Piezoelectric thin film, piezoelectric thin film element, and piezoelectric transducer

A piezoelectric thin film comprising:

• a lower layer;
• and a first piezoelectric layer directly or indirectly stacked on the lower layer,
• wherein the first piezoelectric layer contains a tetragonal crystal 1 of a perovskite-type oxide,
• a (001) plane of the tetragonal crystal 1 is oriented in a normal direction of a surface of the first piezoelectric layer,
• a spacing of (100) planes of the tetragonal crystal 1 is al,
• a spacing of (100) planes of a crystal contained in the lower layer is aL,
• a lattice mismatch rate between the first piezoelectric layer and the lower layer is defined as 100×(aL−a1)/a1,
• the lattice mismatch rate is from 3.0% to 12.1%,
• a rocking curve of diffracted X-rays of the (001) plane of the tetragonal crystal 1 is measured in an out-of-plane direction of the surface of the first piezoelectric layer, and
• a full width at half maximum of the rocking curve is from 1.9° to 5.5°.