Size-distribution model: Size-Spacing Coupling Approximation

Scattering from cylinders of two different sizes using the Size-Spacing Coupling Approximation.

  • The sample is made of cylinders deposited on a substrate.
  • The distribution of particles is made of:
    • 80% of cylinders with radii and heights equal to 5 nm
    • 20% of cylinders with radii and heights equal to 8 nm.
  • The interference function is Radial Paracrystal with a peak distance of 18 nm and a damping length of 1 μm.
  • The wavelength is equal to 1 Å.
  • The incident angles are αi = 0.2° and Φi = 0°.
  • The Size-Spacing Coupling Approximation is implemented using the function setApproximation. By default the Decoupling Approximation is used (see Size-distribution model: Decoupling Approximation).
  • For this size-distribution model, an additional dimensionless parameter, the coupling parameter Kappa, has to be specified. It defines how the distance between particles is linked with their sizes.
Intensity Image: 
Python Script: 
"""
Cylinders of two different sizes in Size-Spacing Coupling Approximation
"""
import numpy
import bornagain as ba
from bornagain import deg, angstrom, nm

phi_min, phi_max = 0.0, 2.0
alpha_min, alpha_max = 0.0, 2.0


def get_sample():
    """
    Returns a sample with cylinders of two different sizes on a substrate.
    The cylinder positions are modelled in Size-Spacing Coupling  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 function
    interference = ba.InterferenceFunctionRadialParaCrystal(
        18.0*nm, 1e3*nm)
    pdf = ba.FTDistribution1DGauss(3 * nm)
    interference.setProbabilityDistribution(pdf)
    interference.setKappa(1.0)

    # assembling the sample
    particle_layout = ba.ParticleLayout()
    particle_layout.addParticle(cylinder1, 0.8)
    particle_layout.addParticle(cylinder2, 0.2)
    particle_layout.setInterferenceFunction(interference)
    particle_layout.setApproximation(ba.ILayout.SSCA)

    air_layer = ba.Layer(m_ambience)
    air_layer.addLayout(particle_layout)
    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, phi_min*deg, phi_max*deg,
                                     200, alpha_min*deg, alpha_max*deg)
    simulation.setBeamParameters(1.0*angstrom, 0.2*deg, 0.0*deg)
    return simulation


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


if __name__ == '__main__':
    result = run_simulation()
    ba.plot_intensity_data(result)