### Large particle formfactor

This example demonstrates, that for large particles (~$1000$ nm) the contribution to the scattered intensity from the form factor oscillates rapidly within one detector bin and analytical calculations (performed for the bin center) give completely a wrong intensity pattern. In this case Monte-Carlo integrations over detector bin should be used.

The simulation generates four plots using different sizes of the particles, (radius $=10$ nm, height $=20$ nm) or (radius $=1$ $\mu$m, height $=2$ $\mu$m), and different calculation methods: analytical calculations or Monte-Carlo integration. The other parameters are identical:

• The sample is made of a monodisperse distribution of cylinders, deposited randomly on a substrate.
• There is no interference between the scattered waves.
• 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 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107  """ Large cylinders in DWBA. This example demonstrates that for large particles (~1000nm) the formfactor oscillates rapidly within one detector bin and analytical calculations (performed for the bin center) give completely wrong intensity pattern. In this case Monte-Carlo integration over detector bin should be used. """ import bornagain as ba from bornagain import deg, angstrom, nm from matplotlib import pyplot as plt default_cylinder_radius = 10*nm default_cylinder_height = 20*nm def get_sample(cylinder_radius, cylinder_height): """ Returns a sample with cylindrical particles on a substrate. """ # 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 cylinder_ff = ba.FormFactorCylinder(cylinder_radius, cylinder_height) cylinder = ba.Particle(m_particle, cylinder_ff) particle_layout = ba.ParticleLayout() particle_layout.addParticle(cylinder, 1.0) 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(integration_flag): """ Returns a GISAXS simulation with defined beam and detector. If integration_flag=True, the simulation will integrate over detector bins. """ 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) simulation.getOptions().setMonteCarloIntegration(integration_flag, 50) simulation.setTerminalProgressMonitor() return simulation def run_simulation(): """ Run simulation and plot results 4 times: for small and large cylinders, with and without integration """ fig = plt.figure(figsize=(12.80, 10.24)) # conditions to define cylinders scale factor and integration flag conditions = [ {'title': "Small cylinders, analytical calculations", 'scale': 1, 'integration': False, 'zmin': 1e-5, 'zmax': 1e2}, {'title': "Small cylinders, Monte-Carlo integration", 'scale': 1, 'integration': True, 'zmin': 1e-5, 'zmax': 1e2}, {'title': "Large cylinders, analytical calculations", 'scale': 100, 'integration': False, 'zmin': 1e-5, 'zmax': 1e10}, {'title': "Large cylinders, Monte-Carlo integration", 'scale': 100, 'integration': True, 'zmin': 1e-5, 'zmax': 1e10} ] # run simulation 4 times and plot results for i_plot, condition in enumerate(conditions): scale = condition['scale'] integration_flag = condition['integration'] sample = get_sample(default_cylinder_radius*scale, default_cylinder_height*scale) simulation = get_simulation(integration_flag) simulation.setSample(sample) simulation.runSimulation() result = simulation.result() # plotting results plt.subplot(2, 2, i_plot+1) plt.subplots_adjust(wspace=0.3, hspace=0.3) zmin = condition['zmin'] zmax = condition['zmax'] ba.plot_colormap(result, zmin=zmin, zmax=zmax, cmap='jet', aspect='auto') plt.text(0.0, 2.1, conditions[i_plot]['title'], horizontalalignment='center', verticalalignment='center', fontsize=12) if __name__ == '__main__': run_simulation() plt.show() 
LargeParticlesFormFactor.py