### Cylinders with size distribution

Scattering from a polydisperse distribution of cylinders in Born Approximation.

• The average radii and heights of the cylinders are equal to $5$ nm.
• The radii of the cylinders vary according to a normal distribution with a standard deviation $\sigma$ equal to $0.2$ times the average radius.
• 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 embedded in air layer, DWBA boils down to BA).
• No interference effects from 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 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71  """ Cylinders with size distribution """ import bornagain as ba from bornagain import deg, angstrom, nm def get_sample(): """ Return a sample with cylinders on a substrate. The cylinders have a Gaussian size distribution. """ m_ambience = ba.HomogeneousMaterial("Air", 0.0, 0.0) m_particle = ba.HomogeneousMaterial("Particle", 6e-4, 2e-8) # cylindrical particle radius = 5*nm height = radius cylinder_ff = ba.FormFactorCylinder(radius, height) cylinder = ba.Particle(m_particle, cylinder_ff) # collection of particles with size distribution nparticles = 100 sigma = 0.2*radius gauss_distr = ba.DistributionGaussian(radius, sigma) sigma_factor = 2.0 par_distr = ba.ParameterDistribution( "/Particle/Cylinder/Radius", gauss_distr, nparticles, sigma_factor) # by uncommenting the line below, the height of the cylinders # can be scaled proportionally to the radius: # par_distr.linkParameter("/Particle/Cylinder/Height") part_coll = ba.ParticleDistribution(cylinder, par_distr) # assembling the sample particle_layout = ba.ParticleLayout() particle_layout.addParticle(part_coll) 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(): """ Create and return GISAXS simulation with beam and detector defined """ simulation = ba.GISASSimulation() simulation.setDetectorParameters(200, 0.0*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') 
CylindersWithSizeDistribution.py