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Interference 2D centered square lattice

Scattering from cylinders positioned in a squared centered lattice.

  • The particles are cylinders with radii and heights of $3$ nm.
  • Their spatial distribution is composed of two square lattices (lattice length $l$), shifted by half a lattice length in both directions:
  • The first square lattice is centered at the origin, with a lattice length of $25$ nm.
  • The second one, with the same lattice spacing and the same type of particles at its nodes is initialized at $x = y = l/2 = 12.5$ nm.
  • The lattices’ base vectors are parallel to the axes of the reference cartesian frame.
  • The wavelength is equal to 0.1 nm.
  • The incident angles are $\alpha_i = 0.2 ^{\circ}$ and $\varphi_i = 0^{\circ}$.

Real-space model

Intensity image

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#!/usr/bin/env python3
"""
2D lattice with disorder, centered square lattice
"""
import bornagain as ba
from bornagain import ba_plot as bp, deg, nm, R3

r = 3*nm  # particle radius
a = 25*nm  # lattice constant


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

    # Define materials
    material_Particle = ba.RefractiveMaterial("Particle", 0.0006, 2e-08)
    material_Substrate = ba.RefractiveMaterial("Substrate", 6e-06, 2e-08)
    material_Vacuum = ba.RefractiveMaterial("Vacuum", 0, 0)

    # Define particles
    ff = ba.Cylinder(r, r)
    particle_1 = ba.Particle(material_Particle, ff)
    particle_2 = ba.Particle(material_Particle, ff)
    particle_2.translate(R3(a/2, a/2, 0))

    # Define composition of particles at specific positions
    basis = ba.Compound()
    basis.addComponent(particle_1)
    basis.addComponent(particle_2)

    # Define 2D lattices
    lattice = ba.SquareLattice2D(a, 0*deg)

    # Define interference functions
    iff = ba.Interference2DLattice(lattice)
    iff_pdf = ba.Profile2DCauchy(48*nm, 16*nm, 0)
    iff.setDecayFunction(iff_pdf)

    # Define particle layouts
    layout = ba.ParticleLayout()
    layout.addParticle(basis)
    layout.setInterference(iff)
    layout.setTotalParticleSurfaceDensity(0.0016)

    # 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(1e9, 0.1*nm, 0.2*deg)
    n = bp.simargs['n']
    detector = ba.SphericalDetector(n, -2*deg, 2*deg, n, 0, 2*deg)
    simulation = ba.ScatteringSimulation(beam, sample, detector)
    return simulation


if __name__ == '__main__':
    bp.parse_args(sim_n=200)
    sample = get_sample()
    simulation = get_simulation(sample)
    result = simulation.simulate()
    bp.plot_simulation_result(result)
Examples/scatter2d/Interference2DCenteredSquareLattice.py