Mössbauer Spectroscopy Models in SpectraFit¶
This notebook demonstrates the use of the built-in Mössbauer spectroscopy models in SpectraFit. Mössbauer spectroscopy is a technique that provides information about chemical, structural, magnetic and electronic states of matter through the analysis of hyperfine interactions between electrons and nuclei.
SpectraFit includes four main Mössbauer models:
- Singlet - For materials with no quadrupole splitting or magnetic hyperfine splitting
- Doublet - For materials with quadrupole splitting but no magnetic hyperfine splitting
- Sextet - For materials with magnetic hyperfine splitting (6 lines)
- Octet - For materials with both magnetic hyperfine and quadrupole interactions (8 lines)
This notebook will demonstrate how to use each model, explain their parameters, and show how to fit experimental data.
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# Import necessary libraries
from __future__ import annotations
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from matplotlib.gridspec import GridSpec
from spectrafit.models.moessbauer import moessbauer_doublet
from spectrafit.models.moessbauer import moessbauer_octet
from spectrafit.models.moessbauer import moessbauer_sextet
# Import SpectraFit models
from spectrafit.models.moessbauer import moessbauer_singlet
# For demonstration of fitting
from spectrafit.plugins import notebook as nb
# Define axis label constant
VELOCITY_LABEL = "Velocity (mm/s)"
# Import notebook plugin for solver approach
# Set plot style
plt.style.use("ggplot")
plt.rcParams["figure.figsize"] = (12, 8)
plt.rcParams["font.size"] = 12
# Import necessary libraries from __future__ import annotations import matplotlib.pyplot as plt import numpy as np import pandas as pd from matplotlib.gridspec import GridSpec from spectrafit.models.moessbauer import moessbauer_doublet from spectrafit.models.moessbauer import moessbauer_octet from spectrafit.models.moessbauer import moessbauer_sextet # Import SpectraFit models from spectrafit.models.moessbauer import moessbauer_singlet # For demonstration of fitting from spectrafit.plugins import notebook as nb # Define axis label constant VELOCITY_LABEL = "Velocity (mm/s)" # Import notebook plugin for solver approach # Set plot style plt.style.use("ggplot") plt.rcParams["figure.figsize"] = (12, 8) plt.rcParams["font.size"] = 12
/tmp/ipykernel_2546/2040819219.py:10: UserWarning: Mössbauer models are experimental features and still need scientific validation. from spectrafit.models.moessbauer import moessbauer_doublet
/home/runner/work/spectrafit/spectrafit/.venv/lib/python3.10/site-packages/dtale/utils.py:18: UserWarning: pkg_resources is deprecated as an API. See https://setuptools.pypa.io/en/latest/pkg_resources.html. The pkg_resources package is slated for removal as early as 2025-11-30. Refrain from using this package or pin to Setuptools<81. from pkg_resources import parse_version
1. Understanding Mössbauer Model Parameters¶
Before we start using the models, let's understand the key parameters in Mössbauer spectroscopy:
- Isomer Shift (δ): Reflects the s-electron density at the nucleus and is sensitive to oxidation state and coordination chemistry.
- Quadrupole Splitting (ΔEQ): Arises from the interaction between the nuclear quadrupole moment and the electric field gradient at the nucleus.
- Magnetic Hyperfine Splitting: Results from the interaction between the nucleus and a magnetic field, splitting spectral lines.
- Line Width (FWHM): Natural line width plus instrumental broadening.
- Background: Constant background level in the spectrum.
These parameters provide critical information about the electronic structure, oxidation state, spin state, and local coordination environment of atoms in materials.
2. Create Velocity Scale for Mössbauer Models¶
Mössbauer spectra are typically plotted with velocity (mm/s) on the x-axis. Let's create a standard range for our demonstrations:
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# Create a velocity scale in mm/s
velocity = np.linspace(-10, 10, 1000) # Range -10 to 10 mm/s
# Create a velocity scale in mm/s velocity = np.linspace(-10, 10, 1000) # Range -10 to 10 mm/s
3. Model 1: Mössbauer Singlet¶
A singlet is the simplest Mössbauer pattern, consisting of a single absorption peak. It occurs in materials with cubic crystal symmetry and no magnetic ordering, where there's only an isomer shift but no quadrupole or magnetic hyperfine splitting.
Examples: Fe metal at room temperature (though technically a very narrow, unresolved doublet).
