Atomic Resolution Strain Imaging of IFE First-Wall Tungsten with Bragg Coherent Diffraction Imaging

I.What this is

Inertial Fusion Energy reactors expose first-wall materials like tungsten to intense radiation and thermal cycling. The damage that matters happens atom by atom — a vacancy here, an interstitial there — so measuring it means imaging at that scale.

We simulate irradiated tungsten nanograins, compute the X-ray diffraction they would produce, and then hand a solver only those intensities and ask it to put the atoms back. The truth is never shown to the solver; it is used afterwards, to grade. This page shows what that looks like — the reconstructions running, and how often they succeed.

II.Going deeper

Three companion pages carry the detail this one compresses. If coherent diffraction is new to you, start with How BCDI works.

III.Watch it reconstruct

Every run is recorded two ways, and they answer different questions.

The same crystal, twice — one works, one does not

These two runs got the same 9,334-atom grain, the same three Bragg peaks and the same photon budget. They differ only in a random seed, which makes them two independent repeats of one experiment. The first found every atom to 0.0017 Å. The second never found a single one.

26,067 atoms, recovered exactly

The largest exact recovery in the archive: count error zero out of 26,067 atoms, mean position error 0.0008 Å — about one three-thousandth of a tungsten bond.

No bulk damage in this one. It was set up as a helium cell — 30 ions at 100 eV — but zero of the 30 are present in the final state. He→W transfers at most 8.34 % of the ion's energy, so 100 eV delivers 8.3 eV against tungsten's ~90 eV displacement threshold, and higher energies embed nothing at all because the ion outruns the grain. Read this as the cleanest large reconstruction, not as damage recovery. Real damage is next →

22,000 atoms with real cascade damage

For damage that actually exists at this scale the primary knock-on atom has to be a tungsten atom, not a helium ion — same mass, so no 8.34 % transfer penalty, and a few-hundred-eV recoil clears the ~90 eV displacement threshold easily. Grain g09 was run as a complete dose ladder, and measuring each truth against that grain's own pristine control gives a clean monotone trend:

Two things to take from that table. Damage rises with energy exactly as you would expect — 23, 33, 49 vacant sites — and every damaged rung converged while the undamaged control failed outright, at χ²/floor 137 and a position error of 0.70 Å. Same grain, same code, same peaks. The videos below are the 800 eV rung, the most heavily damaged 22,000-atom reconstruction in the archive that reached the noise floor.

A 1,000 eV cascade, seen atom by atom

The a-CNA view earning its keep. This grain took a 1,000 eV primary knock-on atom deep into its interior — the most violent cascade in the 5,000-atom library — and it is also the tightest fit in the whole archive at χ²/floor 1.08. Heavily damaged grains reconstruct better than clean ones, which is not what anyone expected; §IV explains why.

And a runaway

The worst run in the archive, and the most instructive. Given a 24,800-atom truth at 4.6× the usual photon dose, it produced 34,125 atoms — inventing 9,325 — and ended with an R-factor 63× its noise floor. More photons did not help: this is a search failure, not a data problem.

IV.Convergence

Three things happen at once when a reconstruction succeeds, and the simultaneity is the point. The R-factor reaches the measurement's own noise floor — the residual the true structure would leave, set by photon shot noise. The atom count locks, because adding or removing any atom now makes the fit worse. And the add/remove churn goes to zero, so the run ends itself instead of exhausting its iteration budget.

A failed run has none of the three. It flattens above the floor, stalls short or drifts past the true count, and churns to the cap. The single number that captures it is χ²/floor: this run's fit divided by the fit the truth itself achieves. Near 1 means everything but the shot noise is explained. The archive spans 1.08 to 10,370.

How often it works

This is a success rate per attempt, not a capability limit — when a run lands, it lands exactly. Success falls with size because unknowns grow as three coordinates per atom while usefully-measured intensity does not, and every run here used three Bragg peaks, the bare minimum that can constrain a 3D displacement field. Large grains want more peaks, not more iterations. The 50,000-atom row is unfinished work rather than a wall: 79 of its 82 runs are still improving.

It is not the radiation damage

The obvious guess is that damaged grains are harder, since defects are exactly what the ideal starting lattice lacks. Across the 144-run 5,000-atom library the trend runs the other way: pristine controls converge 62.5 % of the time, 150 eV cascades 65.6 %, 400 eV 78.1 %, and 1,000 eV 87.5 % — with not one outright failure among the 32 deep-cascade runs. The pristine control is the hardest case in the table.

There is almost no partial credit

Accuracy is not spread smoothly from good to bad. Of all 513 runs, 214 land below 0.05 Å and 273 land at or above 0.5 Å — and only 26 (5.1 %) fall in between. In the tightly controlled 5,000-atom library the gap is starker: 129 below, 14 above, and exactly one in the middle.

Continuous error sources produce continuous degradation. A gap that clean means something discrete decides the outcome: the model latches onto the right lattice registry or a wrong one, with no stable state part-way between two sites. That is good news — a discrete failure is one you can detect and retry, not an accuracy limit you live with.

Picking the good run without knowing the answer

Eight independent repeats were run on one 9,334-atom grain — identical truth, identical measurement recipe, one differing random seed, which sets both the shot-noise draw and the subset of voxels the solver fits. Three converged; five did not.

V.Every run, every figure

The nine reconstructions above, scored. Recall is at the loose 2.023 Å tolerance, as archived — read it alongside χ²/floor, not instead of it.

Open the full diagnostic figure set for these nine runs

Each run's nine-panel summary sheet shows the whole pipeline on one page; the others break out individual stages. What the panels mean → Support-oversizing figures are deliberately not published.

he/25k/25k_g04_FLU30x100_focus_s2 — converged, 26,067 atoms, no bulk damage

summary · convergence · measurement · phasing · seed · residual field · atom slabs

lib_5k_g15_L3deep_E1000_s2 — converged, tightest fit in the archive

summary · convergence · measurement · phasing · seed · residual field · cascade damage

10k_s13 vs 10k_s14 — the seed pair

Converged: summary · convergence · measurement · phasing · seed · residual field · atom slabs
Failed: summary · convergence · measurement · phasing · seed · residual field · atom slabs

large/lgE_25k_g09_L3_E800_s2 — converged, 800 eV cascade

summary · convergence · measurement · phasing · seed · residual field · atom slabs

large/lgE_25k_g01_L1_E150_s2 — converged on a hard grain

summary · convergence · measurement · phasing · seed · residual field

he/25k/25k_g01_E3200x3_spread_s1 — a representative 25k stall

Another helium cell that embedded nothing — 0 of 3 ions retained, 4 vacant sites against its pristine control. Its failure is a search failure, not a damage effect.

summary · convergence · measurement · phasing · seed · residual field

lib_5k_g03_L0 — undamaged, and still failed

summary · convergence · measurement · phasing · seed · residual field

25kD_s42 — the runaway

summary · convergence · measurement · phasing · seed · residual field · atom slabs

Acknowledgments