Interference 2D Paracrystal

Scattering from monodisperse cylinders distributed along a two-dimensional square paracrystal.

  • The particles are cylinders with constant radii and heights equal to $5$ nm.
  • They are deposited on a substrate, following a two-dimensional square paracrystalline pattern.
  • This 2D paracrystal is characterized by:
    • a lattice length of $20$ nm along both axes of the reference Cartesian frame,
    • a damping length equal to $0$,
    • “coherent’ domains with a size of $20$ $\mu$m along the axes of the reference Cartesian frame.
  • The incident beam is characterized by a wavelength of $1$ $\unicode{x212B}$ and angles $\alpha_i = 0.2 ^{\circ}$ and $\phi_i = 0^{\circ}$.

Note:

A damping length is used to introduce finite size effects by applying a multiplicative coefficient equal to $exp \left(-\frac{peak\_distance}{damping\_length}\right)$ to the Fourier transform of the probability densities. $damping\_length$ is equal to $0$ by default and, in this case, no correction is applied.

Intensity image

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"""
2D paracrystal
"""
import bornagain as ba
from bornagain import deg, angstrom, nm, micrometer


def get_sample():
    """
    Returns a sample with cylinders on a substrate, forming a 2D paracrystal
    """
    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)

    # collection of particles
    cylinder_ff = ba.FormFactorCylinder(4*nm, 5*nm)
    cylinder = ba.Particle(m_particle, cylinder_ff)

    interference = ba.InterferenceFunction2DParaCrystal.createSquare(
        10.0*nm, 0.0, 20.0*micrometer, 20.0*micrometer)
    pdf = ba.FTDistribution2DCauchy(1.0*nm, 1.0*nm)
    interference.setProbabilityDistributions(pdf, pdf)

    particle_layout = ba.ParticleLayout()
    particle_layout.addParticle(cylinder, 1.0)
    particle_layout.setInterferenceFunction(interference)

    # assembling the sample
    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)
    print(multi_layer.parametersToString())
    print(multi_layer.treeToString())
    return multi_layer


def get_simulation():
    """
    Returns a GISAXS simulation with beam and detector defined.
    """
    simulation = ba.GISASSimulation()
    # coarse grid because this simulation takes rather long
    simulation.setDetectorParameters(200, -2.0*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.setTerminalProgressMonitor()
    simulation.runSimulation()
    return simulation.result()


if __name__ == '__main__':
    result = run_simulation()
    ba.plot_simulation_result(result)
Interference2DParaCrystal.py