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# Basic singlet with default parameters
singlet_default = moessbauer_singlet(velocity)
# Singlet with custom parameters
singlet_custom = moessbauer_singlet(
velocity,
isomer_shift=0.2, # Isomer shift in mm/s
fwhml=0.30, # Line width
amplitude=1.2, # Amplitude
background=0.1, # Constant background
)
# Plot both singlets
plt.figure()
plt.plot(velocity, singlet_default, label="Default Singlet", linewidth=2)
plt.plot(velocity, singlet_custom, label="Custom Singlet", linewidth=2, linestyle="--")
plt.xlabel(VELOCITY_LABEL)
plt.ylabel("Transmission")
plt.title("Mössbauer Singlet Models")
plt.xlim(-4, 4)
plt.legend()
plt.grid(True)
plt.gca().invert_yaxis() # Invert Y-axis as Mössbauer spectra typically show absorption downward
plt.show()
# Basic singlet with default parameters singlet_default = moessbauer_singlet(velocity) # Singlet with custom parameters singlet_custom = moessbauer_singlet( velocity, isomer_shift=0.2, # Isomer shift in mm/s fwhml=0.30, # Line width amplitude=1.2, # Amplitude background=0.1, # Constant background ) # Plot both singlets plt.figure() plt.plot(velocity, singlet_default, label="Default Singlet", linewidth=2) plt.plot(velocity, singlet_custom, label="Custom Singlet", linewidth=2, linestyle="--") plt.xlabel(VELOCITY_LABEL) plt.ylabel("Transmission") plt.title("Mössbauer Singlet Models") plt.xlim(-4, 4) plt.legend() plt.grid(True) plt.gca().invert_yaxis() # Invert Y-axis as Mössbauer spectra typically show absorption downward plt.show()
4. Model 2: Mössbauer Doublet¶
A doublet consists of two absorption peaks resulting from quadrupole splitting in the excited state of the nucleus. This occurs in non-cubic electronic environments where the electric field gradient is non-zero.
Examples: Fe²⁺ and Fe³⁺ compounds such as FeO, Fe₂O₃, ferrous/ferric salts, silicates, etc.
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# Generate two doublet models with different parameters
doublet1 = moessbauer_doublet(
velocity,
isomer_shift=0.3, # Typical for Fe³⁺ in oxides
quadrupole_splitting=0.7, # Moderate quadrupole splitting
fwhml=0.25, # Line width
amplitude=1.0, # Amplitude
background=0.05, # Background
)
doublet2 = moessbauer_doublet(
velocity,
isomer_shift=1.1, # Typical for Fe²⁺ in silicates
quadrupole_splitting=2.2, # Larger quadrupole splitting
fwhml=0.30, # Line width
amplitude=0.8, # Amplitude
background=0.05, # Background
)
# Plot both doublets
plt.figure()
plt.plot(velocity, doublet1, label="Fe³⁺-like doublet", linewidth=2)
plt.plot(velocity, doublet2, label="Fe²⁺-like doublet", linewidth=2, linestyle="--")
plt.xlabel(VELOCITY_LABEL)
plt.ylabel("Transmission")
plt.title("Mössbauer Doublet Models")
plt.xlim(-4, 4)
plt.legend()
plt.grid(True)
plt.gca().invert_yaxis()
plt.show()
# Visualize the effect of changing quadrupole splitting
plt.figure(figsize=(10, 6))
for qs in [0.5, 1.0, 1.5, 2.0]:
doublet = moessbauer_doublet(
velocity,
isomer_shift=0.4,
quadrupole_splitting=qs,
fwhml=0.25,
amplitude=1.0,
)
plt.plot(velocity, doublet, label=f"QS = {qs} mm/s", linewidth=2)
plt.xlabel(VELOCITY_LABEL)
plt.ylabel("Transmission")
plt.title("Effect of Quadrupole Splitting on Mössbauer Doublets")
plt.xlim(-6, 6)
plt.legend()
plt.grid(True)
plt.gca().invert_yaxis()
plt.show()
# Generate two doublet models with different parameters doublet1 = moessbauer_doublet( velocity, isomer_shift=0.3, # Typical for Fe³⁺ in oxides quadrupole_splitting=0.7, # Moderate quadrupole splitting fwhml=0.25, # Line width amplitude=1.0, # Amplitude background=0.05, # Background ) doublet2 = moessbauer_doublet( velocity, isomer_shift=1.1, # Typical for Fe²⁺ in silicates quadrupole_splitting=2.2, # Larger quadrupole splitting fwhml=0.30, # Line width amplitude=0.8, # Amplitude background=0.05, # Background ) # Plot both doublets plt.figure() plt.plot(velocity, doublet1, label="Fe³⁺-like doublet", linewidth=2) plt.plot(velocity, doublet2, label="Fe²⁺-like doublet", linewidth=2, linestyle="--") plt.xlabel(VELOCITY_LABEL) plt.ylabel("Transmission") plt.title("Mössbauer Doublet Models") plt.xlim(-4, 4) plt.legend() plt.grid(True) plt.gca().invert_yaxis() plt.show() # Visualize the effect of changing quadrupole splitting plt.figure(figsize=(10, 6)) for qs in [0.5, 1.0, 1.5, 2.0]: doublet = moessbauer_doublet( velocity, isomer_shift=0.4, quadrupole_splitting=qs, fwhml=0.25, amplitude=1.0, ) plt.plot(velocity, doublet, label=f"QS = {qs} mm/s", linewidth=2) plt.xlabel(VELOCITY_LABEL) plt.ylabel("Transmission") plt.title("Effect of Quadrupole Splitting on Mössbauer Doublets") plt.xlim(-6, 6) plt.legend() plt.grid(True) plt.gca().invert_yaxis() plt.show()
5. Model 3: Mössbauer Sextet¶
A sextet shows six absorption peaks resulting from magnetic hyperfine splitting. This occurs in magnetically ordered materials where there is a significant magnetic field at the nucleus.
