This paper presents the results of an experimental study of the percolation behavior of the complex dielectric constant of ceramic matrix composites (CMC). Samples of piezoactive CMC were obtained by joint sintering of synthesized PZT piezoceramic powder (matrix) and crushed particles of sintered PZT piezoceramics (filler) of different compositions. The experimental dependencies of real and imaginary parts of the complex dielectric constant of CMC on the porosity of piezoceramic matrix and volume content of ceramic filler particles were measured and analyzed. It was shown that the additional porosity of the ceramic matrix resulting from sintering of the CMC masks the dielectric percolation transition, that actually occurs at the volume concentration of ceramic filler close to percolation threshold (V ∼ 1/3).

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1. Introduction

Over the past years, considerable advances have been made to improve the mechanical properties of ceramics using ceramic composite approaches. Numerous technologies based on incorporation of functional ceramics into structural ones and vice-versa have been developed, and a novel design idea has been applied in the field of functional ferroelectric ceramics.^1,2,3,4 However, the problem of property trade-off, i.e., the deterioration of electromechanical properties, remains unsolved. Unlike structural CMC, functional ones have been studied to a much lesser extent, and their use in the electronics industry is currently quite limited. In the last few years, new design concepts and ceramic compositions for composites have been developed in the field of functional CMC.^5,6,7,8 The main problem in developing piezoactive CMC is the compromise between mechanical and functional properties, in particular the deterioration of such important parameters as piezoelectric and electromechanical characteristics.

In Refs. 9–12, new methods for fabrication ceramic/ceramic piezoactive CMC were proposed. Samples of PZT/PZT piezoactive composites, which consisted of a piezoceramic PZT matrix with randomly distributed pre-sintered PZT granules of the same composition were fabricated and studied. Despite obtaining sufficiently high piezoelectric parameters, the use of the same composition of PZT piezoceramics as ceramic matrix and filler did not make it possible to improve significantly the electromechanical and piezoelectric properties, as well as to study percolation transitions in CMC.

In Refs. 13 and 14, we proposed a new fabrication method and presented the results of the finite element modeling and experimental studying of the microstructure and dielectric properties of piezoactive ceramic/ceramic CMC, consisting of a piezoceramic matrix with randomly distributed sintered piezoceramic particles of different compositions.

This paper presents the results of an experimental study of concentration dependences of the complex dielectric constant of the CMC fabricated using previously developed method by joint sintering of synthesized piezoceramic powder and crushed particles of sintered piezoceramics of different compositions.

2. Objects of the Study and Methods of Measurements

CMC fabricated by joint sintering of synthesized piezoceramic powder (matrix) of the composition PbTi $_{0.41}$ $_{0.41}$ Zr $_{0.49}$ $_{0.49}$ Nb $_{0.057}$ $_{0.057}$ Zn $_{0.0235}$ $_{0.0235}$ W $_{0.006}$ $_{0.006}$ Mn $_{0.011}$ $_{0.011}$ O₃ (C1) and crushed particles of sintered piezoceramics (filler) of the composition Pb $_{0.95}$ $_{0.95}$ Sr $_{0.05}$ $_{0.05}$ (Zr $_{0.53}$ $_{0.53}$ Ti $_{0.47})$ $_{0.47})$ O₃ + 1% Nb₂O₅ (C2) was chosen as the object of the study. The filler particle size was equal to 50–100 $μ$ $μ$ m at a concentration of 0–60 vol%. The choice of matrix and filler compositions was determined by the technological (closeness of sintering temperatures of 1220–1240°C) and chemical compatibility of piezoceramic compositions in order to minimize chemical modification and averaging of the CMC composition. Special regimes of mixing and pressing were used for the formation of CMC press-blanks of 23mm in diameter and 16mm in height. Sintering of blanks was carried out at a temperature of 1240°C for 2h in a mode preventing the cracking of the material caused by the difference in the shrinkage coefficients and thermal expansion of the composite components. After sintering, the density of the blanks was determined using the hydrostatic weighing method, as well as by measuring the weight and volume of the samples. The disk-shaped composite samples of 20mm in diameter and 1mm thick were cutted from the blanks. Electrodes were deposited on the main surfaces of the composites by firing a silver-containing paste. CMC samples were polarized in air by applying dc electric field (∼1kV/mm) to the electrodes at a temperature above the Curie point with cooling under the field to room temperature.

Microstructural studies were performed on polished and chipped surfaces of CMC samples using an EQ-MM500T-USB (MTI, USA) digital metallographic microscope and a JEOL JSM-6390LA scanning electron microscope.

