### Interference 1D lattice

In this example we simulate the scattering from infinite 1D repetition of rectangular patches (rectangular grating). This is done by using the interference function of a 1D lattice together with very long boxes.

• By-default, the axis of the one-dimensional lattice coincides with the $x$-axis of the reference cartesian frame, so it coinsides with the beam direction.
• Long boxes are placed along a one-dimensional lattice on top of substrate, the lattice_length parameter corresponds to the grating period.
• The size of boxes is initially chosen to form a grating which is perpendicular to the beam (long side of the box is along $y$-axis).
• Please keep in mind, that length, width, height in the FormFactorBox(length, width, height) constructor correspond to the directions in the $x,y,z$ axes, in that order, so to achieve the desired setup we use the values: length= $10$ nm, width= $10000$ nm, height= $10$ nm.
• The whole grating is rotated at the end by an angle of $45^{\circ}$ with respect to the beam axis. This is achieved by rotating both the 1D lattice and the long boxes (see lines 25 and 34).
• To avoid the problem of rapidly oscillating form factors of long boxes (see this example for more details), the simulation is performed in monte carlo integration mode.
  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  """ Simulation of grating using very long boxes and 1D lattice. Monte-carlo integration is used to get rid of large-particle form factor oscillations. """ import bornagain as ba from bornagain import deg, angstrom, nm def get_sample(lattice_rotation_angle=45*deg): """ Returns a sample with a grating on a substrate, modelled by very long boxes forming a 1D lattice with Cauchy correlations. """ # 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) box_length, box_width, box_height = 10*nm, 10000*nm, 10*nm lattice_length = 30*nm # collection of particles interference = ba.InterferenceFunction1DLattice( lattice_length, lattice_rotation_angle) pdf = ba.FTDecayFunction1DCauchy(1000.0) interference.setDecayFunction(pdf) box_ff = ba.FormFactorBox(box_length, box_width, box_height) box = ba.Particle(m_particle, box_ff) particle_layout = ba.ParticleLayout() particle_layout.addParticle( box, 1.0, ba.kvector_t(0.0, 0.0, 0.0), ba.RotationZ(lattice_rotation_angle)) 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) 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, 2.0*deg) simulation.setBeamParameters(1.0*angstrom, 0.2*deg, 0.0*deg) simulation.getOptions().setMonteCarloIntegration(True, 100) return simulation def run_simulation(): """ Runs simulation and returns intensity map. """ simulation = get_simulation() simulation.setSample(get_sample()) simulation.setTerminalProgressMonitor() simulation.runSimulation() return simulation.result() if __name__ == '__main__': result = run_simulation() ba.plot_simulation_result(result, intensity_min=1e-03, cmap='jet', aspect='auto') 
Interference1DLattice.py