Interference 1D lattice

In this example we simulate the scattering from infinite 1D repetition of rectangular patches (rectangular grating). This is done by using the interference function of a 1D lattice together with very long boxes.

  • By-default, the axis of the one-dimensional lattice coincides with the $x$-axis of the reference cartesian frame, so it coinsides with the beam direction.
  • Long boxes are placed along a one-dimensional lattice on top of substrate, the lattice_length parameter corresponds to the grating period.
  • The size of boxes is initially chosen to form a grating which is perpendicular to the beam (long side of the box is along $y$-axis).
  • Please keep in mind, that length, width, height in the FormFactorBox(length, width, height) constructor correspond to the directions in the $x,y,z$ axes, in that order, so to achieve the desired setup we use the values: length= $10$ nm, width= $10000$ nm, height= $10$ nm.
  • The whole grating is rotated at the end by an angle of $45^{\circ}$ with respect to the beam axis. This is achieved by rotating both the 1D lattice and the long boxes (see lines 25 and 34).
  • To avoid the problem of rapidly oscillating form factors of long boxes (see this example for more details), the simulation is performed in monte carlo integration mode.

Real-space model

Sketch

Intensity image

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#!/usr/bin/env python3
"""
Simulation of grating using very long boxes and 1D lattice.
Monte-carlo integration is used to get rid of
large-particle form factor oscillations.
"""
import bornagain as ba
from bornagain import angstrom, deg, nm, nm2, kvector_t


def get_sample():
    """
    Returns a sample with a grating on a substrate,
    modelled by very long boxes forming a 1D lattice with Cauchy correlations.
    """

    # 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.FormFactorBox(10.0*nm, 10000.0*nm, 10.0*nm)

    # Define particles
    particle = ba.Particle(material_Particle, ff)
    particle_rotation = ba.RotationZ(45.0*deg)
    particle.setRotation(particle_rotation)

    # Define interference functions
    iff = ba.InterferenceFunction1DLattice(30.0*nm, 45.0*deg)
    iff_pdf = ba.FTDecayFunction1DCauchy(1000.0*nm)
    iff.setDecayFunction(iff_pdf)

    # 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, 1.0*angstrom, ba.Direction(0.2*deg, 0.0*deg))
    det = ba.SphericalDetector(200, -1*deg, 1*deg, 200, 0*deg, 2*deg)
    simulation = ba.GISASSimulation(beam, sample, det)
    simulation.getOptions().setMonteCarloIntegration(True, 100)
    if not "__no_terminal__" in globals():
        simulation.setTerminalProgressMonitor()
    return simulation


if __name__ == '__main__':
    import ba_plot
    sample = get_sample()
    simulation = get_simulation(sample)
    ba_plot.run_and_plot(simulation, intensity_min=1e-03)
Interference1DLattice.py