Complex dielectric parameters of CMC elements were measured on standard samples using an Agilent 4294A impedance analyzer and the Piezoelectric Resonance Analysis Program (PRAP).¹⁵ This software uses a generalized form of Smits’s¹⁶ method to determine material properties for any common resonance mode, and a generalized ratio method for the radial mode¹⁷ valid for materials with any mechanical quality factor $Q_{M}$ $Q_{M}$ .

Analysis of experimental piezoresonance spectra of the thickness and radial vibrational modes of disk samples made it possible to obtain dependences of the complex dielectric permittivity’s $ε_{33}^{T}$ $ε_{33}^{T}$ , $ε_{33}^{S}$ $ε_{33}^{S}$ of CMC om the volume content of the filler particles.

3. Results and Discussion

Figure 1 shows an optical photograph of sintered particles of C2 piezoceramics with a size of 50–100 $μ$ $μ$ m, used as a CMC filler. Figure 2 shows, as an example, an optical photograph of the microstructure of sintered CMC C1/C2 with a concentration of ceramic filler particles C2 equal to 53%.

Fig. 1. Optical micrograph of milled particles of sintered C2 piezoceramics with a size of 50–100 $μ$ $μ$ m.

From the microphotograph (Fig. 2) it is clear that CMC C1/C2 is characterized by a random distribution of filler particles of irregular shape (light brown C2 particles in the dark brown C1 matrix). Small dark spots in the ceramic matrix are micropores that arise due to the difference in the shrinkage coefficients of the ceramic matrix and filler during sintering of CMC.

It is also obvious that at a concentration of 53 vol.% C2 particles have fragmentary three-dimensional mechanical contact, which should lead to an elastic percolation transition. The dielectric percolation transition should be observed at a concentration of filler particles of ∼33 vol.%.

Figures 3 and 4 show the dependences of the shrinkage coefficient $K_{sh .}^{diam .}$ $K_{sh .}^{diam .}$ (Fig. 3), measured $ρ^{exper .}$ $ρ^{exper .}$ density, and the relative porosity P (Fig. 4) of CMC on the volume content V% of filler particles of 50–100 $μ$ $μ$ m sizes for CMC samples of cylindrical shape, sintered in the same regime. It is clear from Fig. 3 that $K_{sh}^{diam}$ $K_{sh}^{diam}$ drops rapidly and almost linearly with increasing V due to an increase in the concentration of the nonshrinking phase (pre-sintered C2 piezoceramic particles), which prevents the ceramic matrix from shrinking and leads to microporosity appearance. It is readily seen in Fig. 4 that the density of the ceramic composite drops and relative porosity grows rapidly with concentration V which corresponds well to shrinkage coefficient behavior (Fig. 3).

Fig. 4. Dependences of measured $ρ^{exper}$ $ρ^{exper}$ density, and the relative porosity P% of CMC on the volume content V% of C2 filler particles of 50–100 $μ$ $μ$ m sizes for CMC samples of cylindrical shape, sintered in the same mode.

Figure 5 shows experimental dependences of the real $ε_{33}^{T^{'}} / ε_{0}$ and imaginary $ε_{33}^{T^{''}} / ε_{0}$ parts of the complex dielectric constant of CMC on the volume content V of C2 filler particles in the C1 matrix. From Fig. 5, it is obvious that $ε_{33}^{T^{'}} / ε_{0}$ and $ε_{33}^{T^{''}} / ε_{0}$ increase with growth of filler content V almost linearly and demonstrate a behavior which is not typical for percolation transitions.

Fig. 5. Experimental dependences of the real $ε_{33}^{T^{'}} / ε_{0}$ and imaginary $ε_{33}^{T^{''}} / ε_{0}$ parts of the complex dielectric constant of CMC on the volume content V of C2 filler particles in the C1 matrix.

In Refs. 14, we used the 3-0 and 3-3 connectivity algorithms for finite element modeling of dielectric percolation transitions in CMC. It was shown that taking into account the experimentally observed porosity of the ceramic matrix leads to a change in the concentration dependence of the dielectric constant, but both algorithms used do not detect the expected dielectric percolation transition in the vicinity of the volume concentration of filler particles close to V ∼ 1/3. Based on this, it was concluded that percolation effects for CMC should be modeled using more precise methods that take into account not only the location of the phase elements, but also the features of the internal structure of their constituent elements.

As we showed earlier,¹⁸ the dielectric constant of any type of porous piezoceramics decreases with increasing porosity almost linearly due to the large difference in the dielectric constant of piezoceramics and air. Thus, to identify the dielectric percolation transition in CMC, in this work we additionally studied the dependence of the complex dielectric constant of the ceramic matrix C1 on porosity.

