Rotated pyramids

Scattering from a monodisperse distribution of rotated pyramids.

This example illustrates how the in-plane rotation of non-radially symmetric particles influences
the scattering pattern.

  • The sample is made of pyramids deposited on a substrate.
  • Each pyramid is characterized by a squared-base side length of 10 nm, a height of 5 nm, and a base angle α equal to 54.73°.
  • These particles are rotated in the (x, y) plane by 45°.
  • There is no interference between the scattered waves.
  • The wavelength is equal to 1 Å.
  • The incident angles are αi = 0.2° and Φi = 0°.
Real-space model: 
Intensity Image: 
Python Script: 
"""
Rotated pyramids on top of substrate
"""
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 rotated pyramids on top of a substrate.
    """
    # 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
    pyramid_ff = ba.FormFactorPyramid(10*nm, 5*nm, 54.73*deg)
    pyramid = ba.Particle(m_particle, pyramid_ff)
    transform = ba.RotationZ(45.*deg)
    particle_layout = ba.ParticleLayout()
    particle_layout.addParticle(
        pyramid, 1.0, ba.kvector_t(0.0, 0.0, 0.0), transform)

    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():
    """
    Returns a 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)