Interference 1D Lattice

Scattering from long boxes distributed along a one-dimensional lattice.

  • The particles are long boxes.
  • Each box has a length of 1000nm, a width of 10nm and a height of 15 nm.
  • The particles are placed along a one-dimensional lattice on top of a substrate.
  • They are rotated in the (x,y) plane by 10° with respect the the x-axis of the reference cartesian frame.
  • The 1D lattice is characterized by a lattice length of 30 nm.
  • The lattice's base vector coincides with x-axis of the reference cartesian frame.
  • The wavelength is equal to 24 Å.
  • The incident angles are αi = 0.2° and Φi = 0°.

 

Note:
- By default, the axis of the one-dimensional lattice is the x-axis. A rotation can be applied to the particles (like in this example) or to the 1D lattice.
- In the real-space model picture, the length of the boxes cannot be seen as it is too large, compared to its width and heigth
 

 

Real-space model: 
Intensity Image: 
Python Script: 
"""
Long boxes on a 1D lattice
"""
import numpy
import bornagain as ba
from bornagain import deg, angstrom, nm


def get_sample():
    """
    Returns a sample with a grating on a substrate.
    The structure is modelled by infinitely long boxes forming a 1D 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
    lattice_length = 30.0*nm
    lattice_rotation_angle = 0.0*deg
    interference = ba.InterferenceFunction1DLattice(
        lattice_length, lattice_rotation_angle)
    pdf = ba.FTDecayFunction1DCauchy(20./2./numpy.pi*nm)
    interference.setDecayFunction(pdf)

    box_ff = ba.FormFactorBox(1000*nm, 10*nm, 15.0*nm)
    box = ba.Particle(m_particle, box_ff)
    transform = ba.RotationZ(25.0*deg)
    particle_layout = ba.ParticleLayout()
    particle_layout.addParticle(box, 1.0, ba.kvector_t(0.0, 0.0, 0.0), transform)
    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)
    return multi_layer


def get_simulation():
    """
    Create and return GISAXS simulation with beam and detector defined
    """
    simulation = ba.GISASSimulation()
    simulation.setDetectorParameters(200, -1.0*deg, 1.0*deg,
                                     200, 0.0*deg, 2.0*deg)
    simulation.setBeamParameters(24.0*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.getIntensityData()


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