Simple Diffraction Pattern Simulation Examples

This example demonstrates how to simulate diffraction patterns using the diffsims.generators.simulation_generator.SimulationGenerator class. A single diffraction pattern can be simulated for a single phase or multiple diffraction patterns can be simulated for a single/multiple phases given a rotation.

One Pattern for One Phase

from orix.crystal_map import Phase
from orix.quaternion import Rotation
from diffpy.structure import Atom, Lattice, Structure
import matplotlib.pyplot as plt

from diffsims.generators.simulation_generator import SimulationGenerator

a = 5.431
latt = Lattice(a, a, a, 90, 90, 90)
atom_list = []
for coords in [[0, 0, 0], [0.5, 0, 0.5], [0, 0.5, 0.5], [0.5, 0.5, 0]]:
    x, y, z = coords[0], coords[1], coords[2]
    atom_list.append(Atom(atype="Si", xyz=[x, y, z], lattice=latt))  # Motif part A
    atom_list.append(
        Atom(atype="Si", xyz=[x + 0.25, y + 0.25, z + 0.25], lattice=latt)
    )  # Motif part B
struct = Structure(atoms=atom_list, lattice=latt)
p = Phase(structure=struct, space_group=227)

gen = SimulationGenerator(
    accelerating_voltage=200,
)
rot = Rotation.from_axes_angles(
    [1, 0, 0], 45, degrees=True
)  # 45 degree rotation around x-axis
sim = gen.calculate_diffraction2d(phase=p, rotation=rot)

_ = sim.plot(show_labels=True)  # plot the first (and only) diffraction pattern

sim.coordinates  # coordinates of the first (and only) diffraction pattern

DiffractingVector (18,),  (m-3m)
[[ 4.  0.  0.]
 [ 3.  1.  1.]
 [ 3. -1. -1.]
 [ 1.  3.  3.]
 [ 1.  1.  1.]
 [ 1. -1. -1.]
 [ 1. -3. -3.]
 [ 0.  2.  2.]
 [ 0. -2. -2.]
 [-1.  3.  3.]
 [-1.  1.  1.]
 [-1. -1. -1.]
 [-1. -3. -3.]
 [-3.  1.  1.]
 [-3. -1. -1.]
 [-4.  0.  0.]
 [ 0.  0.  0.]
 [ 0.  0.  0.]]

Simulating Multiple Patterns for a Single Phase

rot = Rotation.from_axes_angles(
    [1, 0, 0], (0, 15, 30, 45, 60, 75, 90), degrees=True
)  # 45 degree rotation around x-axis
sim = gen.calculate_diffraction2d(phase=p, rotation=rot)

_ = sim.plot(show_labels=True)  # plot the first diffraction pattern

_ = sim.irot[3].plot(
    show_labels=True
)  # plot the fourth(45 degrees) diffraction pattern

sim.coordinates  # coordinates of all the diffraction patterns

array([DiffractingVector (10,),  (m-3m)
       [[ 4.  0.  0.]
        [ 2.  2.  0.]
        [ 2. -2.  0.]
        [ 0.  4.  0.]
        [ 0. -4.  0.]
        [-2.  2.  0.]
        [-2. -2.  0.]
        [-4.  0.  0.]
        [ 0.  0.  0.]
        [ 0.  0.  0.]]                 , DiffractingVector (4,),  (m-3m)
                                         [[ 4.  0.  0.]
                                          [-4.  0.  0.]
                                          [ 0.  0.  0.]
                                          [ 0.  0.  0.]]                ,
       DiffractingVector (4,),  (m-3m)
       [[ 4.  0.  0.]
        [-4.  0.  0.]
        [ 0.  0.  0.]
        [ 0.  0.  0.]]                , DiffractingVector (18,),  (m-3m)
                                        [[ 4.  0.  0.]
                                         [ 3.  1.  1.]
                                         [ 3. -1. -1.]
                                         [ 1.  3.  3.]
                                         [ 1.  1.  1.]
                                         [ 1. -1. -1.]
                                         [ 1. -3. -3.]
                                         [ 0.  2.  2.]
                                         [ 0. -2. -2.]
                                         [-1.  3.  3.]
                                         [-1.  1.  1.]
                                         [-1. -1. -1.]
                                         [-1. -3. -3.]
                                         [-3.  1.  1.]
                                         [-3. -1. -1.]
                                         [-4.  0.  0.]
                                         [ 0.  0.  0.]
                                         [ 0.  0.  0.]]                 ,
       DiffractingVector (4,),  (m-3m)
       [[ 4.  0.  0.]
        [-4.  0.  0.]
        [ 0.  0.  0.]
        [ 0.  0.  0.]]                , DiffractingVector (4,),  (m-3m)
                                        [[ 4.  0.  0.]
                                         [-4.  0.  0.]
                                         [ 0.  0.  0.]
                                         [ 0.  0.  0.]]                ,
       DiffractingVector (10,),  (m-3m)
       [[ 4.  0.  0.]
        [ 2.  0.  2.]
        [ 2. -0. -2.]
        [ 0.  0.  4.]
        [ 0. -0. -4.]
        [-2.  0.  2.]
        [-2. -0. -2.]
        [-4.  0.  0.]
        [ 0.  0.  0.]
        [ 0.  0.  0.]]                 ], dtype=object)

Simulating Multiple Patterns for Multiple Phases

p2 = p.deepcopy()  # copy the phase

p2.name = "al_2"

rot = Rotation.from_axes_angles(
    [1, 0, 0], (0, 15, 30, 45, 60, 75, 90), degrees=True
)  # 45 degree rotation around x-axis
sim = gen.calculate_diffraction2d(phase=[p, p2], rotation=[rot, rot])

_ = sim.plot(
    include_direct_beam=True, show_labels=True, min_label_intensity=0.1
)  # plot the first diffraction pattern

_ = (
    sim.iphase["al_2"].irot[3].plot(show_labels=True, min_label_intensity=0.1)
)  # plot the fourth(45 degrees) diffraction pattern

Plotting a Pixelated Diffraction Pattern

dp = sim.get_diffraction_pattern(
    shape=(512, 512),
    calibration=0.01,
)
plt.figure()
_ = plt.imshow(dp)