Two types of cylinders with size distribution

Scattering of a polydisperse distribution of two types of cylinders.

  • The simulation is performed using the Born approximation, i.e. there is no “substrate” layer.
  • The sample is made of polydisperse cylinders of two different sizes: $R_1 = H_1$ and $R_2 = H_2$, where $R_i$ and $H_i$ are the radius and width of cylinder of type $i$.
  • There are 95% of cylinders of type $1$ and 5% of cylinders of type $2$.
  • The polydispersity affects the radii of the cylinders, following a normal distribution. For the small cylinders, their characteristic sizes vary around $R_1 = 5$ nm with a standard deviation $\sigma_1 = 0.2 R_1$. For type 2, the average value $R_2$ is $10$ nm and $\sigma_2 = 0.02 R_2$.
  • There is also no interference between the scattered beams.
  • The incident beam is characterized by a wavelength of $1$ $\unicode{x212B}$.
  • The incident angles $\alpha_i = 0.2 ^{\circ}$ and $\phi_i = 0^{\circ}$.

Real-space model

Intensity image

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"""
Mixture cylinder particles with different size distribution
"""
import bornagain as ba
from bornagain import deg, angstrom, nm


def get_sample():
    """
    Returns a sample with cylinders in a homogeneous medium ("air").
    The cylinders are a 95:5 mixture of two different size distributions.
    """
    # defining materials
    m_air = ba.HomogeneousMaterial("Air", 0.0, 0.0)
    m_particle = ba.HomogeneousMaterial("Particle", 6e-4, 2e-8)

    # collection of particles #1
    radius1 = 5.0*nm
    height1 = radius1
    sigma1 = radius1*0.2

    cylinder_ff1 = ba.FormFactorCylinder(radius1, height1)
    cylinder1 = ba.Particle(m_particle, cylinder_ff1)

    gauss_distr1 = ba.DistributionGaussian(radius1, sigma1)

    nparticles = 150
    sigma_factor = 3.0

    # limits will assure, that generated Radius'es are >=0
    limits = ba.RealLimits.nonnegative()

    par_distr1 = ba.ParameterDistribution(
        "/Particle/Cylinder/Radius", gauss_distr1, nparticles, sigma_factor, limits)
    part_coll1 = ba.ParticleDistribution(cylinder1, par_distr1)

    # collection of particles #2
    radius2 = 10.0*nm
    height2 = radius2
    sigma2 = radius2*0.02

    cylinder_ff2 = ba.FormFactorCylinder(radius2, height2)
    cylinder2 = ba.Particle(m_particle, cylinder_ff2)

    gauss_distr2 = ba.DistributionGaussian(radius2, sigma2)

    par_distr2 = ba.ParameterDistribution(
        "/Particle/Cylinder/Radius", gauss_distr2, nparticles, sigma_factor, limits)
    part_coll2 = ba.ParticleDistribution(cylinder2, par_distr2)

    # assembling the sample
    particle_layout = ba.ParticleLayout()
    particle_layout.addParticle(part_coll1, 0.95)
    particle_layout.addParticle(part_coll2, 0.05)

    air_layer = ba.Layer(m_air)
    air_layer.addLayout(particle_layout)

    multi_layer = ba.MultiLayer()
    multi_layer.addLayer(air_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, cmap='jet', aspect='auto')
TwoTypesOfCylindersWithSizeDistribution.py