Short versionTwo numbers, plotted against each other, are the entire grade catalog.
1 · Two NumbersOne chart, two axes
Neodymium grades get names like N42, N45SH, N38UH. Confusing, until you notice every one of those names decodes to a single point on this plot: how much field the magnet makes, against how much opposing field it survives before that field starts coming back off.
1 · Two NumbersBr and Hci
Br, remanence, is how much flux the magnet puts out at zero opposing field — more Br, stronger magnet, same size. Hci, intrinsic coercivity, is how much reverse field it takes to start erasing that magnetization for good. If you've read the piece on reading a B-H curve, these are two of its four numbers; the other two, Hcb and (BH)max, mostly ride along with these two here.
Rule of thumb: Br sells the spec sheet. Hci decides whether the part still works in six months.
Short versionThe plain N-series is the highest-Br, lowest-Hci corner of the catalog. Fine at room temperature, not fine anywhere hot.
2 · Standard GradesN35 through N52
No suffix means no heavy rare earth added for coercivity, and it shows: N35 up through N52 sit in a narrow band around 11 to 12 kOe, rated to roughly 80°C. The number after the N tracks with energy product — higher number, more flux — and very little else about the grade changes.
In practiceIf a bill of materials just says "52-grade magnet" with nothing else attached, my first question is what temperature it actually sees in service. A fridge magnet couldn't care less. A magnet three millimeters from a winding that's been running for an hour is a different conversation entirely.
Short versionFor decades the only way to buy more Hci was to alloy dysprosium or terbium through the whole grain — and every bit of it fought against the flux you were trying to protect.
3 · The Old WayH, SH, UH, EH, AH
Push a magnet's rated temperature up and it needs more Hci to match, because coercivity falls as a magnet heats. The historic fix: substitute some neodymium with dysprosium or terbium, alloyed through the entire grain. Climb the suffix ladder — M (100°C), H (120°C), SH (150°C), UH (180°C), EH (200°C), AH (230°C) — and the ceiling moves right.
3 · The Old WayWhy it cost flux
Dysprosium and terbium couple antiferromagnetically to the iron in this crystal — their moment points the wrong way. More of them raises coercivity and quietly cancels out some of the very magnetization they were added to protect. Every step right on this chart bought Hci by giving up Br. Follow the old ceiling and it drops the whole way across.
Short versionCoercivity is decided at the grain boundary, in a layer microns thick. The rest of the grain was never the problem — so let's not put the heavies there.
4 · Grain boundary diffusionWhere demagnetizing actually starts
A sintered NdFeB magnet is millions of grains packed together. Reversal — the part of the demagnetizing process Hci measures — doesn't start in the middle of a grain. It nucleates at defects right at the grain boundary, and sweeps across. If you want to prevent that, you work on the grain boundary. Alloying dysprosium through the whole grain to fix a boundary problem is like putting herbicide on your entire lawn to get rid of a few dandelions.
4 · Grain Boundary DiffusionDope the skin, not the block
Grain boundary diffusion applies a dysprosium or terbium compound — a coating, or a melt-spun alloy powder — to the surface of an already-sintered, already-shaped magnet, then heats it just enough for the heavy rare earth to migrate inward along the grain boundaries. It reinforces the boundary layer and mostly stays out of the grain core, where the flux actually lives.
Origin: proposed by Nakamura and coworkers in the early 2000s and commercialized by Hitachi Metals (now Proterial) through most of that decade.[1]
Short versionThe first payoff wasn't a new grade. It was the old grade, made with a fraction of the dysprosium.
5 · First UseSame spec, less rare earth
Hit an existing spec — say N42SH, 20 kOe of coercivity at the 42 energy-product class — with grain boundary diffusion instead of bulk alloying, and you land on the same point on this chart. What changed is underneath it: dysprosium confined to the boundary skin instead of spread through the whole grain buys the same Hci from far less heavy rare earth.
In practiceThis mattered because dysprosium and terbium are the genuinely scarce, geographically concentrated part of this supply chain — not neodymium. A process that gets the same spec sheet out of less of them is a supply chain story before it's a materials science one.
Short versionOnce Hci and Br could move almost independently, the obvious next move was to stop matching the old spec and start beating it.
6 · A New FrontierThen somebody asked the next question
If grain boundary diffusion barely touches Br while it raises Hci, the old ceiling was never a law of the material — it was a limit of bulk alloying. Push the same technique further and you can chase a grade that combines a Br you used to only get at a lower temperature class with an Hci you used to only get by giving that Br away.
6 · A New FrontierGrades that didn't exist before
The result sits above and left of the old dashed line — the Hci of an old H, SH, UH or EH grade, at roughly the Br of the next size up. Still not free: Dy and Tb are still in the part, just far less of it, placed far more efficiently.
Short versionDiffusion reaches as far as diffusion reaches. Grain size and part thickness set the limit, not chemistry.
7 · The LimitA different ceiling, not a missing one
Grain boundary diffusion works from the outside in, along boundaries, so how far it penetrates depends on how fine the grains are and how thick the part is. Patent data on the process puts effective penetration around 2 to 3 millimeters from the surface,[2] which is exactly why it showed up first in thin rings and discs rather than large blocks — and why it pairs so well with the finely jet-milled powder from the sintering process: more grain boundary area per gram, more places for the diffusion to reach.
7 · The LimitThe ceiling nobody diffuses past
There is a real ceiling here, and it isn't a process problem. Nd₂Fe₁₄B's own anisotropy field caps how much coercivity the crystal can hold, full stop — about 75 kOe. Commercial magnets, GBD or not, typically reach only 15 to 20% of that;[3] the gap has its own name, Brown's paradox, and forty years of literature trying to close it. Grain boundary diffusion moved the practical frontier a long way. It never touched the theoretical one.
Next: what any of this costs — below the chart.