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 $1$ $\unicode{x212B}$.
  • 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 deg, nm


def get_sample():
    """
    Returns a sample with cylinders of two different sizes on a substrate.
    The cylinder positions are modelled in Local Monodisperse Approximation.
    """

    # 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.FormFactorCylinder(8.0*nm, 8.0*nm)

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

    # Define interference functions
    iff_1 = ba.InterferenceFunctionRadialParaCrystal(16.8*nm, 1000.0*nm)
    iff_1_pdf = ba.FTDistribution1DGauss(3.0*nm)
    iff_1.setProbabilityDistribution(iff_1_pdf)
    iff_2 = ba.InterferenceFunctionRadialParaCrystal(22.8*nm, 1000.0*nm)
    iff_2_pdf = ba.FTDistribution1DGauss(3.0*nm)
    iff_2.setProbabilityDistribution(iff_2_pdf)

    # Define particle layouts
    layout_1 = ba.ParticleLayout()
    layout_1.addParticle(particle_1, 0.8)
    layout_1.setInterferenceFunction(iff_1)
    layout_1.setWeight(1)
    layout_1.setTotalParticleSurfaceDensity(0.01)
    layout_2 = ba.ParticleLayout()
    layout_2.addParticle(particle_2, 0.2)
    layout_2.setInterferenceFunction(iff_2)
    layout_2.setWeight(1)
    layout_2.setTotalParticleSurfaceDensity(0.01)

    # Define layers
    layer_1 = ba.Layer(material_Vacuum)
    layer_1.addLayout(layout_1)
    layer_1.addLayout(layout_2)
    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(200, 2*deg, 1*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)
ApproximationLMA.py