diffpy.morph: Python tools for model independent comparisons between sets of 1D functions

diffpy$.$morph addresses a need to gain scientific insights from 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, non-trivial 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 PDF data from x-rays and neutrons, though we note that it may be applied to any 1D function in principle.

💡 Research Summary

The paper introduces diffpy.morph, an open‑source Python package designed to compare one‑dimensional scientific spectra in a model‑independent manner. The central problem addressed is that simple subtraction of two spectra (e.g., PDFs, I(Q) curves) often yields difference curves dominated by trivial effects such as thermal expansion, thermal smearing, or experimental inconsistencies, which can mask the scientifically interesting changes associated with structural or chemical transformations.

Core Concept
diffpy.morph applies a sequence of user‑defined “morphs” – simple parametric transformations – to one of the datasets before subtraction. The three basic morphs are:

1. Stretch – uniformly rescales the independent variable (r or Q) by a factor (1 + η)⁻¹, compensating for isotropic lattice expansion or contraction.
2. Scale – multiplies the entire intensity by a constant s, correcting for differences in incident flux, detector efficiency, or sample thickness.
3. Smear – convolves the radial distribution function with a Gaussian of variance σ², mimicking the broadening caused by increased thermal motion.

These transformations are applied via linear interpolation so that data measured on different grids can be compared directly. The morph parameters (η, s, σ) are optimized automatically by minimizing the profile‑weighted agreement factor Rw or maximizing the Pearson correlation coefficient (PCC) between the morphed spectrum and a target spectrum. The optimization uses standard non‑linear least‑squares algorithms (e.g., Levenberg‑Marquardt) provided by SciPy.

Software Architecture

• File handling: Supports common column‑based formats (.xy, .dat, .chi, .gr) with optional headers.
• Grid alignment: Performs linear interpolation to a common r or Q grid before morphing.
• CLI and API: A command‑line interface (diffpy-morph) and a Python module (diffpy.morph) allow both interactive use and integration into automated workflows.
• Visualization: Generates plots of original, morphed, and difference curves, as well as parameter evolution.
• Extensibility: Morph chains can be defined in JSON/YAML, enabling reproducible pipelines.

Demonstrations and Validation

1. Detecting Structural Phase Transitions – PDFs of IrTe₂, Rh‑substituted IrTe₂, and Pt‑substituted IrTe₂ measured at 10 K and 300 K were compared. Without morphing, Rw values (0.5–0.6) were too large to infer any transition. Applying stretch, scale, and smear reduced Rw to <0.05 and flattened the difference curve, revealing that only the pure IrTe₂ sample undergoes a phase transition, while 5 % Pt substitution suppresses it. The same analysis on I(Q) data gave consistent conclusions.

2. Locating Transition Temperature – A temperature series of PDFs (10 K–300 K) for IrTe₂ was analyzed by morphing the lowest‑temperature PDF to each higher‑temperature PDF. The post‑morph Rw and PCC show a clear change in slope between 263 K and 283 K, matching the known triclinic‑to‑trigonal transition around 280 K. This demonstrates that diffpy.morph can pinpoint transition windows without any structural refinement.

3. Comparison with Conventional Refinement – PDFs of SrFe₂As₂ (150 K–246 K) were processed similarly. A sharp drop in Rw and rise in PCC occur between 192 K and 198 K, the temperature range of the tetragonal‑to‑orthorhombic transition reported in the literature. The stretch parameter η remains constant across this interval, indicating that the change is not simple thermal expansion but a genuine symmetry change.

4. Extracting Material Properties – By fitting stretch morphs across a temperature series, the linear thermal expansion coefficient α can be obtained directly from η(T). For nearly harmonic materials, the temperature derivative of α yields an estimate of the Debye temperature, providing a route to thermodynamic parameters without any explicit lattice model.

5. Correcting Experimental Inconsistencies – The authors demonstrate morphing low‑Q‑max data to match a high‑Q‑max reference, enabling consistent high‑throughput data reduction and facilitating the construction of large PDF databases.

Broader Applicability
Although the examples focus on neutron and X‑ray PDF data, the authors emphasize that any 1D function can be treated similarly. Potential extensions include subtracting hydrogen contributions from neutron density‑of‑states spectra, or correcting illumination differences in 2‑D image histograms for computer‑vision tasks.

Key Advantages

• Model independence: No need for crystallographic models or refinement software to detect subtle changes.
• Speed: Morphing and optimization are computationally cheap, suitable for real‑time analysis during data collection.
• Open source & reproducibility: BSD‑licensed, available on PyPI and conda‑forge, with version‑controlled parameter files.
• Flexibility: Users can define arbitrary morph chains, combine with other analysis tools, or embed in automated pipelines.

Conclusion
diffpy.morph provides a powerful, accessible framework for extracting scientifically relevant differences from 1D spectra by systematically removing trivial, well‑understood variations through simple parametric transformations. Its ability to reveal hidden structural transitions, estimate thermodynamic parameters, and harmonize heterogeneous datasets makes it a valuable addition to the toolbox of materials scientists, chemists, and any researcher working with one‑dimensional experimental data.