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.. _sphx_glr_examples_2D_simulation(macro_amorphous)_plot_1_I=2.5.py:
Czjzek distribution, 27Al (I=5/2) 3QMAS
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
27Al (I=5/2) 3QMAS simulation of amorphous material.
In this section, we illustrate the simulation of a quadrupolar MQMAS spectrum arising
from a distribution of the electric field gradient (EFG) tensors from amorphous
material. We proceed by employing the Czjzek distribution model.
.. code-block:: python
import matplotlib as mpl
import matplotlib.pyplot as plt
import numpy as np
from mrsimulator import Simulator
from mrsimulator.methods import ThreeQ_VAS
from mrsimulator.models import CzjzekDistribution
from mrsimulator.utils.collection import single_site_system_generator
from scipy.stats import multivariate_normal
# global plot configuration
mpl.rcParams["figure.figsize"] = [4.5, 3.0]
Generate probability distribution
---------------------------------
.. code-block:: python
# The range of isotropic chemical shifts, the quadrupolar coupling constant, and
# asymmetry parameters used in generating a 3D grid.
iso_r = np.arange(101) / 1.5 + 30 # in ppm
Cq_r = np.arange(100) / 4 # in MHz
eta_r = np.arange(10) / 9
# The 3D mesh grid over which the distribution amplitudes are evaluated.
iso, Cq, eta = np.meshgrid(iso_r, Cq_r, eta_r, indexing="ij")
# The 2D amplitude grid of Cq and eta is sampled from the Czjzek distribution model.
Cq_dist, e_dist, amp = CzjzekDistribution(sigma=1).pdf(pos=[Cq_r, eta_r])
# The 1D amplitude grid of isotropic chemical shifts is sampled from a Gaussian model.
iso_amp = multivariate_normal(mean=58, cov=[4]).pdf(iso_r)
# The 3D amplitude grid is generated as an uncorrelated distribution of the above two
# distribution, which is the product of the two distributions.
pdf = np.repeat(amp, iso_r.size).reshape(eta_r.size, Cq_r.size, iso_r.size)
pdf *= iso_amp
pdf = pdf.T
The two-dimensional projections from this three-dimensional distribution are shown
below.
.. code-block:: python
_, ax = plt.subplots(1, 3, figsize=(9, 3))
# isotropic shift v.s. quadrupolar coupling constant
ax[0].contourf(Cq_r, iso_r, pdf.sum(axis=2))
ax[0].set_xlabel("Cq / MHz")
ax[0].set_ylabel("isotropic chemical shift / ppm")
# isotropic shift v.s. quadrupolar asymmetry
ax[1].contourf(eta_r, iso_r, pdf.sum(axis=1))
ax[1].set_xlabel(r"quadrupolar asymmetry, $\eta$")
ax[1].set_ylabel("isotropic chemical shift / ppm")
# quadrupolar coupling constant v.s. quadrupolar asymmetry
ax[2].contourf(eta_r, Cq_r, pdf.sum(axis=0))
ax[2].set_xlabel(r"quadrupolar asymmetry, $\eta$")
ax[2].set_ylabel("Cq / MHz")
plt.tight_layout()
plt.show()
.. image:: /examples/2D_simulation(macro_amorphous)/images/sphx_glr_plot_1_I=2.5_001.png
:alt: plot 1 I=2.5
:class: sphx-glr-single-img
Simulation setup
----------------
Let's create the site and spin system objects from these parameters. Use the
:func:`~mrsimulator.utils.collection.single_site_system_generator` utility function to
generate single-site spin systems.
.. code-block:: python
spin_systems = single_site_system_generator(
isotopes="27Al",
isotropic_chemical_shifts=iso,
quadrupolar={"Cq": Cq * 1e6, "eta": eta}, # Cq in Hz
abundance=pdf,
)
len(spin_systems)
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
5770
Simulate a :math:`^{27}\text{Al}` 3Q-MAS spectrum by using the `ThreeQ_MAS` method.
.. code-block:: python
mqvas = ThreeQ_VAS(
channels=["27Al"],
spectral_dimensions=[
{
"count": 512,
"spectral_width": 26718.475776, # in Hz
"reference_offset": -4174.76184, # in Hz
"label": "Isotropic dimension",
},
{
"count": 512,
"spectral_width": 2e4, # in Hz
"reference_offset": 2e3, # in Hz
"label": "MAS dimension",
},
],
)
Create the simulator object, add the spin systems and method, and run the simulation.
.. code-block:: python
sim = Simulator()
sim.spin_systems = spin_systems # add the spin systems
sim.methods = [mqvas] # add the method
sim.config.number_of_sidebands = 1
sim.run()
data = sim.methods[0].simulation
The plot of the corresponding spectrum.
.. code-block:: python
ax = plt.subplot(projection="csdm")
cb = ax.imshow(data / data.max(), cmap="gist_ncar_r", aspect="auto")
plt.colorbar(cb)
ax.set_ylim(-20, -50)
ax.set_xlim(80, 20)
plt.tight_layout()
plt.show()
.. image:: /examples/2D_simulation(macro_amorphous)/images/sphx_glr_plot_1_I=2.5_002.png
:alt: plot 1 I=2.5
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