# Size-distribution model: Decoupling Approximation

Scattering from a distribution of cylinders of two different sizes using the Decoupling Approximation.

• The sample is made of cylinders deposited on a substrate.
• The distribution of particles is made of:
• 80% of cylinders with radii and heights equal to 5 nm
• 20% of cylinders with radii and heights equal to 8 nm.
• The interference function is Radial Paracrystal with a peak distance of 18 nm and a damping length of 1 μm.
• The wavelength is equal to 1 Å.
• The incident angles are αi = 0.2° and Φi = 0°.
Intensity Image:
Python Script:
```"""
Cylinders of two different sizes in Decoupling Approximation
"""
import bornagain as ba
from bornagain import deg, angstrom, nm

def get_sample():
"""
Returns a sample with cylinders of two different sizes on a substrate.
The cylinder positions are modelled in Decoupling Approximation.
"""
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)

# cylindrical particle 1
radius1 = 5*nm
height1 = radius1
cylinder_ff1 = ba.FormFactorCylinder(radius1, height1)
cylinder1 = ba.Particle(m_particle, cylinder_ff1)

# cylindrical particle 2
radius2 = 8*nm
height2 = radius2
cylinder_ff2 = ba.FormFactorCylinder(radius2, height2)
cylinder2 = ba.Particle(m_particle, cylinder_ff2)

# interference function
interference = ba.InterferenceFunctionRadialParaCrystal(
18.0*nm, 1e3*nm)
pdf = ba.FTDistribution1DGauss(3 * nm)
interference.setProbabilityDistribution(pdf)

# assembling the sample
particle_layout = ba.ParticleLayout()
particle_layout.addParticle(cylinder1, 0.8)
particle_layout.addParticle(cylinder2, 0.2)
particle_layout.setInterferenceFunction(interference)

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, 0.0*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.getIntensityData()

if __name__ == '__main__':
result = run_simulation()
ba.plot_intensity_data(result)

```