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## Über dieses Buch

This book is devoted to the systematic description of the role of microgeometry of modern piezo-active composites in the formation of their piezoelectric sensitivity. In five chapters, the authors analyse kinds of piezoelectric sensitivity for piezo-active composites with specific connectivity patterns and links between the microgeometric feature and piezoelectric response. The role of components and microgeometric factors is discussed in the context of the piezoelectric properties and their anisotropy in the composites. Interrelations between different types of the piezoelectric coefficients are highlighted. This book fills a gap in piezoelectric materials science and provides readers with data on the piezoelectric performance of novel composite materials that are suitable for sensor, transducer, hydroacoustic, energy-harvesting, and other applications.

## Inhaltsverzeichnis

### Chapter 1. The Piezoelectric Medium and Piezoelectric Sensitivity

The piezoelectric effect and related electromechanical properties are described, and examples of modern piezoelectric materials and their sensitivity are considered. Full sets of electromechanical constants of various piezoelectric materials are given for comparison. Examples of electromechanical coupling factors and figures of merit are also considered to show links between the piezoelectric sensitivity and these parameters. Among materials exhibiting the important piezoelectric properties, of interest are domain-engineered relaxor-ferroelectric single crystals, poled ferroelectric ceramics and piezo-active composites based on ferroelectrics. The importance of the piezoelectric sensitivity in piezotechnical applications is briefly discussed.
Vitaly Yu. Topolov, Christopher R. Bowen, Paolo Bisegna

### Chapter 2. Effective Piezoelectric Coefficients : From Microgeometry to Anisotropy

Piezoelectric coefficients dij are most widespread to describe the piezoelectric effect, electromechanical properties and other related parameters. The effective piezoelectric coefficients $$d_{ij}^{*}$$ and their links to sensitivity are discussed for piezo-active composites with various connectivity patterns. Examples of the piezoelectric sensitivity of the 2–2-type, 1–3-type, 1–1-type, 0–3-type, and 3–β composites based on ferroelectics are considered. The role of the microgeometry in forming the piezoelectric sensitivity and anisotropy of the piezoelectric coefficients $$d_{3j}^{*}$$ is analysed. Ways to improve the piezoelectric sensitivity in terms of $$d_{ij}^{*}$$ are discussed in connection with potential piezotechnical applications.
Vitaly Yu. Topolov, Christopher R. Bowen, Paolo Bisegna

### Chapter 3. Microgeometry of Composites and Their Piezoelectric Coefficients

Piezoelectric coefficients gij represent a link between an external mechanical stress applied to a sample and an electric field formed by polarisation charges of the sample as a result of the direct piezoelectric effect. The piezoelectric coefficients gij also characterise a link between a strain and electric displacement at the converse piezoelectric effect. The piezoelectric sensitivity associated with gij is of importance for sensor, energy-harvesting, acoustic, and hydroacoustic applications, for piezo-ignition systems, etc. Examples of the effective piezoelectric coefficients $$g_{ij}^{*}$$, max$$g_{33}^{*}$$ and their links to the piezoelectric coefficients $$d_{ij}^{*}$$ are discussed for piezo-active composites with various connectivity patterns (2–2-type, 1–3-type, 1–1-type, 0–3-type, and 3–β composites). The important role of the microgeometric factor and polymer component at achieving the large values of $$g_{ij}^{*}$$ of the composite is shown.
Vitaly Yu. Topolov, Christopher R. Bowen, Paolo Bisegna

### Chapter 4. Piezoelectric Coefficients and : Combination of Properties at Specific Microgeometry

Piezoelectric coefficients eij are used to describe a link between an external mechanical strain and a piezoelectric polarisation caused by the direct piezoelectric effect. The piezoelectric coefficients eij are of importance to analyse a link between a mechanical stress and an external electric field at the converse piezoelectric effect. Examples of the piezoelectric sensitivity of composites with various connectivity patterns are discussed in terms of the effective piezoelectric coefficients $$e_{ij}^{*}$$ and relations between the piezoelectric coefficients $$e_{ij}^{*}$$ and $$d_{ij}^{*}$$. Of specific interest are a non-monotonic behaviour of $$e_{ij}^{*}$$, large values of $$| {e_{ij}^{*} } |$$ and considerable anisotropy of $$e_{3j}^{*}$$ as well as their links to the microgeometry and properties of components.
Vitaly Yu. Topolov, Christopher R. Bowen, Paolo Bisegna

### Chapter 5. Piezoelectric Coefficients : New Opportunities to Improve Sensitivity

Piezoelectric coefficients hij characterise a link between an external mechanical strain applied to a sample and an electric field caused by the direct piezoelectric effect. At the converse piezoelectric effect, the piezoelectric coefficients hij characterise the link between a mechanical stress in the sample and electric displacement. Examples of the volume-fraction behaviour of the effective piezoelectric coefficients $$h_{ij}^{*}$$ and the piezoelectric sensitivity associated with $$h_{ij}^{*}$$ are analysed for the 2–2-type, 1–3-type and 0–3-type composites based on ferroelectrics. Relations between the piezoelectric coefficients $$h_{ij}^{*}$$ and $$e_{ij}^{*}$$ and some cases of the large anisotropy of $$h_{3j}^{*}$$ are discussed for some composites.
Vitaly Yu. Topolov, Christopher R. Bowen, Paolo Bisegna

### Chapter 6. Improving Piezoelectric Sensitivity

The piezoelectric sensitivity of the composite is described in terms of four types of the piezoelectric coefficients, $$d_{ij}^{*}$$, $$e_{ij}^{*}$$, $$g_{ij}^{*}$$, and $$h_{ij}^{*}$$. The role of each type of the piezoelectric coefficients and its merit in determining the PS in composites with various microgeometric features are discussed. Diagrams that link electric and mechanical fields and contain the four types of the piezoelectric coefficients are represented for the direct and converse piezoelectric effects. Examples of orders-of-magnitude of the aforementioned piezoelectric coefficients are given for modern composites based on single crystals. Some ways for improving the piezoelectric sensitivity of the composites are discussed.
Vitaly Yu. Topolov, Christopher R. Bowen, Paolo Bisegna

### Backmatter

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