Diffraction Module¶
Overview
Computes a 2D diffraction pattern. |
Details
The freud.diffraction
module provides functions for computing the
diffraction pattern of particles in systems with long range order.
Stability
freud.diffraction
is unstable. When upgrading from version 2.x to
2.y (y > x), existing freud scripts may need to be updated. The API will be
finalized in a future release.
- class freud.diffraction.DiffractionPattern(grid_size=512, output_size=None)¶
Bases:
freud.util._Compute
Computes a 2D diffraction pattern.
The diffraction image represents the scattering of incident radiation, and is useful for identifying translational and/or rotational symmetry present in the system. This class computes the static structure factor \(S(\vec{k})\) for a plane of wavevectors \(\vec{k}\) orthogonal to a view axis. The view orientation \((1, 0, 0, 0)\) defaults to looking down the \(z\) axis (at the \(xy\) plane). The points in the system are converted to fractional coordinates, then binned into a grid whose resolution is given by
grid_size
. A highergrid_size
will lead to a higher resolution. The points are convolved with a Gaussian of width \(\sigma\), given bypeak_width
. This convolution is performed as a multiplication in Fourier space. The computed diffraction pattern can be accessed as a square array of shape(output_size, output_size)
.The \(\vec{k}=0\) peak is always located at index
(output_size // 2, output_size // 2)
and is normalized to have a value of \(S(\vec{k}=0) = 1\) (not \(N\), a common convention). The remaining \(\vec{k}\) vectors are computed such that each peak in the diffraction pattern satisfies the relationship \(\vec{k} \cdot \vec{R} = 2 \pi N\) for some integer \(N\) and lattice vector of the system \(\vec{R}\). See the reciprocal lattice Wikipedia page for more information.This method is based on the implementations in the open-source GIXStapose application and its predecessor, diffractometer [JJ17].
- Parameters
grid_size (unsigned int) – Resolution of the diffraction grid (Default value = 512).
output_size (unsigned int) – Resolution of the output diffraction image, uses
grid_size
if not provided orNone
(Default value =None
).
- compute(self, system, view_orientation=None, zoom=4, peak_width=1, reset=True)¶
Computes diffraction pattern.
- Parameters
system – Any object that is a valid argument to
freud.locality.NeighborQuery.from_system
.view_orientation ((\(4\))
numpy.ndarray
, optional) – View orientation. Uses \((1, 0, 0, 0)\) if not provided orNone
(Default value =None
).zoom (float) – Scaling factor for incident wavevectors (Default value = 4).
peak_width (float) – Width of Gaussian convolved with points, in system length units (Default value = 1).
reset (bool) – Whether to erase the previously computed values before adding the new computations; if False, will accumulate data (Default value: True).
- property diffraction¶
(
output_size
,output_size
)numpy.ndarray
: Diffraction pattern.
- property k_values¶
k-values.
- Type
(
output_size
, )numpy.ndarray
- property k_vectors¶
(
output_size
,output_size
, 3)numpy.ndarray
: k-vectors.
- plot(self, ax=None, cmap='afmhot', vmin=4e-6, vmax=0.7)¶
Plot Diffraction Pattern.
- Parameters
ax (
matplotlib.axes.Axes
, optional) – Axis to plot on. IfNone
, make a new figure and axis. (Default value =None
)cmap (str) – Colormap name to use (Default value =
'afmhot'
).vmin (float) – Minimum of the color scale (Default value = 4e-6).
vmax (float) – Maximum of the color scale (Default value = 0.7).
- Returns
Axis with the plot.
- Return type
- to_image(self, cmap='afmhot', vmin=4e-6, vmax=0.7)¶
Generates image of diffraction pattern.
- Parameters
- Returns
RGBA array of pixels.
- Return type
((output_size, output_size, 4)
numpy.ndarray
)