The widely used Bruggeman equations correlate tortuosity factors of porous media with their porosity. Finding diverse application from optics to bubble formation, it received considerable attention in fuel cell and battery research, recently. The ability to estimate tortuous mass transport resistance based on porosity alone is attractive, because direct access to the tortuosity factors is notoriously difficult. The correlation, however, has limitations, which are not widely appreciated owing to the limited accessibility of the original manuscript. We retrace Bruggeman's derivation, together with its initial assumptions, and comment on validity and limitations apparent from the original work to offer some guidance on its use.

https://cyberleninka.org/article/n/1375237.pdf

On the origin and application of the Bruggeman correlation for analysing transport phenomena in electrochemical systems

Lead-free (Ba0.85Ca0.15)(Ti0.9Zr0.1)O3 (BCTZ) piezoelectric ceramics were prepared by conventional oxide-mixed method at various calcination and sintering temperatures. Both calcination and sintering temperatures have a significant effect on the density and grain size, which are closely related with piezoelectric and other properties of ceramics. The calcination temperature has a great influence on the grain boundary, which also plays an important role in piezoelectric properties. With increased calcination and sintering temperature, the ferroelectric and piezoelectric properties have enhanced significantly. The BCTZ ceramics calcined at 1300 °C and sintered at 1540 °C exhibit optimal electrical properties: d33 = 650 pC/N, d31 = 74 pC/N, kp = 0.53, kt = 0.38, k31 = 0.309, s 11 E = 14.0 × 10 − 12  m 2 /N , ɛr = 4500, Pr = 11.69 μC/cm2, which is a promising lead-free piezoelectric candidate.

Enhanced piezoelectric properties of (Ba0.85Ca0.15)(Ti0.9Zr0.1)O3 lead-free ceramics by optimizing calcination and sintering temperature

Freeze casting is a promising technique to fabricate porous materials with complex pore shapes and component geometries. This review is aimed to elaborate the fundamental principles of the porous microstructure evolution and critical factors that influence the fundamental physics involved in freeze casting of particulate suspensions. The discussion separately analyses homogeneous and directional freeze casting for both aqueous and non-aqueous systems. The effects of additives, freezing conditions, suspension solids loading and particle size on pore shape, size and morphology evolution are discussed. Special techniques based on modified freeze casting, such as freeze tape casting, double sided freeze casting and field directed freeze casting, are also included.

Freeze casting of porous materials: review of critical factors in microstructure evolution

Freeze casting – A review of processing, microstructure and properties via the open data repository, FreezeCasting.net

A review of fabrication strategies and applications of porous ceramics prepared by freeze-casting method

Porous PZT ceramics have drawn an increasing amount of interest in recent years due to their superior properties compared with the dense material. However, researchers have usually dedicated effort to 0–3 and 3–3 type porous PZT ceramics and little attention has been focused on 1–3 type. The 1–3 type porous PZT ceramics with high porosity were fabricated in this study by freeze-casting process. All samples possessed high piezoelectric coefficient (d33) with high porosity owing to the special one-dimensional ordered porous structure along the poling direction. The d33 values increased by either improving the pore channel orientation level or decreasing pore size. The relative permittivity improved only with the enhancement of pore channel orientation level. The acoustic impedances ranged from 1.45 to 1.35 MRayls which could match well with those of biological tissue or water; therefore, this material would be beneficial in hydrophone applications.

Effects of pore size and orientation on dielectric and piezoelectric properties of 1–3 type porous PZT ceramics

Effects of sintering behavior on microstructure and piezoelectric properties of porous PZT ceramics

Porous lead zirconate titanate (PZT) ceramics are of great interest for hydrophones and medical imaging applications. The 0–3 type and 3–3 type porous PZT ceramics have been extensively discussed these years but the 1–3 type PZT ceramics have seldom been reported. This paper describes the fabrication process to obtain such 1–3 type porous PZT ceramics with one-dimensional pore channels by using tert-butyl alcohol-based directional freeze-casting method, and presents analysis of both microstructure and functional properties. The 1–3 type porous PZT ceramics with porosity ranging from 28.1% to 68.7% were fabricated by adjusting initial solid loading. With the increase of porosity, relative permittivity (ɛr) decreased slightly and longitude piezoelectric coefficient (d33) exhibited only a small decline, which could be attributed to the special 1–3 type porous structure. The resultant samples with 61.3% porosity possessed a high value of hydrostatic figure of merit, >100 times higher than that of dense materials. The acoustic impedance (Z) showed a linear dependence on porosity with the lowest magnitude reaching 1.3 MRayls (106 kg·(m2·s)−1), matching very well with biological tissue or water.

Piezoelectric Properties of the 1–3 Type Porous Lead Zirconate Titanate Ceramics

Porous lead zirconate titanate (PZT) ceramics with three-dimensionally interconnected pores were prepared using a novel tert-butyl alcohol-based gel-casting process, an unconventional technique in acquiring high-porosity ceramics. In the present work, PZT ceramics with porosity ranging from 31.3% to 58.6% were fabricated by adjusting the initial solid loading and sintering temperature. The fabricated samples were characterized in terms of both porous structure and functional properties to clarify the underlying correlation. With the increase of porosity, relative permittivity (er) decreased to a significantly low value compared with dense PZT ceramics while the longitude piezoelectric coefficient (d33) exhibited a moderate decline, which could be attributed to the unique structure with homogeneous pore distribution. As a result, the resultant samples possessed a high value of hydrostatic figure of merit, 4100 times higher than that of dense materials. The acoustic impedance (Z) showed a linear dependence on porosity with the lowest magnitude reaching 3.0 MRayls (10 6 kg . (m 2 . s) –1 ), hopefully leading to enhanced coupling with biological tissue or water.

Porous PZT Ceramics with High Hydrostatic Figure of Merit and Low Acoustic Impedance by TBA‐Based Gel‐Casting Process

Porous PZT ceramics were prepared by two approaches: burnable plastic spheres (BURPS) process with varied percentages (2.5, 5.0, 7.5, 10.0, and 12.5 wt%) of stearic acid as the pore-forming agent and tert-butyl alcohol-based gel casting with different initial solid loadings (10, 15, 20, and 25 vol%). The resultant samples were characterized to evaluate effects of different preparation techniques on the microstructure and electrical properties of porous PZT ceramics. Two batches of samples possessed different pore size and morphology. Dielectric and piezoelectric properties basically showed a descending trend with increasing porosity and the results agreed with the theoretical prediction. Relative permittivity possessed different values even at the same level of porosity due to the difference in pore size and pore morphology. Piezoelectric constant d33 was generally larger for samples by gel casting than for those by the BURPS process mainly induced by the variety in the preparation processes. However, the acoustic impedance exhibited a linear decrease with an increasing porosity regardless of different pore size or morphology introduced by different preparation techniques.

Rui Guo

Papers

Effects of pore size and orientation on dielectric and piezoelectric properties of 1–3 type porous PZT ceramics

Effects of sintering behavior on microstructure and piezoelectric properties of porous PZT ceramics

Piezoelectric Properties of the 1–3 Type Porous Lead Zirconate Titanate Ceramics

Porous PZT Ceramics with High Hydrostatic Figure of Merit and Low Acoustic Impedance by TBA‐Based Gel‐Casting Process

Microstructure and Electrical Properties of Porous PZT Ceramics Fabricated by Different Methods