Wollastonite, ²⁹Si (I=1/2)¶

²⁹Si (I=1/2) spinning sideband simulation.

Wollastonite is a high-temperature calcium-silicate, \(\beta−\text{Ca}_3\text{Si}_3\text{O}_9\), with three distinct \(^{29}\text{Si}\) sites. The \(^{29}\text{Si}\) tensor parameters were obtained from Hansen 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 BlochDecaySpectrum
from mrsimulator.spin_system.tensors import SymmetricTensor
from mrsimulator.method import SpectralDimension

Step 1: Create the sites.

Si29_1 = Site(
    isotope="29Si",
    isotropic_chemical_shift=-89.0,  # in ppm
    shielding_symmetric=SymmetricTensor(zeta=59.8, eta=0.62),  # zeta in ppm
)
Si29_2 = Site(
    isotope="29Si",
    isotropic_chemical_shift=-89.5,  # in ppm
    shielding_symmetric=SymmetricTensor(zeta=52.1, eta=0.68),  # zeta in ppm
)
Si29_3 = Site(
    isotope="29Si",
    isotropic_chemical_shift=-87.8,  # in ppm
    shielding_symmetric=SymmetricTensor(zeta=69.4, eta=0.60),  # zeta in ppm
)

Step 2: Create the spin systems from these sites. Again, we create three single-site spin systems for better performance.

spin_systems = [
    SpinSystem(sites=[Si29_1]),
    SpinSystem(sites=[Si29_2]),
    SpinSystem(sites=[Si29_3]),
]

Step 3: Create a Bloch decay spectrum method.

method = BlochDecaySpectrum(
    channels=["29Si"],
    magnetic_flux_density=14.1,  # in T
    rotor_frequency=1500,  # in Hz
    spectral_dimensions=[
        SpectralDimension(
            count=2048,
            spectral_width=25000,  # in Hz
            reference_offset=-10000,  # in Hz
            label=r"$^{29}$Si resonances",
        )
    ],
)

# A graphical representation of the method object.
plt.figure(figsize=(4, 2))
method.plot()
plt.show()

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="70 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 1.162 seconds)

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