Hyperfine distribution
[1]:
# import packages
import nexus as nx
import numpy as np
import matplotlib.pyplot as plt
mat_Fe = nx.Material.Template(nx.lib.material.Fe)
layer_Fe = nx.Layer(id = "Fe",
material = mat_Fe,
thickness = 3000, # in nanometer
roughness = 100, # in nanometer
)
site = nx.Hyperfine(magnetic_field = 33,
magnetic_theta = 0
)
mat_Fe.hyperfine_sites = [site]
sample = nx.Sample(layers = [layer_Fe])
beam = nx.Beam()
beam.LinearSigma()
exp = nx.Experiment(beam = beam,
objects = [sample],
isotope = nx.moessbauer.Fe57
)
time_spectrum = nx.TimeSpectrum(experiment = exp,
time_length = 200,
time_step = 0.2
)
time_axis, intensity = time_spectrum.Calculate()
plt.semilogy(time_axis, intensity, label = 'no dist')
# define a distribution from the library
# we have to define the number of points and the full width half maxmim for a Gaussian distribution
gauss_dist = nx.lib.distribution.Gaussian(points = 31,
fwhm = 1 # this can also be a fittable Var
)
# apply the distribution to the hyperfine parameter
site.SetMagneticFieldDistribution(gauss_dist)
time_axis, intensity = time_spectrum.Calculate()
# plot the results
plt.semilogy(time_axis, intensity, label = 'with dist')
plt.xlabel('time (ns)')
plt.ylabel('Intensity ($\Gamma$/ns)')
plt.legend()
plt.show()
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C:\Users\lbocklag\AppData\Local\Temp\ipykernel_21632\2364976630.py:57: SyntaxWarning: invalid escape sequence '\G'
plt.ylabel('Intensity ($\Gamma$/ns)')
[2]:
# create a random distribution in the magnetic field angles
site.SetRandomDistribution("mag", "2Dsp", 101)
plt.semilogy(*time_spectrum.Calculate(), label = 'with dist and 2D')
plt.xlabel('time (ns)')
plt.ylabel('Intensity ($\Gamma$/ns)')
plt.legend()
plt.show()
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C:\Users\lbocklag\AppData\Local\Temp\ipykernel_21632\1008142218.py:8: SyntaxWarning: invalid escape sequence '\G'
plt.ylabel('Intensity ($\Gamma$/ns)')
[3]:
# define an asymmetric Gaussian distribution from the lib.distribution.
asym_gauss_dist = nx.lib.distribution.AsymmetricGaussian(points = 101,
hwhm_low = nx.Var(value = 0.5, min = 0, max = 2, fit = True),
hwhm_high = nx.Var(value = 1, min = 0, max = 2, fit = True)
)
# Call of the distribution function.
# The .delta and .weight attributes of asym_gauss_dist are set by the call.
asym_gauss_dist.DistributionFunction()
# get the full width half maximum from the set sigma value
print("FWHM = {}".format(asym_gauss_dist.GetFWHM()))
plt.plot(asym_gauss_dist.delta, asym_gauss_dist.weight)
plt.xlabel('delta value')
plt.ylabel('weight')
plt.show()
FWHM = 1.5
[4]:
# define a hyperfine site
site = nx.Hyperfine(magnetic_field = 10)
# define target parameter
site.SetMagneticFieldDistribution(asym_gauss_dist)
# calc the actual distribution values
real_distribution_values = np.array(asym_gauss_dist.delta) + site.magnetic_field.value
plt.plot(real_distribution_values, asym_gauss_dist.weight)
plt.xlabel('delta value')
plt.ylabel('weight')
plt.show()
[5]:
magnetic_distribution_values, weight = site.GetMagneticFieldDistribution()
plt.plot(magnetic_distribution_values, weight)
plt.xlabel('delta value')
plt.ylabel('weight')
plt.show()
[6]:
site = nx.Hyperfine(quadrupole = 0.2)
