### Hexagonal lattices with basis

Scattering from two hexagonal close packed layers of spheres.

• The sample is made of spherical particles deposited on a substrate.
• These $10$-nanometer-radius particles are positioned in a hexagonal close packed structure:
• each layer is generated using a two-dimensional hexagonal lattice with a lattice length of $20$ nm and its $a$-axis parallel to the $x$-axis of the reference Cartesian frame.
• the vertical stacking is done by specifying the position of a “seeding” particle for each layer: $(0,0,0)$ for the first layer and $(R,R,\sqrt{3}R)$ for the second layer, $R$ being the radius of the spherical particle.
• 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 67 68 69 70 71 72 73  #!/usr/bin/env python3 """ Spheres on two hexagonal close packed layers """ import bornagain as ba from bornagain import deg, nm, kvector_t def get_sample(): """ Returns a sample with spheres on a substrate, forming two hexagonal close packed layers. """ # 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) # Define form factors ff_1 = ba.FormFactorFullSphere(10*nm) ff_2 = ba.FormFactorFullSphere(10*nm) # Define particles particle_1 = ba.Particle(material_Particle, ff_1) particle_2 = ba.Particle(material_Particle, ff_2) particle_2_position = kvector_t(10*nm, 10*nm, 17.3205080757*nm) particle_2.setPosition(particle_2_position) # Define composition of particles at specific positions basis = ba.ParticleComposition() basis.addParticle(particle_1) basis.addParticle(particle_2) # Define 2D lattices lattice = ba.HexagonalLattice2D(20*nm, 0) # Define interference functions iff = ba.InterferenceFunction2DLattice(lattice) iff_pdf = ba.FTDecayFunction2DCauchy(10*nm, 10*nm, 0) iff.setDecayFunction(iff_pdf) # Define particle layouts layout = ba.ParticleLayout() layout.addParticle(basis) layout.setInterferenceFunction(iff) 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, 0.1*nm, ba.Direction(0.2*deg, 0)) detector = ba.SphericalDetector(200, -1*deg, 1*deg, 200, 0, 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) 
HexagonalLatticesWithBasis.py