EuPhO 2024, Експеримент — Задача 3. Task E.3 - Small area behaviour

Task E.3 - Small area behaviour

We can use the setup from the task E.2c, but instead of loading the whole surface of the piezo, we will use the wooden stick to poke into a hole of the plywood cover and measure $F_s$ with the scales as before.

By plotting $U_p(F_s)$ (Fig. 8), we find it has almost the same dependence as in part E2.c with the slope coefficient $\beta_s = (3.37 \pm 0.1)\,\mathrm{V/N}$ almost the same as $\beta$ from part E2.c.

It seems counter-intuitive that limiting the area drastically does not change the response, because the top electrode of the piezo is thin and flexible. What we are observing in this experiment can be explained as follows. Pressing with a stick creates a voltage across the piezo that leads to a mechanical stress radially inside the crystal. The thick bottom electrode prevents the crystal bottom part contracting radially. At the same time, the top electrode is thin, and would be free to contract if there were no wooden plate. Such a contraction would cause the piezo crystal to curve into a bowl-like shape. The wooden cover plate prevents that happening; this means that the mechanical stress will grow along the rim of the piezo disc, and decrease at the point where we press. As a result, the pressure is effectively distributed over the entire piezo crystal. Therefore the correct answer to this part is that there are no significant changes in the response.

E.3 - Small area effects

Special cases and penalties

• Penalty: Without an explicit drawing or written description that the stick was put through the hole, the corresponding 0.5 and the 0.2 for the result will not be awarded, since there is no proof that the measurement are meaningful for this part. The same holds for approaches that only put smaller areas of the wooden cover plate under pressure.
• Adequate measurements of $U_p$ should have at least three points for different forces and it should be concludable (but does not need to be calculated explicitely by the student) from that data that the slope is the same as in E.2c within the error margins. For 2 measurements we award 0.2 and for one 0.1 points, still.
• Penalty: Without a reproducable way to measure piezo voltage responses to applied forces in E2.c, (especially if E2.c was not done or measurements were only attempted with a voltmeter directly attached to the piezo without anything else), the measurements and conclusion in this task are not meaningful. Therefore, the student can only receive max. 0.5 points for the idea of applying pressure through the whole but nothing else. Otherwise the student receives 0 points total.