# define a asymmetric Gaussian distribution object from nexus.lib.distribution.
dist = nx.lib.distribution.PosGaussian(points = 101,
fwhm = nx.Var(0.5, min = 0, max = 2, fit = True),
target_var = site.quadrupole
)
site.SetQuadrupoleDistribution(dist)
values, weight = site.GetQuadrupoleDistribution()
plt.plot(values, weight)
plt.xlabel('delta value')
plt.ylabel('weight')
plt.show()
[7]:
mat_Fe = nx.Material.Template(nx.lib.material.Fe)
layer_Fe = nx.Layer(id = "Fe",
material = mat_Fe,
thickness = 3000, # in nanometer
roughness = 100, # in nanometer
)
site = nx.Hyperfine(quadrupole = 1.0)
mat_Fe.hyperfine_sites = [site]
sample = nx.Sample(layers = [layer_Fe])
beam = nx.Beam()
beam.LinearSigma()
exp = nx.Experiment(beam = beam,
objects = [sample],
isotope = nx.moessbauer.Fe57
)
time_spectrum = nx.TimeSpectrum(experiment = exp,
time_length = 200,
time_step = 0.2,
max_detuning = 0)
fig, axs = plt.subplots(2,2, sharex=True, sharey=True)
fig.suptitle('Random distributions efg')
site.SetRandomDistribution("efg", "3D", 401)
axs[0,0].semilogy(*time_spectrum.Calculate(), label = '3D')
axs[0,0].legend()
axs[0,0].set_ylabel('Intensity ($\Gamma$/ns)')
site.SetRandomDistribution("efg", "2Dsp", 401)
axs[0,1].semilogy(*time_spectrum.Calculate(), label = '2Dsp')
axs[0,1].legend()
site.SetRandomDistribution("efg", "2Dsk", 401)
axs[1,0].semilogy(*time_spectrum.Calculate(), label = '2Dsk')
axs[1,0].legend()
axs[1,0].set_xlabel('time (ns)')
axs[1,0].set_ylabel('Intensity ($\Gamma$/ns)')
site.SetRandomDistribution("efg", "2Dpk", 401)
axs[1,1].semilogy(*time_spectrum.Calculate(), label = '2Dpk')
axs[1,1].legend()
axs[1,1].set_xlabel('time (ns)')
fig.show()
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C:\Users\lbocklag\AppData\Local\Temp\ipykernel_21632\285753287.py:35: SyntaxWarning: invalid escape sequence '\G'
axs[0,0].set_ylabel('Intensity ($\Gamma$/ns)')
C:\Users\lbocklag\AppData\Local\Temp\ipykernel_21632\285753287.py:47: SyntaxWarning: invalid escape sequence '\G'
axs[1,0].set_ylabel('Intensity ($\Gamma$/ns)')
C:\Users\lbocklag\AppData\Local\Temp\ipykernel_21632\285753287.py:55: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
fig.show()
[8]:
mat_Fe = nx.Material.Template(nx.lib.material.Fe)
layer_Fe = nx.Layer(id = "Fe",
material = mat_Fe,
thickness = 3000, # in nanometer
roughness = 100, # in nanometer
)
site = nx.Hyperfine(magnetic_field = 33)
mat_Fe.hyperfine_sites = [site]
sample = nx.Sample(layers = [layer_Fe])
beam = nx.Beam()
beam.LinearSigma()
exp = nx.Experiment(beam = beam,
objects = [sample],
isotope = nx.moessbauer.Fe57)
time_spectrum = nx.TimeSpectrum(experiment = exp,
time_length = 200,
time_step = 0.2,
max_detuning = 0)
fig, axs = plt.subplots(2,2)
fig.suptitle('Random distributions mag')
site.SetRandomDistribution("mag", "3D", 401)
axs[0,0].semilogy(*time_spectrum.Calculate(), label = '3D')
axs[0,0].legend()
axs[0,0].set_ylabel('Intensity ($\Gamma$/ns)')
site.SetRandomDistribution("mag", "2Dsp", 401)
axs[0,1].semilogy(*time_spectrum.Calculate(), label = '2Dsp')
axs[0,1].legend()
site.SetRandomDistribution("mag", "2Dsk", 401)
