### Hexagonal lattices with basis

Scattering from two layers of spheres distributed along a hexagonal close packed structure.

• The sample is made of spherical particles deposited on a substrate.
• These $10$-nanometer-radius particles are distributed along 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 $\phi_i = 0^{\circ}$.
  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 62 63 64 65 66 67 68  """ Spheres on two hexagonal close packed layers """ import numpy import bornagain as ba from bornagain import deg, angstrom, nm def get_sample(): """ Returns a sample with spheres on a substrate, forming two hexagonal close packed layers. """ 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) radius = 10.0*nm sphere_ff = ba.FormFactorFullSphere(radius) sphere = ba.Particle(m_particle, sphere_ff) particle_layout = ba.ParticleLayout() pos0 = ba.kvector_t(0.0, 0.0, 0.0) pos1 = ba.kvector_t(radius, radius, numpy.sqrt(3.0)*radius) basis = ba.ParticleComposition() basis.addParticles(sphere, [pos0, pos1]) particle_layout.addParticle(basis) interference = ba.InterferenceFunction2DLattice.createHexagonal(radius*2.0) 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(): """ Returns a 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) 
HexagonalLatticesWithBasis.py