Introduction to neutron reflectometry fitting

Introduction to neutron reflectometry fitting

The aim of this course, and the companion lecture, are to give an introduction to the following subjects:

  • the Fourier transform and how a Born approximation approach may be used to analyse neutron reflectometry data;

  • the logic of model-dependent analysis;

  • neutron reflectometry “slab models” and their traditional parameterisation;

  • reparameterisation of these models to include chemical and physical insight; and

  • the process and problems associated with fitting in a model-dependent analysis procedure.

It is assumed that this reader has been introduced to the technique of neutron reflectometry, such as what this technique can be used to study and the data collection methodology.

This material was developed by Andrew McCluskey from the European Spallation Source. If you have any questions, please get in touch. Thanks to Drs Maximilian Skoda, Andrew Caruana, Stephen Hall, and Andrew Nelson for feedback on this material.


In this course, we make use of the Python programming language heavily to show mathematics and plot figures. The aim is that the course should not require knowledge of Python to understand the content. If you are not comfortable with Python, feel free to skip the code blocks, but make sure to pay attention to the plots that are produced.


Some particularly useful books and papers for reflectometry analysis, and data analysis in general include:

  • Elementary Scattering Theory: For X-ray and Neutron Users by Devinder Sivia [Siv11];

  • Current Opinion in Colloid & Interface Science, 42, 2019 covers a range of applications in soft and biological matter including [Lak19, Sko19, WC19];

  • Some interesting reviews of magnetic reflectometry analysis include [FM05, TZ07, ZTBT07]; and

  • Data Analysis: A Bayesian Tutorial by Devinder Sivia and John Skilling [SJ06].

This list is not exhaustive and we suggest searching for and reading relevant work in your field once you understand the basics.


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M. Björck. Fitting with differential evolution: an introduction and evaluation. J. Appl. Crystallogr., 44(6):1198–1204, 2011. doi:10.1107/s0021889811041446.


R. A. Campbell, Y. Saaka, Y. Shao, Y. Gerelli, R. Cubitt, E. Nazaruk, D. Matyszewska, and M. J. Lawrence. Structure of surfactant and phospholipid monolayers at the air/water interface modeled from neutron reflectivity data. J. Colloid Interface Sci., 531:98–108, 2018. doi:10.1016/j.jcis.2018.07.022.


M. R. Fitzsimmons and C. F. Majkrzak. Applications of polarized neutron reflectometry to studies of artificially structured magnetic materials. In Y. Zhou, editor, Neutron, X-Rays and Light. Scattering Methods Applied to Soft Condensed Matter, pages 107–155. Springer, 2005.


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J. H. Lakey. Recent advances in neutron reflectivity studies of biological membranes. Curr. Opin. Colloid Interface Sci., 42:33–40, 2019. doi:10.1016/j.cocis.2019.02.012.


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A. R. McCluskey, A. Sanchez-Fernandez, K. J. Edler, S. C. Parker, A. J. Jackson, R. A. Campbell, and T. Arnold. Bayesian determination of the effect of a deep eutectic solvent on the structure of lipid monolayers. Phys. Chem. Chem. Phys., 21(11):6133–6141, 2019. doi:10.1039/c9cp00203k.


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D. S. Sivia and Skilling J. Data Analysis: A Bayesian tutorial. Oxford University Press, 2 edition, 2006. ISBN 978-0-19-856832-2.


M. W. A. Skoda. Recent developments in the application of x-ray and neutron reflectivity to soft-matter systems. Curr. Opin. Colloid Interface Sci., 42:41–54, 2019. doi:10.1016/j.cocis.2019.03.003.


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