BornAgain ≻ git-main ≻ Documentation ≻ Reference ≻ Sample model ≻ Particles ≻ Form factor ≻ Custom formfactor

Custom formfactor

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 0.1 nm.
  • The incident angles are $\alpha_i = 0.2 ^{\circ}$ and $\varphi_i = 0^{\circ}$.

Real-space model

Intensity image

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104

#!/usr/bin/env python3
"""
Custom form factor in DWBA.
"""
import cmath
import bornagain as ba
from bornagain import ba_plot as bp, deg, angstrom, nm


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


class CustomFormfactor:
    """
    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):
        """ arguments and initialization for the formfactor """

        # parameters describing the form factor
        self.L = L
        self.H = H

    def formfactor(self, q:'C3'):
        """ main scattering function """

        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 spanZ(self, rotation):
        """ upper and lower z-positions of a custom shape """

        return ba.Span(0, self.H)


def get_sample():
    """
    Sample with particles, having a custom formfactor, on a substrate.
    """

    # materials
    vacuum = ba.RefractiveMaterial("Vacuum", 0, 0)
    material_substrate = ba.RefractiveMaterial("Substrate", 6e-6, 2e-8)
    material_particle = ba.RefractiveMaterial("Particle", 6e-4, 2e-8)

    # collection of particles
    ff = CustomFormfactor(20*nm, 15*nm)
    particle = ba.Particle(material_particle, ff)
    particle_layout = ba.ParticleLayout()
    particle_layout.addParticle(particle)
    vacuum_layer = ba.Layer(vacuum)
    vacuum_layer.addLayout(particle_layout)
    substrate_layer = ba.Layer(material_substrate)

    """ NOTE:
    Slicing of custom formfactor is not possible.
    all layers must have number of slices equal to 1.
    It is a default situation; otherwise use
    ```
    my_layer.setNumberOfSlices(1)
    ```

    Furthermore, a custom particle should not cross layer boundaries;
    that is, the z-span should be within a single layer
    """

    # assemble sample
    sample = ba.Sample()
    sample.addLayer(vacuum_layer)
    sample.addLayer(substrate_layer)
    return sample


def get_simulation(sample):
    beam = ba.Beam(1e9, 1*angstrom, 0.2*deg)
    n = 100
    det = ba.SphericalDetector(n, -1*deg, 1*deg, n, 0, 2*deg)
    simulation = ba.ScatteringSimulation(beam, sample, det)

    # Deactivate multithreading:
    # Currently BornAgain cannot access the Python interpreter
    # from a multi-threaded C++ function
    simulation.options().setNumberOfThreads(1)

    return simulation


if __name__ == '__main__':
    sample = get_sample()
    simulation = get_simulation(sample)
    result = simulation.simulate()
    bp.plot_datafield(result)
    bp.plt.show()
auto/Examples/scatter2d/CustomFormfactor.py