Examples: Ferromagnetic or antiferromagnetic materials like α-Fe (metallic iron), Fe₃O₄ (magnetite), α-Fe₂O₃ (hematite).
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# Create a wider velocity scale for sextet
velocity_wide = np.linspace(-12, 12, 1000)
# Generate sextet patterns for different magnetic materials
sextet_iron = moessbauer_sextet(
velocity_wide,
isomer_shift=0.0, # Metallic iron
magnetic_field=33.0, # ~33T for metallic iron at room temperature
quadrupole_shift=0.0, # No quadrupole effect in cubic structure
fwhml=0.30, # Line width
amplitude=1.0, # Amplitude
background=0.05, # Background
)
sextet_hematite = moessbauer_sextet(
velocity_wide,
isomer_shift=0.38, # Typical for Fe³⁺ in hematite
magnetic_field=51.5, # ~51.5T for hematite at room temperature
quadrupole_shift=-0.21, # Small quadrupole effect
fwhml=0.30, # Line width
amplitude=1.0, # Amplitude
background=0.05, # Background
)
# Plot sextets
plt.figure(figsize=(12, 6))
plt.plot(velocity_wide, sextet_iron, label="Metallic Iron Sextet", linewidth=2)
plt.plot(velocity_wide, sextet_hematite, label="Hematite Sextet", linewidth=2, linestyle="--")
plt.xlabel(VELOCITY_LABEL)
plt.ylabel("Transmission")
plt.title("Mössbauer Sextet Models")
plt.legend()
plt.grid(True)
plt.gca().invert_yaxis()
plt.show()
# Visualize the effect of changing magnetic field strength
plt.figure(figsize=(12, 6))
for field in [20.0, 30.0, 40.0, 50.0]:
sextet = moessbauer_sextet(
velocity_wide,
isomer_shift=0.3,
magnetic_field=field,
fwhml=0.30,
amplitude=1.0,
)
plt.plot(velocity_wide, sextet, label=f"Field = {field} T", linewidth=2)
plt.xlabel(VELOCITY_LABEL)
plt.ylabel("Transmission")
plt.title("Effect of Magnetic Field Strength on Mössbauer Sextets")
plt.legend()
plt.grid(True)
plt.gca().invert_yaxis()
plt.show()
# Create a wider velocity scale for sextet velocity_wide = np.linspace(-12, 12, 1000) # Generate sextet patterns for different magnetic materials sextet_iron = moessbauer_sextet( velocity_wide, isomer_shift=0.0, # Metallic iron magnetic_field=33.0, # ~33T for metallic iron at room temperature quadrupole_shift=0.0, # No quadrupole effect in cubic structure fwhml=0.30, # Line width amplitude=1.0, # Amplitude background=0.05, # Background ) sextet_hematite = moessbauer_sextet( velocity_wide, isomer_shift=0.38, # Typical for Fe³⁺ in hematite magnetic_field=51.5, # ~51.5T for hematite at room temperature quadrupole_shift=-0.21, # Small quadrupole effect fwhml=0.30, # Line width amplitude=1.0, # Amplitude background=0.05, # Background ) # Plot sextets plt.figure(figsize=(12, 6)) plt.plot(velocity_wide, sextet_iron, label="Metallic Iron Sextet", linewidth=2) plt.plot(velocity_wide, sextet_hematite, label="Hematite Sextet", linewidth=2, linestyle="--") plt.xlabel(VELOCITY_LABEL) plt.ylabel("Transmission") plt.title("Mössbauer Sextet Models") plt.legend() plt.grid(True) plt.gca().invert_yaxis() plt.show() # Visualize the effect of changing magnetic field strength plt.figure(figsize=(12, 6)) for field in [20.0, 30.0, 40.0, 50.0]: sextet = moessbauer_sextet( velocity_wide, isomer_shift=0.3, magnetic_field=field, fwhml=0.30, amplitude=1.0, ) plt.plot(velocity_wide, sextet, label=f"Field = {field} T", linewidth=2) plt.xlabel(VELOCITY_LABEL) plt.ylabel("Transmission") plt.title("Effect of Magnetic Field Strength on Mössbauer Sextets") plt.legend() plt.grid(True) plt.gca().invert_yaxis() plt.show()
6. Model 4: Mössbauer Octet¶
An octet pattern occurs when both magnetic hyperfine interactions and quadrupole interactions are significant, leading to eight absorption lines. This is observed in materials with complex magnetic structures and non-cubic crystal environments.
