### Two types of cylinders with size distribution

Scattering of a polydisperse distribution of two types of cylinders.

• The simulation is performed using the Born approximation, i.e. there is no “substrate” layer.
• The sample is made of polydisperse cylinders of two different sizes: $R_1 = H_1$ and $R_2 = H_2$, where $R_i$ and $H_i$ are the radius and width of cylinder of type $i$.
• There are 95% of cylinders of type $1$ and 5% of cylinders of type $2$.
• The polydispersity affects the radii of the cylinders, following a normal distribution. For the small cylinders, their characteristic sizes vary around $R_1 = 5$ nm with a standard deviation $\sigma_1 = 0.2 R_1$. For type 2, the average value $R_2$ is $10$ nm and $\sigma_2 = 0.02 R_2$.
• There is also no interference between the scattered beams.
• The incident beam is characterized by a wavelength of $1$ $\unicode{x212B}$.
• The incident angles $\alpha_i = 0.2 ^{\circ}$ and $\varphi_i = 0^{\circ}$.
  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  #!/usr/bin/env python3 """ Mixture cylinder particles with different size distribution """ import bornagain as ba from bornagain import deg, nm def get_sample(): """ Returns a sample with cylinders in a homogeneous medium ("Vacuum"). The cylinders are a 95:5 mixture of two different size distributions. """ # Define materials material_Particle = ba.HomogeneousMaterial("Particle", 0.0006, 2e-08) material_Vacuum = ba.HomogeneousMaterial("Vacuum", 0, 0) # Define form factors ff_1 = ba.FormFactorCylinder(5*nm, 5*nm) ff_2 = ba.FormFactorCylinder(10*nm, 10*nm) # Define particles particle_1 = ba.Particle(material_Particle, ff_1) particle_2 = ba.Particle(material_Particle, ff_2) # Define particles with parameter following a distribution distr_1 = ba.DistributionGaussian(5*nm, 1*nm) par_distr_1 = ba.ParameterDistribution("/Particle/Cylinder/Radius", distr_1, 150, 3, ba.RealLimits.nonnegative()) particle_distrib_1 = ba.ParticleDistribution(particle_1, par_distr_1) distr_2 = ba.DistributionGaussian(10*nm, 0.2*nm) par_distr_2 = ba.ParameterDistribution("/Particle/Cylinder/Radius", distr_2, 150, 3, ba.RealLimits.nonnegative()) particle_distrib_2 = ba.ParticleDistribution(particle_2, par_distr_2) # Define particle layouts layout = ba.ParticleLayout() layout.addParticle(particle_distrib_1, 0.95) layout.addParticle(particle_distrib_2, 0.05) 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, 0.1*nm, ba.Direction(0.2*deg, 0)) detector = ba.SphericalDetector(200, 2*deg, 1*deg, 1*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) 
TwoTypesOfCylindersWithSizeDistribution.py