### 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 $\varphi_i = 0^{\circ}$.
• 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  """ Cylinder form factor in Born approximation """ import bornagain as ba from bornagain import deg, nm def get_sample(): """ Returns a sample with cylinders in a homogeneous environment ("Vacuum"), implying a simulation in plain Born approximation. """ # Define materials material_Particle = ba.HomogeneousMaterial("Particle", 0.0006, 2e-08) material_Vacuum = ba.HomogeneousMaterial("Vacuum", 0.0, 0.0) # Define form factors ff = ba.FormFactorCylinder(5.0*nm, 5.0*nm) # Define particles particle = ba.Particle(material_Particle, ff) # Define particle layouts layout = ba.ParticleLayout() layout.addParticle(particle, 1.0) layout.setWeight(1) layout.setTotalParticleSurfaceDensity(0.01) # Define layers layer = ba.Layer(material_Vacuum) layer.addLayout(layout) # Define sample sample = ba.MultiLayer() sample.addLayer(layer) return sample def get_simulation(sample): beam = ba.Beam(1.0, 0.1*nm, ba.Direction(0.2*deg, 0*deg)) detector = ba.SphericalDetector(200, -2*deg, 2*deg, 200, 0*deg, 2*deg) simulation = ba.GISASSimulation(beam, sample, detector) return simulation if __name__ == '__main__': import ba_plot sample = get_sample() simulation = get_simulation(sample) ba_plot.run_and_plot(simulation) 
CylindersInBA.py