Direct Ink writing of dense and complex shaped
doped-BaTiO3 ceramics for acoustic transducer
applications

N Mezdar, L Seveyrat, A Borta-Boyon, Laurent Gremillard, M Q Le, Pierre-Jean Cottinet

► To cite this version:

N Mezdar, L Seveyrat, A Borta-Boyon, Laurent Gremillard, M Q Le, et al.. Direct Ink writing of dense and complex shaped doped-BaTiO3 ceramics for acoustic transducer applications. Materials & Design, 2025, 260, pp.115076. 10.1016/j.matdes.2025.115076. hal-05493174

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# Direct Ink writing of dense and complex shaped doped-BaTiO₃ ceramics for acoustic transducer applications

N. Mezdar<sup>a,b,c,*</sup> <sup>●</sup>, L. Seveyrat<sup>a</sup> <sup>●</sup>, A. Borta-Boyon<sup>d</sup>, L. Gremillard<sup>b,●</sup>, M.Q. Le<sup>a</sup>, Pierre-Jean Cottinet<sup>a</sup>

## ARTICLE INFO

### Keywords:

- Additive manufacturing

- Barium titanate

- Piezoelectric

- Ceramic

- Ferroelectric

- Composite

## ABSTRACT

Barium titanate is a well-known ferroelectric ceramic due to its dielectric and piezoelectric properties allowing its integration in a wide range of fields such as biomedical or Defence applications as actuators, sensors, acoustic transducer and many other devices. The enhancement of the performance of these devices requires materials with increasingly complex shapes which is restricted by current machining steps. This communication reports on the elaboration of BaTiO₃-based materials by DIW through high loaded slurries consisting in 79 %wt barium titanate (BT) with various PVB content from 0 %wt to 0.25 %wt whose rheological behaviour ensures good ink print-ability depending on the printing strategy and the characterization of the printed parts. Dense ceramic cuboids manufactured by layer-by-layer (LbL-DIW) material deposition with a PVB-containing ink, reaching 95% relative density. Piezoelectric and dielectric properties are close those obtained conventionally with d₃₃ values up to 245 pC/N, similar relative permittivity and dielectric losses inferior to 1% as needed for transducer applications. In addition, the integration of this manufacturing technique for the elaboration of piezoelectric 1-3 composites are discussed in this study through both ink's parameter leading the feasibility of ceramic parts for piezoelectric composite such as 1-3 composite by vertical extrusion (V-DIW).

## 1. Introduction

Piezoelectric materials play an essential role in numerous applications. Their piezoelectric properties enable the conversion from mechanical energy to electrical energy (direct piezoelectric effect), and inversely (indirect effect). As a result they are used for sensor applications [1–3], actuators [4,5], energy harvesting [6,7] or vibrations damping [8]. They are also key compounds in the medical [9–12] and maritime fields [13,14], and through their use in ultrasonic transducer devices [15–18] since their first applications as sonars in 1917 through a quartz-based device [19].

For a long time, lead zirconate titanate (PZT) has dominated the piezoelectric ceramic research and the market thanks to his excellent performances linked to high piezoelectric coefficient, strong electromechanical coupling factors, and high Curie temperature [20]. However, lead and its derivatives are subject to environmental and human health concerns. As a result, the European Union restrict their uses in

devices through various regulations, such as the Restriction of Hazardous Substances Directive (RoHS) and Registration, Evaluation, Authorization and Restriction of Chemicals regulation [21]. In response, numerous candidates were investigated to substitute PZT by lead-free piezoelectric ceramics. The last few years, some of them have emerged as promising alternatives, such as sodium-potassium-niobate based ceramics (KNN) [22], bismuth-based materials (BKT-BNT) [23], and barium titanate (BT) together with its derivatives [24–27].

In addition to research dedicated to PZT substitutes, the shaping of piezoelectric ceramics has undergone significant development in recent years. Historically, piezoceramics were manufactured by a conventional route that includes raw materials' preparation, shaping by die pressing, thermal treatments, and final machining operations (e.g., sawing and grinding to obtain the desired geometry). Nevertheless, improving the properties of piezoelectric devices increasingly requires complex geometries that conventional shaping methods cannot easily accommodate, thus limiting design flexibilities. In addition, these machining

<footnote><sup>a</sup> Univ Lyon, INSA-Lyon, LGEF, EA682, F-69621 Villeurbanne, France</footnote>

<footnote><sup>b</sup> Univ Lyon, INSA Lyon, Université Lyon1, CNRS, MATEIS, UMR5510, Villeurbanne 69621, France</footnote>

<footnote><sup>c</sup> Thales Defense Mission Systems, 06560 Valbonne, France</footnote>

<footnote><sup>d</sup> Thales Research & Technology, 91120 Palaiseau, Île-de-France, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: nael.mezdar@insa-lyon.fr, nael.mezdar@thalesgroup.com (N. Mezdar).</footnote>
operations often generate a large amount of waste from sintered ceramic. This matter is especially critical for piezoelectric composites with 1–3 connectivity, which are the focus of our research. Such composites consist of pillar structures commonly used in transducer applications [17].

Several techniques are being explored to overcome these issues, each with specific constraints and advantages. Among them, additive manufacturing (or 3D printing) has emerged as a promising family of processes. It enables the manufacture of 3D objects directly from a predefined digital model, with a precisely controlled amount of material. Currently, the most-known techniques for printing piezoelectric ceramics are Binder-Jetting (BJ) [28,29], Selective Laser Sintering (SLS) [30,31], Inkjet-printing (IJP) [32,33], Stereolithography (SLA) [34,35], Fused Deposition Modelling (FDM) [36,37], and robocasting (also called Direct Ink Writing, DIW) [38,39].

DIW technology is based on the layer-by-layer deposition of an ink, also known as a paste or slurry. The ink is extruded through narrow nozzles under pressure, employing a digital model to control the printing head’s movement. This ink is mostly composed by the ceramic powder and organic constituents to provide suitable rheological properties for the printing process [40], as well as to control the microstructure and mechanical properties of the final part [41]. DIW also allows rapid prototyping, multi-material printing, and low implementation cost. In comparison with SLA, DIW does not require consideration of critical parameters like particles color or refractive index that can drastically affect SLA printing performance [42,43].

Although the DIW technique appears to be a well-suited method for obtaining dense piezoelectric ceramic structures [44,45], only a few studies have been reported on this topic to date [46]. Preliminary results from our team on barium titanate were firstly presented in the work by Damamme et al. [39], demonstrating excellent density and good piezoelectric properties were achieved with the robocasted ceramics. However, the ink formulation used in that study was not yet well optimized, particularly with respect to shape fidelity in complex geometries, such as 1–3 piezoelectric composites, as well as the role and amount of the polyvinyl butyral (PVB) binder.

Therefore, this work specifically addresses this research gap by investigating the effect of PVB content on the rheological, microstructural, and functional properties of BaTiO₃ inks for robocasting. By investigating the work of Damamme et al. [39], this study aims to establish a comprehensive understanding of how PVB optimization can improve printability and enable the fabrication of complex, high-fidelity structures suitable for advanced piezoelectric composite designs [47].

To improve printability and shape fidelity during ink deposition, it is essential to control the ceramic ink formulation and tailor its rheological behavior. The inks must display a shear-thinning behavior during the printing process, meaning that their viscosity must decrease under shear stress. This facilitates smooth extrusion through the nozzle without clogging. After deposition, the ink should rapidly recover to ensure sufficient shape retention, which is crucial to maintain the printed shape. As a matter of fact, the yield stress of the ink must be high enough to support the stacking of successive layers [48].

