paramagnetism – Richard Mudhar

Arduino millis() interrupt frequency measurement blues

A cautionary tale for those trying to measure frequency using Arduino

For the paramagnetism project, I need to measure the frequency of the oscillator accurately. I did that with a 16F628 PIC last time, but I am after an easier life, and the obvious choice here is Arduino. I get serial output, a way to use I2C OLED displays rather than bit-banging a Hitachi character display 1980’s style, and all that extra wiring, what’s not to like?

The lack of consistency, that’s what. I count the number of 16MHz Arduino UNO R3 clock cycles that have elapsed with every rising edge on D2 in an interrupt service routine – the code is at the end of the post. Once I have seen 16 rising edges pass, I copy that value over, set TCNT1 to zero and start over. The first result will be garbage, after that it should be OK. Every half a second I print a copy of the last result out. This measures the period, in 1/16MHz segments. I collect 2300 results, of which the first 10 are like so

freq,cnt
4793.92, 53398
4794.01, 53399
4795.35, 53400
4794.37, 53396
4794.01, 53400
4794.01, 53400
4794.01, 53400
4794.01, 53400
4793.92, 53401
4793.83, 53402

and you can see right from the get-go that there is trouble in Paradise. These are two crystal oscillators. One is the 16MHz in the Arduino board, the other is a SEI 2.4576MHz oscillator block, which I divided by 512 using a CD4060 to get 4.8kHz

Okay, so the oscillator¹ is 24 years old. Just to eliminate this going bad I ran a scope on the 1/512 output, in persistence mode

It was OK, even on many more cycles in persistence mode.

Paramagnetism revisited

Been nearly ten years since I last looked at this. Most people’s interest in paramagnetism seemed to be soil testing with the Phil Callahan Soil Meter (PCSM), mine was investigating megalithic sites. I have Fabrice to thank for this and much useful information about the PCSM. I had unsatisfactory results in the field, lacking sensitivity. This was probably due to a bad choice of coil design. Looking at Bartington’s MS2D surface scanning probe, it’s clear I should have designed this more like a metal detector search coil.

Bartington’s MS2D surface scanning probe shows how it’s done

Which explains why I shelved this project after dismal results at Gors-Fawr I recall.

Gors Fawr measurement fail. I expected this value to be a lot higher

Sadly Philip Callahan passed in November 2017, it seems interest has dropped away without such an eloquent protagonist. For the first time i though I would look at soil, which you can enclose in a solenoid, which takes away a lot of the handwaving. I bought some rock dust from Allgood Farm on ebay and thought I’d investigate. Before we go on I should emphasise that Allgood don’t say anything about paramagnetism in their description –

Volcanic rock dust is rich in essential minerals and trace elements like magnesium, iron, and calcium that plants need to grow.
Slow Release: These minerals are released slowly over time, providing a long-term nutrient supply.

so this is about mineralisation, not paramagnetism. The last volcanic activity in Britain was 50 million years ago, so volcanic rock from the UK won’t be highly paramagnetic, because much will have eroded over 50mn years 😉

the sample was tested inside the coil, separated for clarity in the picture

I used a discrete component Franklin oscillator. I am also testing a LM358 oscillator, on the same breadboard

opamp and discrete Franklin oscillators on a solderless breadboard

It’s tasteless as hell to make these oscillators on a breadboard, but the discrete component oscillator had a tendency to squegging at these low frequencies so it helped debug that. I have this on DL4YHF’s Spectrum Lab

and you can see there’s some scintillation, whether this can be improved by building this on Veroboard remains to be seen. Using Spectrum Lab I measured the frequency f2 at 5.4886 kHz and f1 with sample at 5.4861 kHz.

Using χ = (f1²-f2²)/(f1² × 4 π) from last time¹ I infer the susceptibility is

(5488.6² – 5486.1²)/(5488.6² × 4 π) = 7.25E-05 = 72 µCGS. Probably +/- 5µCGS given the scintillation in frequency. Definitely paramagnetic, probably not stupendously so. I need to find some powdered materials to calibrate this with. And test the Franklin discrete component oscillator and the LM358 version for stability when soldered, rather than bodged on a breadboard 😉

My coil was ~1.2mH and resonated at ~5.5 kHz with a 1 µF mylar capacitor and the stray coupling capacitors of the Franklin oscillator. To be continued

Note the χ_m terminology then is wrong, it should be χ_v, the dimensionless volume susceptibility ↩

Measuring paramagnetism 3 – a portable instrument

In Part 2 I described a flat coil sensor which changes inductance according to the magnetic susceptibility of what is in front of it. To make this useful in the field I need something to display the change.

the field instrument. The black button stores the calibration frequency with no sample, the red button takes the reading and displays the result after 4 seconds

I was going to count the high-frequency microcontroller clock over, say 500 periods of the low-frequency sensor signal. That turns out to be a terrible way to do this. I don’t have the gear to measure it, but I suspect the jitter from slicing the 1.5kHz sensor signal is too high. The result is that the third significant digit twitters a lot. By counting changes in the sliced sensor signal (thus doubling the frequency) over a fixed period I get the twitter down to one part in >12000 counts¹ over a four-second signal acquisition time. Continue reading “Measuring paramagnetism 3 – a portable instrument”

Measuring paramagnetism 2 – a new sensor

Part 1

Since I will be taking the sensor to the rock I’m going to temporarily give up on getting an absolute measurement, and take a leaf out of Bartington’s book from last time and use a flat coil. I will never be able to contain the sample in the magnetic field¹ as I might be able to in a solenoid, to the effective susceptibility will always be lower than 1. One day I may be able to calibrate this and find a fixing factor, but for now I will look for relative differences.

Continue reading “Measuring paramagnetism 2 – a new sensor”

Measuring paramagnetism

There are two approaches to measuring paramagnetism that seem to be common. One is to use a balance to measure the slight attraction to a magnet – put sample in a balance, apply magnetic field, look for difference in weight of sample using a Gouy balance or use a torsion balance to observe the attraction in a horizontal plane which takes out the static weight of the sample.

The trouble with these two is the attraction due to paramagnetism is weak compared to the weight of the sample – these are lab bench instruments and the electromagnet consumes a lot of power. Although taking samples of soil is easy enough to bring back to the lab, one really shouldn’t be taking a hammer and chisel to ancient monuments to get a sample for a Gouy balance 😉

It's not really right to go chiselling a lump off this to insert into a Gouy balance... — It’s not really right to go chiselling a lump off megaliths that have survived thousands of years to insert into a Gouy balance…

The other way of measuring volume magnetic susceptibility is to stick the sample into a coil and measure the inductance – with a different configuration of the coil as a search coil it can be used to measure susceptibility at the rockface.

Continue reading “Measuring paramagnetism”

Paramagnetic soil ponderings and perambulations

Paramagnetism is a reasonably straightforward characteristic of materials – if there are unpaired electrons in the atoms then the element will be paramagnetic and weakly drawn to a magnet. This demo of oxygen being paramagnetic is great – so far so scientific. Compounds can change this – water is diamagnetic although H2O is clearly contains oxygen.

A lump of paramegnetic rock (the coin is ~2cm dia) — A lump of paramagnetic rock (the coin is ~2cm dia)

When applied to soil and the growth of plants, however, paramagnetic effects fall into the domain of the woo-woo rather than the analytic 🙂 Igneous rock and volcanic soils tend to be notably paramagnetic. Philip Callahan is the go-to source, and this extract from a 1995 Acres USA article is a high-level spin on his take : Continue reading “Paramagnetic soil ponderings and perambulations”