### Spheres on Hexagonal Lattice

Scattering from spheres distributed along a hexagonal lattice.

• The sample is made of spherical particles with radii of $10$ nm deposited on a substrate along a hexagonal lattice.
• This two-dimensional lattice is characterized by a lattice length of $20$ nm. Its a-axis coincides with the x-axis of the reference Cartesian frame.
• 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  #!/usr/bin/env python3 """ Spheres on a hexagonal lattice """ import bornagain as ba from bornagain import deg, nm def get_sample(): """ Returns a sample with spherical particles on a substrate, forming a hexagonal 2D lattice. """ # 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.FormFactorFullSphere(10.0*nm) # Define particles particle = ba.Particle(material_Particle, ff) # Define 2D lattices lattice = ba.BasicLattice2D(20.0*nm, 20.0*nm, 120.0*deg, 0.0*deg) # Define interference functions iff = ba.InterferenceFunction2DLattice(lattice) iff_pdf = ba.FTDecayFunction2DCauchy(10.0*nm, 10.0*nm, 0.0*deg) iff.setDecayFunction(iff_pdf) # Define particle layouts layout = ba.ParticleLayout() layout.addParticle(particle, 1.0) layout.setInterferenceFunction(iff) layout.setWeight(1) layout.setTotalParticleSurfaceDensity(0.00288675134595) # 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, -1*deg, 1*deg, 200, 0*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) 
SpheresAtHexLattice.py