The components of the ink and their ratio are essential. Ceramic suspensions are typically composed of ceramic powder with an adequate grain size and high solid loading, a solvent to disperse the particles, a dispersant to prevent particle agglomeration, a binder and a plasticizer to control viscosity and shape retention. Based on the formulation developed by Damamme et al. [39], this study aims to investigate and optimize the amount of polyvinyl butyral (PVB) binder to enable the manufacture of more complex structures involving the robocasting technique.

The first part of this work focuses on understanding the role of PVB in the formulation used for robocasting. This is followed by the second part that analyzes the microstructural characteristics of printed ceramics. Finally, the third part examines their functional dielectric and piezoelectric properties.

## 2. Materials and methods

### 2.1. Ceramic paste preparation

The powder used in this study, recently developed by Thales [49], was a tri-doped barium titanate (BaTiO₃) with the chemical composition (Ba₀.99Ca₀.01)(Ti₀.99Co₀.005Nb₀.005)O₃·δ, featuring a submicron grain size with an average d₅₀ of around 500 nm. It also contains 1 mol% of Li₂CO₃ (Aldrich, 97 %) as a sintering aid. Details of the powder synthesis process are provided in our previous work [39].

An organic vehicle was made from a mixture of terpineol isomers (mix of α, β and γ terpineol, H₂O: 0.1 %, Sigma-Aldrich, 86480) as a solvent and polyethylene glycol with a molecular weight of 200 g·mol⁻¹ (PEG200, Merck, 807483) as a plasticizer with a mass ratio of 9:2. Then 2,2-butoxyethoxy-ethyl acetate (BEEA, 99.5 %, Sigma-Aldrich, 307048), was added as a dispersant, and polyvinyl butyral similar to a Butvar® B-98 (PVB, Sigma-Aldrich, P110010) as a binder. The organic solution was blended in a SpeedMixer (Hauschild GmbH & Co.KG) by several cycles of 2 min at 2300 rpm until the complete dissolution of the binder.

The doped-BaTiO₃ powder was incorporated into the organic vehicle in two sequential steps. Initially, 50 wt% of the powder was mixed for 1 min 30 s at 2300 rpm under dynamic vacuum. The remaining powder was then added and processed under identical conditions. Due to high rotational speed, the pot and resulting ink experienced a significant increase in the temperature. To prevent thermal degradation and maintain formulation stability, the paste was cooled down using a dedicated cooling system. Afterwards, it was transferred into a 5 mL syringe and blended again for 30 s at 200 rpm to ensure uniformity.

Five ink formulations were selected in this paper to investigate the use of different amounts of PVB in the DIW process for piezoceramics printing. They are labelled by their ceramic filling rate and PVB percentage. The reference ink C79_P0 contains no binders whereas C79_P0.25, C79_P1, C79_P2, and C79_P3 contain 0.25 wt%, 1 wt%, 2 wt%, and 3 wt% of PVB respectively. The compositions of those samples (all include 79 wt% ceramic powder) are detailed in Table 1.

For better highlight performance of additive manufacturing, conventional samples based on process of doped-BT pressed cylinder (labelled Btd_P) were also prepared. The ceramic powder was mixed with an aqueous solution of 10 wt% of polyvinyl alcohol (PVA, Rho-doviol® 4/125, Prolabo, 94 %) in an agate mortar respectively with a ratio of 10:1. The mixture was then spread on a sheet of paper and dried in an oven at 60 °C for 1 h. The pressing of the pellets is carried out by introducing 1.5 g of binded powder into a 16 mm diameter matrix at a 10-bar pressure for 1 min using a uniaxial hydraulic press.

The chosen system is quite complex given its four organic components. Terpineol is a fairly viscous solvent with a relatively high evaporation temperature, which promotes more gradual drying. BEEA, as a dispersant and co-solvent, with a decomposition temperature slightly higher than that of terpineol, stabilizes the powder suspension and plays an important role in the ink’s rheology. PVB is a thermoplastic polymer often used to provide cohesion between piezoelectric material particles. Its solubility in terpineol is improved by the presence of BEEA. The PEG 200 plasticizer increases the mobility of the polymer chains and reduces viscosity at high shear rates.

Since the ratios of all the components could not be changed, the

<table><caption>**Table 1**
Compositions of the different doped-BT pastes.</caption><thead><tr><th>Pastename</th><th>Powder (wt %)</th><th>Terpineol + PEG200 (wt%)</th><th>BEEA (wt %)</th><th>PVB (wt %)</th></tr></thead><tbody><tr><td>C79_P0</td><td>79.3</td><td>16.9</td><td>3.8</td><td>0</td></tr><tr><td>C79_P0.25</td><td>79.3</td><td>16.6</td><td>3.8</td><td>0.25</td></tr><tr><td>C79_P1</td><td>79.3</td><td>15.9</td><td>3.8</td><td>1</td></tr><tr><td>C79_P2</td><td>79.3</td><td>14.9</td><td>3.8</td><td>2</td></tr><tr><td>C79_P3</td><td>79.3</td><td>13.9</td><td>3.8</td><td>3</td></tr></tbody></table>
powder and BEEA ratios were kept constant. The PVB rate was first set at 3 % and the rate terpineol – PEG200 was adjusted and then reduced taking into account the first printing results.

## 2.2. Printing and post-treatments of ceramics

Ceramic parts were printed onto glass plates using Direct Ink Writing (DIW) technology through a robocasting system (3Dinks, LLC, USA). The glass plates were covered with coconut oil to allow easy removal after drying. The part design was carried out via RobocadV4 software and directly sliced into an Aerobasic 3200 code that is very similar to standard G-code. The printing process was performed at room temperature (~ 20 °C).

The printed geometry consisted of an 8-layer stack forming a square-based rectangular cuboid of 15 × 15mm² area and 2.9mm height. For each layer, a perimeter was printed and then filled using a rectilinear infill pattern with an alternating cross-hatching angle of 90°. Several printing parameters were adjusted to ensure optimal printability: 410-µm-diameter nozzles and a 5 mm.s⁻¹ printing speed were set to ensure consistent ink flow. To avoid defects caused by inter-filament porosity, a 14 % overlap along the z-axis was chosen (i.e., corresponding to a 360 µm layer height), along with a 14 % in-plane overlap, resulting in a 360 µm center-to-center distance between adjacent filaments.

To prevent the tail effect observed after printing each layer, the "BOD" (Back-Off Distance) parameter that controls the piston's retraction was set to 0.3 mm. Some parts were printed atop a pre-fabricated scaffold structure comprising four layers with a 50 % infill rate and 0.36 mm layer height. These scaffolds were intentionally designed to prevent drying troubles and minimize eventual cracks formation. Such specimens are hereafter referred to as CX_PY_S. During the thermal treatment step, gas released as a result of solvent evaporation can be trapped between the bottom surface of the printed part and the underlying glass support. This entrapment can lead to heterogeneous and differential drying behavior. The scaffold support illustrated in Fig. 1 was therefore introduced to promote this gas release by controlling the porosity of the bottom layer.

