Study On The Relation Between The Dielectric Constant And The Lattice Distortion Of PZT And PT

From the discovery of PZT in 1950's, it has been extensively used in ceramics as an important ferroelectric and piezoelectric material. The work of this paper is mainly to deeply study the relation between the dielectric constant and lattice distortion of PZT and PT, based on their thermodynamic theory. We comprehensively investigate and discuss the relation in the tetragonal,rhombohedral and coexistence phase region of PZT. We also study the relation between the dielectric constant and lattice distortion of the PT tetragonal and cubic phase region. The contents studied as follows:1.From thermodynamic theory of PZT, we established the equation among the dielectric constant, composition x and the lattice distortion c/a of the PZT ferroelectric tetragonal phase region .Next, we attest that the lattice distortion c/a is a function of composition x. Thence , the direct relation between the dielectric constant and the lattice distortion c/a can be attained. We determine all physical parameters in the two connected equations from the experimental data.2.From thermodynamic theory of PZT, we establish the two connected equations, where, one equation is on the dependent relation between the dielectric constant and composition x , another equation is on the dependent relation between the lattice distortion and composition x of the PZT high-temperature rhombohedral phase region. We determine all physical parameters in the two connected equations from the experimental data.3.Base on the results of the PZT ferroelectric tetragonal and high-temperature rhombohedral phase region, we investigate and discuss the relation between the dielectric constant and the lattice distortion in phase coexistence region . Next, we use the phase statistical distribution model and determine the fitting value of the volume fraction of the tetragonal phase to composition x in the equation. We determine other physical parameters in the two connected equations from the experimental data.4.The theoretical results are compared with the related experimental data, The theoretical prediction of the relation between the dielectric constantand the lattice distortion agree well with the experimental data, though some warp exists. Detailed results are shown as follows:(1)The theoretical curve is compared with the experimental data, The theoretical results agree well with the experimental data, especially for c/a>1.0281. When the value of c/a is less than 1.0281, the relative error between the theoretical value and the experimental values gradually increases. The reason is clear. The PZT system lies in the border between the tetragonal phase and the rhombohedral phase region. Along with c/a farther decreases, the PZT system gradually enters into the mixed phase between the tetragonal phase and the rhombohedral phase, transitions to the rhombohedral phase region later. Thus , the theoretical expressions for the PZT the tetragonal phase must bring some warp when the PZT system lies this region. In substance, at this time the lattice distortion c/a gradually decreases, the structure of the PZT system relatively more slack, the structure relatively more active , which makes incline to move. At the action of the outside electric field or outside force, ferroelectric polarization inclines to reverse, which lead the warp to crease at last.(2)The theoretical curve is compared with the experimental data, The theoreticalresults agree well with the experimental data, especially for >1.74107. When the value of is less than 1.74107, the relative error between the theoretical value and the experimental values gradually increases. Along with farther decreases, the PZT system gradually enters into the mixed phase region between the tetragonal phase region and the rhombohedral phase region, farther transitions to the tetragonal phase region. Thus, the relative error between the theoretical value applied to the rhombohedral phase region and the experimental values must be more error in this region.(3)Using the phase statisti...