Note
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²⁷Al MAS NMR of YAG (1st and 2nd order Quad)¶
The following is a quadrupolar lineshape fitting example for the 27Al MAS NMR of Yttrium aluminum garnet (YAG) crystal. The following experimental dataset is a part of DMFIT [1] examples. We thank Dr. Dominique Massiot for sharing the dataset.
import csdmpy as cp
import matplotlib.pyplot as plt
from lmfit import Minimizer
from mrsimulator import Simulator, Site, SpinSystem
from mrsimulator.method.lib import BlochDecaySpectrum
from mrsimulator import signal_processor as sp
from mrsimulator.utils import spectral_fitting as sf
from mrsimulator.utils import get_spectral_dimensions
from mrsimulator.spin_system.tensors import SymmetricTensor
Import the dataset¶
host = "https://nmr.cemhti.cnrs-orleans.fr/Dmfit/Help/csdm/"
filename = "27Al Quad MAS YAG 400MHz.csdf"
experiment = cp.load(host + filename)
# standard deviation of noise from the dataset
sigma = 0.4895381
# For spectral fitting, we only focus on the real part of the complex dataset
experiment = experiment.real
# Convert the coordinates along each dimension from Hz to ppm.
_ = [item.to("ppm", "nmr_frequency_ratio") for item in experiment.dimensions]
# plot of the dataset.
plt.figure(figsize=(8, 4))
ax = plt.subplot(projection="csdm")
ax.plot(experiment, color="black", linewidth=0.5, label="Experiment")
ax.set_xlim(1200, -1200)
plt.grid()
plt.tight_layout()
plt.show()
Create a fitting model¶
Guess model
Create a guess list of spin systems.
Al_1 = Site(
isotope="27Al",
isotropic_chemical_shift=76, # in ppm
quadrupolar=SymmetricTensor(Cq=6e6, eta=0.0), # Cq in Hz
)
Al_2 = Site(
isotope="27Al",
isotropic_chemical_shift=1, # in ppm
quadrupolar=SymmetricTensor(Cq=5e5, eta=0.3), # Cq in Hz
)
spin_systems = [
SpinSystem(sites=[Al_1], name="AlO4"),
SpinSystem(sites=[Al_2], name="AlO6"),
]
Method
# Get the spectral dimension parameters from the experiment.
spectral_dims = get_spectral_dimensions(experiment)
MAS = BlochDecaySpectrum(
channels=["27Al"],
magnetic_flux_density=9.395, # in T
rotor_frequency=15250, # in Hz
spectral_dimensions=spectral_dims,
experiment=experiment, # add the measurement to the method.
)
# Optimize the script by pre-setting the transition pathways for each spin system from
# the method.
for sys in spin_systems:
sys.transition_pathways = MAS.get_transition_pathways(sys)
Guess Spectrum
# Simulation
# ----------
sim = Simulator(spin_systems=spin_systems, methods=[MAS])
sim.config.decompose_spectrum = "spin_system"
sim.run()
# Post Simulation Processing
# --------------------------
processor = sp.SignalProcessor(
operations=[
sp.IFFT(),
sp.apodization.Gaussian(FWHM="300 Hz"),
sp.FFT(),
sp.Scale(factor=50),
]
)
processed_dataset = processor.apply_operations(dataset=sim.methods[0].simulation).real
# Plot of the guess Spectrum
# --------------------------
plt.figure(figsize=(8, 4))
ax = plt.subplot(projection="csdm")
ax.plot(experiment, color="black", linewidth=0.5, label="Experiment")
ax.plot(processed_dataset, linewidth=2, alpha=0.6)
ax.set_xlim(1200, -1200)
plt.grid()
plt.legend()
plt.tight_layout()
plt.show()
Least-squares minimization with LMFIT¶
Use the make_LMFIT_params() for a quick
setup of the fitting parameters.
params = sf.make_LMFIT_params(sim, processor, include={"rotor_frequency"})
print(params.pretty_print(columns=["value", "min", "max", "vary", "expr"]))
Out:
Name Value Min Max Vary Expr
SP_0_operation_1_Gaussian_FWHM 300 -inf inf True None
SP_0_operation_3_Scale_factor 50 -inf inf True None
mth_0_rotor_frequency 1.525e+04 1.515e+04 1.535e+04 True None
sys_0_abundance 50 0 100 True None
sys_0_site_0_isotropic_chemical_shift 76 -inf inf True None
sys_0_site_0_quadrupolar_Cq 6e+06 -inf inf True None
sys_0_site_0_quadrupolar_eta 0 0 1 True None
sys_1_abundance 50 0 100 False 100-sys_0_abundance
sys_1_site_0_isotropic_chemical_shift 1 -inf inf True None
sys_1_site_0_quadrupolar_Cq 5e+05 -inf inf True None
sys_1_site_0_quadrupolar_eta 0.3 0 1 True None
None
Solve the minimizer using LMFIT
minner = Minimizer(sf.LMFIT_min_function, params, fcn_args=(sim, processor, sigma))
result = minner.minimize()
result
The best fit solution¶
best_fit = sf.bestfit(sim, processor)[0].real
residuals = sf.residuals(sim, processor)[0].real
# Plot the spectrum
plt.figure(figsize=(8, 4))
ax = plt.subplot(projection="csdm")
ax.plot(experiment, color="black", linewidth=0.5, label="Experiment")
ax.plot(residuals, color="gray", linewidth=0.5, label="Residual")
ax.plot(best_fit, linewidth=2, alpha=0.6)
ax.set_xlim(1200, -1200)
plt.grid()
plt.legend()
plt.tight_layout()
plt.show()
Total running time of the script: ( 0 minutes 9.569 seconds)