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 $\alpha$ equal to $54.73^{\circ}$.
  • These particles are rotated in the $(x, y)$ plane by $45^{\circ}$.
  • There is no interference between the scattered waves.
  • The wavelength is equal to $1$ $\unicode{x212B}$.
  • The incident angles are $\alpha_i = 0.2 ^{\circ}$ and $\phi_i = 0^{\circ}$.

Real-space model

Intensity image

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"""
Rotated pyramids on top of substrate
"""
import bornagain as ba
from bornagain import deg, angstrom, nm


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, -2.0*deg, 2.0*deg,
                                     200, 0.0*deg, 2.0*deg)
    simulation.setBeamParameters(1.0*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.result()


if __name__ == '__main__':
    result = run_simulation()
    ba.plot_simulation_result(result)
RotatedPyramids.py