# Rotated pyramids

Scattering from a monodisperse distribution of rotated pyramids.

This example illustrates how the in-plane rotation of non-radially symmetric particles influences
the scattering pattern.

• The sample is made of pyramids deposited on a substrate.
• Each pyramid is characterized by a squared-base side length of 10 nm, a height of 5 nm, and a base angle α equal to 54.73°.
• These particles are rotated in the (x, y) plane by 45°.
• There is no interference between the scattered waves.
• The wavelength is equal to 1 Å.
• The incident angles are αi = 0.2° and Φi = 0°.
Real-space model:
Intensity Image:
Python Script:
```"""
Rotated pyramids on top of substrate
"""
import bornagain as ba
from bornagain import deg, angstrom, nm

def get_sample():
"""
Returns a sample with rotated pyramids on top of 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
pyramid_ff = ba.FormFactorPyramid(10*nm, 5*nm, 54.73*deg)
pyramid = ba.Particle(m_particle, pyramid_ff)
transform = ba.RotationZ(45.*deg)
particle_layout = ba.ParticleLayout()
pyramid, 1.0, ba.kvector_t(0.0, 0.0, 0.0), transform)

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

multi_layer = ba.MultiLayer()
return multi_layer

def get_simulation():
"""
Returns a GISAXS simulation with beam and detector defined.
"""
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)
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)

```