### Interference 2D Paracrystal

Scattering from monodisperse cylinders distributed along a two-dimensional square paracrystal.

• The particles are cylinders with constant radii and heights equal to $5$ nm.
• They are deposited on a substrate, following a two-dimensional square paracrystalline pattern.
• This 2D paracrystal is characterized by:
• a lattice length of $20$ nm along both axes of the reference Cartesian frame,
• a damping length equal to $0$,
• “coherent’ domains with a size of $20$ $\mu$m along the axes of the reference Cartesian frame.
• The incident beam is characterized by a wavelength of $1$ $\unicode{x212B}$ and angles $\alpha_i = 0.2 ^{\circ}$ and $\phi_i = 0^{\circ}$.

Note:

A damping length is used to introduce finite size effects by applying a multiplicative coefficient equal to $exp \left(-\frac{peak\_distance}{damping\_length}\right)$ to the Fourier transform of the probability densities. $damping\_length$ is equal to $0$ by default and, in this case, no correction is applied.

  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  """ 2D paracrystal """ import bornagain as ba from bornagain import deg, angstrom, nm, micrometer def get_sample(): """ Returns a sample with cylinders on a substrate, forming a 2D paracrystal """ 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) # collection of particles cylinder_ff = ba.FormFactorCylinder(4*nm, 5*nm) cylinder = ba.Particle(m_particle, cylinder_ff) interference = ba.InterferenceFunction2DParaCrystal.createSquare( 10.0*nm, 0.0, 20.0*micrometer, 20.0*micrometer) pdf = ba.FTDistribution2DCauchy(1.0*nm, 1.0*nm) interference.setProbabilityDistributions(pdf, pdf) particle_layout = ba.ParticleLayout() particle_layout.addParticle(cylinder, 1.0) particle_layout.setInterferenceFunction(interference) # assembling the sample 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) print(multi_layer.parametersToString()) print(multi_layer.treeToString()) return multi_layer def get_simulation(): """ Returns a GISAXS simulation with beam and detector defined. """ simulation = ba.GISASSimulation() # coarse grid because this simulation takes rather long simulation.setDetectorParameters(200, -2.0*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.setTerminalProgressMonitor() simulation.runSimulation() return simulation.result() if __name__ == '__main__': result = run_simulation() ba.plot_simulation_result(result) 
Interference2DParaCrystal.py