### Cylinders in Born Approximation

Scattering from a monodisperse distribution of cylinders using the Born approximation.

• The cylinders are all identical with radii and heights equal to $5$ nanometers.
• The wavelength is equal to $1$ $\unicode{x212B}$.
• The incident angles are equal to $\alpha_i = 0.2 ^{\circ}$ and $\phi_i = 0^{\circ}$.
• There is no substrate (particles are embedded in the air layer), hence no refraction, hence no distorted waves, hence DWBA boils down to regular Born approximation.
• Scattering is not affected by inter-particle correlations (dilute-particles approximation).
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55  """ Cylinder formfactor in Born approximation """ import bornagain as ba from bornagain import deg, angstrom, nm def get_sample(): """ Returns a sample with cylinders in a homogeneous environment ("air"), implying a simulation in plain Born approximation. """ # defining materials m_ambience = ba.HomogeneousMaterial("Air", 0.0, 0.0) 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) particle_layout = ba.ParticleLayout() particle_layout.addParticle(cylinder, 1.0) air_layer = ba.Layer(m_ambience) air_layer.addLayout(particle_layout) multi_layer = ba.MultiLayer() multi_layer.addLayer(air_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, cmap='jet', aspect='auto') 
CylindersInBA.py