# Optimization of direct ink writing of Si N suspensions for the fabrication of self-supported structure

Flavie Lebas, Sylvain Marinel, Elisa Jaumouillé, Christelle Bilot, Romuald Herbinet, Loïc Le Pluart, Raphaël Laloo, Claude Estournès, Charles Manière

► To cite this version:

Flavie Lebas, Sylvain Marinel, Elisa Jaumouillé, Christelle Bilot, Romuald Herbinet, et al. Optimization of direct ink writing of Si N suspensions for the fabrication of self-supported structure. Progress in Additive Manufacturing, 2025, 10.1007/s40964-025-01212-3. http://dx.doi.org/10.1007/s40964-025-01212-3

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# Optimization of direct ink writing of Si₃N₄ suspensions for the fabrication of self-supported structure

Flavie Lebas¹, Sylvain Marinel¹, Elisa Jaumouillé¹, Christelle Bilot¹, Romuald Herbinet²,

Loïc Le Pluart², Raphaël Laloo³, Claude Estournes³, Charles Manière¹

¹Université Caen Normandie, ENSICAEN, CNRS, Normandie Univ, CRISMAT UMR6508, F-14000 CAEN, France

²Université Caen Normandie, ENSICAEN, CNRS, Normandie Univ, LCMT UMR6507, F-14000 Caen, France

³CIRIMAT, Université de Toulouse, Toulouse INP, CNRS, 118 route de Narbonne 31062 Toulouse Cedex 9, France

* Corresponding authors: flavie.lebas@ensicaen.fr, charles.maniere@ensicaen.fr

## Abstract

Si₃N₄ is an advanced ceramic highly attractive for applications in aeronautics, aerospace, and other industries. Additive manufacturing (AM) is suitable for producing advanced ceramic parts with complex shapes, eliminating the need for machining to achieve the final component (near-net shape concept), thereby reducing costs. In this context, direct ink writing (DIW), which involves the extrusion of low organic aqueous suspensions, is well-suited for the rapid printing of large shapes with varying wall thicknesses. In this work, the formulation of a Si₃N₄ aqueous suspension has been fully developed. The optimal adding amounts of dispersant, ceramic loading, and organic binders have been determined to achieve suitable rheological properties for DIW. The suspension rheology has been adjusted to produce tall, self-supported, thinner parts, such as radomes, which are particularly challenging due to their sensitivity to slumping. These parts were sintered at 1850°C in N₂ atmosphere and exhibit a distinctive microstructure with typical non-equiaxed Si₃N₄ needle-like grains. The microhardness value of 1505 HV and the flexural strength of 374 MPa were comparable to Si₃N₄ ceramics fabricated through conventional processing.

## Graphical abstract

<figure><img src="image_2.png" /></figure>

## Keywords

Ceramic additive manufacturing, Direct ink writing, Silicon nitride, Aqueous suspensions, Rheology
# 1. Introduction

Si₃N₄ is a highly attractive ceramic material due to its exceptional properties, including mechanical strength, hardness, toughness, wear resistance, and thermal shock resistance. Si₃N₄ is usually produced through liquid-phase sintering, using Y₂O₃ and Al₂O₃ compounds as additives [1–3]. Without these additives, solid-state sintering of Si₃N₄ is unsuitable for achieving full densification because of the low self-diffusivity of this covalent material [4,5]. Regarding its application, Si₃N₄ ceramics are widely used in various structural applications, such as automotive engine components (e.g., turbines, valves, cam rollers and bearings), radomes [6–8], insulators, aerospace system, and medical devices [3–5,9].

