Table A1.

Values of the piezoelectric, dielectric and elastic constants of the AT-cut Quartz.

Dielectric Matrix $\left[{\epsilon }^S\right]$	$\left(\begin{array}{ccc}39.21& 0& 0\\ 0& 39.82& 0.86\\ 0& 0.86& 40.42\end{array}\right)·{10}^{-12}$
Elastic Matrix $\left[c^E\right]$	$\left(\begin{array}{cccccc}86.74& -8.25& 27.15& -3.66& 0& 0\\ -8.25& 129.77& -7.42& 5.7& 0& 0\\ 27.15& -7.42& 102.83& 9.92& 0& 0\\ -3.66& 5.7& 9.92& 38.61& 0& 0\\ 0& 0& 0& 0& 68.81& 2.53\\ 0& 0& 0& 0& 2.53& 29.01\end{array}\right) ·{10}^9$
Piezoelectric Matrix $\left[e\right]$	$\left(\begin{array}{c}0.171\\ 0\\ 0\end{array} \begin{array}{c}-0.152\\ 0\\ 0\end{array} \begin{array}{c}-0.0187\\ 0\\ 0\end{array} \begin{array}{c}0\\ 0.108\\ -0.0761\end{array} \begin{array}{c}0\\ -0.095\\ 0.067\end{array}\right)$