Electromechanical coupling coefficient k31eff for arbitrary aspect ratio resonators made of [001] and [011] poled (1−x)Pb(Mg1/3Nb2/3)O3–xPbTiO3 single crystals

The dependence of k31eff on the aspect ratio G=l1/l2 has been calculated for resonators made of [001] poled 0.67Pb(Mg1/3Nb2/3)O3–0.33PbTiO3 (PMN-0.33PT) and [011] poled 0.71Pb(Mg1/3Nb2/3)O3–0.29PbTiO3 (PMN-0.29PT). Based on the derived unified formula, the lateral electromechanical energy conversion efficiency |k31eff|2 decreases with G for [001] poled PMN-0.33PT but increases with G for [011] poled PMN-0.29PT.