Cylinders and Prisms

Scattering from a mixture of cylinders and prisms without interference.

  • The sample comprises a substrate on which are deposited, in equal proportion, cylinders and prisms.
  • All particles are made of the same material.
  • Each type of particle has the same orientation.
  • The cylinders are $5$ nm high and $5$ nm in radius.
  • Each prism is $5$ nm high with an equilateral triangular base, whose side length is equal to $10$ nm.
  • There is no interference between the waves scattered by these particles. The distribution is therefore diluted.
  • The incident neutron beam is characterized by a wavelength of $1$ $\unicode{x212B}$.
  • The incident angles are $\alpha_i = 0.2 ^{\circ}$ and $\varphi_i = 0^{\circ}$.
  • The simulation is performed using the Distorted Wave Born Approximation (due to the presence of a substrate).

Real-space model

Intensity image

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
"""
Mixture of cylinders and prisms without interference
"""
import bornagain as ba
from bornagain import deg, nm


def get_sample():
    """
    Returns a sample with uncorrelated cylinders and prisms on a substrate.
    """

    # Define materials
    material_Particle = ba.HomogeneousMaterial("Particle", 0.0006, 2e-08)
    material_Substrate = ba.HomogeneousMaterial("Substrate", 6e-06, 2e-08)
    material_Vacuum = ba.HomogeneousMaterial("Vacuum", 0.0, 0.0)

    # Define form factors
    ff_1 = ba.FormFactorCylinder(5.0*nm, 5.0*nm)
    ff_2 = ba.FormFactorPrism3(10.0*nm, 5.0*nm)

    # Define particles
    particle_1 = ba.Particle(material_Particle, ff_1)
    particle_2 = ba.Particle(material_Particle, ff_2)

    # Define interference functions
    iff = ba.InterferenceFunctionNone()

    # Define particle layouts
    layout = ba.ParticleLayout()
    layout.addParticle(particle_1, 0.5)
    layout.addParticle(particle_2, 0.5)
    layout.setInterferenceFunction(iff)
    layout.setWeight(1)
    layout.setTotalParticleSurfaceDensity(0.01)

    # Define layers
    layer_1 = ba.Layer(material_Vacuum)
    layer_1.addLayout(layout)
    layer_2 = ba.Layer(material_Substrate)

    # Define sample
    sample = ba.MultiLayer()
    sample.addLayer(layer_1)
    sample.addLayer(layer_2)

    return sample


def get_simulation(sample):
    beam = ba.Beam(1.0, 0.1*nm, ba.Direction(0.2*deg, 0*deg))
    detector = ba.SphericalDetector(100, 2*deg, 0*deg, 1*deg)
    simulation = ba.GISASSimulation(beam, sample, detector)
    return simulation


if __name__ == '__main__':
    import ba_plot
    sample = get_sample()
    simulation = get_simulation(sample)
    ba_plot.run_and_plot(simulation)
CylindersAndPrisms.py