axs[1,0].semilogy(*time_spectrum.Calculate(), label = '2Dsk')
axs[1,0].legend()
axs[1,0].set_xlabel('time (ns)')
axs[1,0].set_ylabel('Intensity ($\Gamma$/ns)')
site.SetRandomDistribution("mag", "2Dpk", 401)
axs[1,1].semilogy(*time_spectrum.Calculate(), label = '2Dpk')
axs[1,1].legend()
axs[1,1].set_xlabel('time (ns)')
fig.show()
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C:\Users\lbocklag\AppData\Local\Temp\ipykernel_21632\3227972485.py:34: SyntaxWarning: invalid escape sequence '\G'
axs[0,0].set_ylabel('Intensity ($\Gamma$/ns)')
C:\Users\lbocklag\AppData\Local\Temp\ipykernel_21632\3227972485.py:46: SyntaxWarning: invalid escape sequence '\G'
axs[1,0].set_ylabel('Intensity ($\Gamma$/ns)')
C:\Users\lbocklag\AppData\Local\Temp\ipykernel_21632\3227972485.py:55: UserWarning: FigureCanvasAgg is non-interactive, and thus cannot be shown
fig.show()
[9]:
delta = np.linspace(-5, 5, 6) # absolute differences to the target value
weight = np.linspace(0.1, 1, 6) # some weight values
array_dist = nx.lib.distribution.Array(delta, weight)
site = nx.Hyperfine(magnetic_field = 30, # distribution will range from 25 to 35
magnetic_theta = 90,
magnetic_phi = 30
)
site.SetMagneticFieldDistribution(array_dist)
# Print all combinations applied to the site
print(site)
# print each parameter combination due to distributions stored in site.BareHyperfines
for elem in site.BareHyperfines:
print(elem)
Hyperfine .id:
.weight = 1.0
.isomer_shift = 0.0 dist points: 1
.magnetic_field = 30.0 dist points: 6
.magnetic_theta = 90.0 dist points: 1
.magnetic_phi = 30.0 dist points: 1
.quadrupole = 0.0 dist points: 1
.quadrupole_alpha = 0.0 dist points: 1
.quadrupole_beta = 0.0 dist points: 1
.quadrupole_gamma = 0.0 dist points: 1
.quadrupole_asymmetry = 0.0 dist points: 1
.isotropic = False 3D distribution in mag and efg. Random mag or efg distributions are ignored.
random magnetic distribution: none dist points: 1
random quadrupole distribution: none dist points: 1
total number of distribution points: 6
BareHyperfine Parameters:
.weight = 0.030303030303030307
.isomer_shift (mm/s) = 0.0
.magnetic_field (T) = 25.0
.magnetic_theta (rad) = 1.5707963267948966
.magnetic_phi (rad) = 0.5235987755982988
.quadrupole (mm/s) = 0.0
.quadrupole_alpha (rad) = 0.0
.quadrupole_beta (rad) = 0.0
.quadrupole_gamma (rad) = 0.0
.quadrupole_asymmetry = 0.0
.isotropic = False
BareHyperfine Parameters:
.weight = 0.08484848484848487
.isomer_shift (mm/s) = 0.0
.magnetic_field (T) = 27.0
.magnetic_theta (rad) = 1.5707963267948966
.magnetic_phi (rad) = 0.5235987755982988
.quadrupole (mm/s) = 0.0
.quadrupole_alpha (rad) = 0.0
.quadrupole_beta (rad) = 0.0
.quadrupole_gamma (rad) = 0.0
.quadrupole_asymmetry = 0.0
.isotropic = False
BareHyperfine Parameters:
.weight = 0.1393939393939394
.isomer_shift (mm/s) = 0.0
.magnetic_field (T) = 29.0
.magnetic_theta (rad) = 1.5707963267948966
.magnetic_phi (rad) = 0.5235987755982988
.quadrupole (mm/s) = 0.0
.quadrupole_alpha (rad) = 0.0
.quadrupole_beta (rad) = 0.0
.quadrupole_gamma (rad) = 0.0
.quadrupole_asymmetry = 0.0
.isotropic = False
BareHyperfine Parameters:
