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

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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#!/usr/bin/env python3
"""
2D paracrystal
"""
import bornagain as ba
from bornagain import deg, nm


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

    # Define materials
    material_Particle = ba.HomogeneousMaterial("Particle", 0.0006, 2e-08)
    material_Substrate = ba.HomogeneousMaterial("Substrate", 6e-06, 2e-08)
    material_Vacuum = ba.HomogeneousMaterial("Vacuum", 0.0, 0.0)

    # Define form factors
    ff = ba.FormFactorCylinder(4.0*nm, 5.0*nm)

    # Define particles
    particle = ba.Particle(material_Particle, ff)

    # Define 2D lattices
    lattice = ba.BasicLattice2D(10.0*nm, 10.0*nm, 90.0*deg, 0.0*deg)

    # Define interference functions
    iff = ba.InterferenceFunction2DParaCrystal(lattice, 0.0*nm, 20000.0*nm,
                                               20000.0*nm)
    iff.setIntegrationOverXi(True)
    iff_pdf_1 = ba.FTDistribution2DCauchy(1.0*nm, 1.0*nm, 0.0*deg)
    iff_pdf_2 = ba.FTDistribution2DCauchy(1.0*nm, 1.0*nm, 0.0*deg)
    iff.setProbabilityDistributions(iff_pdf_1, iff_pdf_2)

    # Define particle layouts
    layout = ba.ParticleLayout()
    layout.addParticle(particle, 1.0)
    layout.setInterferenceFunction(iff)
    layout.setWeight(1)
    layout.setTotalParticleSurfaceDensity(0.01)

    # Define layers
    layer_1 = ba.Layer(material_Vacuum)
    layer_1.addLayout(layout)
    layer_2 = ba.Layer(material_Substrate)

    # Define sample
    sample = ba.MultiLayer()
    sample.addLayer(layer_1)
    sample.addLayer(layer_2)

    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, 2*deg, 200, 0*deg, 2*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)
Interference2DParaCrystal.py