Additive manufacturing (AM) has recently demonstrated significant potential for producing advanced ceramic components with intricate geometries that are challenging or impossible to achieve using conventional machining techniques, such as lattice structures or encapsulated parts [10]. Among the various AM processes available, selecting the most suitable method depends on specific requirements such as material density, surface finish, size, geometric complexity, and the properties of the ceramic material itself [11,12]. The fabrication of silicon nitride (Si₃N₄) ceramics through AM is particularly advantageous for applications involving small production runs, where traditional machining methods would be excessively time-consuming and costly. This is particularly relevant in aerospace applications, where component production often does not require mass manufacturing [13–15]. Furthermore, AM is highly suitable for creating parts with internal channels, which are essential in industries such as aerospace and defense [16,17]. In this context, radomes present an intriguing case study due to their self-supporting geometries, considerable height, and typically thin walls. These characteristics pose challenges, such as deformation under the part's weight if the ceramic suspension does not possess suitable rheological properties [18]. This study investigates the fabrication of a radome using the Direct Ink Writing (DIW) technique, highlighting the importance of precise adjustment of organic additives in the Si₃N₄ suspension to accommodate complex geometries.

Direct ink writing (DIW), also known as robocasting, is an AM method patented in 2000 by J. Cesarano and Paul D. Calvert at Sandia National Laboratories [19]. This technique involves creating green parts by extruding a paste filament through a syringe. It builds the component layer by layer based on a CAD (Computer Assisted Design) model. The advantage of DIW lies in its ability to work with highly charged, viscous aqueous ceramic pastes containing low organic content (<2%) and its uses of various nozzle sizes (0.2-2mm) [20,21]. This simple, rapid, and cost-effective extrusion technology holds strong potential for manufacturing parts with varying thicknesses and sizes. In addition, this method enables the formulation of a suspension with a very low content of organic additives, which is not necessarily the case of
all approaches based on the same technology. This low content of organic additives is clearly
a great advantage as they can be easily and rapidly removed during the debinding process.
Finally, robocasting offers great flexibility in the materials that can be printed, such as
advanced ceramics, including alumina, zirconia, and silicon nitride (Si₃N₄), as demonstrated in
the review [20].

A few papers have already reported the fabrication of Si₃N₄ by DIW [1,3,4,22], as this
process holds great promise for producing near-net-shape parts, opening the door to
numerous applications and opportunities. The printing of Si₃N₄ by DIW in the literature has
particularly focused on lattice structures. Zhao et al. [3] printed grid-like architectures by
varying the center-to-center distance between the extruded filaments, thereby achieving a
porous yet “solid” structure. To study the residual pore structure in silicon nitride bars printed
by DIW, Deiner et al. [4] printed bars using various patterns (aligned, hexagonal, diagonal,
bouligand). Faria et al. [1] successfully printed cylindrical parts by printing all layers in the same
direction and superimposing them. Previous studies have primarily focused on the fabrication
of relatively well-supported geometries. In contrast, fabricating radome shapes presents
significant challenges and requires careful adjustment of the suspension's rheological
properties, particularly ensuring sufficient yield stress to support the high-aspect-ratio
structures [18,23].

In this context, the aim of this work is to develop a Si₃N₄ formulation capable of
producing high-aspect-ratio radome shapes with overhangs using a simple and robust
process. The primary objective is to optimize the rheological properties of the Si₃N₄ paste to
place it within the printable zone. This printable zone corresponds to a range of viscosity values
high enough to ensure proper shape retention, allowing the successive deposition of layers
without collapse. Subsequently, the optimized paste will be used to print radome shapes,
evaluating their feasibility and making further adjustments to the formulation as needed. This
study investigates the processes of printing, debinding, sintering, and characterizing complex
ceramic parts, with a particular focus on identifying and controlling the key parameters required
for the successful direct ink writing of high-aspect-ratio Si₃N₄ radome structures.

**2. Materials and methods**

**2.1. Methods**

The flowchart (Fig. 1) illustrates the methodology used to develop an aqueous Si₃N₄
suspension suitable for printing overhanging structures, such as radomes. These shapes are
characterized by thin walls and significant height, requiring precise adjustment of the
suspension composition to ensure the printing of self-supported parts without deformation. The
study consists of eight stages: selection of the formulation components, determination of optimal dispersant conditions, preparation and rheological characterization of the suspension, and an initial optimization step to approximate the reference properties of clay, known for its excellent plasticity. Following initial printing tests, a second adjustment may be made to ensure that radome shapes - the most challenging structures in this study - maintain stability during the printing process. Finally, the printed parts undergo debinding and sintering.

