Dielectric and light scattering spectroscopy of incommensurate phases in crystals

Petzelt, J.

doi:10.1080/01411598108241319

Cited by 76 publications

(30 citation statements)

References 220 publications

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“…These experimental results correspond to the flexocoupling constants of the order of a few hundred volts 6 and customarily discussed in terms of the static bulk flexoelectric effect. At the same time, the upper bounds (17) and (18) suggest that so high values of the flexocoupling constants would have lead to the formation of the incommensurate phase in these materials. 15 Since no incommensurate phase been reported, either in BaTiO 3 or in SrTiO 3 , the high flexoelectric response in perovskite ceramics can hardly be due to the static bulk flexoelectric effect.…”

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confidence: 99%

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Upper bounds for flexoelectric coefficients in ferroelectrics

Yudin

Ahluwalia

Tagantsev

2014

Applied Physics Letters

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Flexoelectric effect is the response of electric polarization to the mechanical strain gradient. At the nano-scale, where large strain gradients are expected, the flexoelectric effect becomes appreciable and may substitute piezoelectric effect in centrosymmetric materials. These features make flexoelectricity of growing interest during the last decade. At the same time, the available theoretical and experimental results are rather contradictory. In particular, experimentally measured flexoelectric coefficients in some ferroelectric materials largely exceed theoretically predicted values. Here, we determine the upper limits for the magnitude of the static bulk contribution to the flexoelectric effect in ferroelectrics, the contribution which was customarily considered as the dominating one. The magnitude of the upper bounds obtained suggests that the anomalously high flexoelectric coupling documented for perovskite ceramics can hardly be attributed to a manifestation of the static bulk effect. V C 2014 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4865208] Flexoelectric effect is the response of electric polarization to the mechanical strain gradient. It can be viewed as higher-order effect with respect to piezoelectricity, which is the response of polarization to strain itself. However at the nano-scale, where large strain gradients are expected, the flexoelectric effect becomes appreciable. Besides, in contrast to piezoelectric effect, flexoelectricity is allowed by symmetry in any material. Due to these features flexoelectricity has attracted growing interest during the last decade. On the other hand, the available theoretical and experimental results are rather contradictory, attesting to a limited understanding in the field. In particular, often experimentally measured flexoelectric coefficients largely exceed theoretically predicted values. It is important to distinguish different contributions to the effect: bulk and surface contributions; static and dynamic contributions. The relative magnitude of these contributions is discussed in a recent review article.

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“…17 While the inequalities obtained indicate the upper bounds for flexoelectric constants in materials where incommensurate phase does not form, they may also be used to understand materials where such phases indeed form. 8,18 …”

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confidence: 99%

Upper bounds for flexoelectric coefficients in ferroelectrics

Yudin

Ahluwalia

Tagantsev

2014

Applied Physics Letters

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“…For the latter, more information is needed, but it is clear that the space group is neither that reported for/3-nor that reported for a'-Sr2SiO4. modulated in the b direction, some with an approximately 2x period [(NH4)2BeF4 (Petzelt, 1981)] but most with an approximately 3 x period [Rb2ZnCL and Rb2ZnBr4 (Hogervorst & de ~/olff, 1982); K2ZnCI4 (Kucharczyk, Paciorek & Kalicifiska-Karut, 1981); K2SeO4 (Petzelt, 1981); etc.] -cf.…”

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confidence: 99%

A preliminary electron-microscope study of the β⇄α' transformation of distrontium silicate, Sr₂SiO₄

Stenberg¹,

Hyde²

1986

Acta Crystallogr Sect B

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Some electron-microscope observations (mainly electron diffraction) confirm the suggestion [Barbier & Hyde (1985). Acta Cryst. B41,383-390] that a modulated structure is likely to intervene in the/3-~-a'-Sr2SiO4 transformation. The diffraction patterns from beam-heated crystals indicate two apparently incommensurate modulations, ql = 0.39b* and q2 = 0.30b*. There are also variations in the monoclinic angle,/3, of the unit cell, and changes in symmetry as indicated by systematic absences of Bragg reflections. While many questions remain unanswered, it is clear that previous understanding and explanations of the transformation must be augmented by the inclusion of periodic modulation of the structure(s)-for Sr~SiO4, and probably for Ca_~SiO4 also.

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“…Already in 1970 [18], Axe et al pointed out that the phonon dispersion curves for the ferroelectric KTaO 3 suggest that mode coupling (which is, as presently known, due to flexoelectricity) can lead to the formation of the incommensurate state in perovskite ferroelectrics. In fact, a large number of ferroelectric materials are known to exhibit modulated phases [19][20][21]. Prior studies of incommensurate phases in ferroelectrics revealed the presence of one-dimensional modulations/stripe domain patterns.…”

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confidence: 99%

Influence of flexoelectric coupling on domain patterns in ferroelectrics

et al. 2014

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Using Ginzburg-Landau theory and two-dimensional (2D) phase field simulations, we analyze the influence of flexoelectric coupling on the domain patterns in ferroelectrics. The phase field simulations predict that a high strength of the flexoelectric coupling leads to formation of a fine structure in domain patterns in ferroelectrics. The fine structure forms when the coupling strength exceeds a critical value and is related to local transition into an incommensurate phase. Depending on the parameters, a structure with stripe patterns with antiparallel polarizations or another one, not seen before, with two-dimensional arrays of alternating vortices is found. Complex domain configurations with coexisting phases and unusual domain walls between them are observed. Although the incommensurate phase does not form for weaker couplings, the influence of flexoelectricity on bulk domain patterns can still be significant. The results of the calculations are rationalized using an analytical model. Directions for the modulation wave vectors in the fine structure are found in the framework of a linear analysis, while the type of the structure-stripes or vortices-is determined by anharmonicity.

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Dielectric and light scattering spectroscopy of incommensurate phases in crystals

Cited by 76 publications

References 220 publications

Upper bounds for flexoelectric coefficients in ferroelectrics

Upper bounds for flexoelectric coefficients in ferroelectrics

A preliminary electron-microscope study of the β⇄α' transformation of distrontium silicate, Sr₂SiO₄

Influence of flexoelectric coupling on domain patterns in ferroelectrics

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Dielectric and light scattering spectroscopy of incommensurate phases in crystals

Cited by 76 publications

References 220 publications

Upper bounds for flexoelectric coefficients in ferroelectrics

Upper bounds for flexoelectric coefficients in ferroelectrics

A preliminary electron-microscope study of the β⇄α' transformation of distrontium silicate, Sr2SiO4

Influence of flexoelectric coupling on domain patterns in ferroelectrics

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Product

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A preliminary electron-microscope study of the β⇄α' transformation of distrontium silicate, Sr₂SiO₄