After printing, the samples were subjected to a two-temperature stage drying process via a Memmert UF55Plus oven. The first step involved a 16-hour dwell at 40 °C, followed by a 6-hours dwell at 100 °C, with a controlled heating rate of 1 °C.min⁻¹. Once the drying procedure was over, the samples were debinded in a Nabertherm oven for 4 h at 600 °C with the same heating rate, ensuring the complete removal of residual organic compounds, confirmed by Fig. 2.

As observed in Fig. 2, a slight difference in mass at the very beginning of the two curves occurs around 50 °C but it seems to be a measurement artifact. Both inks exhibit two main mass losses. The first corresponds to terpineol and PEG, between 70 and 250 °C, with a maximum around 150 °C, as confirmed by the DTG curve (in red). The second corresponds to BEEA, much less important, occurring within 250 and 350 °C, because of its higher boiling point than terpineol and PEG200. It is worth noting that the departure of PVB cannot be visualized for C79_P0.25, as it

<figure><img src="image_4.png" /><figcaption>Fig. 2. TGA and DTG curves of C79_P0 and C79_P0.25 inks from 30 to 600 °C using a heating rate of 1 °C.min⁻¹.</figcaption></figure>

represents only 0.25 wt% of the ink mass.

Subsequently, sintering was carried out in air at 1150 °C for 4 h and a faster rate of 3 °C.min⁻¹ to densify the ceramic structures.

The surfaces of the printed ceramics were ground with SiC abrasive discs to obtain a smooth and flat surface suitable for electrode deposition. A silver ink was then applied to the polished faces using a 10 µm mesh sieve, followed by a thermal treatment at 500 °C for 1 h. Poling was conducted using "Field Cooling" method, which allows the reorientation of the ferroelectric domains during their formation. The samples were immersed in a bath of insulating silicone oil and heated to 150 °C, i.e., over its Curie temperature. Next, an electric field of 1 kV. mm⁻¹ was applied perpendicular to the electrode surfaces during cooling down to 40 °C, a temperature above the orthorhombic transition. Once the bath reached 40 °C, the field was gradually reduced to zero.

## 2.3. Characterization methods

### 2.3.1. Rheology measurements

Rheology investigations were conducted using an Anton Paar MCR302 rheometer equipped with a 25 mm parallel plate and a 1 mm gap. All measurements were performed at 20 °C using pastes aged for 24 h. Each specimen was subjected to four different rheological tests, enabling the determination of key parameters as defined in Eqs 1–4.

An oscillatory strain sweep was employed to assess the storage modulus (G') and the loss modulus (G'') as a function of shear strain from 0.1 % to 100 %, at an angular frequency (ω) set to 10 rad.s⁻¹. It allowed the identification of G' and G'' in the Linear Visco-Elastic Region (LVER), denoted as G'eq. It is also possible to determine the yield point (τy), defined as the shear stress at the end of the LVER where G' = 0.90G'eq; and the flow point (τf), defined by the condition G' = G''.

<figure><img src="image_5.png" /><figcaption>Fig. 1. Schematic illustration of the drying process of printed ceramic parts: (a) with a supporting scaffold, and (b) without a scaffold. The scaffold increases the surface area available for drying in the lower part of the sample and facilitates the removal of organics, thereby promoting more homogeneous drying throughout the entire thickness of the ceramic piece.</figcaption></figure>
The complex shear modulus ($G^*$) represents the overall viscoelastic behavior of the material and is defined by the relation:

$$G^* = G'(\omega) + iG''(\omega) \qquad (1)$$

Other criteria have been proposed in the literature to estimate the printability of ceramic pastes for robocasting. One such criterion is the ratio $\Phi > 20$ (Eq. (2)) derived from the thesis works of Fielden [50], which serves as an indicator of the material's structural rigidity relative to its yield point. Another is the Flow transitional index (FTI) introduced by Rocha et al. [51] that should be under 20 to ensure good extrudability and shape fidelity (Eq. (3)).

$$\Phi = \frac{G'_{eq}}{\tau_y} \qquad (2)$$

$$FTI = \frac{\tau_y}{\tau_f} \qquad (3)$$

Three Interval Thixotropy tests (3ITT) were conducted to assess the thixotropic behavior of the paste. The test measures the complex viscosity ($\eta^*$) of the ceramic ink under three successive conditions: (i) at rest, using an extremely low shear strain of 0.03%; (ii) under high shear with 100% strain for 10 s, to simulate the extrusion through the nozzle; and (iii) again at rest, to estimate the time-dependent recovery of the initial complex viscosity ($\eta^*$).

A rotational test known as flow curve test was conducted to measure the shear stress as a function of the shear rate. The results were fitted with the Herschel Bulkley model (Eq. (4)) that describes the flow behavior of the paste

$$\tau = \tau_0 + k(\dot{\gamma})^n \qquad (4)$$

where $\tau$ is the shear stress (Pa), $\tau_0$ is the yield stress (Pa), $k$ is the consistency index (Pa.s$^n$), $\dot{\gamma}$ is the shear rate ($s^{-1}$) and $n$ is the flow index.

### 2.3.2. Microstructural characterization

The densities of the sintered specimens were determined via pycnometry using a cell calibrated to 24.62 mL. The relative densities were calculated as the ratio between the measured ceramic density and the theoretical value of barium titanate (i.e., 6.02 g.cm$^{-3}$). Other measurements were also made using Archimede immersion method.

Microstructures were observed by Scanning Electron Microscopy (SEM) using a Hitachi FlexSEM 1000 II SEM, operated in backscattered electron (BSE) mode with a 20 kV acceleration voltage. To investigate the grain size within the material, the ceramic samples were mirror-polished and subjected to thermal etching at 1100 °C (i.e., below the sintering temperature) for 15 min. The samples were then cooled in water at ambient temperature. The grain sizes were determined by image analysis through Fiji software with a population nearby 550 grains using multiple images for each batch of samples to determine the grain size distribution and visualize the dispersion of the values more precisely. The grains were measured individually, considering the largest diagonal of each grain. Macroscopic observations were also conducted using AM7915MZT Dino-Lite USB Digital Microscope and the associated software DinoCapture 2.0.

X-ray diffraction (XRD) was performed on the ceramic samples to identify their crystalline phases and structures including space group and lattice parameter. The device used was an X'Pert Pro MPD Panalytical diffractometer configured in Bragg-Brentano geometry. The diffractograms were recorded over an angular (2θ) range of 10° to 90°, with a step size of 0.016°, a step time of 150 s and a rotating sample holder (60 rpm). On one hand, phase identification and peak indexing were carried out using HighScore software in combination with the Crystallographic Open Database (COD). On the other hand, lattice constant was determined and refined through X'Pert Plus software (Phillips Analytical B.V.) using the first 26 reflections and the TREOR

indexing method [52].

### 2.3.3. Piezoelectric and dielectric measurements

The dielectric capacitance, from which the relative permittivity ($\epsilon_r$) of a material is deduced according to Eq. (5), was measured at a frequency of 1 kHz and an applied voltage of 1 V via an RLC meter HP4284A equipped with an Agilent 16034E connector.

$$\epsilon_r = \frac{\epsilon_{33}^T}{\epsilon_0} \quad \text{and} \quad \epsilon_{33}^T = \frac{C_{LF} \times e}{S} \qquad (5)$$

Here, $\epsilon_{33}^T$ and $\epsilon_0$ are respectively the permittivity of the material and of the vacuum permittivity ($\epsilon_0 = 8.85 \cdot 10^{-12} F \cdot m^{-1}$), $C_{LF}$ is the dielectric capacitance (F), $S$ is the surface area of the electrodes (m$^2$), and $e$ is the sample's thickness (m). Dielectric losses (denoted tan δ) correspond to energy losses due to current leakage [53], and are expressed as the ratio between the imaginary part ($\epsilon''$) to the real part ($\epsilon'$) of the complex permittivity. Piezoelectric coefficient $d_{33}$ (strain and polarization along thickness direction, also the z-axis) was measured using a Piezotest PM300 piezometer, based on the Berlincourt method [54]. The sample was clamped with a preloading force of approximately 11 N between two probes vibrating at 110 Hz.

