Conductivity of HOT Bathroom Tiles


In “Casting Day Fuzzy Feeling” part 1 I found very hot bathroom tiles conduct electricity, so the ceramic shield that I built for my aluminium furnace was pretty much useless. It got me thinking “How useless”: Was the glowing hot porcelain conducting electricity going to kill me? I spent w-aaaaaaaaa-y too long trying to work this out!

I found this paper, “Temperature Dependence of Electrical Conductivity of a Green Porcelain Mixture”[1] online. This paper was really the most useful information I found on porcelain’s thermoelectrometric properties (yep, I found the word for it!).

The paper really focuses on green porcelain, which is the porcelain before its fired. But the authors, once they have gone to 900℃ then measure the conductivity as the (now sintered) material cools.

I think the gist of the paper is that as you heat/sinter the green porcelain interesting things happen at ‘A’, ‘B’ and ‘C’ in the graphs below, and these causes glitches in the conductivity curve. I think those changes are irreversible, so the cooling curve is smooth. I am assuming that if you heated it up again, you would see a smooth curve the same as the ‘cooling curve’ from the paper.

Clear as mud right?

Conductivity Data for Sintered Porcelain

‘Conductivity’ data points heating green porcelain up, circled in red (Figure 5 in [1]) NOT what I was after, but what is happening at A, B and C is actually pretty interesting – you’ll have to look at the actual paper for that! But this (I think) is the green porcelain being cooked to form the sintered ’tile’ material.

…Same data a different way (An Arrhenius Plot) plus the cooling curve. (Figure 4 in [1])

The images above, in the original PDF, were raster images, so I digitized it to get the numbers. I used the data in the first graph to sense-check the data I got out of the Arrhenius plot since the y-axis is labelled as log (σT), which I pretty sure is an error – should be log σ – since the value are the same as for the top graph.

Here is my take on the values:

 

Conductivity vs Resistivity vs Resistance vs Impedance

I had to do a little learning on this:

  • Conductivity (Seimens per metre) is the reciprocal of resistivity (Ohm-metre).
  • Resistivity (and its reciprocal Conductivity) characterise the material. Resistance(R ) and conductance include geometrical properties. So ‘copper’ has a resistivity, and 200mm of copper wire a resistance.
  • Impedance is for alternating current as resistance id for DC. In the paper [1], they go through some exercise to convert impedance to resistance in an equivalent DC circuit…
  • …also the impedance seems to be affected by the AC frequency. The bearing of this gets me a little lost. For instance the paper [1] they measure impedances over the 1.3MHz–1mHz range at the different temps and then use some magic (involving impedance spectra, equivalent CPE circuit and Nyquist plot. Eh?)to derive the conductivity. Hum?

And that’s pretty much it.

Steinhart-Hart

A bit of a digression but I came across the Steinhart-Hart Equation for thermistors when I was making my solar shower. The Steinhart–Hart equation is a model of the resistance of a semiconductor at different temperatures. I wondered if I could curve fit the Steinhart-Hart equation to the ‘cooling’ data. the orange dashed line showed what I ended up with – I cheated a little and left the T=100℃, 800℃ and 850℃ values out of the curve fit.

It kind of fits though right? I read somewhere that the Steinhart-Hart equation is only really good for/ accurate over a temperature range of ~200℃.

Just thought it was interesting.

Conclusion

Main Conclusion: Ceramics are weird. the more you try and understand, the more lost you get. And the statement ‘ceramics are insulator’ just is not true. At low temperatures, ceramics are insulators.

I am not sure if I can call me tiles semi-conductors or not. As far as the definition of a semiconductor goes it seems we meet the criteria:

 A solid substance that has a conductivity between that of an insulator and that of most metals, either due to the addition of an impurity or because of temperature effects.

Wikipedia has a list some resistivities/ conductivities of some common conductors, insulators and things in between (semiconductors and electrolytes). Comparing these with the values for the sintered porcelain (the ‘cooling’ curve):

  • Porcelain @100C: I reckon its okay to assume my tiles would have an insulator hat on. We kind of knew that though right?!? But it is the worst of what I would call an insulator on the Wiki list: glass is the next best. Porcelain at 100℃ it about the same as ‘Air’ at 20℃.s
  • @ 400C:  Between de-ionised water and damp wood at 20℃.
  • @ 900C: Sitting between drinking water and seawater. You hear about people and pets dying of electrocution swimming in electrified water.

So, as if I needed it confirmed, my ceramic shield is a pretty-shit electrical shield.

Other Stuff I Learnt

International Annealed Copper Standard (IACS)

This was kind of interesting – a standard conductivity for copper. From Wikipedia: The standard is most often used as a comparative property in the specification of the conductivity of other metals. 

Even at 1200C my tiles are <<1% of the conductivity of IAC copper.

 

 

 

 

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