68 lines
1.9 KiB
Python
68 lines
1.9 KiB
Python
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"""
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=======================
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Spin-lattice relaxation
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=======================
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Example for
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"""
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import numpy as np
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from matplotlib import pyplot as plt
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from nmreval.distributions import ColeDavidson
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from nmreval.nmr import Relaxation, RelaxationEvaluation
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from nmreval.nmr.coupling import Quadrupolar
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from nmreval.utils.constants import kB
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# Define temperature range
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inv_temp = np.linspace(3, 9, num=30)
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temperature = 1000/inv_temp
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# spectral density parameter
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ea = 0.45
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tau = 1e-21 * np.exp(ea / kB / temperature)
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gamma_cd = 0.1
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# interaction parameter
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omega = 2*np.pi*46e6
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delta = 120e3
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eta = 0
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r = Relaxation()
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r.set_distribution(ColeDavidson) # the only parameter that has to be set beforehand
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t1_values = r.t1(omega, tau, gamma_cd, mode='bpp',
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prefactor=Quadrupolar.relax(delta, eta))
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# add noise
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rng = np.random.default_rng(123456789)
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noisy = (rng.random(t1_values.size)-0.5) * 0.5 * t1_values + t1_values
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# set parameter and data
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r_eval = RelaxationEvaluation()
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r_eval.set_distribution(ColeDavidson)
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r_eval.set_coupling(Quadrupolar, (delta, eta))
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r_eval.data(temperature, noisy)
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r_eval.omega = omega
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t1_min_data, _ = r_eval.calculate_t1_min() # second argument is None
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t1_min_inter, line = r_eval.calculate_t1_min(interpolate=1, trange=(160, 195), use_log=True)
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fig, ax = plt.subplots()
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ax.semilogy(1000/t1_min_data[0], t1_min_data[1], 'rx', label='Data minimum')
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ax.semilogy(1000/t1_min_inter[0], t1_min_inter[1], 'r+', label='Parabola')
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ax.semilogy(1000/line[0], line[1])
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found_gamma, found_height = r_eval.get_increase(t1_min_inter[1], idx=0, mode='distribution')
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print(found_gamma)
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plt.axhline(found_height)
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plt.show()
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#%%
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# Now we found temperature and height of the minimum we can calculate the correlation time
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plt.semilogy(1000/temperature, tau)
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tau_from_t1, opts = r_eval.correlation_from_t1()
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print(opts)
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plt.semilogy(1000/tau_from_t1[:, 0], tau_from_t1[:, 1], 'o')
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plt.show()
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