1],
marker='o', color='blue', s=25)
plt.scatter(red_points[:, 0],
red_points[:, 1],
marker='o', color='red', s=25)

plt.scatter(blue_points[iface.ref_point_ids, 0],
blue_points[iface.ref_point_ids, 1],
marker='o', color='cyan', s=25)
plt.scatter(red_points[iface.point_ids, 0],
red_points[iface.point_ids, 1],
marker='o', color='black', s=25)

plt.show()