Powder refinement

The powder layer lives in xtalforge-analysis: measured patterns, peaks, indexing, Le Bail/Pawley extraction and a least-squares structural refinement.

rietx inventory

Task 7.1 is a study, not a port. rietx_inventory() returns a RietxBridge with the documented capabilities (pattern IO, background, profile, Le Bail, Pawley, Rietveld, indexing), the MIT license and the source note. The acceptance metrics are AcceptanceMetrics { max_rwp, max_position_error } and check_acceptance rejects values outside them. RIETX_LICENSE_NOTE, ACCEPTANCE_MAX_RWP and ACCEPTANCE_MAX_POSITION_ERROR are the public constants. The exact rietx sources are not vendored; the native implementation is a simplified model documented in the module comments and the roadmap's known-gaps section.

Instrument

Instrument { geometry, zero_shift, displacement, ka2_ratio, polarization, sample_radius } applies a zero shift and the sample-displacement correction, and doublet splits a reflection into the Kα1/Kα2 pair. Geometry is BraggBrentano or DebyeScherrer. doublet_checked validates the ratio.

Le Bail

le_bail(structure, observed, &LebailOptions) subtracts a SNIP background, shares every observed point among the reflections in proportion to their calculated profile (the Le Bail partition) and returns LebailResult { intensities, intensity_esds, positions, pattern, r_factor, rwp, chi_squared }. The intensity esds are the diagonal of (A^T W A)^-1 scaled by the reduced chi-squared; above 128 reflections the covariance diagonal is used instead of the exact inverse. See Le Bail extraction. Python powder_lebail(text, pattern_text) and WASM powder_lebail_info(text, pattern_text) return positions, intensities, intensity_esds, r_factor, rwp and chi_squared, like xtalforge --json powder lebail.

Pawley

pawley_refine(structure, observed, &PawleyOptions) fits the whole pattern with one free intensity per allowed reflection, a Chebyshev background and optional free cell, zero-shift, size and strain parameters. It returns PawleyResult { reflections, cell, cell_esds, zero_shift, zero_shift_esd, size, strain, rp, rwp, rexp, chi_squared, pattern, converged, iterations }; every PawleyReflection carries hkl, d, two_theta, intensity and esd. The linear intensities and their covariance are solved exactly for each non-linear point and the cell/zero/width model is refined by variable projection. See Pawley fit for the conventions and limits.

Whole-range and structural refinement

refine_phase(structure, observed, &RietveldOptions, &RefineOptions) runs the McCusker stages: the scale and background analytically, then the zero shift and free cell numbers, the profile width, and the structure. RefineOptions selects them with refine_positions, refine_adps, refine_occupancies, refine_zero, refine_cell, refine_width, refine_texture, texture_axis and doublet. Positions move only along the directions free_directions(operations, frac) allows for each Wyckoff site, the cell ties of the metric family are restored after every move, and a March-Dollase coefficient is refined about texture_axis.

It refuses to refine more parameters than the observed peaks support and returns RefinedPhase { structure, rwp, parameters, parameter_esds, stages, converged, iterations }. parameter_esds holds the covariance-based esds of the free parameters, and stages is the order that actually ran. combined_objective(energy, rwp, weight) is the energy-plus-fit objective of Task 7.9.1. See Rietveld refinement for the stage details, the Wyckoff rules and the documented deviations.

Cells and extinction

free_cell_parameters(number) returns the free cell parameters for the crystal system of a space-group number (triclinic 6, monoclinic 4, orthorhombic 3, tetragonal/hexagonal 2, cubic 1); TrigonalSetting and free_cell_parameters_with_setting choose the trigonal setting, and CELL_PARAMETER_NAMES holds the names. extinction_symbol(number) returns the Bravais extinction letter for the 14 Bravais types.

Automatic run

run_automatic(structure, observed, &AutomaticOptions) finds the peaks, runs the general metric-family indexing, builds the leading-cell table, extracts Le Bail intensities, fits a Pawley model of the best (cell, class) and fits the phase, recording every step in order in AutomaticResult { peaks, index, leading_cells, lebail, pawley, phase, steps }.

For each of the first AutomaticOptions::leading_cells indexing candidates (default 5) the extinction classes of its crystal system are enumerated: groups with the same reflection-condition signature are one class, its representative is the group with the most operations, and a class is refuted when an indexed reflection violates it. Every surviving class is fitted with Le Bail and ranked by BIC against the absence-free lattice class; the leading AutomaticOptions::classes classes (default 3) are Pawley fitted.

leading_cells holds one row per fitted (cell, class): its IndexedCell, cell_rank, class_rank, class_symbol, delta_bic, Pawley pawley_rwp, pawley_cell_esds and the space_groups that share the class. The table is sorted by Pawley Rwp; fits within 1 % of each other are a tie and are ordered by the indexing and class ranks, as in the reference. The steps list contains peaks, index, leading_cells, le_bail, pawley and rietveld (a Pawley fit the cell makes impossible is recorded as pawley_skipped). It refuses fewer than three points or peaks, a zero leading_cells and a zero classes. IndexedPeak is one indexed reflection. is_systematically_absent(operations, hkl) is the underlying reflection-condition test; see Extinction screening.

Indexing

index_pattern(peaks, wavelength, &IndexingOptions) solves the cubic, tetragonal, hexagonal, orthorhombic and monoclinic families, refines each candidate and ranks them by coverage, symmetry and M20, with F_N and the coverage fraction reported. figures_of_merit, predict_reflections and match_peaks expose the individual pieces. The definitions and the ranking rules are on the indexing algorithm page.

Surfaces

xtalforge powder {index,lebail,pawley,rietveld,automatic,cells,rietx}; powder index --general prints the ranked metric families, --background subtracts a SNIP background and keeps lines above 1 % of the strongest and five times the noise (PeakOptions::noise_limited, the same search run_automatic uses), --refine-peaks fits each line; powder pawley prints the full fit with Rwp and esds, and powder rietveld --refine runs the McCusker stages (--occupancies and --texture add those parameters; --no-doublet models one wavelength instead of the Cu K alpha 1/K alpha 2 doublet that the CLI uses by default, as Python's doublet=False does). Python powder_index, powder_lebail, powder_pawley, powder_automatic, powder_refine, powder_cells, rietx; WASM powder_index_info, powder_lebail_info, powder_pawley_info, powder_pawley_width_info (with refine_size/refine_strain; both Pawley results carry size, strain and the fitted calculated profile), powder_automatic_info (its cell is only the quick cubic-index edge kept for the 1.0 signature; best_cell is the Pawley-refined cell of the leading candidate, or its indexed cell when the Pawley stage was skipped; Python powder_automatic and xtalforge --json powder automatic carry the same best_cell), powder_refine_info, powder_cells_info, rietx_inventory_info.