Iron Powder Example

This example demonstrates how to use nbragg to analyze neutron transmission through an iron powder sample.

Dataset Overview

The iron powder example showcases the analysis of Bragg edges in a polycrystalline iron sample. We’ll walk through the entire process from data loading to fitting and interpretation.

Data Preparation

First, load the transmission data and use the .plot method to plot and inspect the data.

import nbragg

# Load transmission data
data = nbragg.Data.from_transmission("iron_powder.csv")
data.plot()

The user can also inspect the data in a table format by calling:

data.table

	wavelength	trans	err
0	0.501098	0.148315	0.004449
1	0.505493	0.147728	0.004432
2	0.509889	0.147725	0.004432
3	0.514284	0.148043	0.004441
4	0.518680	0.148369	0.004451

Cross-Section Configuration

We’ll use the NCrystal cross-section for alpha-iron and use the .plot method to visualize the cross-section:

# Define iron cross-section
xs = nbragg.CrossSection.from_material("Fe_sg229_Iron-alpha.ncmat")
xs.plot()

Model Creation and Fitting

Create a transmission model with background and response variations:

# Create transmission model
model = nbragg.TransmissionModel(
    xs,
    vary_background=True,
    vary_response=True
)

# Perform fitting
result = model.fit(data)

Visualization

Display the fit results using the command:

result.plot()

To visualize the instrumental response after fitting, use:

model.response.plot(params=result.params)

Fit Summary

In a Jupyter Notebook, typing result displays the following fit summary as an interactive HTML table:

Fit Result

Model: Model(transmission)

Fit Statistics

Fitting Method	leastsq
# Function Evals	57
# Data Points	1138
# Variables	7
Chi-square	1728.82713
Reduced Chi-square	1.52858279
Akaike Info Criterion	489.878468
Bayesian Info Crit.	525.137662
R-squared	-345.832688

Parameters

Name	Value	Standard Error	Relative Error	Initial Value	Min	Max	Vary
thickness	1.97199144	0.02039823	(1.03%)	1.0	0.0	5.0	True
norm	0.78300304	0.00980444	(1.25%)	1.0	0.1	10.0	True
temp	300.000000	0.00000000	(0.00%)	300.0	77.0	1000.0	False
α1	2.58192159	0.06909434	(2.68%)	3.67	0.001	1000.0	True
β1	3.82826196	0.12721525	(3.32%)	3.06	0.001	1000.0	True
b0	-0.0221435	0.00722197	(32.61%)	0.0	-1e6	1e6	True
b1	0.00684805	0.00222445	(32.48%)	0.0	-1e6	1e6	True
b2	0.03639802	0.00512610	(14.08%)	0.0	-1e6	1e6	True

Correlations

Parameter 1	Parameter 2	Correlation
b0	b1	-0.9968
thickness	norm	+0.9825
b0	b2	-0.9725
b1	b2	+0.9670
α1	β1	+0.6106
norm	b0	+0.5964
norm	b1	-0.5791
thickness	b0	+0.5467
thickness	b1	-0.5268
norm	b2	-0.4251
thickness	b2	-0.3591
α1	b2	+0.1194
α1	b1	+0.1181
α1	b0	-0.1071

Key Observations

The iron powder sample shows multiple Bragg edges
Variations in background and instrumental response are accounted for
The model provides insights into material structure

Additional Notes

Ensure you have the correct NCrystal material file
Calibrate your instrumental response carefully
The quality of fitting depends on data resolution