# Interference 1D Lattice

Scattering from long boxes distributed along a one-dimensional lattice.

• The particles are long boxes.
• Each box has a length of 1000nm, a width of 10nm and a height of 15 nm.
• The particles are placed along a one-dimensional lattice on top of a substrate.
• They are rotated in the (x,y) plane by 10° with respect the the x-axis of the reference cartesian frame.
• The 1D lattice is characterized by a lattice length of 30 nm.
• The lattice's base vector coincides with x-axis of the reference cartesian frame.
• The wavelength is equal to 24 Å.
• The incident angles are αi = 0.2° and Φi = 0°.

Note:
- By default, the axis of the one-dimensional lattice is the x-axis. A rotation can be applied to the particles (like in this example) or to the 1D lattice.
- In the real-space model picture, the length of the boxes cannot be seen as it is too large, compared to its width and heigth

Real-space model:
Intensity Image:
Python Script:
```"""
Long boxes on a 1D lattice
"""
import numpy
import bornagain as ba
from bornagain import deg, angstrom, nm

def get_sample():
"""
Returns a sample with a grating on a substrate.
The structure is modelled by infinitely long boxes forming a 1D lattice.
"""
# 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
lattice_length = 30.0*nm
lattice_rotation_angle = 0.0*deg
interference = ba.InterferenceFunction1DLattice(
lattice_length, lattice_rotation_angle)
pdf = ba.FTDecayFunction1DCauchy(20./2./numpy.pi*nm)
interference.setDecayFunction(pdf)

box_ff = ba.FormFactorBox(1000*nm, 10*nm, 15.0*nm)
box = ba.Particle(m_particle, box_ff)
transform = ba.RotationZ(25.0*deg)
particle_layout = ba.ParticleLayout()
particle_layout.addParticle(box, 1.0, ba.kvector_t(0.0, 0.0, 0.0), transform)
particle_layout.setInterferenceFunction(interference)

# assembling the sample
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, -1.0*deg, 1.0*deg,
200, 0.0*deg, 2.0*deg)
simulation.setBeamParameters(24.0*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)

```