### 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 $\varphi_i = 0^{\circ}$.

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  #!/usr/bin/env python3 """ 2D paracrystal """ import bornagain as ba from bornagain import deg, nm def get_sample(): """ Returns a sample with cylinders on a substrate, forming a 2D paracrystal """ # 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, 0.0) # Define form factors ff = ba.FormFactorCylinder(4.0*nm, 5.0*nm) # Define particles particle = ba.Particle(material_Particle, ff) # Define 2D lattices lattice = ba.BasicLattice2D(10.0*nm, 10.0*nm, 90.0*deg, 0.0*deg) # Define interference functions iff = ba.InterferenceFunction2DParaCrystal(lattice, 0.0*nm, 20000.0*nm, 20000.0*nm) iff.setIntegrationOverXi(True) iff_pdf_1 = ba.FTDistribution2DCauchy(1.0*nm, 1.0*nm, 0.0*deg) iff_pdf_2 = ba.FTDistribution2DCauchy(1.0*nm, 1.0*nm, 0.0*deg) iff.setProbabilityDistributions(iff_pdf_1, iff_pdf_2) # Define particle layouts layout = ba.ParticleLayout() layout.addParticle(particle, 1.0) layout.setInterferenceFunction(iff) layout.setWeight(1) layout.setTotalParticleSurfaceDensity(0.01) # Define layers layer_1 = ba.Layer(material_Vacuum) layer_1.addLayout(layout) 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, 0.1*nm, ba.Direction(0.2*deg, 0*deg)) detector = ba.SphericalDetector(200, -2*deg, 2*deg, 200, 0*deg, 2*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) 
Interference2DParaCrystal.py