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, 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 = lattice length/2 = 12.5 nm.
  • The lattices' base vectors are parallel to the axes of the reference cartesian frame.
  • The wavelength is equal to 1 Å.
  • The incident angles are αi = 0.2° and Φi = 0°.
Real-space model: 
Intensity Image: 
Python Script: 
"""
2D lattice with disorder, centered square lattice
"""
import numpy
import bornagain as ba
from bornagain import deg, angstrom, nm

phi_min, phi_max = -2.0, 2.0
alpha_min, alpha_max = 0.0, 2.0


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, phi_min*deg, phi_max*deg,
                                     200, alpha_min*deg, alpha_max*deg)
    simulation.setBeamParameters(1.0*angstrom, 0.2*deg, 0.0*deg)

    return simulation


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


if __name__ == '__main__':
    result = run_simulation()
    ba.plot_intensity_data(result)