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#!/usr/bin/env python3
# /// script
# requires-python = ">=3.10"
# dependencies = ["bornagain>=25,<26"]
# ///
"""
Cylindrical mesocrystal with hexagonal lattice and two-material basis.
Test to investigate intensity changes with different numbers of slices.
"""
import math
import numpy as np
import bornagain as ba
ba.require_versions("bornagain>=25,<26")
from bornagain import deg, nm, nm2, R3
def get_sample(n_slices=1):
# Materials (zero absorption)
particle1_color = (0.86, 0.24, 0.18)
particle1_mat = ba.RefractiveMaterial("Particle1", particle1_color, 4e-05, 0)
particle2_color = (0.25, 0.65, 0.35)
particle2_mat = ba.RefractiveMaterial("Particle2", particle2_color, 8e-06, 0)
substrate_color = (0.28, 0.57, 0.82)
substrate_mat = ba.RefractiveMaterial("Substrate", substrate_color, 6e-06, 0)
vacuum = ba.Vacuum()
# Basis particles
inner_ff = ba.FuzzySphere(4.7*nm, .4*nm)
inner_particle1 = ba.Particle(particle1_mat, inner_ff)
inner_particle2 = ba.Particle(particle2_mat, inner_ff)
# 3D lattice
lattice_a = 6.21
lattice_c = 6.57
sigma_a = 1.16
position_variance = sigma_a/math.sqrt(3)
lattice = ba.HexagonalLattice(lattice_a*2, lattice_c*2*2.3)
bas_a = lattice.basisVectorA()
bas_b = lattice.basisVectorB()
bas_c = lattice.basisVectorC()
# Basis composition
position_0 = R3(0, 0, 0)
position_1 = 1.0/3*(2*bas_a + bas_b + bas_c)
basis = ba.Compound()
basis.addComponent(inner_particle1, position_0)
basis.addComponent(inner_particle2, position_1)
# Crystal
crystal = ba.Crystal(basis, lattice, position_variance)
# Mesocrystal: shaped crystal
outer_ff = ba.Cylinder(20*nm, 50*nm)
outer_particle = ba.Mesocrystal(crystal, outer_ff)
# Layers
layer_1 = ba.Layer(vacuum)
layer_1.deposit2D(ba.Dilute2D(0.0001/nm2, outer_particle))
if n_slices > 1:
layer_1.setNumberOfSlices(n_slices)
layer_2 = ba.Layer(substrate_mat)
# Sample
sample = ba.Sample()
sample.addLayer(layer_1)
sample.addLayer(layer_2)
return sample
def simulate_horizontal_cut(n_slices=1, reciprocal=False):
"""
Simulate with Nx1 detector for horizontal cut at alpha_f=0.92 deg.
"""
sample = get_sample(n_slices)
beam = ba.Beam(1e9, 0.1*nm, 0.2*deg)
n = 200
# Single bin centered at alpha_f=0.92 deg
detector = ba.SphericalDetector(n, -2*deg, 2*deg, 1, 0.91*deg, 0.93*deg)
simulation = ba.ScatteringSimulation(beam, sample, detector)
if reciprocal:
simulation.options().setMesoReciprocalSum(True, 2.5)
return simulation.simulate()
def simulate_vertical_cut(n_slices=1, reciprocal=False):
"""
Simulate with 1xN detector for vertical cut at phi_f=0 deg.
"""
sample = get_sample(n_slices)
beam = ba.Beam(1e9, 0.1*nm, 0.2*deg)
n = 200
# Single bin centered at phi_f=0 deg
detector = ba.SphericalDetector(1, -0.01*deg, 0.01*deg, n, 0, 2*deg)
simulation = ba.ScatteringSimulation(beam, sample, detector)
if reciprocal:
simulation.options().setMesoReciprocalSum(True, 2.5)
return simulation.simulate()
def simulate_depthprobe(n_slices=1, reciprocal=False):
"""
Simulate intensity vs depth.
"""
sample = get_sample(n_slices)
n = 100
alpha_f = 0.001*deg if reciprocal else 0.0064*deg
scan = ba.AlphaScan([alpha_f])
scan.setWavelength(0.1*nm)
z_axis = ba.EquiDivision("z (nm)", n, -20*nm, 120*nm)
simulation = ba.DepthprobeSimulation(scan, sample, z_axis)
if reciprocal:
simulation.options().setMesoReciprocalSum(True, 2.5)
return simulation.simulate(), alpha_f/deg
def get_sld_profile(n_slices=1):
"""
Returns the SLD profile of the resampled sample.
