Crystalline extinction

IRMA can apply an optional crystalline-extinction correction to the coherent-elastic Bragg edges of an iel=10 (generalized-elastic) evaluation: the MF7/MT2 cross section in which each family of reciprocal-lattice planes adds a step at its Bragg-edge energy. The correction is off by default, and when it is disabled the tape carries the ideal-crystal Bragg edges, byte-identical to a run without the feature.

What extinction is

In an ideal (kinematic) crystal the coherent-elastic cross section is the Bragg sum over reciprocal-lattice planes. A real crystallite diffracts so efficiently that, once a beam is strongly Bragg-scattered, it is depleted before it can scatter again, so the measured Bragg-peak intensity is lower than the kinematic value. This reduction is called extinction.

IRMA multiplies each plane's kinematic intensity by an extinction factor y(x, θ) ∈ (0, 1]:

\[ \sigma_{\rm coh}^{\rm el}(E) \;=\; \frac{1}{E}\sum_{2d \ge \lambda} \delta_{hkl}\, y_{hkl}(\lambda) \]

with \(\delta_{hkl}\) the kinematic edge strength of plane family \(hkl\) and \(y_{hkl}\) its extinction factor.

Extinction acts through two mechanisms. Both are described in the mosaic picture of a real crystal, which models a crystallite as a stack of small, slightly misoriented perfect blocks:

Primary extinction: multiple scattering within one perfect mosaic block. Driven by the crystallite size l.
Secondary extinction: beam depletion from block to block across the specimen. Driven by the mosaic spread g and the grain size L.

The dimensionless argument x (the extinction strength the model computes from l, g, L, and the wavelength) grows with wavelength (x ∝ λ² and higher powers), so extinction is strongest at long wavelengths (low energies) and dies out above ~0.1 eV. Above that cutoff σ_ext = σ_kin, so the high-energy edges are unchanged.

Extinction is a property of the specimen, not of the material: l, g, and L describe a particular specimen. They come from a fit to a measured transmission (as in Xu 2025) or from measured microstructure (electron backscatter diffraction, EBSD), and the same material in a different form has different extinction. Do not treat an extinction-corrected tape as a generic material library.

Extinction vs. texture

Extinction and texture (preferred orientation) both reduce some Bragg peaks, but they are different physics. Extinction attenuates reflections in an orientation-independent way and reduces the total coherent-elastic cross section. Texture redistributes intensity between reflections and conserves the total. IRMA models extinction only; texture has no place in an orientation-averaged ENDF/TSL evaluation.

Models

Five models are available, ported from the NCrystal CrysXT plugin: two Sabine forms and three Becker-Coppens (BC) forms.

Model	Mechanisms	Parameters
`Sabine_uncorr`	primary + secondary (uncorrelated block)	`l`, (`g`,`L`)
`Sabine_corr`	primary + secondary (correlated block)	`l`, (`g`,`L`)
`BC_pure`	primary or secondary	`l` or (`g`,`L`)
`BC_mix`	coupled primary + secondary	`l`, `g`, `L`
`BC_mod`	secondary only (no primary factor)	`l`, `g`, `L`

BC_pure is the simplest entry point: BC_pure l=8550 gives pure primary extinction from a single crystallite-size parameter. BC_mix and BC_mod couple the two mechanisms and therefore require l>0, g>0 and L>0: the secondary term is parameterized by the block size l, so l is needed even though BC_mod applies no primary factor.

The Becker-Coppens models take a recipe. The default, std, is the updated BC2025 recipe (Kittelmann 2026); cls is the original BC1974 closed forms, which can be numerically fragile at strong extinction. The Sabine models are analytic and ignore recipe. The tilt distribution, the assumed shape of the block-misorientation spread, is Gauss/Lorentz/Fresnel for Becker-Coppens and rect/tri for Sabine (defaults: Gauss and rect).

Enabling it: the extinction card

Cards are the numbered records of the input file; the input file reference shows the complete layout with the extinction card in place. Add the optional extinction card as the last card of the iel=10 elastic block (after Cards 6d/6e, or Card 6g for inelastic_mode=1/2), before Card 7:

extinction <model> l=<Å> g=<rad⁻¹> L=<Å> [dist=<...>] [rec=cls|std] [rmse_tol=<frac>]

Example (examples/tsl/be_iel10_extinction.input):

2.28660 2.28660 3.58330 90.0 90.0 120.0/   $ Card 6c: Be hcp cell
4 9 8.93478 7.79 0.0018 2/                  $ Card 6d
0.33333333 0.66666667 0.75  0.66666667 0.33333333 0.25/   $ Card 6d continued: the two fractional positions
extinction BC_mix l=8550 g=170 L=75750 dist=Gauss rec=std rmse_tol=1e-3 /
150 400 1/                                  $ Card 7

Fields:

