Introduction¶
Here we present an open-source Python library which focuses on fitting the neutron resonance signal for neutron imaging measurements. In this package, by defining the sample information such as elements and thickness in the neutron path, one can extract elemental/isotopic information of the sample. Various sample types such as layers of single elements (Ag, Co, etc. in solid form), chemical compounds (UO2, Gd2O3, etc.), or even multiple layers of both types.
The energy dependent cross-section data used in this library are from National Nuclear Data Center, a published online database. Evaluated Nuclear Data File (ENDF/B) [1] is currently supported and more evaluated databases will be added in future.
Python packages used are: SciPy [2], NumPy [3], Matplotlib [4], Pandas [5] Periodictable [6], lmfit [7] and ImagingReso [8].
Statement of need¶
Neutron imaging is a powerful tool to characterize material non-destructively. And based on the unique resonance features, it is feasible to identify elements and/or isotopes resonance with incident neutrons. However, a dedicated user-friendly fitting tool for resonance imaging is missing, and ResoFit we presented here could fill this gap.
Installation instructions¶
Install ResoFit by typing the following command in Terminal:
pip install ResoFit
or by typing the following command under downloaded directory in Terminal:
python setup.py
Example usage¶
Example of usage is presented in tutorial.ipynb under /notebooks
directory.
Calculation algorithm¶
The neutron transmission calculation algorithm of neutron transmission T(E), is base on Beer-lambert law [9]-[10]:
\(N_i\) : number of atoms per unit volume of element \(i\),
\(d_i\) : effective thickness along the neutron path of element \(i\),
\(\sigma_{ij}\left( E \right)\) : energy-dependent neutron total cross-section for the isotope \(j\) of element \(i\),
\(A_{ij}\) : abundance for the isotope \(j\) of element \(i\).
For solid materials the number of atoms per unit volume can be calculated from:
\(N_A\) : Avogadro’s number,
\(C_i\) : molar concentration of element \(i\),
\(\rho_i\) : density of the element \(i\),
\(m_{ij}\) : atomic mass values for the isotope \(j\) of element \(i\).
References¶
[1] M. B. Chadwick et al., “ENDF/B-VII.1 Nuclear Data for Science and Technology: Cross Sections, Covariances, Fission Product Yields and Decay Data,” Nuclear Data Sheets, vol. 112, no. 12, pp. 2887–2996, Dec. 2011.
[2] T. E. Oliphant, “SciPy: Open Source Scientific Tools for Python,” Computing in Science and Engineering, vol. 9. pp. 10–20, 2007.
[3] S. van der Walt et al., “The NumPy Array: A Structure for Efficient Numerical Computation,” Computing in Science & Engineering, vol. 13, no. 2, pp. 22–30, Mar. 2011.
[4] J. D. Hunter, “Matplotlib: A 2D Graphics Environment,” Computing in Science & Engineering, vol. 9, no. 3, pp. 90–95, May 2007.
[5] W. McKinney, “Data Structures for Statistical Computing in Python,” in Proceedings of the 9th Python in Science Conference, 2010, pp. 51–56.
[6] P. A. Kienzle, “Periodictable V1.5.0,” Journal of Open Source Software, Jan. 2017.
[7] M. Newville, A. Nelson, A. Ingargiola, T. Stensitzki, R. Otten, D. Allan, Michał, Glenn, Y. Ram, MerlinSmiles, L. Li, G. Pasquevich, C. Deil, D.M. Fobes, Stuermer, A. Beelen, O. Frost, A. Stark, T. Spillane, S. Caldwell, A. Polloreno, stonebig, P.A. Brodtkorb, N. Earl, colgan, R. Clarken, K. Anagnostopoulos, B. Gamari, A. Almarza, lmfit/lmfit-py 0.9.7, (2017). doi:10.5281/zenodo.802298.
[8] Y. Zhang and J. C. Bilheux, “ImagingReso”.
[9] M. Ooi et al., “Neutron Resonance Imaging of a Au-In-Cd Alloy for the JSNS,” Physics Procedia, vol. 43, pp. 337–342, 2013.
[10] A. S. Tremsin et al., “Non-Contact Measurement of Partial Gas Pressure and Distribution of Elemental Composition Using Energy-Resolved Neutron Imaging,” AIP Advances, vol. 7, no. 1, p. 15315, 2017.