The dielectric and piezoelectric properties were measured at ambient temperature under 1 kHz, one day after the poling process. In addition, the temperature dependence of dielectric constant was evaluated over a range from -10 °C to 150 °C with a heating rate of 1 °C.min$^{-1}$ rate. Measurements were carried out using an impedance analyzer (HP 4194A) connected to a temperature-controlled oven (Vötsch VT7004), enabling to deduce the Curie temperature of the printed ceramic.

The number of printed parts used and tested for the different characterizations, such as density or functional properties measurements, varies from N = 4 up to N = 14.

## 3. Results and discussion

### 3.1. Shaping of ceramics and rheological behaviors

Fig. 3 shows the different printing tests depending on the paste formulations. All formulations show good flow behavior, without clogging, and can be easily deposited onto the substrate. However, pastes with more than 0.25 wt% of PVB appear to lose their shape after printing. Indeed, C79_P0 and C79_P0.25 still retain their printed geometry while C79_P1, C79_P2, and C79_P3 exhibit noticeable sagging. This effect can be linked to an additional effect of the PVB binder, which—as highlighted in previous studies [55–57]—plays a role of dispersing agent. Through the steric stabilization of the particles, PVB reduces the paste’s viscosity.

Interestingly, a tiny sagging effect of filaments is actually desirable, as it improves the contact between filaments and prevents void formation. In the case of C79_P3, the sagging effect decreases at the end of the printing part, indicating that the dispersing effect of PVB may be dominant only at its lower concentration, and can be overcome at higher levels, to some extent. In other words, the rheological issues associated with PVB addition could be managed by further raising its content. However, it would also increase the amount of organic matter that needs to be considered during pyrolysis, potentially complicating the thermal treatment process.

The sagging effect of C79_P0 and C79_P0.25 was investigated by monitoring the horizontal diameter observation of their filaments, using a 1.19 nozzle diameter, over time, as illustrated in Fig. 4. For both inks, the initial filament diameters were similar, measuring 1.410 and 1.413 mm respectively for C79_P0 and C79_P0.25. This analysis highlights that the free-PVB filaments (C79_P0) do not show any significant variations over time, suggesting a rapid recovery of the ink’s viscoelastic properties that limits post-deposition deformation. In contrast, the small content of PVB (0.25 wt%) implies moderate but measurable sagging effect,
<figure><img src="image_6.png" /><figcaption>Fig. 3. (a) 3D printer (3Dinks, LLC, USA), and (b) printing of doped BaTiO₃ with different formulations including printed scaffold support. From 1 wt% PVB, shape retention is lost due to altered rheological behavior.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 4. From left to right: schematic of the experimental setup camera – 3D printer used for in situ monitoring of the sagging effect during filament extrusion. Evolution of the horizontal filament diameter over time for the C79_P0 and C79_P0.25 ink formulations using a 1.19 nozzle diameter.</figcaption></figure>

characterized by an increase in the horizontal diameter of approximately 4 % (56 µm), which stabilized after about 15 s from the initial state. No further changes were observed beyond this time.

Consequently, due to their superior shape retention, only the C79_P0 and C79_P0.25 ceramic parts were selected for thermal treatment and further investigation.

Fig. 5 shows the effect of PVB on the viscoelastic properties of three different formulations containing 0, 0.25 and 1 wt% PVB, according to an oscillatory strain sweep test. Measurement results are also summarized in Table 2. The binder-free formulation C79_P0 reveals slightly higher storage (G') and loss modulus (G'') than its C79_P0.25 counterpart, with value of 6.7 × 10⁶ Pa versus 4.7 × 10⁶ Pa for G' and above 10⁶ Pa versus 9 × 10⁵ Pa for G'', within the Linear Viscoelastic Region (LVER). These stiffness values are substantially higher than 10⁴ Pa, a threshold limit commonly reported in the literature that is necessary to ensure adequate mechanical integrity and maintain the printed shape during robocasting [40].

In both formulations, increasing strain involves the end of the LVER

with a decrease in G' at the yield point (τ_y). As displayed in Figs. 5b, a yield point at 377 Pa appears for the C79_P0, corresponding to the stress required to disrupt the tri-dimensional structure of the paste, leading to irreversible deformation. Adding a small amount of PVB results in a modest increase of τ_y up to 506 Pa, as observed for the C79_P0.25. Despite having a similar stiffness at rest, this increase in the yield point suggests that the tri-dimensional network is reinforced by the polymer's chains, offering higher resistance to external forces and thereby enhancing the ink's resiliency. These yield point values are in line with literature recommendations for robocasting [41,58], which typically find minimum values of 200 Pa or more [40].

Beyond the LVER, a slight increase in G'' occurs, followed by a decrease in both G' and G'', reflecting an overall reduction in complex modulus (G''), which is characteristic of shear-thinning behavior. This fact leads to a cross-over at the flow point (τ_f), where the inks transit from ''solid-like'' to ''liquid-like'' state. The flow points occur at 112 Pa and 494 Pa respectively for CP79_P0 and C79_P0.25, notably lower than their corresponding yield points. Such discrepancy can be explained by the structural reorganization of ink during deformation, coupled with
<figure><img src="image_8.png" /><figcaption>Fig. 5. Storage and loss modulus as function of (a) shear strain and (b) shear stress for three formulations with various PVB content. All measurements were obtained by oscillatory strain sweep test using a 25 mm diameter parallel plate at 20 °C and ω = 10rad.s⁻¹.</figcaption></figure>

<caption>**Table 2**</caption>

Summary of the rheological measurements obtained by oscillatory Dynamic strain Sweep (DSS) test.

<table><thead><tr><th>Samples</th><th>G' at rest (Pa)</th><th>Yield point τ<sub>y</sub> (Pa)</th><th>Flow point τ<sub>f</sub> (Pa)</th><th>Φ</th><th>FTI</th></tr></thead><tbody><tr><td>C79_P0</td><td>6.7 x 10<sup>6</sup></td><td>377</td><td>112</td><td>17772</td><td>3.4</td></tr><tr><td>C79_P0.25</td><td>4.7 x 10<sup>6</sup></td><td>506</td><td>494</td><td>9289</td><td>1.0</td></tr><tr><td>C79_P1</td><td>212</td><td>0.4</td><td>42</td><td>525</td><td>&lt; 0.1</td></tr></tbody></table>

stress relaxation phenomenon that transiently reduces shear stress before stabilization and its subsequent increase. For both inks, the structural integrity factor (Φ) is found above 20 and the flow transition index (FTI) is estimated below 20, confirming suitable viscoelastic behavior of the developed inks for robocasting applications.

On the other hand, C79_P1 also seems to reach acceptable values of Φ and FTI, despite the significant sagging effect clearly observed in Fig. 3b.

