Really, the unit [pm/V ] is used in practice. Usually, such inverse characteristic as coefficient of specific piezosensitivity [V/pm] is measured.

I disagree with Serge! Piezoelectricity is the property of generating charges under a mechanical stress : charges are expressed in coulombs, they can only be turned into volts by adding a "charge amplifier" electronic circuit ; stress is expressed in pascals but can be turned in other physical units if the shape coefficient of the piezoelectric material, its polarization, and the whole sensor assembly design are properly factored: pC/N is then the valid unit to express the "sensitivity" of a calibrated force piezo-sensor, pC/ms-2 (or Pc/"g" for the old bad habit of using g as acceleration unit) for piezo-accelerometers, Pc/Pa for piezo pressure sensors etc.. It is only when you assemble a complete transduction chain with preamps etc. that you can ultimately express the calibration in physical units per volt (ms-2/V for accelerometers, N/V for force transducers , Pa/V for pressure transducers etc.)

There is no way to relate directly your piezo-sensitivity into physical units/V without assessing the transduced design including all the electronic conversion gains...

Bernard Garnier Thank you for your answer.

I want to further clarify that I measured the piezoelectric coefficient value from PFM in pm/V which uses indirect piezoelectric effect. Is it safe to say that if we can generate the charges via direct piezoelectric effect then we get the value in pC/N?

Also, the value I got in pm/V can not be, in that case, compared to values in literature in pC/N, right?

Thank you for your help!

For piezoelectric materials, there are piezoelectric effect and inverse piezoelectric effect.

Piezoelectric effect means if we give a force to piezoelectric materials then the charges will be generate in the surface of materials, so the "pC/N" is used to describe this force to charge "piezoelectric effect".

In contrast, the inverse piezoelectric means if we give a voltage to piezoelectric materials then it will produce strain, so the "pm/V" is used to describe this voltage to strain "inverse piezoelectric effect".

The "inverse piezoelectric effect" equal to the "piezoelectric electric effect" theoretically.

Lin Guo Thank you for providing the clarity!

pm/V and pCb/N are idential dimensions. Look at the relation that 1 V is equal to the electrical voltage between two points of a conductor in which, at a current of 1A, a power of 1 W is produced between the two points. I.e:

1Volt =1Watt/1Ampere

1 Watt = 1 Joule/Second 1 Joule = 1Newton ∙ 1Meter

1 Ampere = 1 Coulomb/Second

1Volt=(1 Joule/Second )/(1 Coulomb/Second)=(1 Joule )/(1 Coulomb)

=1 (N∙m)/Cb

therefore 1 V/m=1 N/Cb and pm/V=pCb/N

When you use a piezo element as a sensor, the pCb/N (charge per applied force) is more convenient. When you use it as a drive element you better take pm/V which means the contraction in pm per Volt applied. The material constant is the same in both cases.

You may find more on this on my website:

https://www.f3lix-tutorial.com/piezo-constants

Piezoelectric Coefficient is the charge developed on the surface of Piezoelectric material per unit force applied on it. So in SI system, the unit become coulomb/Newton. Since the charge developed per unit force is small and so, we take unit as pC/N.

Also, [charge/Force] = [charge/(charge x electric field)] = inverse of potential gradient. So the unit become pm/V.

Thus both the units have same dimension and are correct to measure Piezoelectric coefficient. pC/N is easily understandable by the students as it is related to the basic definition.

The numerical values cant be exchanged unless the sensitivity of PFM and d33 meter have a linear relation.

The dimensions pm/V and pC/N, represent the piezoelectric coefficient, are physically equivalent pairs of converse effects which have been clarified by several scholars above.

There are generally differences in experimental results between the pm/V and pC/N. For ferroelectrics, the typical measurement method is the inverse piezoelectric coefficient(pm/V) expressed by butterfly loops(normalization of electrostrain on applied electric field) and the piezoelectric coefficient(pC/N) measured by quasi-static piezoelectric instruments.

Such two piezoelectric coefficients have dimensional consistency, but in terms of numerical value, the inverse piezoelectric coefficient is usually larger than the piezoelectric coefficient (sometimes several times larger, depending on the piezoelectric crystal).

The contribution of electrostrain is divided into two parts: intrinsic contributions and extrinsic contributions. Intrinsic contributions originate from piezoelectric and electrostrictive effects. Extrinsic contributions come from the switching of non-180° domains and volume changes produced by the non-ferroelectric to ferroelectric phase change. In addition, the inverse piezoelectric coefficient is partially contributed by ferroelectric domain flipping and undergoes polarization state reorientation switching (ferroelectric phase switching), while the piezoelectric coefficient does not undergo this phase switching(it only expresses polarization current under a small continuous alternating stress).

Therefore, the inverse piezoelectric coefficient(pm/V) and the piezoelectric coefficient(pC/N) are often referred to as the large signal piezoelectric coefficient and the small signal piezoelectric coefficient, respectively.

Finally, a unit of physical quantity describe a certain physical process, and in describing experimental data, dimensions should follow the experimental process.

I hope these answers are useful to you.