SaM - Compact Piezoelectric Coefficient Matrix for PZT • Dependence of Piezoelectricity on Temperature • Curie Temperature

Remeber:

Piezoelectric coefficient matrix (in compact notation) for PZT (Lead Zirconate Titanate):${\overline{\overline{d}}}_{\text{PZT}}=\left[\begin{array}{lccccc}0& 0& 0& 0& d_{15}& 0\\ 0& 0& 0& d_{24}& 0& 0\\ d_{31}& d_{32}& d_{33}& 0& 0& 0\end{array}\right]$The real matrix dimensions are $[3\times 3\times 3]$.

==Piezoelectric materials have to be operated under the Curie temperature==.

Curie Temperature: is the temperature at which, usually, there is a phase transition from an asymmetrical to a symmetrical crystal. For PZT this temperature is $T_C=250°\text{C}$.

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Piezoelectric materials have to be operated under the Curie temperature, which is the temperature at which, usually, there is a phase transition from an asymmetrical to a symmetrical crystal, for PZT this temperature is 250 degrees, and etc.:

• NOTE: for quartz used at temperature higher than $200$ degrees its behavior becomes highly dependent on temperature.
• The last thing is that the structure of the $d$ matrix, which is the charge piezoelectric coefficient.
  This matrix here actually has a sparse nature.
• For instance this is the shape that this matrix takes obviously with respect to the crystallographic axis, for PZT.
• Notice this is a matrix which is $3\times 6$, while we defined it as a $3\times 3\times 3$, because it relates a vector to a tensor (which is a $3\times 3$), so $3\times 3\times 3$, is the right dimension/size of the matrix, but since everything is symmetrical, the part related to the mechanical behavior, 2 indexes can be collapsed into one so in compact notation we can use for a couple of indexes the same rule that we have used for the elastic matrix.
• And you see here that we have many many zeroes, so only in some specific direction there is really a coupling between the electrical and mechanical response.
  (So a sparse matrix)