{"id":2357,"date":"2015-07-20T11:10:52","date_gmt":"2015-07-20T11:10:52","guid":{"rendered":"http:\/\/www.richardmudhar.com\/?p=2357"},"modified":"2018-09-11T22:22:20","modified_gmt":"2018-09-11T22:22:20","slug":"measuring-paramagnetism","status":"publish","type":"post","link":"https:\/\/www.richardmudhar.com\/blog\/2015\/07\/measuring-paramagnetism\/","title":{"rendered":"Measuring paramagnetism"},"content":{"rendered":"

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<\/a> or use a torsion balance to observe the attraction in a horizontal plane which takes out the static weight of the sample.<\/p>\n

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 \ud83d\ude09<\/p>\n

\"It's<\/a>
It’s not really right to go chiselling a lump off megaliths that have survived thousands of years to insert into a Gouy balance…<\/figcaption><\/figure>\n

The other way of measuring volume magnetic susceptibility is to stick the sample into a coil and measure the inductance – with a different configuration\u00a0 of the coil as a search coil it can be used to measure susceptibility at the rockface.<\/p>\n

<\/p>\n

For a solenoid<\/p>\n

L = \u00b50<\/sub>\u00b5r<\/sub>N2<\/sup>A\/l<\/em><\/em><\/p>\n

L being the inductance,N the number of turns, A is the cross-sectional area and little l being the length – all of which are constants in any sensor<\/p>\n

\u00b50<\/sub><\/em> being the permeability of free space,\u00a0\u00b50=<\/sub>4\u03c0\u00d710-7<\/sup> N A-2<\/sup> <\/em><\/p>\n

\u00b5r<\/sub><\/em> is the effective relative permeability of the sample such that<\/p>\n

\u00b5<\/em>r<\/sub><\/em>= <\/em>\u03c7m<\/sub><\/em>+1 where
\n<\/em><\/p>\n

\u03c7m<\/sub><\/em> is the effective magnetic susceptibility of the sample<\/p>\n

I suspect this is the method used by the Phil Callahan Soil Meter (PCSM)<\/p>\n

\"the<\/a>
the Phil Callahan Soil Meter<\/figcaption><\/figure>\n

Bartington Instruments<\/a> seem to be the go-to guys for magnetic susceptibility instrumentation. From them I learned that one shouldn’t use too high a frequency, which is a bear, My initial prototype ran at 52kHz which is ten to a hundred times too high.<\/p>\n

How do you measure the inductance of a coil?<\/h4>\n

You resonate it with a capacitance and observe the frequency. It’s easy to measure frequency. The obvious way is that of time immemorial – I used a Colpitts oscillator of grid dip oscillator fame<\/p>\n

\"Colpitts<\/a>
Colpitts oscillator<\/figcaption><\/figure>\n

and measured frequency with a frequency counter via a high impedance scope probe (10M\/10pf) on the collector of the transistor. A respectably clean sine wave is to be seen<\/p>\n

\"A<\/a>
A roughly 52kHz sinewave of more than 12V is to be seen at the collector<\/figcaption><\/figure>\n
\"The<\/a>
The frequency is not particularly stable long-term – that it’s within 0.015% of the frequency just before I measured the sample after an hour is surprising. The first digit is a zero – my camera seems to hate the red LED display of this 30-year old frequency counter<\/figcaption><\/figure>\n

The first thing to note is this is not a big effect – 52,473 Hz unloaded as opposed to 52,441 with the sample. The sensor is a jam jar wound with enamelled wire<\/p>\n

\"sensor<\/a>
sensor design<\/figcaption><\/figure>\n

From the resonant frequency<\/p>\n

f=1\/(2\u03c0\u221a(LC))<\/p>\n

from which I infer the coil was about 0.56mH. Through a whole load of manipulating the formula for inductance<\/p>\n

 <\/p>\n

\"\"<\/p>\n

I can derive that if L1 is the inductance of the empty jar and L2 is the inductance of the jar with sample then the effective magnetic susceptibility of the sample\u00a0\u03c7m<\/sub><\/em> is (L2-L1)\/L1, which I then have to divide by 4\u03c0<\/a> to convert from SI to CGS is about 97 \u00b5CGS<\/em>1<\/a><\/sup> Phil Callahan would not approve…
\n<\/em><\/p>\n

All volcanic soil & rock is paramagnetic, (from 200 to 2,000 \u00b5CGS). According to Dr. Callahan\u2019s research, a soil magnetic susceptibility reading of 0 – 100 \u00b5CGS would be poor; 100 – 300 \u00b5CGS good; 300 – 800 \u00b5CGS very good; & 800 -1200 \u00b5CGS above excellent. This force can be added to soil, where it has eroded away, by spreading ground-up paramagnetic rock (basalt, granite, etc.) into the soil<\/em>.<\/p>\n

Philip Callahan from the Pike Agri-Lab website<\/a><\/p>\n<\/blockquote>\n

This generally squares with this chart I pinched from Bartington’s manual for the MS2 susceptibility system<\/a>–<\/p>\n

\"1507_sus\"<\/a>100 will take you to the granites and metamorphic rocks and 800 gets you about halfway to the left hand side.<\/p>\n

There again, my sample takes up less than a quarter of the volume of the solenoid I guess, so if it filled the jar it would creep into very good category. That shows one area that needs thought – filling the sample vessel. A look at Bartington’s susceptibility product range<\/a> of sensors is instructive – it shows me I want something like the MS2F point probe and maybe a search-coil-like MS2D surface scanning probe eventually. Bartington are good enough to tell me the frequency ranges\u00a0 – the MS2F is 580Hz and the MS2D loop is 958Hz – presumably there are issues of getting the inductance high enough for the loop, hence going up in frequency. Or maybe the higher frequency suits the application better – Bartington seem to know their stuff.<\/p>\n

Room for improvement<\/h4>\n