Figure 6 shows the experimental dependences of the real $ε_{33}^{T^{'}} / ε_{0}$ and imaginary $ε_{33}^{T^{''}} / ε_{0}$ parts of the complex dielectric constant on the relative porosity P of porous ceramics C1 specially manufactured using the previously developed method of burning out of porosifier agent.¹⁸

These values correspond to dielectric loss tangent $t g δ = ε_{33}^{T^{''}} / ε_{33}^{T^{'}}$ equal to 0.003 and 0.02. Thus, in contrast to the real part of the dielectric constant, the values of the imaginary part and the dielectric loss tangent tend to values typical for the piezoceramic filler material, without exhibiting percolation behavior.

It is obvious from Fig. 6 that $ε_{33}^{T^{'}} / ε_{0}$ and $ε_{33}^{T^{''}} / ε_{0}$ drop rapidly and almost linearly with increasing P. The obtained dependences (Fig. 5) were used to correct the experimental dependences of the real $ε_{33}^{T^{'}} / ε_{0}$ and imaginary $ε_{33}^{T^{''}} / ε_{0}$ parts of the complex dielectric constant of CMC on the volume content V of C2 filler particles in the C1 matrix.

Figures 7 and 8 show the experimental (1) and corrected on additional porosity (2) dependences of the real $ε_{33}^{T^{'}} / ε_{0}$ and imaginary $ε_{33}^{T^{''}} / ε_{0}$ parts of the complex dielectric constant of CMC on the volume content V of C2 filler particles in the C1 matrix.

Fig. 7. Experimental (1) and corrected on additional porosity (2) dependences of the real $ε_{33}^{T^{'}} / ε_{0}$ part of the complex dielectric constant of CMC on the volume content V of C2 filler particles in the C1 matrix.

Taking into account the dependence of the real part of dielectric constant $ε_{33}^{T^{'}} / ε_{0}$ of the piezoceramic matrix C1 on porosity allows us to normalize the obtained dependences to initial porosity of the ceramic matrix (Fig. 5). The resulting corrected dependence corresponds to the classical dielectric percolation transition at a C2 filler particle concentration of V ∼ 1/3. The real part of the corrected dielectric constant $ε_{33}^{T^{'}} / ε_{0}$ of CMC increases sharply with increasing V (Fig. 7, curve 2) from the value $ε_{33}^{T^{'}} / ε_{0} = 1120$ , typical for the piezoceramics of the C1 matrix, to the value $ε_{33}^{T^{'}} / ε_{0} = 1600$ , typical for the dense piezoceramics C2.

However, in this case, the change in dielectric constant occurs in a limited range of values typical for the matrix and filler materials.

The imaginary part of dielectric constant of CMC $ε_{33}^{T^{''}} / ε_{0}$ (Fig. 8) grows rapidly and almost linearly with increasing V. Taking into account the porosity of the piezoceramic matrix CMC (Fig. 5) only leads to a change in the slope of the dependence $ε_{33}^{T^{''}} / ε_{0}$ on V without any anomalies near the percolation threshold. It should be noted that the values $ε_{33}^{T^{''}} / ε_{0}$ for the C1 piezoceramics, and for dense piezoceramics C2, are equal to approximately 2 and 32 correspondingly.

Thus, we can conclude that the additional porosity of the ceramic matrix resulting from sintering of CMC masks the dielectric percolation transition that actually occurs at the volume concentration of ceramic filler close to percolation threshold (V ∼ 1/3).

4. Conclusion

This paper presents the results of a study of CMC obtained by joint sintering of synthesized piezoceramic powder (matrix) and crushed particles of sintered piezoceramics (filler) of different compositions. The experimental dependences of the real $ε_{33}^{T^{'}} / ε_{0}$ and imaginary $ε_{33}^{T^{''}} / ε_{0}$ parts of the complex dielectric constant of CMC on the volume content V of ceramic filler particles in the ceramic matrix were obtained. Analysis of the concentration and porosity dependences of the complex dielectric constant of CMC showed that at the concentration of piezoceramic filler particles close to V ∼ 1/3 a classical dielectric percolation transition occurs. We showed that the additional porosity of the ceramic matrix resulting from sintering of the CMC masks the dielectric percolation transition occurring at the concentration of filler particles close to percolation threshold (V ∼ 1/3).

Acknowledgments

The study was financially supported by the Russian Science Foundation Grant No. 24-22-00063, https://rscf.ru/project/24-22-00063/ at the Southern Federal University.

ORCID

A. N. Rybyanets https://orcid.org/0000-0002-8974-6153

N. A. Shvetsova https://orcid.org/0000-0001-5896-1339

I. A. Shvetsov https://orcid.org/0000-0003-2990-8314

N. A. Kolpacheva https://orcid.org/0000-0001-6553-1767

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Vol. 15, No. 02

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Received 26 April 2024

Revised 29 May 2024

Accepted 17 June 2024

Published: 22 July 2024

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This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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