### 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 $\phi_i = 0^{\circ}$.
  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  """ Spheres on a hexagonal lattice """ import bornagain as ba from bornagain import deg, angstrom, nm def get_sample(): """ Returns a sample with spherical particles on a substrate, forming a hexagonal 2D lattice. """ m_air = 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) sphere_ff = ba.FormFactorFullSphere(10.0*nm) sphere = ba.Particle(m_particle, sphere_ff) particle_layout = ba.ParticleLayout() particle_layout.addParticle(sphere) interference = ba.InterferenceFunction2DLattice.createHexagonal(20.0*nm) pdf = ba.FTDecayFunction2DCauchy(10*nm, 10*nm) interference.setDecayFunction(pdf) particle_layout.setInterferenceFunction(interference) air_layer = ba.Layer(m_air) air_layer.addLayout(particle_layout) substrate_layer = ba.Layer(m_substrate, 0) 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, -1.0*deg, 1.0*deg, 200, 0.0*deg, 1.0*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) 
SpheresAtHexLattice.py