### Interference - Superposition of Square Lattices

This example demonstrates how to perform a simulation of scattering from cylinders distributed in a square lattice fashion. The resultant 2D lattice is a sum of rotated lattices with different disorder.

This example is similar to Interference of a rotated square lattice.

  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 74 75 76  # 2D lattice with different disorder (IsGISAXS example #6), sum of rotated lattices import numpy import bornagain as ba from bornagain import deg, angstrom, nm def get_sample(): """ Returns a sample with cylinders on a substrate, forming a 2D lattice with different disorder rotated lattice """ m_ambience = 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) air_layer = ba.Layer(m_ambience) substrate_layer = ba.Layer(m_substrate) p_interference_function = \ ba.InterferenceFunction2DLattice.createSquare(25.0*nm) pdf = ba.FTDecayFunction2DCauchy(300.0*nm/2.0/numpy.pi, 100.0*nm/2.0/numpy.pi) p_interference_function.setDecayFunction(pdf) particle_layout = ba.ParticleLayout() ff_cyl = ba.FormFactorCylinder(3.0*nm, 3.0*nm) position = ba.kvector_t(0.0, 0.0, 0.0) cylinder = ba.Particle(m_particle, ff_cyl.clone()) cylinder.setPosition(position) particle_layout.addParticle(cylinder, 1.0) particle_layout.setInterferenceFunction(p_interference_function) air_layer.addLayout(particle_layout) 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. Assigns additional distribution to lattice rotation angle. """ simulation = ba.GISASSimulation() simulation.setDetectorParameters(100, 0.0*deg, 2.0*deg, 100, 0.0*deg, 2.0*deg) simulation.setBeamParameters(1.0*angstrom, 0.2*deg, 0.0*deg) simulation.setSample(get_sample()) xi_min = 0.0*deg xi_max = 240.0*deg xi_distr = ba.DistributionGate(xi_min, xi_max) # assigns distribution with 3 equidistant points to lattice rotation angle simulation.addParameterDistribution("*/SquareLattice/Xi", xi_distr, 3) return simulation def run_simulation(): """ Runs simulation and returns intensity map. """ simulation = get_simulation() simulation.runSimulation() return simulation.result() if __name__ == '__main__': result = run_simulation() ba.plot_simulation_result(result, cmap='jet', aspect='auto') 
Interference2DLatticeSumOfRotated.py