# Electrical charge equilibrium and the piezoelectric effect

About the piezoelectric effect: if I press a crystal the electrical charges segregate and an electrical voltage appears on the other two faces of the crystal.
See this link for example: http://www.explainthatstuff.com/piezoelectricity.html

If I connect the two opposite faces with a wire, an electrical current will flow.
The questions is what happens next, if I keep the crystal pressed (with or without the wire connected - I think it's the same thing)?
I mean, the mechanical stress is still present, but the electrical charges in the deformed crystal are now in some kind of equilibrium?
How is that possible, if pressing the crystal deformed the crystal structure so that the electrical charges are “separated” ?
What happens now if I disconnect the wire and release the crystal?
Would that disturb again and produce a new disequilibrium in electrical charges?
What would be the new equilibrium?

So you might want to read this wiki article I like to think of a piezo as a voltage source (pressure dependent), with a series capacitance, (and then some leakage resistance.)
When you squeeze it you generate some voltage on the cap, but it leaks off. When you release the pressure then you get opposite sign of voltage for a time. (That assumes you are squeezing and releasing slowly.)

The mentioned link shows it very well. If the crystal is not deformed the (ionic) crystal is in equilibrium in all regards (mechanical, potential, electric, ..), if deformed an electrical polarization is induced (dipole moment) and it needs some effort to keep this state (force).

Analogon: It is like you have a sphere at the minimum $$x_0$$ of a parabolic potential, you bring the ball off the equilibrium $$x_1$$ and hold it. Now you have a dynamic equilibrium, but the ball still keeps the additional potential energy and is not in its original equilibrium state.

If you release the polarization will be gone and the state left of the diagram is reached again, now it is in equilibrium state again (idealized for non ferroelectric materials, there are hysterisis effects for the latter one, but not e.g. for quartz crystals).

I highly recommend to use one of the free available electronic circuit simulators e.g. LTSpice VII (very old, but easy to use and precise). Here you will see dynamic behaviour of voltage and current in case of different loads. You even you simulate an energy harvester. Take a simple equivalent circuit diagram (in internet you will find several approaches, take the simplest with one internal C and R) for a piezo e.g. C around some pF and R around 50 Ohm.

For a simple gas fire lighter you have $$U = d * \frac{l}{A}*F$$ with d piezoelectr. constant, l length of 2 piezos (sandwich structure), A area where force F applies, equal to sigma.

d = 0.012 Vm/N

l = 0.028 m

$$F = \sigma * A\,\, N$$

$$U = d * l * \sigma = 0.012 * 0.028 * 30^6 = 10,080\, V\, or\, 10\, kV$$ which will give you a nice sparc in ambient atmospheric pressure.