### Size-distribution model: local monodisperse approximation

Scattering from cylinders of two different sizes using the Local Monodisperse Approximation (LMA).

• The sample is made of cylinders deposited on a substrate.
• The cylinders are of two different sizes:
• 80% of Type $1$: radius $R_1 = 5$ nm, height $H_1 = 5$ nm. The interference function is a radial paracrystal with a peak distance equal to $16.8$ nm and a damping length of $1$ $\mu$m.
• 20% of Type $2$: radius $R_2 = 8$ nm, height $H_2 = 8$ nm. The interference function is also a radial paracrystal but with a peak distance of $22.8$ nm and a damping length equal to $1$ $\mu$m.
• Each type of cylinders is associated with a “particle layout”.
• The LMA is used since the sample is made of two domains containing particles of the same size and shape.
• The wavelength is equal to $1$ $\unicode{x212B}$.
• The incident angles are $\alpha_i = 0.2 ^{\circ}$ 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 68 69 70 71  #!/usr/bin/env python3 """ Cylinders of two different sizes in Local Monodisperse Approximation """ import bornagain as ba from bornagain import deg, nm def get_sample(): """ Returns a sample with cylinders of two different sizes on a substrate. The cylinder positions are modelled in Local Monodisperse Approximation. """ # Define materials material_Particle = ba.HomogeneousMaterial("Particle", 0.0006, 2e-08) material_Substrate = ba.HomogeneousMaterial("Substrate", 6e-06, 2e-08) material_Vacuum = ba.HomogeneousMaterial("Vacuum", 0, 0) # Define form factors ff_1 = ba.FormFactorCylinder(5*nm, 5*nm) ff_2 = ba.FormFactorCylinder(8*nm, 8*nm) # Define particles particle_1 = ba.Particle(material_Particle, ff_1) particle_2 = ba.Particle(material_Particle, ff_2) # Define interference functions iff_1 = ba.InterferenceFunctionRadialParaCrystal(16.8*nm, 1000*nm) iff_1_pdf = ba.FTDistribution1DGauss(3*nm) iff_1.setProbabilityDistribution(iff_1_pdf) iff_2 = ba.InterferenceFunctionRadialParaCrystal(22.8*nm, 1000*nm) iff_2_pdf = ba.FTDistribution1DGauss(3*nm) iff_2.setProbabilityDistribution(iff_2_pdf) # Define particle layouts layout_1 = ba.ParticleLayout() layout_1.addParticle(particle_1, 0.8) layout_1.setInterferenceFunction(iff_1) layout_1.setTotalParticleSurfaceDensity(0.01) layout_2 = ba.ParticleLayout() layout_2.addParticle(particle_2, 0.2) layout_2.setInterferenceFunction(iff_2) layout_2.setTotalParticleSurfaceDensity(0.01) # Define layers layer_1 = ba.Layer(material_Vacuum) layer_1.addLayout(layout_1) layer_1.addLayout(layout_2) layer_2 = ba.Layer(material_Substrate) # Define sample sample = ba.MultiLayer() sample.addLayer(layer_1) sample.addLayer(layer_2) 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) 
ApproximationLMA.py