### Size-distribution model: size-spacing coupling approximation

Scattering from cylinders of two different sizes using the Size-Spacing Coupling Approximation.

• The sample is made of cylinders deposited on a substrate.
• The distribution of particles is made of:
• 80% of cylinders with radii and heights equal to $5$ nm
• 20% of cylinders with radii and heights equal to $8$ nm.
• The interference function is Radial Paracrystal with a peak distance of $18$ nm and a damping length of $1$ $\mu$m.
• The wavelength is equal to $1$ $\unicode{x212B}$.
• The incident angles are $\alpha_i = 0.2 ^{\circ}$ and $\phi_i = 0^{\circ}$.
• The Size-Spacing Coupling Approximation is implemented using the function setApproximation. By default the Decoupling Approximation is used (see Size-distribution model: Decoupling Approximation).
• For this size-distribution model, an additional dimensionless parameter, the coupling parameter Kappa, has to be specified (see line 33). It defines how the distance between particles is linked with their sizes.
  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  """ Cylinders of two different sizes in Size-Spacing Coupling 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 Size-Spacing Coupling 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 function interference = ba.InterferenceFunctionRadialParaCrystal(18.0*nm, 1e3*nm) pdf = ba.FTDistribution1DGauss(3 * nm) interference.setProbabilityDistribution(pdf) interference.setKappa(1.0) # assembling the sample particle_layout = ba.ParticleLayout() particle_layout.addParticle(cylinder1, 0.8) particle_layout.addParticle(cylinder2, 0.2) particle_layout.setInterferenceFunction(interference) air_layer = ba.Layer(m_ambience) air_layer.addLayout(particle_layout) 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, cmap='jet', aspect='auto') 
ApproximationSSCA.py