# Size-distribution model: Local Monodisperse Approximation

Scattering from cylinders of two different sizes using the Local Monodisperse Approximation (LMA).

• The sample is made of cylinders deposited on a substrate.
• The cylinders are of two different sizes:
• 80% of Type 1: radius R1 = 5nm, height H1 = 5 nm. The interference function is a radial paracrystal with a peak distance equal to 16.8 nm and a damping length of 1 μm.
• 20% of Type 2: radius R2 = 8 nm, height H2 = 8 nm. The interference function is also a radial paracrystal but with a peak distance of 22.8 nm and a damping length equal to 1 μm.
• Each type of cylinders is associated with a "particle layout".
• The LMA is used since the sample is made of two domains containing particles of the same size and shape.
• 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 Local Monodisperse 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 Local Monodisperse 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
cylinder1 = ba.Particle(m_particle, cylinder_ff1)

# cylindrical particle 2
cylinder2 = ba.Particle(m_particle, cylinder_ff2)

# interference function1
16.8*nm, 1e3*nm)
pdf = ba.FTDistribution1DGauss(3 * nm)
interference1.setProbabilityDistribution(pdf)

# interference function2
22.8*nm, 1e3*nm)
interference2.setProbabilityDistribution(pdf)

# assembling the sample
particle_layout1 = ba.ParticleLayout()
particle_layout1.setInterferenceFunction(interference1)

particle_layout2 = ba.ParticleLayout()
particle_layout2.setInterferenceFunction(interference2)

air_layer = ba.Layer(m_ambience)
substrate_layer = ba.Layer(m_substrate)
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)

```