Examples: Some complex iron oxides, iron-bearing minerals with distorted crystal structures, or materials with mixed valence states.
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# Generate octet patterns
octet1 = moessbauer_octet(
velocity_wide,
isomer_shift=0.35, # Fe³⁺-like isomer shift
magnetic_field=45.0, # Strong magnetic field
quadrupole_shift=0.6, # Significant quadrupole interaction
efg_vzz=1.5e21, # Electric field gradient parameter
efg_eta=0.3, # EFG asymmetry parameter
fwhml=0.30, # Line width
amplitude=1.0, # Amplitude
background=0.05, # Background
angle_theta_phi={"theta": 0.3, "phi": 0.2}, # Orientation angles
)
octet2 = moessbauer_octet(
velocity_wide,
isomer_shift=0.28, # Different isomer shift
magnetic_field=35.0, # Different magnetic field
quadrupole_shift=0.4, # Different quadrupole shift
efg_vzz=1.2e21, # Different electric field gradient
efg_eta=0.5, # Different asymmetry
fwhml=0.35, # Line width
amplitude=0.9, # Amplitude
background=0.05, # Background
angle_theta_phi={"theta": 0.5, "phi": 0.1}, # Different orientation angles
)
# Plot octets
plt.figure(figsize=(12, 6))
plt.plot(velocity_wide, octet1, label="Octet Model 1", linewidth=2)
plt.plot(velocity_wide, octet2, label="Octet Model 2", linewidth=2, linestyle="--")
plt.xlabel(VELOCITY_LABEL)
plt.ylabel("Transmission")
plt.title("Mössbauer Octet Models")
plt.legend()
plt.grid(True)
plt.gca().invert_yaxis()
plt.show()
# Generate octet patterns octet1 = moessbauer_octet( velocity_wide, isomer_shift=0.35, # Fe³⁺-like isomer shift magnetic_field=45.0, # Strong magnetic field quadrupole_shift=0.6, # Significant quadrupole interaction efg_vzz=1.5e21, # Electric field gradient parameter efg_eta=0.3, # EFG asymmetry parameter fwhml=0.30, # Line width amplitude=1.0, # Amplitude background=0.05, # Background angle_theta_phi={"theta": 0.3, "phi": 0.2}, # Orientation angles ) octet2 = moessbauer_octet( velocity_wide, isomer_shift=0.28, # Different isomer shift magnetic_field=35.0, # Different magnetic field quadrupole_shift=0.4, # Different quadrupole shift efg_vzz=1.2e21, # Different electric field gradient efg_eta=0.5, # Different asymmetry fwhml=0.35, # Line width amplitude=0.9, # Amplitude background=0.05, # Background angle_theta_phi={"theta": 0.5, "phi": 0.1}, # Different orientation angles ) # Plot octets plt.figure(figsize=(12, 6)) plt.plot(velocity_wide, octet1, label="Octet Model 1", linewidth=2) plt.plot(velocity_wide, octet2, label="Octet Model 2", linewidth=2, linestyle="--") plt.xlabel(VELOCITY_LABEL) plt.ylabel("Transmission") plt.title("Mössbauer Octet Models") plt.legend() plt.grid(True) plt.gca().invert_yaxis() plt.show()
7. Comparison of All Mössbauer Models¶
Let's compare all four models side by side to see the progression in complexity:
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# Create a figure with 2x2 grid for all models
fig = plt.figure(figsize=(14, 10))
gs = GridSpec(2, 2, figure=fig)
# Singlet plot
ax1 = fig.add_subplot(gs[0, 0])
singlet = moessbauer_singlet(velocity, isomer_shift=0.2, fwhml=0.25, amplitude=1.0)
ax1.plot(velocity, singlet, "b-", linewidth=2)
ax1.set_title("Mössbauer Singlet")
ax1.set_xlabel(VELOCITY_LABEL)
ax1.set_ylabel("Transmission")
ax1.set_xlim(-4, 4)
ax1.invert_yaxis()
ax1.grid(True)
# Doublet plot
ax2 = fig.add_subplot(gs[0, 1])
doublet = moessbauer_doublet(velocity, isomer_shift=0.3, quadrupole_splitting=1.0, fwhml=0.25, amplitude=1.0)
