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Triangular Ripples in a Rectangular Lattice

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

  • Each particle has a triangular profile (“Ripple2” 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 $\varphi_i = 0^{\circ}$.

Scattering intensity

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#!/usr/bin/env python3
"""
 Sample from the article D. Babonneau et. al., Phys. Rev. B 85, 235415, 2012 (Fig.3)
"""
import bornagain as ba
from bornagain import ba_plot as bp, deg, nm


def get_sample():
    """
    A sample with a grating on a substrate, modelled by triangular ripples
    forming a 1D Paracrystal.
    """

    # Materials
    particle_color = (0.86, 0.24, 0.18)
    particle_mat = ba.RefractiveMaterial("Particle", particle_color, 0.0006, 2e-08)
    substrate_color = (0.28, 0.57, 0.82)
    substrate_mat = ba.RefractiveMaterial("Substrate", substrate_color, 6e-06, 2e-08)
    vacuum = ba.Vacuum()

    # Particles
    ff = ba.SawtoothRippleBox(100*nm, 20*nm, 4*nm, -3*nm)
    particle = ba.Particle(particle_mat, ff)

    # 2D lattices
    lattice = ba.BasicLattice2D(200*nm, 50*nm, 90*deg, 0)
    layout = ba.Crystal2D(particle, lattice)
    profile = ba.Profile2DGauss(160*nm, 16*nm, 0)
    layout.setDecayFunction(profile)

    # Layers
    layer_1 = ba.Layer(vacuum)
    layer_1.deposit2D(layout)
    layer_2 = ba.Layer(substrate_mat)

    # Sample
    sample = ba.Sample()
    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, -2*deg, 2*deg, n, 0., 3*deg)
    simulation = ba.ScatteringSimulation(beam, sample, detector)
    return simulation


if __name__ == '__main__':
    sample = get_sample()
    ba.showSample3D(sample, sample_size=1200*nm, seed=0)
    simulation = get_simulation(sample)
    result = simulation.simulate()
    bp.plot_datafield(result, unit_aspect=1)
    bp.plt.show()
auto/Examples/scatter2d/TriangularRipple.py