Interference 2D centered square lattice

Scattering from cylinders distributed along 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 $1$ $\unicode{x212B}$.
  • The incident angles are $\alpha_i = 0.2 ^{\circ}$ and $\phi_i = 0^{\circ}$.

Real-space model

Intensity image

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"""
2D lattice with disorder, centered square lattice
"""
import numpy
import bornagain as ba
from bornagain import deg, angstrom, nm


def get_sample():
    """
    Returns a sample with cylinders on a substrate,
    forming a 2D centered square lattice
    """
    # defining materials
    m_ambience = ba.HomogeneousMaterial("Air", 0.0, 0.0)
    m_substrate = ba.HomogeneousMaterial("Substrate", 6e-6, 2e-8)
    m_particle = ba.HomogeneousMaterial("Particle", 6e-4, 2e-8)

    # collection of particles
    interference = ba.InterferenceFunction2DLattice.createSquare(25.0*nm)
    pdf = ba.FTDecayFunction2DCauchy(300.0*nm/2.0/numpy.pi,
                                     100.0*nm/2.0/numpy.pi)
    interference.setDecayFunction(pdf)

    particle_layout = ba.ParticleLayout()
    position1 = ba.kvector_t(0.0, 0.0, 0.0)
    position2 = ba.kvector_t(12.5*nm, 12.5*nm, 0.0)
    cylinder_ff = ba.FormFactorCylinder(3.*nm, 3.*nm)
    cylinder = ba.Particle(m_particle, cylinder_ff)
    basis = ba.ParticleComposition()
    basis.addParticles(cylinder, [position1, position2])
    particle_layout.addParticle(basis)
    particle_layout.setInterferenceFunction(interference)

    # assembling the sample
    air_layer = ba.Layer(m_ambience)
    air_layer.addLayout(particle_layout)
    substrate_layer = ba.Layer(m_substrate)

    multi_layer = ba.MultiLayer()
    multi_layer.addLayer(air_layer)
    multi_layer.addLayer(substrate_layer)

    print(multi_layer.treeToString())
    return multi_layer


def get_simulation():
    """
    Create and return GISAS simulation with beam and detector defined
    """
    simulation = ba.GISASSimulation()
    simulation.setDetectorParameters(200, -2.0*deg, 2.0*deg,
                                     200, 0.0*deg, 2.0*deg)
    simulation.setBeamParameters(1.0*angstrom, 0.2*deg, 0.0*deg)

    return simulation


def run_simulation():
    """
    Runs simulation and returns intensity map.
    """
    simulation = get_simulation()
    simulation.setSample(get_sample())
    simulation.runSimulation()
    return simulation.result()


if __name__ == '__main__':
    result = run_simulation()
    ba.plot_simulation_result(result, cmap='jet', aspect='auto')
Interference2DCenteredSquareLattice.py