Wollastonite, ²⁹Si (I=1/2), MAF¶

²⁹Si (I=1/2) magic angle flipping.

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 numpy as np
import matplotlib.pyplot as plt

from mrsimulator import Simulator, SpinSystem, Site
from mrsimulator import signal_processor as sp
from mrsimulator.spin_system.tensors import SymmetricTensor
from mrsimulator.method import Method, SpectralDimension, SpectralEvent, RotationEvent

Create the sites and spin systems

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

spin_systems = [SpinSystem(sites=[s]) for s in sites]

Use the generic Method class to simulate a 2D magic-angle Flipping (MAF) spectrum by customizing the method parameters, as shown below.

Here, we include an empty RotationEvent. An empty RotationEvent has zero rotation angle that does not allow mixing of the transitions from the first and second SpectralEvent. Since all spin systems in this example have a single site, defining no mixing between the two spectral events is superfluous. We include it such that the method is applicable with multi-site spin systems.

maf = Method(
    name="Magic Angle Flipping",
    channels=["29Si"],
    magnetic_flux_density=14.1,  # in T
    rotor_frequency=np.inf,
    spectral_dimensions=[
        SpectralDimension(
            count=128,
            spectral_width=2e4,  # in Hz
            label="Anisotropic dimension",
            events=[
                SpectralEvent(
                    rotor_angle=90 * np.pi / 180,  # in rads
                    transition_queries=[{"ch1": {"P": [-1], "D": [0]}}],
                ),
                RotationEvent(),
            ],
        ),
        SpectralDimension(
            count=128,
            spectral_width=3e3,  # in Hz
            reference_offset=-1.05e4,  # in Hz
            label="Isotropic dimension",
            events=[
                SpectralEvent(
                    rotor_angle=54.735 * np.pi / 180,  # in rads
                    transition_queries=[{"ch1": {"P": [-1], "D": [0]}}],
                )
            ],
        ),
    ],
    affine_matrix=[[1, -1], [0, 1]],
)

# A graphical representation of the method object.
plt.figure(figsize=(5, 2.5))
maf.plot()
plt.show()

Create the Simulator object, add the method and spin system objects, and run the simulation.

sim = Simulator(spin_systems=spin_systems, methods=[maf])
sim.run()

Add post-simulation signal processing.

csdm_dataset = sim.methods[0].simulation
processor = sp.SignalProcessor(
    operations=[
        sp.IFFT(dim_index=(0, 1)),
        sp.apodization.Gaussian(FWHM="50 Hz", dim_index=0),
        sp.apodization.Gaussian(FWHM="50 Hz", dim_index=1),
        sp.FFT(dim_index=(0, 1)),
    ]
)
processed_dataset = processor.apply_operations(dataset=csdm_dataset).real
processed_dataset /= processed_dataset.max()

The plot of the simulation after signal processing.

plt.figure(figsize=(4.25, 3.0))
ax = plt.subplot(projection="csdm")
cb = ax.imshow(processed_dataset.T, aspect="auto", cmap="gist_ncar_r")
plt.colorbar(cb)
ax.invert_xaxis()
ax.invert_yaxis()
plt.tight_layout()
plt.show()

Total running time of the script: (0 minutes 0.487 seconds)

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