Effective Coercive Field of PMN-PT Single Crystal Inside a Curved Array Ultrasonic Transducer at High Frequencies

The effective coercive field
${E}_{\text {c}}^{\text {eff}} $
has been investigated as a function of frequency
${f}$
from 10 kHz to 4 MHz for [001]c poled 0.71Pb(Mg1/3Nb2/3)O3-0.29PbTiO3 (PMN-0.29PT) single crystals inside an ultrasonic curved array transducer. The results show that
${E}_{\text {c}}^{\text {eff}} $
monotonically increase with
${f}$
in the form of
${f} ^{\beta }$
, reached more than 6 kV/cm at 4 MHz, which is three times of conventionally defined coercive field (~2 kV/cm). The
$\beta $
value changes at about 400 kHz due to the transition from non-180° domain switching to 180° domain switching. Our results showed that the
${E}_{\text {c}}^{\text {eff}} $
of PMN-0.29PT single crystals under clamped boundary conditions is larger than that of under free boundary conditions, which revealed the fact that strain confinemfent hinders domain switching in ferroelectric crystals. These quantitative results of
${E}_{\text {c}}^{\text {eff}} $
versus
${f}$
can provide very useful guidelines for the design of high-frequency medical array transducers using PMN-PT single crystals.