BornAgain ≻ 21 ≻ Documentation ≻ Reference ≻ Sample model ≻ Particle assemblies ≻ Others ≻ Size-distribution model: size-spacing coupling approximation

Size-distribution model: size-spacing coupling approximation

Scattering from cylinders of two different sizes using the Size-Spacing Coupling Approximation.

  • The sample is made of cylinders deposited on a substrate.
  • The distribution of particles is made of:
    • 80% of cylinders with radii and heights equal to $5$ nm
    • 20% of cylinders with radii and heights equal to $8$ nm.
  • The interference function is Radial Paracrystal with a peak distance of $18$ nm and a damping length of $1$ $\mu$m.
  • The wavelength is equal to 0.1 nm.
  • The incident angles are $\alpha_i = 0.2 ^{\circ}$ and $\varphi_i = 0^{\circ}$.
  • The Size-Spacing Coupling Approximation is implemented using the function setApproximation. By default the Decoupling Approximation is used (see Size-distribution model: Decoupling Approximation).
  • For this size-distribution model, an additional dimensionless parameter, the coupling parameter Kappa, has to be specified (see line 33). It defines how the distance between particles is linked with their sizes.

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
63
64
65

#!/usr/bin/env python3
"""
Cylinders of two different sizes in Size-Spacing Coupling Approximation
"""
import bornagain as ba
from bornagain import ba_plot as bp, deg, nm


def get_sample():
    """
    A sample with cylinders of two different sizes on a substrate.
    The cylinder positions are modelled in Size-Spacing Coupling  Approximation.
    """

    # Materials
    material_particle = ba.RefractiveMaterial("Particle", 0.0006, 2e-08)
    material_substrate = ba.RefractiveMaterial("Substrate", 6e-06, 2e-08)
    vacuum = ba.RefractiveMaterial("Vacuum", 0, 0)

    # Form factors
    ff_1 = ba.Cylinder(5*nm, 5*nm)
    ff_2 = ba.Cylinder(8*nm, 8*nm)

    # Particles
    particle_1 = ba.Particle(material_particle, ff_1)
    particle_2 = ba.Particle(material_particle, ff_2)

    # Interference functions
    iff = ba.InterferenceRadialParacrystal(18*nm, 1000*nm)
    iff.setKappa(1)
    iff_pdf = ba.Profile1DGauss(3*nm)
    iff.setProbabilityDistribution(iff_pdf)

    # Particle layouts
    layout = ba.ParticleLayout()
    layout.addParticle(particle_1, 0.8)
    layout.addParticle(particle_2, 0.2)
    layout.setInterference(iff)
    layout.setTotalParticleSurfaceDensity(0.01)

    # Layers
    layer_1 = ba.Layer(vacuum)
    layer_1.addLayout(layout)
    layer_2 = ba.Layer(material_substrate)

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

    return sample


def get_simulation(sample):
    beam = ba.Beam(1e9, 0.1*nm, 0.2*deg)
    detector = ba.SphericalDetector(200, 2*deg, 1*deg, 1*deg)
    simulation = ba.ScatteringSimulation(beam, sample, detector)
    return simulation


if __name__ == '__main__':
    sample = get_sample()
    simulation = get_simulation(sample)
    result = simulation.simulate()
    bp.plot_simulation_result(result)
auto/Examples/scatter2d/ApproximationSSCA.py