<figure><img src="image_3.png" /><figcaption>Fig. 1. Flowchart of the method used to determine optimal suspension to print challenging self-supported parts.</figcaption></figure>

### 2.1.1. Raw materials

A mix of three inorganic powders was used composed of 89.3wt% silicon nitride (Si₃N₄, P95L, VestaSi, sweden), 7.0 wt% yttrium oxide (Y₂O₃, Grade C, Höganäs, sweden) and 3.7wt% aluminium oxide (Al₂O₃, P172LSB Altéo, France) [1]. The addition of yttrium oxide and alumina is an essential eutectic mix to fully sinter the silicon nitride by liquid phase sintering. Two dispersants were used to stabilize the suspensions: Dolapix A88 (Zschimmer & Schwarz, Germany) and the solution PEI (polyethyleneimine, 50wt% water) (Sigma-Aldrich-Merck, Germany Mw 2000). Faria *et al* [1] have already found that adding the PEI compound is
necessary to better stabilise the slurry. Additionally, Zhang and al [24] have shown that PEI is
an effective dispersant for Si₃N₄ particles in aqueous media. The Dolapix/PEI ratio was also
kept constant as done by Faria *et al.* [1]. The amount of dispersants must be optimized to
ensure complete coverage of the particles surfaces, providing effective electrosteric repulsion
[25–27]. Finally, carboxylmethylcellulose (CMC, Sigma-Aldrich-Merck, Germany) is a
multifunctional additive (binder, viscosity agent, *etc..*) [28,29] and is also added to our
suspensions. It is primarily used mainly as a binder to increase the viscosity and stabilize the
suspension.

2.1.2. Optimization of dispersant concentration

The optimal quantity of dispersant was determined by measuring the viscosity of suspension containing 40 vol% of ceramics with different amounts of Dolapix A88 (0 to 0.7 wt% based on total solids content). As previously mentioned, the Dolapix/PEI weight ratio was kept constant at 2.5, meaning that the amount of PEI changes in proportion to the variation in Dolapix content.

2.1.3. Suspensions preparation

In the literature, the most common process for preparing the suspension involves first preparing a solution of organics and additives, followed by the gradual addition of the inorganic powder mixture. This process works, but it is time-consuming and requires the use of different mixing machines [1,3,4]. The process proposed in this work is simplified through the use of a one-step ball milling method, as described in reference [30], which offers significant time savings and reduces equipment requirements. This approach also minimizes handling steps, thereby limiting the risk of air entrapment during mixing. The one-step ball milling process is described as follows. All the inorganic powders and CMC powder are weighted in the appropriate proportions. The mixture is then placed in a 100 ml agate bowl and mixed manually before adding water and dispersants (Dolapix A88 and PEI), which were previously weighted in a beaker. The mixture is briefly mixed manually before the addition of agate balls. The milling configuration consists of 2/3 void and 1/3 paste and balls. The material to ball volume ratio is 3:2. This high solid-loading configuration ensures intimate contact between the ceramic powder and the grinding media, maximizing the milling efficiency. Such a setup favors effective particle size reduction and promotes homogeneity in the paste, while the high shear conditions and close contact between the viscous suspension and the (20 mm large) balls contribute to the destruction and removal of air bubbles. The resulting paste is not only well dispersed but also free from entrapped gas, which is essential for achieving a stable and continuous
extrusion during printing. The grinding-milling process is then carried out in a planetary mono
mill (Pulverisette 6, Fritsch, Germany) for 1 hour, rotating at 350 min⁻¹. The higher the solid
loading rate, the more difficult the mixing becomes due to solid/liquid heterogeneities.
Therefore, it may be beneficial to increase the mixing time to 1,5 hours to better homogenize
the paste and grind the agglomerations. This helps reduce viscosity by breaking up the
agglomerates, thus improving the extrudability of the paste. At the end of the mixing stage, no
degassing step is required. The paste is collected using a Maryse and stored in a plastic bottle.

