### 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 $\phi_i = 0^{\circ}$.
  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 72 73 74 75 76 77 78 79 80 81 82 83  """ Cylinders of two different sizes in Local Monodisperse Approximation """ import bornagain as ba from bornagain import deg, angstrom, 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. """ m_ambience = ba.HomogeneousMaterial("Air", 0.0, 0.0) m_substrate = ba.HomogeneousMaterial("Substrate", 6e-6, 2e-8) m_particle = ba.HomogeneousMaterial("Particle", 6e-4, 2e-8) # cylindrical particle 1 radius1 = 5*nm height1 = radius1 cylinder_ff1 = ba.FormFactorCylinder(radius1, height1) cylinder1 = ba.Particle(m_particle, cylinder_ff1) # cylindrical particle 2 radius2 = 8*nm height2 = radius2 cylinder_ff2 = ba.FormFactorCylinder(radius2, height2) cylinder2 = ba.Particle(m_particle, cylinder_ff2) # interference function1 interference1 = ba.InterferenceFunctionRadialParaCrystal( 16.8*nm, 1e3*nm) pdf = ba.FTDistribution1DGauss(3 * nm) interference1.setProbabilityDistribution(pdf) # interference function2 interference2 = ba.InterferenceFunctionRadialParaCrystal( 22.8*nm, 1e3*nm) interference2.setProbabilityDistribution(pdf) # assembling the sample particle_layout1 = ba.ParticleLayout() particle_layout1.addParticle(cylinder1, 0.8) particle_layout1.setInterferenceFunction(interference1) particle_layout2 = ba.ParticleLayout() particle_layout2.addParticle(cylinder2, 0.2) particle_layout2.setInterferenceFunction(interference2) air_layer = ba.Layer(m_ambience) air_layer.addLayout(particle_layout1) air_layer.addLayout(particle_layout2) substrate_layer = ba.Layer(m_substrate) multi_layer = ba.MultiLayer() multi_layer.addLayer(air_layer) multi_layer.addLayer(substrate_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) 
ApproximationLMA.py