Therefore, these two parameters alone are not sufficient to determine the printability of an ink regarding the dimensional stability of the printed parts. Indeed, the complex shear modulus (G*) shows a drastic decrease, resulting from an abrupt drop in both G*eq and G*eq values respectively at 212 Pa and 80 Pa. Those values are revealed to be insufficient to ensure a good retention of the printed shape. At higher strain (i.e., above 6 %), both moduli increase, suggesting the onset of a shear-thickening effect.

Fig. 6a displays a shear-thinning behavior profile of both C79_P0 and C79_P0.25 inks, confirmed by fitting the flow curves with the Herschel-Buckley model. The flow indices n < 1, with 0.23 and 0.25 respectively, indicate non-Newtonian, shear-thinning behavior. As k is a numerical value that is dependent on the flow index, n, it can't be used alone as a fluid property parameter [59]. Furthermore, these graphs exhibit a hysteresis loop, confirming that the rheological properties of the ink depend on their shear history. Two different values of yield stress are observed depending on whether the shear rate is increasing or decreasing. Static yield stress (τ<sub>0</sub><sup>STAT</sup>), representing the shear stress

<figure><img src="image_9.png" /><figcaption>Fig. 6. (a) Flow curves at 20 °C for C79_P0 and C79_P0.25 inks with increasing and decreasing shear rate ramps including flow parameters. Both inks reveal flow indices "n" inferior to 1 with respectively 0.23 and 0.25. Static yield stresses of 1672 Pa (binder-free) and 2019 Pa for (0.25 wt% PVB), and dynamic yield stresses of 305 and 172 Pa, respectively. The parameter k is 874 Pa.s<sup>0.23</sup> for C79_P0 and 1247 Pa.s<sup>0.25</sup> for C79_P0.25. (b) The complex viscosities obtained by oscillatory test with three intervals of strain depending on the time for C79_P0 and C79_P0.25. Oscillatory tests were carried out at 20 °C and ω = 10rad.s⁻¹.</figcaption></figure>
required to initiate flow, can be estimated from the slope of the increasing shear rate. On the other hand, dynamic yield stress ($\tau_{0}^{DYN}$), characterizing the minimal stress needed to maintain flow, is obtained from the y-intercept of the fit curve [60].

As revealed in Figs. 6a, a slight increase in static yield stress is observed with a small addition of PVB, from 1672 for C79_P0 ink to 2019 for Pa C79_P0.25 ink. This increase is probably originated from the interaction of polymer chains within particles, which strengthens the tri-dimensional network at rest and thus raises the stress necessary to break down the ink structure to initiate the flow. Nevertheless, such an addition of PVB induces a decrease in the dynamic yield stress, from 305 down to 172 Pa with respect to C79_P0 and C79_P0.25. This phenomenon can be explained by the reorganization of the tri-dimensional network under shear. Indeed, as shear increases, the polymer chains tend to align, leading to decreased resistance to flow after shearing.

While the static yield stress characterizes the minimum stress required to initiate ink flow, the dynamic yield stress defines the minimum stress needed to maintain the flow and, in the resilience, to retain the shape of printed parts against gravitational forces. Given this, the theoretical maximum printable height ($h_{max}$) with no collapse of the structure is expressed by the following relation (Eq. (6), proposed by M'Barki et al. [61]):

$$h_{max} = \frac{\tau_{0}^{DYN}}{\rho g} \qquad (6)$$

where $\tau_{0}^{DYN}$ denotes the dynamic yield stress, $\rho$ is the ink density, and $g$ is the constant acceleration due to gravity. Based on those parameters, $h_{max}$ for C79_P0 and C79_P0.25 pastes can be used for structures with

height equal to 11 and 6 mm, respectively. These values are supposed to be sufficient in the case of printing pillars with low diameter/height ratios, as recommended for 1–3 piezocomposite like-structures. To a certain extent, the lower dynamic yield stress of C79_P0.25 ink correlates with an improvement in the density of the sintered ceramic. The fact is that the filaments can flow more easily during printing, allowing them to better fill the gaps between layers.

The inks' thixotropic behavior is illustrated in Fig. 6b, showing the time evolution of the complex viscosity ($\eta^{*}$) during a three-interval thixotropy test (3ITT). The recovery of $\eta^{*}$ is assessed after characteristic periods of 30 and 100 s, providing insights into the inks' structural rebuild capabilities following shear. C79_P0 ink (the black curve) exhibits a sharp decrease in $\eta^{*}$ by nearly 2 decades of magnitude during the second interval, followed by a fast regeneration. The recovery rate is recorded at 77 % after 30 s, and 81 % after 100 s. In contrast, the C79_P0.25 formulation, comprising 0.25 wt% PVB (the red curve), initially displays a higher complex viscosity at rest and experiences less fluidization during 100 % deformation step.

However, its recovery is much slower, with a regeneration of only 21 % after 30 s, i.e., over three times lower than its PVB-free counterpart. After 100 s, its recovery rate reaches just 32 %. Accordingly, such a slower recovery is somehow beneficial for printing dense components. It gives ink more time to flow and adequately heal defects or fill gaps between successive layers before regaining the target structure.

## 3.2. Microstructural characterizations

After printing, the ceramic parts are subject to thermal treatments to progressively remove the organic compounds during the drying and

<figure><img src="image_10.png" /><figcaption>Fig. 7. (a) Schematic representation of the three thermal treatment steps after printing process. (b) Relative density using Archimede immersion method and pycnometry, and porosity from ground samples SEM images analysis of printed samples compared to the pressed sample. (c) Printed part cores observed by digital microscopy with different PVB rate after grinding. Enhanced structure is revealed on the top face while scaffold support underneath helps prevent the formations of large cracks.</figcaption></figure>
debinding steps. This is followed by sintering, which promotes densifi-
cation and is typically accompanied by an increase of the grain size.
These processing steps are illustrated in Fig. 7a, while Fig. 7b displays
the relative density measured by pycnometry after sintering. For com-
parison, the density of pressed parts (denoted BTd_P) is included as a
reference, reaching 98.6 %, and is considered almost fully dense. As
demonstrated in Fig. 7b, all printed samples exhibit relative density
above 90 wt%, confirming the feasibility of the robocasting method for
additive manufacturing of dense ceramics. Notably, the addition of 0.25
wt% PVB gives rise to a significant increase in density: from 90.5 % for
C79_P0 to 94.0 % for C79_P0.25, both without scaffold support.

As previously discussed in Subsection 3.1, such an improvement is mainly attributed to the slower viscosity recovery of the PVB-containing paste. This behavior enables the filling of small inter-filament voids after deposition, thereby reducing defects and porosity, as confirmed by digital microscope images in Fig. 7c. As expected, the C79_P0.25 sample shows a smooth surface with few macroscopic defects, limited to residual porosity, after grinding. In contrast, printing with the binder-free ink leads to smaller densities, which induce a higher prevalence of defects such as cracks and pores. These cracks likely originate during the drying and debinding stages, probably because the absence of PVB compromises the material’s cohesion and mechanical integrity, rendering it unable to withstand thermal treatments effectively. The resulting microstructural degradation is directly correlated with the reduced relative density observed in the C79_P0 sample. Eventually, the incorporation of a small amount of PVB appears to mitigate crack formation throughout drying, particularly in unsupported samples.