.weight = 0.19393939393939397
.isomer_shift (mm/s) = 0.0
.magnetic_field (T) = 31.0
.magnetic_theta (rad) = 1.5707963267948966
.magnetic_phi (rad) = 0.5235987755982988
.quadrupole (mm/s) = 0.0
.quadrupole_alpha (rad) = 0.0
.quadrupole_beta (rad) = 0.0
.quadrupole_gamma (rad) = 0.0
.quadrupole_asymmetry = 0.0
.isotropic = False
BareHyperfine Parameters:
.weight = 0.24848484848484848
.isomer_shift (mm/s) = 0.0
.magnetic_field (T) = 33.0
.magnetic_theta (rad) = 1.5707963267948966
.magnetic_phi (rad) = 0.5235987755982988
.quadrupole (mm/s) = 0.0
.quadrupole_alpha (rad) = 0.0
.quadrupole_beta (rad) = 0.0
.quadrupole_gamma (rad) = 0.0
.quadrupole_asymmetry = 0.0
.isotropic = False
BareHyperfine Parameters:
.weight = 0.30303030303030304
.isomer_shift (mm/s) = 0.0
.magnetic_field (T) = 35.0
.magnetic_theta (rad) = 1.5707963267948966
.magnetic_phi (rad) = 0.5235987755982988
.quadrupole (mm/s) = 0.0
.quadrupole_alpha (rad) = 0.0
.quadrupole_beta (rad) = 0.0
.quadrupole_gamma (rad) = 0.0
.quadrupole_asymmetry = 0.0
.isotropic = False
[10]:
values = np.linspace(1, 30, 6) # absolute values
weight = np.square(values) # some dependence on values
array_dist = nx.lib.distribution.Array(values, weight)
array_dist.DistributionFunction()
site = nx.Hyperfine(magnetic_field = 0, # zero because absolute values are assumed
magnetic_theta = 90,
magnetic_phi = 30)
site.SetMagneticFieldDistribution(array_dist)
print(site)
for elem in site.BareHyperfines:
print(elem)
Hyperfine .id:
.weight = 1.0
.isomer_shift = 0.0 dist points: 1
.magnetic_field = 0.0 dist points: 6
.magnetic_theta = 90.0 dist points: 1
.magnetic_phi = 30.0 dist points: 1
.quadrupole = 0.0 dist points: 1
.quadrupole_alpha = 0.0 dist points: 1
.quadrupole_beta = 0.0 dist points: 1
.quadrupole_gamma = 0.0 dist points: 1
.quadrupole_asymmetry = 0.0 dist points: 1
.isotropic = False 3D distribution in mag and efg. Random mag or efg distributions are ignored.
random magnetic distribution: none dist points: 1
random quadrupole distribution: none dist points: 1
total number of distribution points: 6
BareHyperfine Parameters:
.weight = 0.0004925623091321052
.isomer_shift (mm/s) = 0.0
.magnetic_field (T) = 1.0
.magnetic_theta (rad) = 1.5707963267948966
.magnetic_phi (rad) = 0.5235987755982988
.quadrupole (mm/s) = 0.0
.quadrupole_alpha (rad) = 0.0
.quadrupole_beta (rad) = 0.0
.quadrupole_gamma (rad) = 0.0
.quadrupole_asymmetry = 0.0
.isotropic = False
BareHyperfine Parameters:
.weight = 0.022776081174268544
.isomer_shift (mm/s) = 0.0
.magnetic_field (T) = 6.8
.magnetic_theta (rad) = 1.5707963267948966
.magnetic_phi (rad) = 0.5235987755982988
.quadrupole (mm/s) = 0.0
.quadrupole_alpha (rad) = 0.0
.quadrupole_beta (rad) = 0.0
.quadrupole_gamma (rad) = 0.0
.quadrupole_asymmetry = 0.0
.isotropic = False
BareHyperfine Parameters:
.weight = 0.07819919219781303
.isomer_shift (mm/s) = 0.0
.magnetic_field (T) = 12.6
.magnetic_theta (rad) = 1.5707963267948966
.magnetic_phi (rad) = 0.5235987755982988
.quadrupole (mm/s) = 0.0
.quadrupole_alpha (rad) = 0.0
.quadrupole_beta (rad) = 0.0
.quadrupole_gamma (rad) = 0.0
.quadrupole_asymmetry = 0.0