ax2.plot(velocity, doublet, "g-", linewidth=2)
ax2.set_title("Mössbauer Doublet")
ax2.set_xlabel(VELOCITY_LABEL)
ax2.set_ylabel("Transmission")
ax2.set_xlim(-4, 4)
ax2.invert_yaxis()
ax2.grid(True)
# Sextet plot
ax3 = fig.add_subplot(gs[1, 0])
sextet = moessbauer_sextet(velocity_wide, isomer_shift=0.0, magnetic_field=33.0, fwhml=0.25, amplitude=1.0)
ax3.plot(velocity_wide, sextet, "r-", linewidth=2)
ax3.set_title("Mössbauer Sextet")
ax3.set_xlabel(VELOCITY_LABEL)
ax3.set_ylabel("Transmission")
ax3.set_xlim(-12, 12)
ax3.invert_yaxis()
ax3.grid(True)
# Octet plot
ax4 = fig.add_subplot(gs[1, 1])
octet = moessbauer_octet(
velocity_wide, isomer_shift=0.35, magnetic_field=45.0, quadrupole_shift=0.6,
efg_vzz=1.5e21, efg_eta=0.3, fwhml=0.25, amplitude=1.0,
)
ax4.plot(velocity_wide, octet, "c-", linewidth=2)
ax4.set_title("Mössbauer Octet")
ax4.set_xlabel(VELOCITY_LABEL)
ax4.set_ylabel("Transmission")
ax4.set_xlim(-12, 12)
ax4.invert_yaxis()
ax4.grid(True)
plt.tight_layout()
plt.show()
# Create a figure with 2x2 grid for all models fig = plt.figure(figsize=(14, 10)) gs = GridSpec(2, 2, figure=fig) # Singlet plot ax1 = fig.add_subplot(gs[0, 0]) singlet = moessbauer_singlet(velocity, isomer_shift=0.2, fwhml=0.25, amplitude=1.0) ax1.plot(velocity, singlet, "b-", linewidth=2) ax1.set_title("Mössbauer Singlet") ax1.set_xlabel(VELOCITY_LABEL) ax1.set_ylabel("Transmission") ax1.set_xlim(-4, 4) ax1.invert_yaxis() ax1.grid(True) # Doublet plot ax2 = fig.add_subplot(gs[0, 1]) doublet = moessbauer_doublet(velocity, isomer_shift=0.3, quadrupole_splitting=1.0, fwhml=0.25, amplitude=1.0) ax2.plot(velocity, doublet, "g-", linewidth=2) ax2.set_title("Mössbauer Doublet") ax2.set_xlabel(VELOCITY_LABEL) ax2.set_ylabel("Transmission") ax2.set_xlim(-4, 4) ax2.invert_yaxis() ax2.grid(True) # Sextet plot ax3 = fig.add_subplot(gs[1, 0]) sextet = moessbauer_sextet(velocity_wide, isomer_shift=0.0, magnetic_field=33.0, fwhml=0.25, amplitude=1.0) ax3.plot(velocity_wide, sextet, "r-", linewidth=2) ax3.set_title("Mössbauer Sextet") ax3.set_xlabel(VELOCITY_LABEL) ax3.set_ylabel("Transmission") ax3.set_xlim(-12, 12) ax3.invert_yaxis() ax3.grid(True) # Octet plot ax4 = fig.add_subplot(gs[1, 1]) octet = moessbauer_octet( velocity_wide, isomer_shift=0.35, magnetic_field=45.0, quadrupole_shift=0.6, efg_vzz=1.5e21, efg_eta=0.3, fwhml=0.25, amplitude=1.0, ) ax4.plot(velocity_wide, octet, "c-", linewidth=2) ax4.set_title("Mössbauer Octet") ax4.set_xlabel(VELOCITY_LABEL) ax4.set_ylabel("Transmission") ax4.set_xlim(-12, 12) ax4.invert_yaxis() ax4.grid(True) plt.tight_layout() plt.show()
8. Simulating Complex Mössbauer Spectra with Multiple Components¶
Real Mössbauer spectra often contain multiple components from different iron sites or different iron-bearing phases. Let's simulate a complex spectrum containing multiple components:
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# Simulate a complex spectrum with multiple components
velocity_complex = np.linspace(-12, 12, 1000)
# Component 1: Fe3+ doublet (e.g., from a silicate mineral)
fe3_doublet = moessbauer_doublet(
velocity_complex,
isomer_shift=0.35,
quadrupole_splitting=0.7,
fwhml=0.30,
amplitude=0.6,
background=0.0,
)
# Component 2: Fe2+ doublet (e.g., from another mineral phase)
fe2_doublet = moessbauer_doublet(
velocity_complex,
isomer_shift=1.15,
quadrupole_splitting=2.2,
fwhml=0.35,
amplitude=0.4,
background=0.0,
)
