ScatterSim:Examples:002Lattice

# The next step is creating a lattice

from ScatterSim.NanoObjects import SphereNanoObject, PolydisperseNanoObject
# We'll import a few lattices, cubic, FCC, BCC and Diamond
from ScatterSim.LatticeObjects import SimpleCubic, FCCLattice, BCCLattice, DiamondTwoParticleLattice
# import the peak shape for the peaks, tunable
from ScatterSim.PeakShape import PeakShape

import numpy as np
import matplotlib.pyplot as plt

TBA <source lang="python">

1. Let's use our polydisperse sphere nanoobject since it's more realistic
2. In general though, you'll want to start with simpler objects to reduce computation time
3. but this one should be okay...

pargs_polysphere = dict(radius= 1, sigma_R=.04)

polysphere = PolydisperseNanoObject(SphereNanoObject, pargs_polysphere, argname='radius', argstdname='sigma_R')

1. The peak shape
2. delta is sigma of a Gaussian, and nu is FWHM of a Lorentzian
3. Generally, you'll want to keep one zero and vary the other (to get a Gaussian or Lorentzian)
4. but when finalizing a fit, you may want to play with intermediate values

peak = PeakShape(delta=0.03, nu=0.01)

1. now define your lattices
2. lattices, to first order are just defined by 6 parameters:
3. lattice_spacing_a, lattice_spacing_b and lattice_spacing_c (the unit vector spacings)
4. alpha, beta, gamma (the angles the unit vectors make with the axes)
5. We'll deal with simple lattices, so all unit vectors are aligned with x, y and z axes, and same length

lattice_spacing = 10. # 10 times radius (1 nm) lat_sc = SimpleCubic([polysphere], lattice_spacing_a=lattice_spacing) lat_fcc = FCCLattice([polysphere], lattice_spacing_a=lattice_spacing) lat_bcc = BCCLattice([polysphere], lattice_spacing_a=lattice_spacing) lat_diamond = DiamondTwoParticleLattice([polysphere], lattice_spacing_a=lattice_spacing)

q = np.linspace(.4, 4, 1000)

1. Now compute the intensity, it will take some time...

Z0_sc = lat_sc.intensity(q, peak) Pq_sc = lat_sc.form_factor_squared_isotropic(q)

c_sc = .1

1. note Gq is same for all three here (just depends on sigma_D, it's an exponential decay...)

Gq_sc = lat_sc.G_q(q)

Sq_sc = c_sc*Z0_sc/Pq_sc*Gq_sc + (1-Gq_sc)

print("Finished calculating Simple Cubic")

Z0_fcc = lat_fcc.intensity(q, peak) Pq_fcc = lat_fcc.form_factor_squared_isotropic(q) Gq_fcc = lat_fcc.G_q(q)

Sq_fcc = c_sc*Z0_fcc/Pq_fcc*Gq_fcc + (1-Gq_fcc)

print("Finished calculating Face Centered Cubic")

Z0_bcc = lat_bcc.intensity(q, peak) Pq_bcc = lat_bcc.form_factor_squared_isotropic(q) Gq_bcc = lat_bcc.G_q(q)

Sq_bcc = c_sc*Z0_bcc/Pq_bcc*Gq_bcc + (1-Gq_bcc)

print("Finished calculating Body Centered Cubic") Z0_diamond = lat_diamond.intensity(q, peak) Pq_diamond = lat_diamond.form_factor_squared_isotropic(q) Gq_diamond = lat_diamond.G_q(q)

Sq_diamond = c_sc*Z0_diamond/Pq_diamond*Gq_diamond + (1-Gq_diamond)

print("Finished calculating Diamond") plt.figure(0, figsize=(10,8));plt.clf() plt.subplot(2,2,1) plt.title("Simple Cubic Structure Factor") plt.plot(q, Sq_sc) plt.subplot(2,2,2) plt.title("Face Centered Cubic Structure Factor") plt.plot(q, Sq_fcc) plt.subplot(2,2,3) plt.title("Body Centered Cubic Structure Factor") plt.plot(q, Sq_bcc) plt.subplot(2,2,4) plt.title("Diamond Structure Factor") plt.plot(q, Sq_diamond)

1. Same, but loglog plot (sometimes easier to see)

plt.figure(1, figsize=(10,8));plt.clf() plt.subplot(2,2,1) plt.title("Simple Cubic Structure Factor") plt.loglog(q, Sq_sc) plt.subplot(2,2,2) plt.title("Face Centered Cubic Structure Factor") plt.loglog(q, Sq_fcc) plt.subplot(2,2,3) plt.title("Body Centered Cubic Structure Factor") plt.loglog(q, Sq_bcc) plt.subplot(2,2,4) plt.title("Diamond Structure Factor") plt.loglog(q, Sq_diamond)