Calculating electric field produced by micro crystalline piezoelectric grains

Hi,

I'm researching a potential masters project involving incorporating piezoelectric crystals into a ceramic so that when a load is experienced the electric field generated encourages the electroplastic effect in the bulk phase so that it becomes more plastic and inhibits crack formation.

The basic equation relating electric displacement and field is the starting point, I don't have a good grasp on electric displacement. It mentions dipole density which I guess forms a matrix that you adjust with a strain vector that coupled with some factors can produce a measurable charge displacement? yeah I'm really lost.

If someone understands this maths, could you help me with figuring out what a grain of say quartz under a say 0.1% strain would produce as an electric field?

currently im looking to produce a charge density of i think 40A/cm? which i foresee as difficult due to the potentially very high resistance of the ceramic. at this stage im looking at the ceramic used in ceramic knives, although im yet to find out what that is.

Answers and Replies

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I found some examples of calculations on here. so thats good.

a quartz crystal of 2mm size can produce a field at its surface of 44kV/cm^2. which from looking into electroplastic effect is very useable.

Ceramics however tend to be most effected by electroplastic (EP)effect near their glass transition temperature, which for NaCl ~300 C.

Metals however are quite affected by EP at room temperature, as long as the electric field strength is high, 2-100kV/cm^2.

So, what use is a conductive material that will soften proportionally to the strain induced?

I don't claim to have much expertise in this area, but the electric field within the piezo crystal does not extend more than the space charge region on its exterior (angstroms). I'm not sure you would expect to see any electric field developed in adjacent non-piezo grains, assuming you're making a granular composite.

if its that small, how do electric lighters form such a spark?

In the case of a conducting material, would the space charge be conducted? I am unclear what I'm trying to say, would it redistribute the electron cloud?...curses

I think what i mean is will an electron wind be generated?

Poled piezo crystals generate an internal voltage difference upon mechanical deformation that exactly cancels the internal charge distribution of the non-centrosymmetric crystal structure. As long as the deformation is maintained, so is the internal voltage difference. By hooking up an external circuit to this crystal, you are essentially shorting it. I don't think you'd want to create a composite having embedded piezo crystals where the matrix phase was conductive (though, again, I could be wrong).

By not want are you saying it would be electrified? wouldn't the random orientation of the piezo crystals negate each other? so you would only get localized currents.

what about a piezomagnetic material? it would produce a changing magnetic field under shock which would induce an electric field