Coesite, ¹⁷O (I=5/2)¶

¹⁷O (I=5/2) quadrupolar spectrum simulation.

Coesite is a high-pressure (2-3 GPa) and high-temperature (700°C) polymorph of silicon dioxide \(\text{SiO}_2\). Coesite has five crystallographic \(^{17}\text{O}\) sites. In the following, we use the \(^{17}\text{O}\) EFG tensor information from Grandinetti et al. [1]

import matplotlib.pyplot as plt

from mrsimulator import Simulator, SpinSystem, Site
from mrsimulator import signal_processor as sp
from mrsimulator.method.lib import BlochDecayCTSpectrum
from mrsimulator.spin_system.tensors import SymmetricTensor
from mrsimulator.method import SpectralDimension

Step 1: Create the sites.

# default unit of isotropic_chemical_shift is ppm and Cq is Hz.
O17_1 = Site(
    isotope="17O",
    isotropic_chemical_shift=29,
    quadrupolar=SymmetricTensor(Cq=6.05e6, eta=0.000),
)
O17_2 = Site(
    isotope="17O",
    isotropic_chemical_shift=41,
    quadrupolar=SymmetricTensor(Cq=5.43e6, eta=0.166),
)
O17_3 = Site(
    isotope="17O",
    isotropic_chemical_shift=57,
    quadrupolar=SymmetricTensor(Cq=5.45e6, eta=0.168),
)
O17_4 = Site(
    isotope="17O",
    isotropic_chemical_shift=53,
    quadrupolar=SymmetricTensor(Cq=5.52e6, eta=0.169),
)
O17_5 = Site(
    isotope="17O",
    isotropic_chemical_shift=58,
    quadrupolar=SymmetricTensor(Cq=5.16e6, eta=0.292),
)

# all five sites.
sites = [O17_1, O17_2, O17_3, O17_4, O17_5]

Step 2: Create the spin systems from these sites. For optimum performance, we create five single-site spin systems instead of a single five-site spin system. The abundance of each spin system is taken from above reference. Here we are iterating over both the sites and abundance list concurrently using a list comprehension to construct a list of SpinSystems

abundance = [0.83, 1.05, 2.16, 2.05, 1.90]
spin_systems = [SpinSystem(sites=[s], abundance=a) for s, a in zip(sites, abundance)]

Step 3: Create a central transition selective Bloch decay spectrum method.

method = BlochDecayCTSpectrum(
    channels=["17O"],
    rotor_frequency=14000,  # in Hz
    spectral_dimensions=[
        SpectralDimension(
            count=2048,
            spectral_width=50000,  # in Hz
            label=r"$^{17}$O resonances",
        )
    ],
)

The above method is set up to record the \(^{17}\text{O}\) resonances at the magic angle, spinning at 14 kHz and 9.4 T (default, if the value is not provided) external magnetic flux density. The resonances are recorded over 50 kHz spectral width using 2048 points.

Step 4: Create the Simulator object and add the method and spin system objects.

sim = Simulator()
sim.spin_systems = spin_systems  # add the spin systems
sim.methods = [method]  # add the method

Step 5: Simulate the spectrum.

sim.run()

# The plot of the simulation before signal processing.
plt.figure(figsize=(4.25, 3.0))
ax = plt.subplot(projection="csdm")
ax.plot(sim.methods[0].simulation.real, color="black", linewidth=1)
ax.invert_xaxis()
plt.tight_layout()
plt.show()

Step 6: Add post-simulation signal processing.

processor = sp.SignalProcessor(
    operations=[
        sp.IFFT(),
        sp.apodization.Exponential(FWHM="30 Hz"),
        sp.apodization.Gaussian(FWHM="145 Hz"),
        sp.FFT(),
    ]
)
processed_dataset = processor.apply_operations(dataset=sim.methods[0].simulation)

# The plot of the simulation after signal processing.
plt.figure(figsize=(4.25, 3.0))
ax = plt.subplot(projection="csdm")
ax.plot(processed_dataset.real, color="black", linewidth=1)
ax.invert_xaxis()
plt.tight_layout()
plt.show()

Total running time of the script: ( 0 minutes 0.490 seconds)

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