Open Access

diffpy.morph: Python tools for model-independent comparisons between sets of one-dimensional functions

Andrew Yang ^1,*, Christopher L. Farrow ¹, Pavol Juhás ², Luis Kitsu Iglesias ^3,4, Chia-Hao Liu¹, Samuel D. Marks ^5,6, Vivian R. K. Wall⁷, Joshua Safin ⁸, Sean M. Drewry⁸ et al.

Caden Myers ¹, Dillon F. Hanlon ⁹, Nicholas Leonard ⁹, Cedomir Petrovic ^10,†, Ahhyun Jeong ¹¹, Dmitri V. Talapin ¹¹, Linda F. Nazar ¹², Haidong Zhou ¹³, Samuel W. Teitelbaum⁹, Tim B. van Driel ¹⁴, Soham Banerjee¹, Emil S. Bozin ¹⁵, Michael F. Toney^4,6,16, Katharine Page ^8,17, Naomi S. Ginsberg^{7,18,19,20,21}, and Simon J. L. Billinge ^1,‡,§

¹Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA
²Google Research, Google, Mountain View, California 94043, USA
³Electrochemical Energy Systems Laboratory, Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland
⁴Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, Colorado 80309, USA
⁵Advanced Photon Source, Argonne National Laboratory, Lemont, Illinois 60439, USA
⁶Materials Science and Engineering Program, University of Colorado Boulder, Boulder, Colorado 80309, USA
⁷Department of Chemistry, University of California, Berkeley, California 94720, USA
⁸Department of Materials Science and Engineering, The University of Tennessee, Knoxville, Tennessee 37996, USA
⁹Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
¹⁰Brookhaven National Laboratory, Upton, New York 11973, USA
¹¹Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA
¹²Department of Chemistry, University of Waterloo, Waterloo, Canada ON N2L 3G1
¹³Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996, USA
¹⁴SLAC National Accelerator Laboratory, Stanford University, Menlo Park, California 94025, USA
¹⁵Center for Solid State Physics and New Materials, Institute of Physics Belgrade, 11080 Belgrade, Serbia
¹⁶Renewable and Sustainable Energy Institute, University of Colorado Boulder, Boulder, Colorado 80309, USA
¹⁷Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
¹⁸Department of Physics, University of California, Berkeley, California 94720, USA
¹⁹Molecular Biophysics and Integrated Bioimaging Division and Materials Sciences and Chemical Sciences Divisions, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
²⁰Kavli Energy NanoSciences Institute, University of California, Berkeley, California 94720, USA
²¹STROBE, NSF Science & Technology Center, University of California, Berkeley, California 94720, USA

^*Present address: Department of Applied Physics and Materials Science, California Institute of Technology, Pasadena, California 91125, USA.
^†Present address: Shanghai Key Laboratory of Material Frontiers Research in Extreme Environments (MFree), Shanghai Advanced Research in Physical Sciences (SHARPS), Shanghai 201203, People's Republic of China.
^‡Contact author: sbillinge@ucsb.edu
^§Present address: Materials Department, University of California, Santa Barbara, California 93106, USA.

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Phys. Rev. Materials 10, 113801 – Published 5 November, 2026

DOI: https://doi.org/10.1103/t39r-v3lx

Abstract

diffpy.morph addresses a need to gain scientific insights from one-dimensional (1D) scientific spectra in model-independent ways. A powerful approach for this is to take differences between pairs of spectra and look for meaningful changes that might indicate underlying chemical, structural, or other modifications. The challenge is that the difference curve may contain uninteresting differences such as experimental inconsistencies and benign physical changes such as the effects of thermal expansion. diffpy.morph allows researchers to apply simple transformations, or “morphs,” to one of the datasets to remove the unwanted differences, revealing, when they are present, nontrivial differences. diffpy.morph is an open-source Python package available on the Python Package Index and conda-forge. Here, we describe its functionality and apply it to solve a range of experimental challenges on diffraction and pair distribution function data from x-rays and neutrons, though we note that it may be applied to any 1D function in principle.

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References (63)

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Phys. Rev. Materials 10, 113801– Published 5 November, 2026

Vol. 10, Iss. 11 — November 2026

Received 1 February 2026
Accepted 22 July 2026

DOI: https://doi.org/10.1103/t39r-v3lx

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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diffpy.morph: Python tools for model-independent comparisons between sets of one-dimensional functions

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