Spheres on Hexagonal Lattice

Scattering from spheres distributed along a hexagonal lattice.

  • The sample is made of spherical particles with radii of 10 nm deposited on a substrate along a hexagonal lattice.
  • This two-dimensional lattice is characterized by a lattice length of 20 nm. Its a-axis coincides with the x-axis 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: 
"""
Spheres on a hexagonal lattice
"""
import numpy
import bornagain as ba
from bornagain import deg, angstrom, nm

phi_min, phi_max = -1.0, 1.0
alpha_min, alpha_max = 0.0, 1.0


def get_sample():
    """
    Returns a sample with spherical particles on a substrate,
    forming a hexagonal 2D lattice.
    """
    m_air = 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)

    sphere_ff = ba.FormFactorFullSphere(10.0*nm)
    sphere = ba.Particle(m_particle, sphere_ff)
    particle_layout = ba.ParticleLayout()
    particle_layout.addParticle(sphere)

    interference = ba.InterferenceFunction2DLattice.createHexagonal(20.0*nm)
    pdf = ba.FTDecayFunction2DCauchy(10*nm, 10*nm)
    interference.setDecayFunction(pdf)

    particle_layout.setInterferenceFunction(interference)

    air_layer = ba.Layer(m_air)
    air_layer.addLayout(particle_layout)
    substrate_layer = ba.Layer(m_substrate, 0)
    multi_layer = ba.MultiLayer()
    multi_layer.addLayer(air_layer)
    multi_layer.addLayer(substrate_layer)
    return multi_layer


def get_simulation():
    """
    Create and return GISAXS 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)