PhD Thesis Arne Lüker final version V4 - Cranfield University

c) Impact of Local Polar Regions.
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Theoretical Considerations and Literature Review
The typically centrosymmetric tunable materials may have local polar regions induced
by various defects and structural imperfections. For example, infrared reflectivity
investigations of SrTiO3 ceramics revealed a clear presence of grain-boundary-induced
polar phase inclusions [19]. Random field defects can also be responsible for the
appearance of local polar regions [20]. In all these polar inclusions, the quasi-Debye
mechanisms is expected to be active. Though the volume fraction of the polar phase is
typically small, this “defects-induced” quasi-Debye mechanism may be important due to
its large (compared to other intrinsic loss mechanisms) contribution per unit of volume.
Though the theory of the “defect-induced” quasi-Debye mechanism is not developed,
using the results on the quasi-Debye loss mechanism should be strongly ε-dependent.
According to Ref. [6] in the ferroelectric phase of a displacive ferroelectric
tan S
3 / 2 2
δ QD ∝ ε P where PS is the spontaneous polarization. In the case of non-polar
tunable material with polar inclusions one can substitute the volume average of the local
polarization squared,
quasi-Debye mechanism as
2
P loc , for
2
P S to evaluate the contribution of the “defect-induced”
3 / 2 2
tanδ
∝ ε P .
[Eq. 2.23]
dQD
loc