Field	Meaning	Default
`<model>`	one of the five models above (required)	—
`l`	crystallite (block) size [Å], primary	`0` (off)
`g`	mosaic spread [rad⁻¹] (the Becker-Coppens mosaic-distribution parameter; it scales as the inverse of the mosaic angular spread), secondary	`0` (off)
`L`	grain size [Å], secondary	`0` (off)
`dist`	tilt distribution	`Gauss` (BC) / `rect` (Sabine)
`rec`	BC recipe `std`/`cls`	`std`
`rmse_tol`	tabulation tolerance	`1e-3`

IRMA validates the card at parse time: the model name, l/g/L ≥ 0, at least one active mechanism, l>0, g>0, and L>0 for BC_mix/BC_mod, and a distribution valid for the model. The card works with every inelastic_mode (0, 1, 2) and with both elastic formats (elastic_mode=1/2), provided MF7/MT2 actually carries coherent Bragg edges to correct. The mixed elastic format (MEF, elastic_mode=2) always does: extinction corrects the per-atom coherent Bragg edges and leaves the incoherent-elastic part untouched. The single-channel elastic format (SEF, elastic_mode=1) writes only the dominant elastic component, and two SEF configurations route MF7/MT2 to the incoherent-elastic builder, which never applies extinction: a single-atom material whose sigma_coh <= sigma_inc (Card 6d), and a polyatomic whose principal scatterer is not the designated-coherent atom. On such an input file IRMA rejects the extinction card at parse time ("extinction would be a silent no-op ...") instead of silently writing an uncorrected tape whose comments claim an extinction correction; switch to elastic_mode=2 (MEF) so MF7/MT2 keeps a coherent-elastic part, or remove the card. The model and parameters are stamped into the MF1/MT451 comments, so the tape records that it is an extinction-corrected, specimen-specific evaluation.

In the GUI

The ENDF Evaluation ▸ Material tab has a Crystalline Extinction (Optional) section under the iel=10 coherent-elastic options: an enable toggle (off by default), the model dropdown, and the l/g/L/distribution/recipe/rmse_tol fields. An ⓘ help glyph on every control (hover for a preview, click for the full text) explains the parameter and links the references. Importing an input file with an extinction card populates the section automatically.

Tape format (MF7/MT2)

Unlike the ideal Bragg-edge staircase, the extinction-corrected σ(E) varies within a Bragg interval below the cutoff, because the factor y depends on wavelength. IRMA keeps the standard histogram (INT=1) cumulative-S form: it reuses the kinematic Bragg edges above the cutoff and splices fine, tolerance-adaptive nodes below it. This is deliberate. NJOY THERMR (and other processors) read MF7/MT2 as a step function regardless of the interpolation flag, so tabulating for that step, and labeling it INT=1, is both smaller and more faithful than a lin-lin table that gets read as a staircase anyway. No NJOY patch is needed.

Extinction adds nodes only below ~0.1 eV; a typical run adds a few hundred points to the table (e.g. Be: ~2.5k vs ~1.7k). rmse_tol trades node count for fidelity (default 1e-3 ≈ 0.04% RMSE on the reconstructed cross section).

Validation

The five models reproduce the CrysXT plugin to 0.000% across nine model/recipe/distribution cases. A frozen CrysXT capture is replayed by the CI gate tests/test_extinction_crysxt_expected.py, so any drift in the port is caught without needing NCrystal/CrysXT at test time. End to end, a real beryllium evaluation processed by NJOY THERMR reproduces the CrysXT coherent-elastic cross section to 0.07% median (cell matched to the reference structure).

The broader beryllium evaluation (its inelastic and cross-section suites against OCLIMAX, Euphonic, and NJOY) is documented in Validation ▸ Beryllium, which also discusses the experimental signature of extinction at the Bragg cutoff.

Attribution & references

The extinction models and recipes are ported, not imported, from the NCrystal CrysXT plugin: the code is reimplemented inside IRMA, and NCrystal/CrysXT is not a dependency.

ncplugin-CrysXT: https://github.com/dddijulio/ncplugin-CrysXT

Read these to understand the physics and how to obtain l/g/L:

T. Kittelmann, D. D. DiJulio, S. Xu & J. I. Marquez Damian, Revisiting Becker-Coppens (1974): updated recipes for estimating extinction factors in spherical crystallites, Acta Cryst. (2026) A82, 163–178. doi:10.1107/S2053273326001245. The BC2025 std recipes.
S. Xu et al., Impact of extinction effects on neutron transmission in solid beryllium metal, J. Appl. Cryst. (2025) 58, 1957–1966. doi:10.1107/S1600576725007939. Concept, motivation, and fitting l/g/L to a measured transmission.
P. J. Becker & P. Coppens, Acta Cryst. (1974) A30, 129.
T. M. Sabine, International Tables for Crystallography (2006), Vol. C, ch. 6.4.