Fig. 7c also highlights a beneficial effect of scaffold support, espe-
cially in reducing defects on the bottom surface of ceramics, ultimately
leading to increased density. Indeed, the relative density increases by
2.3 % for C79_P0_S, and by 0.8 % for C79_P0.25_S as opposed to their
unsupported counterparts. It is worth noting that C79_P0.25_S attains
the highest relative density by pycnometry among the printed samples at
95.9 %. Although this value remains below the ideal one at 98.6 %
achieved by the pressed sample, the observed improvements in this
study underscore the relevance of process optimization based on key
physical parameters.

The relative densities obtained by Archimede immersion method on
samples that have been cut and ground down to their core are also
displayed in Fig. 7b. The measured value as a reference with BTd_P
appears to be the higher 97.5 % as expected. The other densities are

slightly higher when using a scaffold in the case of C79_P0.25, showing
an increase of ~ 1.6 %. Surprisingly, the difference between binder-free
and PVB-containing inks appears small, with values around 90 %. These
Archimede method measurements were conducted in a second time on
thinner samples, cut from the original ones for other characterizations,
and therefore may lead to lower accuracy.

Additional observations were conducted on ground, unetched sam-
ples to evaluate the porosity fraction area for each type of samples. It
reveals that binder-free formulation shows higher porosity area, with
values of 13.4 % and 12.6 % respectively for C79_P0 and C79_P0_S. On
the other hand, PVB-containing parts lead to lower porosity, with 10.3 %
and 11.2 % for samples with and without scaffolds. It seems that the use
of PVB and scaffolds tends to reduce the fraction area of porosity. These
results are consistent with the previous reported on relative densities,
which show the same tendency. In addition, although porosity remains
in all samples, the use of scaffolds for both inks reduces the formation of
cracks in printed ceramic, which manifest as porosity defects.

Fig. 8a presents the SEM images of printed samples, all observed after thermal etching. Among the printed samples, C79_P0 appears highly porous and exhibits visible cracks, consistent with the observations previously discussed in Fig. 7c. Inversely, those printed from the PVB-containing inks are revealed to be less porous. Given that the relative organic content is identical for all ink formulations, the binder-free ink suffers from inhomogeneity. In other words, even a tiny amount of PVB enhances the ink’s rheology and printability, while also favoring dispersion within particles. This improved microstructural uniformity contributes to greater densification during the sintering stage. However, thermal etching induces some cracks, and grains could blow up, provoking distorted apparent porosity in SEM observations including the higher density’s samples. Despite these limitations, qualitative comparison of those micrographs allows for the identification of porosity trends across the different processing conditions.

As observed in the statistical whisker plot of Fig. 8b, the conventional
pressed sample (BTd_P) exhibits with the most optimized printed sample
C79_P0.25_S, the biggest mean values of grain size with respectively 4.6
µm and 4.4 µm. The three other printed samples (without binder and/or
support) possessed lower mean value of around 3.5 µm. Analysis of
central tendencies shows somewhat differences between mean and
median values in all samples, with a maximal discrepancy of 0.4 µm.
This suggests a symmetric grain size distribution, regardless of the
manufacturing method, ink formulation, or the presence of a scaffold as

<figure><img src="image_11.png" /><figcaption>**Fig. 8.** (a) SEM images using BSE – Magnification x1500 of printed C79_P0, C79_P0.25 samples and die-pressed sintered ceramics after mirror polishing and thermal etching treatments. (b) Statistical analysis of grain size distribution of sintered ceramics after thermal etching based on whisker plot. Each configuration was evaluated using 550 grains from different locations to assess variability and reproducibility.</figcaption></figure>
support.

Additionally, dispersion analysis is conducted using Quartile Coefficient of Dispersion (QCD) given by Eq. (7) to compare the variability of each sample. Unlike the sole lecture of minimal and maximal values, it allows better representation of the values variability for each sample's values. The QCD range from 2.8 % (for BTd_P and C79_P0) to 3.4 % (C79_P0.25_S) indicating just slight differences. These values, while associated with similar medians, suggest comparable grain size populations.

$$QCD = \frac{IQR}{Q_1 + Q_3} = \frac{Q_3 - Q_1}{Q_1 + Q_3} \qquad (7)$$

where IQR is the interquartile range, Q1 the 25th percentile (lower quartile) and Q3 the 75th percentile (upper quartile).

X-ray diffraction analysis confirmed the presence of a pure perovskite BaTiO₃ phase in all samples, whether prepared via conventional pressing method or 3D printing. The indexed diffraction peak and the characteristic peak splitting around 45°, i.e., corresponding to the (002) and (200) reflections, confirms a tetragonal structure with space group P4mm at room temperature. As summarized in Table 3, lattice constants show no significant differences between the two shaping routes, further supported by high figure of merit (FoM) in the refinement results.

### 3.3. Functional properties

Dielectric constant measurements as a function of temperature were performed through heating and cooling ramps to determine the Curie temperature ($T_c$) for unpoled ceramics, as summarized in Fig. 9. The ceramic produced via the conventional shaping method exhibited a local maximum in dielectric constant, corresponding to a $T_c$ of 112 °C. On the other hand, the robocasted ceramics, printed with or without scaffold support, showed somewhat higher $T_c$ values, ranging from 114 °C to 117 °C during the heating ramp that can be considered as similar within experimental uncertainty. The orthorhombic-tetragonal transition ($T_o, T$) occurs over a temperature range between 14 °C and 19 °C, with a broader peak while the pressed sample has this transition occurring at 21 °C. It is therefore suggested that the shaping method of piezoelectric ceramics has a slight impact on the $T_c$, likely due to microstructural variations or internal stress. Although additive manufacturing enables the fabrication of complex geometries, it inherently introduces defects that can affect both microstructural and functional properties [39,62]. Nevertheless, these differences observed between conventional die-pressed and 3D-printed ceramics remain relatively minor. Fig. 9 also highlights a thermal hysteresis ($\Delta T$) associated with the orthorhombic-tetragonal and tetragonal-cubic transitions. This phenomenon is commonly reported for ferroelectric ceramics according to its characteristics of a first-order transition with temperature [63,64].

Table 4 also reports on the dielectric and piezoelectric properties of both robocasting and conventionally shaped ceramics. To highlight potential trends in property values, the Fig. 10 displays the different results from Table 4 into a normalized with respect to the reference sample. Relative dielectric constant ($\epsilon_r$) seems to increase with sample's density. Lower permittivity is recorded for binder-free inks, with mean values of 1735 for C79_P0 and 1671 for C79_P0_S, clearly indicating no significant effect observed from the use of scaffold support. As expected, binder-containing formulations give higher permittivity

values owing to their higher densities, reaching 1788 for C79_P0.25 (without scaffold) and 1851 for C79_P0.25_S. Accordingly, the conventionally die-pressed sample displays the highest relative permittivity, at 2004. As previously reported [65], the grain size of tri-doped barium titanate (BaTiO₃) can have a significant effect on the dielectric and piezoelectric properties of the final ceramic. Such an effect is, however, assumed to be negligible due to the minimal differences in grain size observed among those samples.

Dielectric losses ($\tan\delta$) show mean values below 1 % for all samples. As expected, the die-pressed ceramics exhibit lower losses thanks to their minimal defects compared to the 3D-printed counterparts. For acoustic transducer applications, $\tan\delta$ should remain below 3 % to ensure adequate hydrophone performance with minimum energy dissipation, enhancing signal-to-noise ratio, and preventing overheat during operational use [66]. Interestingly, dielectric loss behavior appears ultimately linked to sample density. For instance, the printed C79_P0 sample, which displays lower average density and broader density range (84–94 %), also possesses a wider $\tan\delta$ variation, from 0.45 % to 2.2 %. The incorporation of a scaffold, together with the addition of small amounts of PVB, helps mitigate cracking- and drying-induced defects, thereby narrowing the variation in dielectric loss. Nevertheless, increasing the density above 90 % does not appear to significantly impact this parameter.

