Piezoelectrics

Certain materials are atomically structured such that they can deform and polarize as they do so. This is a useful property that allows us to convert energy between mechanical and electrical domains. Examples of such materials include SiO2SiO_{2} (Quartz) and BaTiO3BaTiO_{3} (Ceramic).

A Compression force on Quartz Generating a a Charge Dipole

When dealing with piezoelectric materials we are usually concerned about the relative amount, direction, and type of force that corresponds to a particular polarization vector. The relation between tense forces ( T1,T2,T3T_1, T_2, T_3 ) and shear forces ( T4,T5,T6T_4, T_5, T_6 ) are represented in a piezoelectric coefficient matrix ( DD ) with a polarization output vector shown below:

[P1P2P3]=[d11d12d13d14d15d16d21d22d23d24d25d26d31d32d33d34d35d36][T1T2T3T4T5T6]\begin{bmatrix} P_1\\P_2\\P_3 \end{bmatrix} = \begin{bmatrix} d_{11}&d_{12}&d_{13}&d_{14}&d_{15}&d_{16} \\ d_{21}&d_{22}&d_{23}&d_{24}&d_{25}&d_{26} \\ d_{31}&d_{32}&d_{33}&d_{34}&d_{35}&d_{36} \\ \end{bmatrix} \begin{bmatrix} T_1\\T_2\\T_3\\T_4\\T_5\\T_6 \end{bmatrix}

This equation is, of course reversible as in T=DT∗PT = D^T*P.

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