Electric-field-enhanced permittivity dependence on temperature and cooling rate

Improving the Electro-Optical Deflection Performance of KTN Crystals Based on the Temperature Compensation Effect

“…τ d and τ o denote the displacement relaxation time and reorientation relaxation time, respectively, and χ d and χ o are the displacement and reorientation polarization rates, respectively. The construction of the lattice phonon dielectric response model and the PNRs reorientation-induced dielectric response model yields as follows ε = n P normals 3 L normals 3 k normalB T ε 0 sech 2 ( P s L s 3 E d c k B T ) + m P normale 3 L normale 3 k normalB T ε 0 sech 2 ( P e L e 3 false( E normald normalc − E normalc normalo false) k B T ) where E dc is the b...…”

“…τ d and τ o denote the displacement relaxation time and reorientation relaxation time, respectively, and χ d and χ o are the displacement and reorientation polarization rates, respectively. The construction of the lattice phonon dielectric response model and the PNRs reorientation-induced dielectric response model yields as follows where E dc is the bias electric field, P s is the polarization strength of the electric dipole, L s is the size of the electric dipole, k B is the Boltzmann constant, n is the number of phonons, L e is the size of the PNRs, P e is the polarization strength of the PNRs, E co is the coercivity field to be overcome for PNR reorientation, and m is the number of PNRs. ε is the total dielectric response contributed by lattice phonon polarization and the PNR reorientation, which is positively correlated with the number of phonons n. As shown in Figure c, the cell model of KTN was simulated using VESTA, and the increase in dielectric constant is attributed to the intensity of polarization, reflecting an increasing content of Nb atoms from left to right, in agreement with the results observed by polarized light microscopy.…”

“…τ o denote the displacement relaxation time and reorientation relaxation time, respectively, and χ d and χ o are the displacement and reorientation polarization rates, respectively. The construction of the lattice phonon dielectric response model and the PNRs reorientation-induced dielectric response model yields as follows47 …”

Cu-Doping-Modified Order State, Ferroelectric Property, Multiscale Inhomogeneities, and Local Structure in the Relaxor KTa1–xNbxO3 Crystal

“…Implementing the cool-down operation from high temperature, the PNRs with zero time-averaged polarization appears near Burns temperature T B and is insensitive to the external electric field because of violent thermal fluctuation . Further cooling the KTN, the PNRs with nonzero polarization begin to form below the intermediate temperature T *, and the field-driven reorientation and vibration dynamics of PNRs has a great influence on the dielectric, ferroelectric, and piezoelectric properties of the KTN crystal …”

“…5 Further cooling the KTN, the PNRs with nonzero polarization begin to form below the intermediate temperature T*, 6 and the field-driven reorientation and vibration dynamics of PNRs has a great influence on the dielectric, ferroelectric, and piezoelectric properties of the KTN crystal. 7 Several features of the PNR need to be focused, including the orientation, field-driven reorientation or vibration, and size distribution. Froḧlich entropy can well describe the order state of the domain structure and signals the features of the considered phase and correlated transitions.…”