# Custom Form Factor

Scattering from a monodisperse distribution of particles, whose form factor is defined by the user.

• This example shows how users can simulate their own particle shape by implementing the analytical expression of its form factor.
• The particular shape used here is a polyhedron, whose planar cross section is a "plus" shape with a side length of 20 nm and a height of 15 nm.
• These particles are distributed on a substrate.
• 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:
```"""
Custom form factor in DWBA.
"""
import bornagain as ba
from bornagain import deg, angstrom, nm
import cmath

def sinc(x):
if abs(x) == 0:
return 1.
else:
return cmath.sin(x)/x

class CustomFormFactor(ba.IFormFactorBorn):
"""
A custom defined form factor.
The particle is a prism of height H,
with a base in form of a Greek cross ("plus" sign) with side length L.
"""
def __init__(self, L, H):
ba.IFormFactorBorn.__init__(self)
# parameters describing the form factor
self.L = L
self.H = H

def clone(self):
"""
IMPORTANT NOTE:
The clone method needs to call transferToCPP() on the cloned object
to transfer the ownership of the clone to the cpp code
"""
cloned_ff = CustomFormFactor(self.L, self.H)
cloned_ff.transferToCPP()
return cloned_ff

def evaluate_for_q(self, q):
qzhH = 0.5*q.z()*self.H
qxhL = 0.5*q.x()*self.L
qyhL = 0.5*q.y()*self.L
return 0.5*self.H*self.L**2*cmath.exp(complex(0., 1.)*qzhH)*\
sinc(qzhH)*(sinc(0.5*qyhL)*(sinc(qxhL)-0.5*sinc(0.5*qxhL))+\
sinc(0.5*qxhL)*sinc(qyhL))

def get_sample():
"""
Returns a sample with particles, having a custom form factor, on 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
ff = CustomFormFactor(20.0*nm, 15.0*nm)
particle = ba.Particle(m_particle, ff)
particle_layout = ba.ParticleLayout()
air_layer = ba.Layer(m_ambience)
substrate_layer = ba.Layer(m_substrate)

# assemble multilayer
multi_layer = ba.MultiLayer()
return multi_layer

def get_simulation():
"""
Returns a GISAXS simulation with beam and detector defined.
IMPORTANT NOTE:
"""
simulation = ba.GISASSimulation()
simulation.setDetectorParameters(100, -1.0*deg, 1.0*deg,
100, 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)

```