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Size-distribution model: local monodisperse approximation

Scattering from cylinders of two different sizes using the Local Monodisperse Approximation (LMA).

  • The sample is made of cylinders deposited on a substrate.
  • The cylinders are of two different sizes:
    • 80% of Type $1$: radius $R_1 = 5$ nm, height $H_1 = 5$ nm. The interference function is a radial paracrystal with a peak distance equal to $16.8$ nm and a damping length of $1$ $\mu$m.
    • 20% of Type $2$: radius $R_2 = 8$ nm, height $H_2 = 8$ nm. The interference function is also a radial paracrystal but with a peak distance of $22.8$ nm and a damping length equal to $1$ $\mu$m.
  • Each type of cylinders is associated with a “particle layout”.
  • The LMA is used since the sample is made of two domains containing particles of the same size and shape.
  • The wavelength is equal to 0.1 nm.
  • The incident angles are $\alpha_i = 0.2 ^{\circ}$ and $\varphi_i = 0^{\circ}$.

Intensity image

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#!/usr/bin/env python3
"""
Cylinders of two different sizes in Local Monodisperse Approximation
"""
import bornagain as ba
from bornagain import ba_plot as bp, deg, nm
import matplotlib.pyplot as plt


def get_sample():
    """
    A sample with cylinders of two different sizes on a substrate.
    The cylinder positions are modelled in Local Monodisperse 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_1 = ba.InterferenceRadialParacrystal(16.8*nm, 1000*nm)
    iff_1_pdf = ba.Profile1DGauss(3*nm)
    iff_1.setProbabilityDistribution(iff_1_pdf)
    iff_2 = ba.InterferenceRadialParacrystal(22.8*nm, 1000*nm)
    iff_2_pdf = ba.Profile1DGauss(3*nm)
    iff_2.setProbabilityDistribution(iff_2_pdf)

    # Particle layouts
    layout_1 = ba.ParticleLayout()
    layout_1.addParticle(particle_1, 0.8)
    layout_1.setInterference(iff_1)
    layout_1.setTotalParticleSurfaceDensity(0.01)
    layout_2 = ba.ParticleLayout()
    layout_2.addParticle(particle_2, 0.2)
    layout_2.setInterference(iff_2)
    layout_2.setTotalParticleSurfaceDensity(0.01)

    # Layers
    layer_1 = ba.Layer(vacuum)
    layer_1.addLayout(layout_1)
    layer_1.addLayout(layout_2)
    layer_2 = ba.Layer(material_substrate)

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

    return sample


def get_simulation(sample):
    beam = ba.Beam(1e9, 0.1*nm, 0.2*deg)
    n = 200
    detector = ba.SphericalDetector(n, 0., 2*deg, n, 0., 2*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)
    plt.show()
auto/Examples/scatter2d/ApproximationLMA.py