Powder patterns and porosity

xtalforge-analysis starts with calculated PXRD (Task 5.1) and the periodic surface-distance grid with porosity numbers (Tasks 5.2/5.3).

PXRD

The Rust entry point is calculate_pxrd; Python exposes pxrd, WASM pxrd_info and the CLI xtalforge pxrd.

use xtalforge_analysis::{PxrdOptions, Radiation, calculate_pxrd};

let pattern = calculate_pxrd(&structure, &PxrdOptions {
    radiation: Radiation::CuKa,
    ..PxrdOptions::default()
})?;

Radiation carries the wavelengths (CuKa, CuKa1, MoKa, CoKa, FeKa, CrKa, AgKa). calculate_pxrd enumerates hkl reflections in the requested 2-theta range, computes d = 1/|hkl @ reciprocal|, structure factors from the P1 atoms, Lorentz-polarization and multiplicity, and samples a Gaussian profile. Pattern { points, reflections } carries the sampled curve and the peak list; Reflection { hkl, d, two_theta, multiplicity, intensity }.

Pareto front

pareto_front(points) returns the indices of the non-dominated (energy, residual) points, minimising both objectives.

Rietveld phase model

fit_phase(structure, observed, &RietveldOptions) simulates the phase from the structure and PXRD engine, then fits its scale and background, returning RietveldPhase { scale, background, rwp, pattern }. The structural refinement is refine_phase(structure, observed, &RietveldOptions, &RefineOptions) in the powder refinement page; it runs the McCusker stages (zero/cell, width, then Wyckoff coordinates, a global isotropic ADP multiplier, occupancies and texture) and returns RefinedPhase { structure, rwp, parameters, parameter_esds, stages, converged, iterations }. free_directions(operations, frac) is the Wyckoff-allowed subspace helper.

Le Bail

le_bail(structure, observed, &LebailOptions) subtracts a SNIP background, partitions the observed intensity among overlapping reflections and iterates the profile sum, returning LebailResult { intensities, positions, pattern, r_factor, rwp, chi_squared, intensity_esds }. The esds come from the inverse of the profile normal matrix scaled by the reduced chi-squared; above 128 reflections only the covariance diagonal is used. See Le Bail extraction.

Indexing

index_pattern(peaks, wavelength, &IndexingOptions) searches the cubic, tetragonal, hexagonal, orthorhombic and monoclinic metric families and returns IndexingResult { candidates }, best first. Each IndexedCell carries the family, the refined CellMetric { a, b, c, alpha, beta, gamma }, the indexed peaks, completeness, mean_error, the de Wolff m20, the Smith-Snyder f_n and the prediction coverage. The search is bounded by max_index, max_volume, min_completeness and max_evaluations.

figures_of_merit(&cell, peaks, wavelength, tolerance) evaluates one cell and predict_reflections(&cell, max_q) / match_peaks(...) expose the prediction and the matching. index_cubic(peaks, wavelength, max_index, tolerance) is the original cubic-only search and keeps returning CubicIndex.

Run xtalforge powder index PATTERN --general for the ranked table. See Powder indexing for the solve, the figures of merit and the ranking rules.

Profiles and background

Profile { kind, center, fwhm, eta, height } evaluates Gaussian, Lorentzian and pseudo-Voigt peaks and samples a range. Background::{Constant, Linear, Quadratic} are the background models.

Least squares

least_squares(initial, &FitOptions, residuals) is a Levenberg-Marquardt fit with finite-difference Jacobians. FitResult { parameters, residuals, chi_squared, iterations, converged } is the result.

Measured patterns and peaks

xtalforge_io::read_xy reads a measured pattern; find_peaks(&points, &PeakOptions) finds local maxima with optional smoothing, a height threshold and a minimum separation, returning Peak { two_theta, intensity, fwhm }. PeakOptions also turns on a SNIP background subtraction (background, background_window) and a per-line Gaussian plus linear background fit (refine, fit_window). background_envelope(&points, window) returns the SNIP envelope and fit_peaks(&points, &positions, &options) fits named positions, which is what an indexing run wants to refine.

Nets

quotient_graph(&CgdEntry, tolerance) reduces a CGD net to nodes, edges and lattice shifts; NetInvariants reports node/edge counts, cycle rank and coordination, and shift_map groups shifts by node pair. NetIndex indexes a CGD file and searches by invariants; components finds connected components (interpenetration candidates) and interpenetrate duplicates a net at a shift. NetFingerprint is the periodicity plus the distinct coordination sequences and point symbols of a quotient graph; fingerprint computes it and QuotientGraph::from_canonical_key rebuilds one RCSR minimal cell from its canonical key. RcsrIndex::from_embedded() holds the full 2019-06-01 catalogue (2,931 entries) and identify returns a RcsrIdentification { fingerprint, names, nearest, nearest_by }; one name is unique, several are an ambiguous set, and none gives the nearest candidates.

Isosurfaces

isosurface(&Grid3, value) extracts a TriangleMesh { vertices, triangles } with marching tetrahedra (six tetrahedra per cell, no ambiguous marching-cube cases). The four crossings of a 2-2 sign pattern are ordered around their quadrilateral, so adjacent tetrahedra share the same diagonal and the surface is watertight. It rejects grids with fewer than two samples along an axis.

Distance grid

distance_grid(structure, radii, spacing) returns a DistanceGrid wrapping xtalforge_io::grid::Grid3. The value is the distance to the nearest atom surface (negative inside an atom), using minimum images. contact_surface, accessible_volume(probe), pore_volume, surface_area, largest_included_diameter and pore_diameter(bin_width) are the porosity numbers; PoreSizeBin is one histogram bin. default_radii uses the element van der Waals radii. PatternPoint is the shared measured-pattern point type, and ProfileKind selects Gaussian, Lorentzian or pseudo-Voigt.

All operations return typed errors for non-positive spacing, missing radii or invalid probe values.

Zeo++, RCSR and overlays

run_zeo(structure, &ZeoOptions) probes zeo++ and parses its Channels output (parse_zeo_channels, parse_zeo_volume); without the binary it returns a typed error. write_zeo_inputs writes the CSSR and the network arguments.

RcsrIndex::from_embedded() holds the full 2019-06-01 RCSR catalogue as a fingerprint index; the full snapshots are in data/rcsr/ and the index is regenerated by examples/build_rcsr_index.rs. identify matches the coordination-sequence and point-symbol invariants, returns every name that shares them, and falls back to the nearest candidates; validate checks the index. QuotientGraph, NetEdge, NetInvariants, NetFingerprint and RcsrEntry are the net types. merge_nets joins two quotient graphs and overlay_net turns one into an Overlay with an OverlayStyle; OverlaySet collects overlays for a viewer.

xtalforge analysis {porosity,nets,zeo,overlay}, Python porosity, net_invariants, zeo_parse and the WASM equivalents expose the same operations.