Concerning the $d_{33}$ piezoelectric coefficient, the die-pressed samples achieve the highest value of 249 pC.N⁻¹. For the 3D-printed samples, they are between 194 and 237 pC.N⁻¹, below the pressed samples ones which was expected given an overall higher porosity. However, the $d_{33}$ coefficients for the printed samples are not completely in agreement with the densities. For instance, the C79_P0 sample, despite its moderate density of 90 %, owns the highest average $d_{33}$, exceeding even that of the more densely optimized C79_P0.25_S (225 pC.N⁻¹). The use of a scaffold unexpectedly results in decreased $d_{33}$ for C79_P0 and has a negligible effect for C79_P0.25. The relationship between density and the $d_{33}$ coefficient is not strictly linear, and certain factors can influence it, particularly for limited porosity ranges (<10–15 %). A slightly different microstructure, such as more homogeneous grains, can reduce internal intergranular stresses and therefore facilitate domain wall mobility. Horchidan et al. [67] presented the highest $d_{33}$ values for porosity rates around 15 %. The distribution and geometry of the pores can also play a role by increasing the compliance of the material. For instance, the work of Zhang [68] demonstrated how porosity influences the distribution of the electric field and modifies the piezoelectric properties. Roscow [69] further studied the effect of pore alignment and morphology using freeze casting on polarization. The free surface can have a significant influence, as it represents an interface (such as a pore), which is a zone without mechanical stress in the material. This contributes to a global relaxation of the internal stresses, modifies the local field during polarization and facilitates the mobility of the domains [69–73]. The surface effect is logically more pronounced in ceramics with small grains and porosities, which is therefore consistent with our observations. This could explain why the $d_{33}$ coefficient does not follow the same increasing trend with density as observed for permittivity. However, combining both PVB and scaffold support seems to reduce the dispersion in $d_{33}$ measurements, thus improving the repeatability to a level comparable to the one of the die-pressed batch. Further research is needed to better understand these observations and the underlying mechanisms.

<table><caption>**Table 3**
Lattice constants of conventional shaped and 3D printed doped BT samples.</caption><thead><tr><th>Samples</th><th>a = b (Å)</th><th>c (Å)</th><th>α=β=γ (°)</th><th>c/a</th><th>Space group</th><th>Crystal system</th><th>FoM (TREOR)</th></tr></thead><tbody><tr><td>BTd_P</td><td>3,9954</td><td>4,0319</td><td>90</td><td>1,00913</td><td>P4mm</td><td>tetragonal</td><td>74</td></tr><tr><td>C79_P0</td><td>3,9974</td><td>4,0310</td><td>90</td><td>1,00840</td><td>P4mm</td><td>tetragonal</td><td>78</td></tr><tr><td>C79_P0_S</td><td>3,9959</td><td>4,0324</td><td>90</td><td>1,00913</td><td>P4mm</td><td>tetragonal</td><td>79</td></tr><tr><td>C79_P0.25</td><td>3,9941</td><td>4,0289</td><td>90</td><td>1,00871</td><td>P4mm</td><td>tetragonal</td><td>146</td></tr><tr><td>C79_P0.25_S</td><td>3,9939</td><td>4,0292</td><td>90</td><td>1,00883</td><td>P4mm</td><td>tetragonal</td><td>116</td></tr></tbody></table>
<figure><img src="image_12.png" /><figcaption>Fig. 9. Temperature dependence of relative dielectric constant during heating and cooling of the different printed ceramic samples at 1 kHz.</figcaption></figure>

<table><caption>**Table 4**
Relative densities by pycnometry, dielectric and piezoelectric properties of die-pressed and 3D-printed samples.</caption><thead><tr><th></th><th></th><th>BTd_P</th><th>C79_P0</th><th>C79_P0_S</th><th>C79_P0.25</th><th>C79_P0.25_S</th></tr></thead><tbody><tr><td rowspan="4">Relative density (%)</td><td>Mean</td><td>98.6</td><td>90.1</td><td>92.8</td><td>94.0</td><td>94.7</td></tr><tr><td>SD</td><td>0.8</td><td>3.2</td><td>2.4</td><td>2.0</td><td>0.8</td></tr><tr><td>Min</td><td>97.1</td><td>84.1</td><td>90.4</td><td>92.2</td><td>93.8</td></tr><tr><td>Max</td><td>99.3</td><td>94.2</td><td>95.1</td><td>96.7</td><td>95.9</td></tr><tr><td rowspan="4">tanδ (%)</td><td>Mean</td><td>0.50</td><td>0.79</td><td>0.62</td><td>0.70</td><td>0.62</td></tr><tr><td>SD</td><td>0.05</td><td>0.50</td><td>0.19</td><td>0.10</td><td>0.18</td></tr><tr><td>Min</td><td>0.45</td><td>0.47</td><td>0.45</td><td>0.61</td><td>0.45</td></tr><tr><td>Max</td><td>0.57</td><td>2.20</td><td>0.82</td><td>0.83</td><td>0.98</td></tr><tr><td rowspan="4">ε<sub>r</sub> = ε<sub>33</sub><sup>T</sup>/ε<sub>0</sub></td><td>Mean</td><td>2004</td><td>1735</td><td>1671</td><td>1788</td><td>1851</td></tr><tr><td>SD</td><td>70</td><td>138</td><td>79</td><td>92</td><td>85</td></tr><tr><td>Min</td><td>1929</td><td>1530</td><td>1582</td><td>1654</td><td>1693</td></tr><tr><td>Max</td><td>2103</td><td>1999</td><td>1733</td><td>1856</td><td>1933</td></tr><tr><td rowspan="4">d<sub>33</sub> (pC.N<sup>-1</sup>)</td><td>Mean</td><td>249</td><td>237</td><td>194</td><td>232</td><td>225</td></tr><tr><td>SD</td><td>3</td><td>20</td><td>20</td><td>15</td><td>5</td></tr><tr><td>Min</td><td>246</td><td>200</td><td>174</td><td>211</td><td>219</td></tr><tr><td>Max</td><td>255</td><td>258</td><td>213</td><td>245</td><td>232</td></tr></tbody></table>

Slight differences in d<sub>33</sub> values were also observed between sample batches, possibly due to variations in powder preparation over time. While not investigated in detail in this study, this factor may partly explain discrepancies with earlier results [39]. Also, it highlights the potential for improving the manufacture of lead-free ceramic components for acoustic applications through controlled processing of this tri-doped barium titanate.

## 4. Towards complex geometries of piezoceramics

Previous results clearly highlighted that the optimal performance in terms of density, permittivity, and piezoelectric coefficient d<sub>33</sub> was obtained using the C79 ink formulation with 0.25 wt% PVB, especially when robocasted onto a scaffold during the printing process. This new configuration allows for improvement of structural integrity and densification through the sintering stage. The ultimate goal is enabling the implementation of such materials into hydrophones or other acoustic sensor devices, which typically need more complex geometries
<figure><img src="image_13.png" /><figcaption>**Fig. 10.** Relative densities by pycnometry, dielectric and piezoelectric properties of die-pressed and 3D-printed samples and the comparative between different types of parts using normalized value to the reference set from BTd_P samples.</figcaption></figure>

to enhance and optimize their performances (Fig. 11.A-D). In particular, the manufacture of piezoelectric ceramics with specific connectivity patterns, such as 3–3 or 1–3 composite structures, is critical for achieving the desired electromechanical coupling and acoustic impedance matching [47].