.isotropic = False
BareHyperfine Parameters:
.weight = 0.16676189537976552
.isomer_shift (mm/s) = 0.0
.magnetic_field (T) = 18.4
.magnetic_theta (rad) = 1.5707963267948966
.magnetic_phi (rad) = 0.5235987755982988
.quadrupole (mm/s) = 0.0
.quadrupole_alpha (rad) = 0.0
.quadrupole_beta (rad) = 0.0
.quadrupole_gamma (rad) = 0.0
.quadrupole_asymmetry = 0.0
.isotropic = False
BareHyperfine Parameters:
.weight = 0.28846419072012613
.isomer_shift (mm/s) = 0.0
.magnetic_field (T) = 24.2
.magnetic_theta (rad) = 1.5707963267948966
.magnetic_phi (rad) = 0.5235987755982988
.quadrupole (mm/s) = 0.0
.quadrupole_alpha (rad) = 0.0
.quadrupole_beta (rad) = 0.0
.quadrupole_gamma (rad) = 0.0
.quadrupole_asymmetry = 0.0
.isotropic = False
BareHyperfine Parameters:
.weight = 0.44330607821889473
.isomer_shift (mm/s) = 0.0
.magnetic_field (T) = 30.0
.magnetic_theta (rad) = 1.5707963267948966
.magnetic_phi (rad) = 0.5235987755982988
.quadrupole (mm/s) = 0.0
.quadrupole_alpha (rad) = 0.0
.quadrupole_beta (rad) = 0.0
.quadrupole_gamma (rad) = 0.0
.quadrupole_asymmetry = 0.0
.isotropic = False
[11]:
# load a Distribution from a file
file_dist = nx.lib.distribution.File("distribution.txt")
site = nx.Hyperfine(magnetic_field = 0, # zero because absolute field values are given
magnetic_theta = 90,
magnetic_phi = 30
)
site.SetMagneticFieldDistribution(file_dist)
for elem in site.BareHyperfines:
print(elem)
BareHyperfine Parameters:
.weight = 0.15
.isomer_shift (mm/s) = 0.0
.magnetic_field (T) = 31.2
.magnetic_theta (rad) = 1.5707963267948966
.magnetic_phi (rad) = 0.5235987755982988
.quadrupole (mm/s) = 0.0
.quadrupole_alpha (rad) = 0.0
.quadrupole_beta (rad) = 0.0
.quadrupole_gamma (rad) = 0.0
.quadrupole_asymmetry = 0.0
.isotropic = False
BareHyperfine Parameters:
.weight = 0.25
.isomer_shift (mm/s) = 0.0
.magnetic_field (T) = 32.2
.magnetic_theta (rad) = 1.5707963267948966
.magnetic_phi (rad) = 0.5235987755982988
.quadrupole (mm/s) = 0.0
.quadrupole_alpha (rad) = 0.0
.quadrupole_beta (rad) = 0.0
.quadrupole_gamma (rad) = 0.0
.quadrupole_asymmetry = 0.0
.isotropic = False
BareHyperfine Parameters:
.weight = 0.4
.isomer_shift (mm/s) = 0.0
.magnetic_field (T) = 33.2
.magnetic_theta (rad) = 1.5707963267948966
.magnetic_phi (rad) = 0.5235987755982988
.quadrupole (mm/s) = 0.0
.quadrupole_alpha (rad) = 0.0
.quadrupole_beta (rad) = 0.0
.quadrupole_gamma (rad) = 0.0
.quadrupole_asymmetry = 0.0
.isotropic = False
BareHyperfine Parameters:
.weight = 0.15
.isomer_shift (mm/s) = 0.0
.magnetic_field (T) = 34.2
.magnetic_theta (rad) = 1.5707963267948966
.magnetic_phi (rad) = 0.5235987755982988
.quadrupole (mm/s) = 0.0
.quadrupole_alpha (rad) = 0.0
.quadrupole_beta (rad) = 0.0
.quadrupole_gamma (rad) = 0.0
.quadrupole_asymmetry = 0.0
.isotropic = False
BareHyperfine Parameters:
.weight = 0.05
.isomer_shift (mm/s) = 0.0
.magnetic_field (T) = 35.2
.magnetic_theta (rad) = 1.5707963267948966
.magnetic_phi (rad) = 0.5235987755982988
.quadrupole (mm/s) = 0.0
.quadrupole_alpha (rad) = 0.0
.quadrupole_beta (rad) = 0.0
.quadrupole_gamma (rad) = 0.0
.quadrupole_asymmetry = 0.0
.isotropic = False