"""
sample = get_sample(n_slices)
n = 200
z_min, z_max = -20*nm, 60*nm
z = np.asarray(ba.generateZValues(n, z_min, z_max))
sld = ba.materialProfileSLD(sample, n, z_min, z_max)
sld_real = np.real(sld)
return z, sld_real
# Color cycle for different N values
colors = ['C0', 'C1', 'C2', 'C3']
if __name__ == '__main__':
# Slice counts to compare
slice_counts = [1, 2, 5, 20]
# Create figure with 2 rows, 4 columns
fig, axes = ba.plt.subplots(
2, 4, figsize=(18, 10), layout="constrained")
# Row 1: Real-space summation (default)
ax = axes[0, 0]
for i, n in enumerate(slice_counts):
result = simulate_horizontal_cut(n_slices=n, reciprocal=False)
ax.semilogy(result.xCenters(), result.flatVector(),
label=f'N={n}', color=colors[i])
ax.set_title('Real-space: Horizontal cut at alpha_f=0.92 deg')
ax.set_xlabel('phi_f (deg)')
ax.set_ylabel('Intensity')
ax.legend()
ax = axes[0, 1]
for i, n in enumerate(slice_counts):
result = simulate_vertical_cut(n_slices=n, reciprocal=False)
ax.semilogy(result.yCenters(), result.flatVector(),
label=f'N={n}', color=colors[i])
ax.set_title('Real-space: Vertical cut at phi_f=0 deg')
ax.set_xlabel('alpha_f (deg)')
ax.set_ylabel('Intensity')
ax.legend()
ax = axes[0, 2]
for i, n in enumerate(slice_counts):
result, alpha_f = simulate_depthprobe(n_slices=n, reciprocal=False)
ax.semilogy(result.yCenters(), result.flatVector(),
label=f'N={n}', color=colors[i])
ax.set_title(f'Real-space: Intensity vs depth at alpha_f={alpha_f:.4f} deg')
ax.set_xlabel('z (nm)')
ax.set_ylabel('Intensity')
ax.legend()
ax = axes[0, 3]
profiles = []
for n in slice_counts:
z, sld = get_sld_profile(n_slices=n)
profiles.append((f'N={n}', z, sld))
ba.plot_material_profile(
profiles, z_unit=nm, ax=ax,
xlabel='z (nm)', ylabel='SLD (real part)')
ax.set_title('Real-space: SLD profile')
ax.legend()
# Row 2: Reciprocal-space (Fourier) summation
ax = axes[1, 0]
for i, n in enumerate(slice_counts):
result = simulate_horizontal_cut(n_slices=n, reciprocal=True)
ax.semilogy(result.xCenters(), result.flatVector(),
label=f'N={n}', color=colors[i])
ax.set_title('Fourier: Horizontal cut at alpha_f=0.92 deg')
ax.set_xlabel('phi_f (deg)')
ax.set_ylabel('Intensity')
ax.legend()
ax = axes[1, 1]
for i, n in enumerate(slice_counts):
result = simulate_vertical_cut(n_slices=n, reciprocal=True)
ax.semilogy(result.yCenters(), result.flatVector(),
label=f'N={n}', color=colors[i])
ax.set_title('Fourier: Vertical cut at phi_f=0 deg')
ax.set_xlabel('alpha_f (deg)')
ax.set_ylabel('Intensity')
ax.legend()
ax = axes[1, 2]
for i, n in enumerate(slice_counts):
result, alpha_f = simulate_depthprobe(n_slices=n, reciprocal=True)
ax.semilogy(result.yCenters(), result.flatVector(),
label=f'N={n}', color=colors[i])
ax.set_title(f'Fourier: Intensity vs depth at alpha_f={alpha_f:.3f} deg')
ax.set_xlabel('z (nm)')
ax.set_ylabel('Intensity')
ax.legend()
ax = axes[1, 3]
profiles = []
for n in slice_counts:
z, sld = get_sld_profile(n_slices=n)
profiles.append((f'N={n}', z, sld))
ba.plot_material_profile(
profiles, z_unit=nm, ax=ax,
xlabel='z (nm)', ylabel='SLD (real part)')
ax.set_title('Fourier: SLD profile')
ax.legend()
ba.showSample3D(get_sample(), sample_size=250*nm, seed=0)
ba.plt.show()
|
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