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

Real-space model

Intensity image

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


def get_sample():
    """
    Returns a sample with cylinders in a homogeneous medium ("Vacuum").
    The cylinders are a 95:5 mixture of two different size distributions.
    """

    # Define materials
    material_Particle = ba.HomogeneousMaterial("Particle", 0.0006, 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(10.0*nm, 10.0*nm)

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

    # Define particles with parameter following a distribution
    distr_1 = ba.DistributionGaussian(5.0*nm, 1.0*nm)
    par_distr_1 = ba.ParameterDistribution("/Particle/Cylinder/Radius",
                                           distr_1, 150, 3.0,
                                           ba.RealLimits.nonnegative())
    particle_distrib_1 = ba.ParticleDistribution(particle_1, par_distr_1)
    distr_2 = ba.DistributionGaussian(10.0*nm, 0.2*nm)
    par_distr_2 = ba.ParameterDistribution("/Particle/Cylinder/Radius",
                                           distr_2, 150, 3.0,
                                           ba.RealLimits.nonnegative())
    particle_distrib_2 = ba.ParticleDistribution(particle_2, par_distr_2)

    # Define particle layouts
    layout = ba.ParticleLayout()
    layout.addParticle(particle_distrib_1, 0.95)
    layout.addParticle(particle_distrib_2, 0.05)
    layout.setWeight(1)
    layout.setTotalParticleSurfaceDensity(0.01)

    # Define layers
    layer = ba.Layer(material_Vacuum)
    layer.addLayout(layout)

    # Define sample
    sample = ba.MultiLayer()
    sample.addLayer(layer)

    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)
TwoTypesOfCylindersWithSizeDistribution.py