# Component 3: Magnetic sextet (e.g., from hematite)
hematite_sextet = moessbauer_sextet(
velocity_complex,
isomer_shift=0.38,
magnetic_field=51.5,
quadrupole_shift=-0.21,
fwhml=0.33,
amplitude=0.7,
background=0.0,
)
# Add a constant background
background = np.ones_like(velocity_complex) * 0.05
# Combine all components
complex_spectrum = fe3_doublet + fe2_doublet + hematite_sextet + background
# Add some noise to simulate experimental data
rng = np.random.default_rng(42) # For reproducibility
noise = rng.normal(0, 0.01, velocity_complex.shape)
noisy_spectrum = complex_spectrum + noise
# Plot the complex spectrum and its components
plt.figure(figsize=(12, 8))
# Plot individual components
plt.plot(velocity_complex, fe3_doublet + 0.05, "g-", linewidth=1.5, label="Fe³⁺ Doublet")
plt.plot(velocity_complex, fe2_doublet + 0.05, "m-", linewidth=1.5, label="Fe²⁺ Doublet")
plt.plot(velocity_complex, hematite_sextet + 0.05, "r-", linewidth=1.5, label="Hematite Sextet")
# Plot the combined spectrum
plt.plot(velocity_complex, noisy_spectrum, "k.", markersize=1, label="Noisy Data")
plt.plot(velocity_complex, complex_spectrum, "b-", linewidth=2, label="Combined Spectrum")
plt.xlabel(VELOCITY_LABEL)
plt.ylabel("Transmission")
plt.title("Complex Mössbauer Spectrum with Multiple Components")
plt.legend()
plt.grid(True)
plt.gca().invert_yaxis()
plt.show()
# Simulate a complex spectrum with multiple components velocity_complex = np.linspace(-12, 12, 1000) # Component 1: Fe3+ doublet (e.g., from a silicate mineral) fe3_doublet = moessbauer_doublet( velocity_complex, isomer_shift=0.35, quadrupole_splitting=0.7, fwhml=0.30, amplitude=0.6, background=0.0, ) # Component 2: Fe2+ doublet (e.g., from another mineral phase) fe2_doublet = moessbauer_doublet( velocity_complex, isomer_shift=1.15, quadrupole_splitting=2.2, fwhml=0.35, amplitude=0.4, background=0.0, ) # Component 3: Magnetic sextet (e.g., from hematite) hematite_sextet = moessbauer_sextet( velocity_complex, isomer_shift=0.38, magnetic_field=51.5, quadrupole_shift=-0.21, fwhml=0.33, amplitude=0.7, background=0.0, ) # Add a constant background background = np.ones_like(velocity_complex) * 0.05 # Combine all components complex_spectrum = fe3_doublet + fe2_doublet + hematite_sextet + background # Add some noise to simulate experimental data rng = np.random.default_rng(42) # For reproducibility noise = rng.normal(0, 0.01, velocity_complex.shape) noisy_spectrum = complex_spectrum + noise # Plot the complex spectrum and its components plt.figure(figsize=(12, 8)) # Plot individual components plt.plot(velocity_complex, fe3_doublet + 0.05, "g-", linewidth=1.5, label="Fe³⁺ Doublet") plt.plot(velocity_complex, fe2_doublet + 0.05, "m-", linewidth=1.5, label="Fe²⁺ Doublet") plt.plot(velocity_complex, hematite_sextet + 0.05, "r-", linewidth=1.5, label="Hematite Sextet") # Plot the combined spectrum plt.plot(velocity_complex, noisy_spectrum, "k.", markersize=1, label="Noisy Data") plt.plot(velocity_complex, complex_spectrum, "b-", linewidth=2, label="Combined Spectrum") plt.xlabel(VELOCITY_LABEL) plt.ylabel("Transmission") plt.title("Complex Mössbauer Spectrum with Multiple Components") plt.legend() plt.grid(True) plt.gca().invert_yaxis() plt.show()
9. Fitting a Mössbauer Spectrum Using SpectraFit¶
Now let's demonstrate how to fit a Mössbauer spectrum using the SpectraFit framework. We'll use the simulated data from the previous section as our "experimental" data.
