Cylinders and Prisms

Scattering from a mixture of cylinders and prisms without interference.

  • The sample comprises a substrate on which are deposited, in equal proportion, cylinders and prisms.
  • All particles are made of the same material.
  • Each type of particle has the same orientation.
  • The cylinders are 5 nm high and 5 nm in radius.
  • Each prism is 5 nm high with an equilateral triangular base, whose side length is equal to 10 nm.
  • There is no interference between the waves scattered by these particles. The distribution is therefore diluted.
  • The incident neutron beam is characterized by a wavelength of 1 Å.
  • The incident angles are αi = 0.2° and Φi = 0°.
  • The simulation is performed using the Distorted Wave Born Approximation (due to the presence of a substrate).

 

Real-space model: 
Intensity Image: 
Python Script: 
"""
Mixture of cylinders and prisms without interference
"""
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, 2.0


def get_sample():
    """
    Returns a sample with uncorrelated cylinders and prisms on a substrate.
    """
    # defining materials
    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)

    # collection of particles
    cylinder_ff = ba.FormFactorCylinder(5*nm, 5*nm)
    cylinder = ba.Particle(m_particle, cylinder_ff)
    prism_ff = ba.FormFactorPrism3(10*nm, 5*nm)
    prism = ba.Particle(m_particle, prism_ff)
    particle_layout = ba.ParticleLayout()
    particle_layout.addParticle(cylinder, 0.5)
    particle_layout.addParticle(prism, 0.5)
    interference = ba.InterferenceFunctionNone()
    particle_layout.setInterferenceFunction(interference)

    # air layer with particles and substrate form multi layer
    air_layer = ba.Layer(m_air)
    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():
    """
    Returns a GISAXS simulation with beam and detector defined.
    """
    simulation = ba.GISASSimulation()
    simulation.setDetectorParameters(100, phi_min*deg, phi_max*deg,
                                     100, 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 resulting 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)