# Coil inductance near the core's Curie temperature

I wound a Gadolinium slug and measured its inductance at various temperatures around its Curie temperature of 19°C (or 20 or 21 or so, references vary). Because of the Curie-Weiss law (Curie–Weiss law - Wikipedia) I expected to see the measurement suddenly shrink to almost nothing as the temperature approached from below. But I got a different behavior. Well below Tc the inductance dropped linearly. Around Tc there was a shoulder, and the curve became quite steep, but then to my surprise it grew ever more gradual again, seemingly falling off like an exponential decay or something. So, it looks like an S curve, or a negative “error function”, though with the upper curve sharpened a bit in shoulder fashion.

Here are some typical rough values of temperature followed by the inductance in microhenrys. Notice how even 20 degrees above Tc there is still some slope; it’s gradually tapering off, and didn’t suddenly switch off.

10°C 240
15°C 210
17°C 200
19°C 195
20°C 190
21°C 150
22°C 110
23°C 80
25°C 60
30°C 40
35°C 32
40°C 30

Maybe I misunderstand what to expect. That would explain why the Curie temperature value ranges over a couple degrees in the literature. What should inductance look like for a wound coil whose core is around its Curie temperature?

Or, maybe something here is messy. I used a cheap inductance meter - could it be heating the core a little, or should I be interested in a high-field value or a limit in the low field?

Thanks!

Here’s some explanation with a couple of graphs that better illustrate why I hoped to find sudden transition behavior: http://www.msm.cam.ac.uk/doitpoms/tlplib/ferromagnetic/curie-weiss.php

Well, for starters, how sure are you that your entire core was at the Curie temperature? If the part you measured the temperature was around 21 or 22, for example, the part deep inside could well have been a few degrees higher.

Also, in in part at least, probably sloppy measurement due to the cheap meter (probably with no Kelvin connections). Our problem here appears to be that you can accurately measure temperature but can’t accurately measure inductance. I, on the other hand, am not equipped to accurately measure temperature but can make very accurate inductance measurements. Is your Mid Atlantic anywhere near mine?

QED, thanks. Your Mid Atlantic is probably 3 hours from mine, but the offer is most kind.

I think the entire core was isothermal far beyond that influence mattering. It has a radius of 3 mm, and I think it has a conductivity of around 50 W/(m K), so it must have a radial relaxation time of about 0.1 seconds, whereas my experiment allowed a few minutes for temperatures to equilibrate. Moreover, I traced the curve going up and going down, and measured no difference.

The second reference makes me think I should be trying to see the saturation magnetization drop to zero, like by magnetically biasing the slug and then evaluating whether the permeability was higher than air for that field. But not sure.