H9 engineering interpretation: what the measured Ms allows, and what it does not

This is the H9 engineering interpretation (quest item 01a08ce9-4854-77c0). It uses only route-measured values from the H9 reproduction capsule and answers one question: if the relaxed Fe3W D022 cell were a perfect magnet — ideal square loop, infinite anisotropy, full density, single domain — what would its measured saturation magnetization allow it to deliver?

The measured input

Route Ms = 1.2691 T on the relaxed cell Fe3W (I4/mmm) - DFT relaxed (route 0a23817e, moments run

Ideal upper-bound energy product

$$(BH)_{max} \le \frac{(\mu_0 M_s)^2}{4\mu_0} = \frac{(1.2691)^2}{4\mu_0}$$

0.320 MJ/m³ = 40.3 MGOe. This is the ceiling for a magnet with this Ms and nothing else wrong. Real magnets reach roughly 70-90% of their ideal bound (microstructure, demagnetizing fields, non-square loops), so a practical device built on this Ms tops out in the high-20s MGOe.

For scale: Nd2Fe14B's own ideal bound is ~0.52 MJ/m³ (Ms 1.61 T; commercial magnets reach 400-475 kJ/m³). The H9 ceiling is 62% of Nd2Fe14B's ceiling. That is the arithmetic consequence of the measured Ms; it is the strongest statement about H9's application ceiling that Ms alone can make, and no synthesis improvement can raise it while Ms stays at 1.27 T.

Anisotropy required for a hard magnet

The hardness parameter $\kappa = \sqrt{K_1 / (\mu_0 M_s^2/2)}$

K1 needed for $\kappa = 1$: 0.641 MJ/m³.

MAE for this structure is not measured. The single MAE submission was admission-rejected by the route's own geometry gate (max stress 0.7832 kbar > 0.5 kbar, MAE run), and per the preregistration that rejected receipt is a geometry/route finding, not a value. So the decisive number for whether H9 is a magnet at all is missing, and the table shows it as missing.

Property table (measured values only)

Sensitivity to the observed Ms

The frozen-settings fixture controls bound the route's Ms bias one-sided upward: bcc Fe +1.0% (2.2386 vs 2.217 µB exp, action 01a08947), L1_0 FePt +~12% (3.1642 vs ~2.83 µB exp, PBE/Mulliken DZP overestimate, action 01a08afd); the MnBi CHGNet-vs-DFT cross-route spread was 1.7%. Taking the envelope as Ms ∈ [0.88, 1.017] × 1.2691 T:

Because $(BH)_{max}$ scales as Ms², a +12% moment overestimate inflates the energy-product bound by ~25%. The honest reading is that the ceiling sits at 0.25-0.33 MJ/m³ with the bias sign known (the route overestimates; the true ceiling is nearer the low end).

What this means (interpretation, clearly labeled)

1. If the H9 structure's anisotropy clears 0.64 MJ/m³, the measured Ms makes a theoretically viable, though not competitive, magnet: κ ≥ 1 but an energy-product ceiling 38% below Nd2Fe14B's ideal bound. As an NdFeB replacement, the measured Ms is already disqualifying on ceiling alone.

2. The one number that decides whether H9 is a magnet at all (MAE) is unmeasured, and the anisotropy bar it must clear (0.64 MJ/m³) is 10x lower than the 6.48 MJ/m³ the same-composition H5 Fe3W anchor returned in a different space group (SG 123, action 01a07785) — cited as context on what this chemistry is capable of, not as a substitute for the missing measurement.

3. Every claim above inherits the one-sided route bias; the low ends of the envelopes are the conservative numbers.