Piezoelectric effect: calculate change of length of crystal

[daskywalker]

Homework Statement

A piezo-electric precision actuator is required that produces a displacement (length change) parallel to the crystal z axis of 1.0nm/V. If a commercial type 5H PZT material is available with d33 = 650. pC/N, what length (along the z axis) is needed for the crystal?

Homework Equations

ε_ij=d_kij*E_k

The Attempt at a Solution

I set the length of the crystal as x and try to solve for it. But since I do not know how much voltage is applied at the piezoelectric device my x's just cancel leaving me with 2 numbers that are supposed to be equal but are obviously not.

 

[mark726]

I would first clarify some assumptions and gather more information in order to accurately solve this problem. Some questions that come to mind are:

1. What is the purpose of the piezo-electric precision actuator? Is it for a specific experiment or application? This information can help determine the appropriate voltage to use.

2. Is the crystal under any external stress or strain? If so, this can affect the length of the crystal and should be taken into account in the solution.

3. Are there any other materials or components involved in the actuator? This can also affect the voltage and displacement.

Once these questions are answered, I would approach the problem by using the given equations and known values to solve for the unknown length. If more information is needed, I would conduct experiments or simulations to determine the appropriate voltage and length for the actuator. I would also consult with other scientists or experts in the field for their insights and recommendations.