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# Prepare the data for fitting
x_data = velocity_complex
y_data = noisy_spectrum
# Convert to DataFrame for SpectraFit notebook plugin
moessbauer_data = pd.DataFrame({
"Velocity": x_data, # mm/s
"Transmission": y_data,
})
# Import axis configuration models
from spectrafit.api.notebook_model import XAxisAPI
from spectrafit.api.notebook_model import YAxisAPI
# Initialize the SpectraFitNotebook with our Mössbauer data and conventional axis configuration
spn = nb.SpectraFitNotebook(
df=moessbauer_data,
x_column="Velocity",
y_column="Transmission",
fname="moessbauer_example",
xaxis_title=XAxisAPI(name="velocity", unit="mm s<sup>-1</sup>"),
yaxis_title=YAxisAPI(name="relative transmission", unit=None, invert=True)
)
# Prepare the data for fitting x_data = velocity_complex y_data = noisy_spectrum # Convert to DataFrame for SpectraFit notebook plugin moessbauer_data = pd.DataFrame({ "Velocity": x_data, # mm/s "Transmission": y_data, }) # Import axis configuration models from spectrafit.api.notebook_model import XAxisAPI from spectrafit.api.notebook_model import YAxisAPI # Initialize the SpectraFitNotebook with our Mössbauer data and conventional axis configuration spn = nb.SpectraFitNotebook( df=moessbauer_data, x_column="Velocity", y_column="Transmission", fname="moessbauer_example", xaxis_title=XAxisAPI(name="velocity", unit="mm s-1"), yaxis_title=YAxisAPI(name="relative transmission", unit=None, invert=True) )
Note: Initializing the SpectraFit environment and loading has to be separate from the model fitting. The model fitting process is done in a separate cell to ensure that the history is preserved correctly and can be shown in RUN chart.
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# Define initial model for fitting using the solver_model approach
initial_model = [
# Component 1: Fe³⁺ doublet
{
"moessbauerdoublet": {
"amplitude": {"value": 1.5, "min": 0.0, "max": 1.0, "vary": True},
"isomershift": {"value": 0.3, "min": 0.0, "max": 0.7, "vary": True},
"quadrupolesplitting": {"value": 0.6, "min": 0.3, "max": 1.0, "vary": True},
"fwhml": {"value": 0.3, "min": 0.2, "max": 0.4, "vary": True},
"center": {"value": 0.0, "min": -0.2, "max": 0.2, "vary": True},
},
},
# Component 2: Fe²⁺ doublet
{
"moessbauerdoublet": {
"amplitude": {"value": 0.3, "min": 0.0, "max": 1.0, "vary": True},
"isomershift": {"value": 1.0, "min": 0.8, "max": 1.3, "vary": True},
"quadrupolesplitting": {"value": 2.0, "min": 1.5, "max": 2.5, "vary": True},
"fwhml": {"value": 0.3, "min": 0.2, "max": 0.5, "vary": True},
"center": {"value": 0.0, "min": -0.2, "max": 0.2, "vary": True},
},
},
# Component 3: Hematite sextet
{
"moessbauersextet": {
"amplitude": {"value": 0.6, "min": 0.3, "max": 1.0, "vary": True},
"isomershift": {"value": 0.4, "min": 0.2, "max": 0.6, "vary": True},
"magneticfield": {"value": 50.0, "min": 45.0, "max": 55.0, "vary": True},
"quadrupoleshift": {"value": -0.2, "min": -0.4, "max": 0.0, "vary": True},
"fwhml": {"value": 0.3, "min": 0.2, "max": 0.5, "vary": True},
"center": {"value": 0.0, "min": -0.2, "max": 0.2, "vary": True},
},
},
]
# Define optimizer and minimizer settings (similar to what was in the parameters dictionary)
optimizer_settings = {
"max_nfev": 1000,
"method": "leastsq",
}
minimizer_settings = {
"nan_policy": "propagate",
"calc_covar": True,
}
# Run the fit using solver_model approach
spn.solver_model(
initial_model=initial_model,
show_peaks=True, # Show individual peaks
show_plot=True, # Display the fit results?
