[cophus]

Pair-angle distribution function (PADF)

PADF from orientation-averaged diffraction, following pypadf (Martin et al.). Primarily Emanuel Tsegaye's work, with Karen Ehrhardt's fixes to the Legendre fit and output.

What's here

• diffraction/padf.py: PairAngleDistributionFunction (per-pattern angular correlation, median subtraction, Legendre fit with |sin θ| weights, spherical Bessel transform, PADF Θ(r, r′, θ) with an optional taper of the Legendre orders to suppress ringing in θ), plot_g2_g3, simple_plot (side-by-side and fixed-r maps), plot_angular_correlation
  • bandlimit_volume: band-limits a model g3 to the measured q range and l_max
  • padf_from_clusters: model PADF from all interatomic vectors of atomic clusters (2-, 3- and 4-body terms, as the diffraction PADF measures)
• diffraction/padf2d.py: PairAngleDistributionFunction2D, an in-plane variant (circular harmonics and Hankel transforms) for 2D samples that only rotate in plane, which also retains odd harmonics when Friedel symmetry is broken, plus padf2d_from_clusters
• diffraction/bispectrum.py: angular bispectrum for Friedel-symmetry breaking
• diffraction/gr_truth.py: three-body g3 histograms of 3D and 2D atomic models (adapted from Arthur McCray's PDFs_3batch)
• diffraction/lattices.py, multislice.py: test-image and pattern simulation (2D lattices, random clusters of 3D structures with Weickenmeier-Kohl scattering factors)
• polar_transform: accepts 2D patterns and 3D stacks as well as 4D-STEM
• PairDistributionFunction: the default background is now a constant plus one power law, B(k) = c + a (1 + k²/s²)^(−p), with positive parameters so the single scattering f(k) = B − c is positive and monotonic, fit with k / I(k) weighting (the error in F(k)). bg_model="power" with two terms, "known" (N⟨f⟩² + c from tabulated scattering factors) and the previous "gaussian" are options. The low-r density correction now acts over the transform window rather than the background fit range.
• core.visualization.show_1d (identical to the copy on diffractive_imaging)

Validation (notebooks, not in the repo)

• bcc Fe / fcc Al, 1600 random orientations: the nearest-neighbor PADF peaks are at 70.4/109.6° and 60.3/90.5/119.7°, and the diagonal and fixed-r maps match the model PADF at the first two shells. A single [001] pattern gives the 90° angles of the projected column lattice instead.
• Amorphous Si (1000-atom WWW continuous random network from atomode): the PADF of 6400 simulated patterns peaks at 109.6° on the nearest-neighbor shell, and the model PADF from all interatomic vectors peaks at 107.6°. A diffraction PADF contains two-, three- and four-body terms, so for amorphous samples the model reference must include all vector pairs (padf_from_clusters), not only triplets. With the known-scattering-factor background (fit at k > 1 1/Å) over the full k range and the low-r correction below 2 Å, g(r) is zero below the first shell and the first peak matches the model (2.30 Å, height 4.0 vs 4.3).
• Amorphous Si, 2D-PADF of the projected patterns: the traces at the first and second neighbor distances correlate at 0.98 and 0.96 with the 2D-PADF calculated from the projected atomic positions.
• 2D lattices (triangular, honeycomb, square, decagonal): the 2D-PADF of a single FFT matches the 2D-PADF calculated from the atomic positions, with peaks at the expected bond angles. In an h-BN multislice series, with q limited to where f(q) > 10⁻³, the odd-harmonic fraction at the bond length increases from 0.003 for one slice to 0.99 for 64 slices, while the centrosymmetric honeycomb stays at 0.000.

🤖 Generated with Claude Code

[cophus]

Testing notebooks for PADF
padf_3d_crystals.ipynb
padf_aSi_01_pdf.ipynb
padf_aSi_02_padf.ipynb
padf2d_lattices.ipynb
a_si_crn.py

[cophus]

Updated notebooks:
padf_aSi_01_pdf.ipynb
padf_aSi_02_padf.ipynb
padf2d_lattices.ipynb
padf_3d_crystals.ipynb