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Calculations and Measurements of the Spatial Piezoelectric Response and of the d 15 Parameter of PZT5A Ceramic
Author(s) -
Kahn Manfred,
Ingel Robert,
Lewis David
Publication year - 1989
Publication title -
journal of the american ceramic society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.9
H-Index - 196
eISSN - 1551-2916
pISSN - 0002-7820
DOI - 10.1111/j.1151-2916.1989.tb06218.x
Subject(s) - piezoelectricity , lead zirconate titanate , polarization (electrochemistry) , ceramic , materials science , tensor (intrinsic definition) , mathematical analysis , trigonometric functions , mineralogy , mathematics , composite material , geometry , ferroelectricity , chemistry , dielectric , optoelectronics
In the analytical section of this paper the magnitudes of the polarization vectors ( Pi ) of lead zirconate titanate are shown as they vary with the angle of an applied uniaxial stress. This is done by applying a directional cosine matrix to the stress tensor σ jk in Pi = d ijk σ jk . In addition the polarization in the direction of a rotating stress is derived from rotating the d ijk tensor. Two‐dimensional as well as three‐dimensional isometric plots of the results are shown. The experimental section describes the preparation of disks poled uniformly at 90° to their thickness and the use of the Berlincourt d 33 meter to measure d 333 as a function of angle. Very good agreement with the calculated results was obtained. The effect of electrodes on the measurement of d 33 and the use of a d 31 parameter to permit a d 15 determination are also demonstrated. The d 333 measurements provided a d 15 value with a resolution of ± 8%. Its average value was within 5% of d 15 values derived with other techniques.