)
# Define initial model for fitting using the solver_model approach initial_model = [ # Component 1: Fe³⁺ doublet { "moessbauerdoublet": { "amplitude": {"value": 1.5, "min": 0.0, "max": 1.0, "vary": True}, "isomershift": {"value": 0.3, "min": 0.0, "max": 0.7, "vary": True}, "quadrupolesplitting": {"value": 0.6, "min": 0.3, "max": 1.0, "vary": True}, "fwhml": {"value": 0.3, "min": 0.2, "max": 0.4, "vary": True}, "center": {"value": 0.0, "min": -0.2, "max": 0.2, "vary": True}, }, }, # Component 2: Fe²⁺ doublet { "moessbauerdoublet": { "amplitude": {"value": 0.3, "min": 0.0, "max": 1.0, "vary": True}, "isomershift": {"value": 1.0, "min": 0.8, "max": 1.3, "vary": True}, "quadrupolesplitting": {"value": 2.0, "min": 1.5, "max": 2.5, "vary": True}, "fwhml": {"value": 0.3, "min": 0.2, "max": 0.5, "vary": True}, "center": {"value": 0.0, "min": -0.2, "max": 0.2, "vary": True}, }, }, # Component 3: Hematite sextet { "moessbauersextet": { "amplitude": {"value": 0.6, "min": 0.3, "max": 1.0, "vary": True}, "isomershift": {"value": 0.4, "min": 0.2, "max": 0.6, "vary": True}, "magneticfield": {"value": 50.0, "min": 45.0, "max": 55.0, "vary": True}, "quadrupoleshift": {"value": -0.2, "min": -0.4, "max": 0.0, "vary": True}, "fwhml": {"value": 0.3, "min": 0.2, "max": 0.5, "vary": True}, "center": {"value": 0.0, "min": -0.2, "max": 0.2, "vary": True}, }, }, ] # Define optimizer and minimizer settings (similar to what was in the parameters dictionary) optimizer_settings = { "max_nfev": 1000, "method": "leastsq", } minimizer_settings = { "nan_policy": "propagate", "calc_covar": True, } # Run the fit using solver_model approach spn.solver_model( initial_model=initial_model, show_peaks=True, # Show individual peaks show_plot=True, # Display the fit results? )
/home/runner/work/spectrafit/spectrafit/spectrafit/report.py:237: UserWarning: ## WARNING ######################### Uncertainties could not be estimated #################################### /home/runner/work/spectrafit/spectrafit/spectrafit/report.py:237: UserWarning: ## WARNING ######################################################################################## The parameter 'moessbauerdoublet_fwhml_2' is at its boundary and uncertainties cannot be estimated! ################################################################################################### /home/runner/work/spectrafit/spectrafit/spectrafit/report.py:237: UserWarning: ## WARNING #################################################################################################### The parameter 'moessbauersextet_magneticfield_3' is at its initial value and uncertainties cannot be estimated! ###############################################################################################################
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10. Conclusion¶
This notebook has demonstrated the Mössbauer spectroscopy models available in SpectraFit:
- Singlet - For materials with no quadrupole or magnetic splitting
- Doublet - For materials with quadrupole splitting
- Sextet - For materials with magnetic hyperfine splitting
- Octet - For materials with both magnetic and quadrupole interactions
These models can be used individually or combined to analyze complex Mössbauer spectra from various iron-bearing materials.
The key parameters that can be extracted from Mössbauer spectra include:
- Isomer shift (δ) - Related to oxidation state and coordination
- Quadrupole splitting (ΔEQ) - Related to site symmetry and valence state
- Magnetic hyperfine field (Bhf) - Related to magnetic ordering
- Line widths - Related to local environments and dynamics
SpectraFit provides a flexible framework for fitting these models to experimental data and extracting physically meaningful parameters. The solver_model approach from the notebook plugin offers a particularly streamlined workflow for efficient data analysis, parameter extraction, and result visualization.