Interference 2D Square Lattice

Scattering from cylindrical particles distributed along a square lattice.

  • Cylinders with radii and heights of 3 nanometers are deposited on a substrate.
  • Because of the presence of the substrate layer the simulation is run using the DWBA.
  • The particles are distributed along a square lattice with a lattice length of 25 nm.
  • The main axes are parallel to the x-axis and y-axis of the reference cartesian frame, respectively.
  • The lattice is initialized by placing a cylinder at the origin.
  • The incident beam is characterized by a wavelength of 1 Å.
  • The incident angles are αi = 0.2° and Φi = 0°.
Real-space model: 
Intensity Image: 
Python Script: 
Cylinders on a 2D 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 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,

    cylinder_ff = ba.FormFactorCylinder(3.*nm, 3.*nm)
    cylinder = ba.Particle(m_particle, cylinder_ff)
    particle_layout = ba.ParticleLayout()

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

    multi_layer = ba.MultiLayer()
    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()
    return simulation.getIntensityData()

if __name__ == '__main__':
    result = run_simulation()