# Cylinders with size distribution

Scattering from a polydisperse distribution of cylinders in Born Approximation.

• The average radii and heights of the cylinders are equal to 5 nm.
• The radii of the cylinders vary according to a normal distribution with a standard deviation σ equal to 0.2 times the average radius.
• The wavelength is equal to 1 Å.
• The incident angles are equal to αi = 0.2°and Φi = 0°.
• There is no substrate (particles embedded in air layer, DWBA boils down to BA).
• No interference effects from inter-particle correlations (dilute-particles approximation).
Real-space model:
Intensity Image:
Python Script:
```"""
Cylinders with size distribution
"""
import bornagain as ba
from bornagain import deg, angstrom, nm

def get_sample():
"""
Return a sample with cylinders on a substrate.
The cylinders have a Gaussian size distribution.
"""
m_ambience = ba.HomogeneousMaterial("Air", 0.0, 0.0)
m_particle = ba.HomogeneousMaterial("Particle", 6e-4, 2e-8)

# cylindrical particle
cylinder = ba.Particle(m_particle, cylinder_ff)

# collection of particles with size distribution
nparticles = 100

sigma_factor = 2.0
par_distr = ba.ParameterDistribution(
# by uncommenting the line below, the height of the cylinders
#   can be scaled proportionally to the radius:
part_coll = ba.ParticleDistribution(cylinder, par_distr)

# assembling the sample
particle_layout = ba.ParticleLayout()

air_layer = ba.Layer(m_ambience)
multi_layer = ba.MultiLayer()
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)

```