Rheological analyses of both ink formulations indicated that the composition of each ink (with different amounts of PVB) highly depends on the target architecture and geometries. For instance, cylindrical and rectangular cuboidal lattice structures, along with a 1–3-2 composite ceramic structure (Fig. 11.F), were successfully printed via layer-by-layer extrusion (LbL-DIW) using the C79_P0 formulation. The diameter of the pillars after sintering was about 2.4 mm. However, the fabrication of finer features as in the case of thinner pillars remains constrained by the printing resolution allowed by the use of either ink formulations when extruded through nozzle diameters of 410 µm, thus limiting the achievable minimum feature size. While the pillar height is theoretically driven by the rheological properties of ink (i.e., its yield stress and viscoelastic recovery), the pillar’s aspect ratio (width/height) can be practically tuned by adjusting the extrusion diameter. This parameter is particularly relevant in the design of 1–3 piezocomposites for acoustic transducer field, where the aspect ratio governs the hydrostatic performance as well as the electromechanical coupling efficiency [74].

To overcome the limitations of conventional layer-by-layer printing

<figure><img src="image_14.png" /><figcaption>**Fig. 11.** Printed doped-BaTiO₃ complex parts using two different material deposition strategies: LbL-DIW and V-DIW. (A) rectangular cuboid lattice structure from C79_P0, (B) cylindrical lattice structure from C79_P0, (C) pillars on rectangular cuboid for 1–3-2 composites by C79_P0, and (D) layer by layer deposited rectangular cuboid from C79_P0.25 with (E) vertically printed pillars using C79_P0 for 1–3-2 composites, (F) Printing, sintered and embedded part of 1–3-2 composite structure by LbL deposition in resin, and (G) Printing, sintered and surrounded by an epoxy resin 1–3-2 composite structure made by both LbL and V-DIW methods.</figcaption></figure>
in fabricating high-aspect-ratio features, the Vertical DIW (V-DIW) technique [38], as illustrated in Fig. 11.E, was explored for the fabrication of pillar structures. A custom G-code script was developed, incorporating key parameters including the rheological properties of ink, nozzle diameters, target component height, with the specific objective of manufacturing 1–3 piezocomposite architectures. This fabrication approach combined two DIW strategies. The bottom part consisted of a rectangular cuboid, analogue to the C79_P0.25_S sample previously described in subsection 3.1. As suggested, the integration of a scaffold support during the printing process somehow enhances the final material properties. Such a configuration gives rise to higher sintered densities, lower dielectric losses, and improves both dielectric permittivity and piezoelectric response.

Following the fabrication of the bottom structure, a secondary
deposition step was carried out using the C79_P0 formulation to print
pillars. A nozzle with a 1.6 mm diameter was used, with the intended
pillar diameter set equal to the extrusion filament diameter. It is worth
noting that the actual printed pillar diameter exceeded the nozzle size,
reaching approximately 1.8 mm due to the over-extrusion parameter set
in the G-code.

The binder-free formulation proved particularly well-suited for ver-
tical printing, thanks to its excellent dynamic yield stress that involves
the extrusion of stable structures up to 11 mm height. Moreover, the
3ITT testing confirmed its superior structural recovery, characterized by
the fastest restoration of its complex viscosity and storage modulus
among all tested inks. It helps prevent the shape deformation while
vertically printing and allows an easy separation between the nozzle and
the pillar apex at the end of the extrusion.

As illustrated in Fig. 11.G, the V-DIW approach appears more suit-
able for the fabrication of pillar array and 1–3 composites. This tech-
nique allows the manufacture of smooth surface pillars without any
layer stacks, reducing the risk of defects throughout shrinkage. Addi-
tionally, the method offers greater design flexibility by enabling a wider
range of aspect ratios. Notably, V-DIW allowed the fabrication of thinner
pillars with post-sintering diameters as small as 1.7 mm, significantly
lower than the 2.4 mm achieved with LbL-DIW.

As previously discussed, the V-DIW technique offers an efficient
approach toward tailoring pillar dimensions, especially with smaller
diameters for a desired height. The development and characterization of
complete piezocomposites and their properties using this method
remain the subject of ongoing investigation.

5. Conclusion

In this work, doped barium titanate ceramics with simple geometries
were successfully fabricated via direct ink writing (DIW) using highly
loaded slurries, achieving good shape fidelity. Rheological investigation
and printability observations of terpineol-based inks with different
amounts of PVB binder allowed a comprehension of the binder's influ-
ence on ink behavior such as viscous abilities, thixotropy, and me-
chanical strengths throughout thermal treatments. The best results in
terms of density, dielectric and piezoelectric properties, were obtained
with the ink formulation containing 0.25 wt% PVB. After sintering at
1150 °C, the samples achieved a relative density of approximately 95 %,
with a relative permittivity (ε<sub>r</sub>) of 1856 and a piezoelectric charge co-
efficient (d<sub>33</sub>) of 245 pC/N. These values are only slightly lower than
those typically obtained through conventional ceramic processing.
Dielectric losses remained below 1 %, confirming that the developed
materials are of high interests for acoustic transducers, particularly
throughout their integration into piezoelectric composites.

Scaffold-based drying aids were also successfully employed to pre-
vent crack formation during the drying stage as well as to enhance
densification. Furthermore, it was demonstrated that, due to its distinct
rheological and thixotropic behavior, the binder-free ink was found to
be more appropriate for fabricating size-tailored structures, such as the
narrow pillars required in 1–3-2 piezocomposite architectures. On the

other hand, the binder-containing ink appeared more suitable for pro-
ducing dense and mechanically robust base layers within such com-
posites. Eventually, binder-free ink proved advantageous for printing
fine-featured elements with high dimensional fidelity.

Such an ink formulation reveals a promising strategy for additive
manufactured of lead-free piezoelectric composites via DIW approach.
Future work will focus on further optimization of the composite fabri-
cation process including the refinement of thermal treatment protocols
based on thermogravimetric and dilatometric analyses. The standardi-
zation of powder batches will also be essential to further advance the
development of efficient and environmentally friendly acoustic
transducers.

CRediT authorship contribution statement

**N. Mezdar:** Writing – original draft, Formal analysis, Data curation, Conceptualization. **L. Seveyrat:** Writing – review & editing. **A. Borta-Boyon:** Writing – review & editing, Resources. **L. Gremillard:** Writing – review & editing. **M.Q. Le:** Writing – review & editing. **Pierre-Jean Cottinet:** Writing – review & editing, Supervision, Resources.

Funding

This material is based upon work supported by the ANRT (Associa-
tion nationale de la recherche et de la technologie) with a CIFRE
fellowship No. 2023/0216. This work is principally financed by Thales.
The project is also partially supported by Institute Carnot I@L.

Declaration of competing interest

The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.

Acknowledgements

The authors acknowledge the ANRT (Association nationale de la recherche et de la technologie) for supporting this work through the CIFRE fellowship No. 2023/0216. The authors would like to thank Thales Research&Technology, Thales Defense Mission Systems and Institute Carnot I@L for the financial supports. They also would like to thank Marion Technologies for the provision of BT doped powder.

Data availability

Data will be made available on request.

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