### Interference 2D centered square lattice

Scattering from cylinders distributed along a squared centered lattice.

• The particles are cylinders with radii and heights of $3$ nm.
• Their spatial distribution is composed of two square lattices (lattice length $l$), shifted by half a lattice length in both directions:
• The first square lattice is centered at the origin, with a lattice length of $25$ nm.
• The second one, with the same lattice spacing and the same type of particles at its nodes is initialized at $x = y = l/2 = 12.5$ nm.
• The lattices’ base vectors are parallel to the axes 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 62 63 64 65 66 67 68 69 70 71 72 73  """ 2D lattice with disorder, centered square lattice """ 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 centered square lattice """ # defining materials 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) # collection of particles interference = ba.InterferenceFunction2DLattice.createSquare(25.0*nm) pdf = ba.FTDecayFunction2DCauchy(300.0*nm/2.0/numpy.pi, 100.0*nm/2.0/numpy.pi) interference.setDecayFunction(pdf) particle_layout = ba.ParticleLayout() position1 = ba.kvector_t(0.0, 0.0, 0.0) position2 = ba.kvector_t(12.5*nm, 12.5*nm, 0.0) cylinder_ff = ba.FormFactorCylinder(3.*nm, 3.*nm) cylinder = ba.Particle(m_particle, cylinder_ff) basis = ba.ParticleComposition() basis.addParticles(cylinder, [position1, position2]) particle_layout.addParticle(basis) particle_layout.setInterferenceFunction(interference) # assembling the sample air_layer = ba.Layer(m_ambience) air_layer.addLayout(particle_layout) substrate_layer = ba.Layer(m_substrate) multi_layer = ba.MultiLayer() multi_layer.addLayer(air_layer) multi_layer.addLayer(substrate_layer) print(multi_layer.treeToString()) return multi_layer def get_simulation(): """ Create and return GISAS simulation with beam and detector defined """ simulation = ba.GISASSimulation() simulation.setDetectorParameters(200, -2.0*deg, 2.0*deg, 200, 0.0*deg, 2.0*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) 
Interference2DCenteredSquareLattice.py