The elastic softening occurring at pure ferroelectric transitions is of piezoelectric origin, and, neglecting fluctuations, can be written as the tensor product [1] Ds^piezo = d+.(1/e).d (1) where s is the compliance, d is the piezoelectric coefficient and e the dielectric permittivity. Then, from elastic and dielectric measurements of an unpoled ceramic it is possible to obtain an angular average of d, though different from the effective d33, d31 and d15 measured on poled samples. Not all ferroelectric transitions produce simple steplike elastic softenings, but when this is the case, their amplitude is a useful measure of the local piezoelectric response in each domain of the unpoled ceramic, and hence of the potential intrinsic piezoelectric response that may be reached after full poling. This allows the piezoelectric response to be evaluated without the need of poling the sample. A quantitative test of the method has been made for the FE tetragonal phase of BaTiO3 [2], and is successful sufficiently far from TC and the next transition to the orthorhombic phase, possibly due the effect of the fluctuations, not included in Eq. (1). The method may be useful when studying new materials, that are difficult to be fully poled for various reasons, or cannot be poled at all, for example due to excessive electrical conductivity. It can also be used to probe effects, otherwise difficult to probe, such as the effect of charge doping on the polar displacements. It has recently been shown by first-principle calculations [3], that the screening from doped electrons or holes can enhance, rather than suppress, the polar displacements. Indeed, we find that, introducing O vacancies in BaTiO3-? and therefore doping electrons, even though the Curie temperature is depressed, the amplitude of the step below TC presents an initial increase of 17% and then stabilizes around the initial amplitude of the undoped sample, for ? up to 0.01. The microscopic state of O deficient BaTiO3-? is complicated, but the most obvious explanation of the effect is that the enhancement of the piezoelectric softening is related to the polar displacements P through d = 2QP^2, assuming a constant electrostrictive coupling Q, and constant e, whose measurement is prevented by the free charges. [1]. Cordero, F. et al., "Piezoelectric softening in ferroelectrics: Ferroelectric versus antiferroelectric PbZr1-xTixO3", Phys. Rev. B, Vol. 93, 174111, 2016. [2]. Cordero, F., "Quantitative evaluation of the piezoelectric response of unpoled ferroelectric ceramics from elastic and dielectric measurements: Tetragonal BaTiO3", J. Appl. Phys., Vol. 123, 094103, 2018. [3]. Zhao, H.J. et al., "Meta-screening and permanence of polar distortion in metallized ferroelectrics", Phys. Rev. B, Vol. 97, 054107, 2018.
Piezoelectric softening at ferroelectric transitions: effect of doping in BaTiO3-d
Francesco Cordero;
2018
Abstract
The elastic softening occurring at pure ferroelectric transitions is of piezoelectric origin, and, neglecting fluctuations, can be written as the tensor product [1] Ds^piezo = d+.(1/e).d (1) where s is the compliance, d is the piezoelectric coefficient and e the dielectric permittivity. Then, from elastic and dielectric measurements of an unpoled ceramic it is possible to obtain an angular average of d, though different from the effective d33, d31 and d15 measured on poled samples. Not all ferroelectric transitions produce simple steplike elastic softenings, but when this is the case, their amplitude is a useful measure of the local piezoelectric response in each domain of the unpoled ceramic, and hence of the potential intrinsic piezoelectric response that may be reached after full poling. This allows the piezoelectric response to be evaluated without the need of poling the sample. A quantitative test of the method has been made for the FE tetragonal phase of BaTiO3 [2], and is successful sufficiently far from TC and the next transition to the orthorhombic phase, possibly due the effect of the fluctuations, not included in Eq. (1). The method may be useful when studying new materials, that are difficult to be fully poled for various reasons, or cannot be poled at all, for example due to excessive electrical conductivity. It can also be used to probe effects, otherwise difficult to probe, such as the effect of charge doping on the polar displacements. It has recently been shown by first-principle calculations [3], that the screening from doped electrons or holes can enhance, rather than suppress, the polar displacements. Indeed, we find that, introducing O vacancies in BaTiO3-? and therefore doping electrons, even though the Curie temperature is depressed, the amplitude of the step below TC presents an initial increase of 17% and then stabilizes around the initial amplitude of the undoped sample, for ? up to 0.01. The microscopic state of O deficient BaTiO3-? is complicated, but the most obvious explanation of the effect is that the enhancement of the piezoelectric softening is related to the polar displacements P through d = 2QP^2, assuming a constant electrostrictive coupling Q, and constant e, whose measurement is prevented by the free charges. [1]. Cordero, F. et al., "Piezoelectric softening in ferroelectrics: Ferroelectric versus antiferroelectric PbZr1-xTixO3", Phys. Rev. B, Vol. 93, 174111, 2016. [2]. Cordero, F., "Quantitative evaluation of the piezoelectric response of unpoled ferroelectric ceramics from elastic and dielectric measurements: Tetragonal BaTiO3", J. Appl. Phys., Vol. 123, 094103, 2018. [3]. Zhao, H.J. et al., "Meta-screening and permanence of polar distortion in metallized ferroelectrics", Phys. Rev. B, Vol. 97, 054107, 2018.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
