### Cosine Ripples in a Rectangular Lattice

Scattering from elongated particles distributed along a two-dimensional rectangular lattice.

• Each particle has a sinusoidal profile (“Ripple1” form factor) with a length of $100$ nm, a width of $20$ nm and a height of $4$ nm.
• They are placed along a rectangular lattice on top of a substrate.
• This lattice is characterized by a lattice length of $200$ nm in the direction of the long axis of the particles and of $50$ nm in the perpendicular direction.
• The lattice’s base vectors coincide with the reference Cartesian frame.
• The wavelength is equal to $1.6$ $\unicode{x212B}$.
• The incident angles are $\alpha_i = 0.3 ^{\circ}$ 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  """ Cosine ripple on a 2D lattice """ import numpy import bornagain as ba from bornagain import deg, angstrom, nm def get_sample(): """ Returns a sample with cosine ripples on a substrate. The structure is modelled as a 2D 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 ripple1_ff = ba.FormFactorRipple1(100*nm, 20*nm, 4*nm) ripple = ba.Particle(m_particle, ripple1_ff) particle_layout = ba.ParticleLayout() particle_layout.addParticle(ripple, 1.0) interference = ba.InterferenceFunction2DLattice( 200.0*nm, 50.0*nm, 90.0*deg, 0.0*deg) pdf = ba.FTDecayFunction2DCauchy( 1000.*nm/2./numpy.pi, 100.*nm/2./numpy.pi) interference.setDecayFunction(pdf) particle_layout.setInterferenceFunction(interference) # assemble 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(): """ characterizing the input beam and output detector """ simulation = ba.GISASSimulation() simulation.setDetectorParameters(100, -1.5*deg, 1.5*deg, 100, 0.0*deg, 2.5*deg) simulation.setBeamParameters(1.6*angstrom, 0.3*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, cmap='jet', aspect='auto') 
CosineRipplesAtRectLattice.py