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Cosine Ripples in a Rectangular Lattice

Scattering from elongated particles positioned in a two-dimensional rectangular lattice.

  • Each particle has a sinusoidal profile (“Ripple1” form factor) with a length of $100$ nm, a width of $20$ nm and a height of $4$ nm.
  • They are placed along a rectangular lattice on top of a substrate.
  • This lattice is characterized by a lattice length of $200$ nm in the direction of the long axis of the particles and of $50$ nm in the perpendicular direction.
  • The lattice’s base vectors coincide with the reference Cartesian frame.
  • The wavelength is equal to 0.16 nm.
  • The incident angles are $\alpha_i = 0.3 ^{\circ}$ and $\varphi_i = 0^{\circ}$.

Real-space model

Intensity image

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#!/usr/bin/env python3
"""
Cosine ripple on a 2D lattice
"""
import bornagain as ba
from bornagain import ba_plot as bp, deg, nm


def get_sample():
    """
    A sample with cosine ripples on a substrate.
    The structure is modelled as a 2D Lattice.
    """

    # Materials
    material_particle = ba.RefractiveMaterial("Particle", 0.0006, 2e-08)
    material_substrate = ba.RefractiveMaterial("Substrate", 6e-06, 2e-08)
    vacuum = ba.RefractiveMaterial("Vacuum", 0, 0)

    # Form factors
    ff = ba.CosineRippleBox(100*nm, 20*nm, 4*nm)

    # Particles
    particle = ba.Particle(material_particle, ff)

    # 2D lattices
    lattice = ba.BasicLattice2D(200*nm, 50*nm, 90*deg, 0)

    # Interference functions
    iff = ba.Interference2DLattice(lattice)
    iff_pdf = ba.Profile2DCauchy(160*nm, 16*nm, 0)
    iff.setDecayFunction(iff_pdf)

    # Particle layouts
    layout = ba.ParticleLayout()
    layout.addParticle(particle)
    layout.setInterference(iff)
    layout.setTotalParticleSurfaceDensity(0.0001)

    # Layers
    layer_1 = ba.Layer(vacuum)
    layer_1.addLayout(layout)
    layer_2 = ba.Layer(material_substrate)

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

    return sample


def get_simulation(sample):
    beam = ba.Beam(1e9, 0.16*nm, 0.3*deg)
    n = 200
    detector = ba.SphericalDetector(n, -1.5*deg, 1.5*deg, n, 0, 2.5*deg)
    simulation = ba.ScatteringSimulation(beam, sample, detector)
    return simulation


if __name__ == '__main__':
    sample = get_sample()
    simulation = get_simulation(sample)
    result = simulation.simulate()
    bp.plot_simulation_result(result)
auto/Examples/scatter2d/CosineRipplesAtRectLattice.py