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 $\phi_i = 0^{\circ}$.

Intensity image

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"""
Cylinders of two different sizes in Local Monodisperse Approximation
"""
import bornagain as ba
from bornagain import deg, angstrom, 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.
    """
    m_ambience = ba.HomogeneousMaterial("Air", 0.0, 0.0)
    m_substrate = ba.HomogeneousMaterial("Substrate", 6e-6, 2e-8)
    m_particle = ba.HomogeneousMaterial("Particle", 6e-4, 2e-8)

    # cylindrical particle 1
    radius1 = 5*nm
    height1 = radius1
    cylinder_ff1 = ba.FormFactorCylinder(radius1, height1)
    cylinder1 = ba.Particle(m_particle, cylinder_ff1)

    # cylindrical particle 2
    radius2 = 8*nm
    height2 = radius2
    cylinder_ff2 = ba.FormFactorCylinder(radius2, height2)
    cylinder2 = ba.Particle(m_particle, cylinder_ff2)

    # interference function1
    interference1 = ba.InterferenceFunctionRadialParaCrystal(
        16.8*nm, 1e3*nm)
    pdf = ba.FTDistribution1DGauss(3 * nm)
    interference1.setProbabilityDistribution(pdf)

    # interference function2
    interference2 = ba.InterferenceFunctionRadialParaCrystal(
        22.8*nm, 1e3*nm)
    interference2.setProbabilityDistribution(pdf)

    # assembling the sample
    particle_layout1 = ba.ParticleLayout()
    particle_layout1.addParticle(cylinder1, 0.8)
    particle_layout1.setInterferenceFunction(interference1)

    particle_layout2 = ba.ParticleLayout()
    particle_layout2.addParticle(cylinder2, 0.2)
    particle_layout2.setInterferenceFunction(interference2)

    air_layer = ba.Layer(m_ambience)
    air_layer.addLayout(particle_layout1)
    air_layer.addLayout(particle_layout2)
    substrate_layer = ba.Layer(m_substrate)
    multi_layer = ba.MultiLayer()
    multi_layer.addLayer(air_layer)
    multi_layer.addLayer(substrate_layer)
    return multi_layer


def get_simulation():
    """
    Create and return GISAXS simulation with beam and detector defined
    """
    simulation = ba.GISASSimulation()
    simulation.setDetectorParameters(200, 0.0*deg, 2.0*deg,
                                     200, 0.0*deg, 2.0*deg)
    simulation.setBeamParameters(1.0*angstrom, 0.2*deg, 0.0*deg)
    return simulation


def run_simulation():
    """
    Runs simulation and returns intensity map.
    """
    simulation = get_simulation()
    simulation.setSample(get_sample())
    simulation.runSimulation()
    return simulation.result()


if __name__ == '__main__':
    result = run_simulation()
    ba.plot_simulation_result(result)
ApproximationLMA.py