midas-saxs

Differentiable small-angle X-ray scattering for MIDAS. Two source terms, one detector:

• Density contrast — voids, gas bubbles, precipitates. Sphere / ellipsoid / cylinder form factors, lognormal polydispersity, Percus-Yevick S(Q), Guinier and Porod analysis. These came from midas_pdf.saxs, which now re-exports them from here, so MIDAS has one definition of "SAXS form factor".
• Strain contrast — dislocation loops, driven by a midas_ddd network read from ExaDiS. Optional extra: pip install 'midas-saxs[dislocations]'.

from midas_saxs import SAXSGeometry, SpherePopulation, simulate_frame

geom = SAXSGeometry(lsd_um=2.0e6, bcy_px=512, bcz_px=512, px_um=75.0,
                    wavelength_A=0.7293, n_pix_y=1024, n_pix_z=1024,
                    beamstop_radius_px=30)
voids = SpherePopulation(radius_A=50.0, number_density_per_A3=1e-8,
                         delta_rho_e_per_A3=-2.45, label="voids")
frame = simulate_frame(geom, particles=[voids], sample_volume_A3=1e15)

dev/paper/loop_vs_void_demo.py renders the five-panel figure that motivates the whole package.

Read this before promising anyone a loop measurement

Three numbers, all reproducible from the demo script.

1. Loops are faint. A dislocation loop of radius R displaces only its relaxation volume pi R^2 b; a void of the same radius displaces 4 pi R^3 / 3. For R = 5 nm in Cu that is 26x in volume and 680x in forward intensity. The loop scatters like a sphere of radius 1.7 nm.

2. What separates a loop from a void is shape, not size. The loop's small-angle amplitude is direction-dependent — kappa dV in its own plane, dV along its normal, with kappa = lambda/(lambda + 2 mu). Intensity is therefore modulated by 1 - kappa^2 (0.84 for lambda = 100, mu = 75). A void is isotropic. Radially averaging a frame destroys exactly this, which is why this package renders 2-D frames and offers azimuthal_profile alongside radial_average.

3. Real voids bury the signature. Measured on the demo: 24 aligned loops alone give an azimuthal contrast of 6.30x (the closed form predicts 1/kappa^2 = 6.25). Add equal-radius voids at the same number density — the physically realistic irradiated case — and the contrast collapses to 1.002x, with the voids outshining the loops by 1089x integrated over the frame.

So: loops are detectable at small angle in a clean matrix, and essentially undetectable alongside a void or bubble population of comparable size. If the question is defect-type discrimination in an irradiated material, near-Bragg diffuse (Huang) scattering is stronger than the small-angle signal by (G/q)^2 ~ 1e4 to 1e7 and is the better measurement.

Scope

Closed dislocation loops only. A cut surface exists only for a closed circuit. Open lines — the deformation population — enclose no area, carry no relaxation volume, and contribute nothing as q -> 0; their small-angle signature is a weak transverse streak that is not modelled. simulate_frame reports how much line length it ignored rather than returning a number that looks complete.

Units

The 1e4 between the last two is easy to lose, so inv_A_to_inv_um / inv_um_to_inv_A exist and strain_source uses them rather than a literal.

Detector geometry

pixel_to_q goes through midas_transforms.apply_tilt_distortion — the same tilt (R_z R_y R_x) and 15-coefficient distortion model the HEDM side uses. That is deliberate: a SAXS geometry and an FF geometry calibrated from the same detector must agree about where q sits. Transmission SAXS has no omega, so lab q is sample q.

Migration note

form_factors, model, wide_band and core_shell moved here from midas_pdf.saxs. Both the package-level path (from midas_pdf.saxs import SAXSModel) and the deep path (from midas_pdf.saxs.form_factors import ...) still resolve, to the same objects — asserted by test_midas_pdf_reexports_the_same_objects. midas_pdf.saxs keeps the genuinely PDF-coupled part: joint SAXS + PDF refinement and its Bayesian variants.

One convention worth knowing: sphere_form_factor_squared returns V^2 |F|^2, not the normalised |F|^2. SpherePopulation.intensity multiplies it by n * delta_rho^2 and nothing else, which is only correct because the volume is already in there.