Solid loading was adjusted by conducting the following experiments: suspension
containing 40%vol, 47%vol and 50%vol. were prepared and characterized in terms of
rheological behavior. Different amounts of carboxylmethylcellulose (CMC) were also tested
(wt% based on the amount of water). Various compositions were tested to balance the solid
loading and CMC content, aiming to achieve the target rheological property area.
The final composition was characterized using a shear stress rate loop test to determine the
static and dynamic yield stress. The viscoelastic behavior was also assessed. Together, these
parameters allowed us to determine whether the suspension can be used to print a self-
supporting structure.

2.1.4. Printing

The direct ink writing machine used in this study is the Eazao Bio (Eazao, China) [31] (Fig.2.a). This machine uses a pneumatic delivery syringe controlled by a manometer and a dispensing switch. The paste, contained in a 30 cm³ syringe, was extruded through a nozzle with a diameter of 1.2 mm at a speed of 20 mm/s. The optimal pressure was controlled by the manometer to regulate the flow, ensuring the printing of a homogeneous and continuous filament. A test is systematically performed before printing parts.
<figure><img src="image_4.png" /><figcaption>Fig. 2. Printability of different parts: a) Eazao Bio [31], b) the printability simulation on Ultimaker Cura software, c) printing of parts, d) 3D drawing of the radom, e) slightly staggered filament layers, f) radome printing</figcaption></figure>

Parts were drawn and saved in a stl file with the software Freecad. To set the printing parameters such as the layer height, filling strategy etc., the software Cura Ultimaker was used. As presented in Fig.2.b), the building layer by layer can be observed. Only the perimeter is printed, without any filling. A GCode program was also saved on a SD card, which was connected to Eazao Bio machine. The layer height must be inferior or equal to 70 % of the nozzle diameter [32,33]. Therefore, the layer height was set to 50% of the nozzle diameter. Using a 1.2 mm nozzle, this corresponds to a layer height of 0.6 mm.

Initially, vertically oriented geometries, such as a flower-shaped part, were printed with a few layers to evaluate critical rheological properties like yield stress and to assess extrusion quality, particularly when curved geometries (Fig. 2.c)). The adhesion of the first filament to the substrate was carefully examined, as well as the quality of subsequent layers in areas with
intricate curves. The layered structure provides an excellent test for determining the printing quality, highlighting potential issues such as insufficient viscosity, which can make successful stacking of layers impossible. This geometry serves as an ideal benchmark for validating the material's rheological properties and extrusion control during printing. For each formulation, the flower-shaped structure was printed. Depending on the results, we adjust the formulation (by increasing the ceramic loading rate or the amount of viscosifying agent) until we obtain satisfactory results. This means obtaining successfully stable stacking of several layers.

Second, the flower-shaped model serves as a preliminary screening tool to assess the rheological suitability of the paste formulation before attempting more demanding structures like the self support structure as radome shape. Its complex geometry with comprising curved, and layered features provides an effective means to evaluate three critical parameters: (i) the viscosity and yield stress, by verifying that the suspension can support multiple stacked layers without collapsing, (ii) the 2D shape fidelity, since the model's fine details and curvatures test the suspension's high shear thinning ability to flow uniformly without agglomerates, nozzle clogging, or distortion, and (iii) the layer stacking capability, essential for building vertically extended, thin-walled components. Successfully printing the flower model confirms that the formulation has both the minimum required structural integrity and flow behavior. This test is therefore crucial to anticipate the feasibility of printing a tall, self-supported structure such as the radome, where layer-by-layer deposition must remain stable under increasing height and overhang.

Afterwards, a self-supported structure was printed. In this work, we define a self-supported structure as a geometry that can be printed without the use of additional support materials, even when it includes overhangs or inclined walls that typically present challenges to stability during printing, drying, and debinding/sintering. In our study, we use a self-supported structure with the following characteristics (Fig.2.d) and e):

- Wall thickness: approximately 1.5 mm, providing sufficient mechanical stability during printing and drying, while remaining representative of lightweight structures.

- Increased overhang angle with about 30° from the vertical axis at the tip, as illustrated by the radome profile.

- Height-to-diameter (aspect) ratio: about 2.5, which increases vertical load and thus the risk of deformation or collapse during printing and sintering. Although this is a single case study and the geometry may appear regular, it still presents several significant challenges. The continuous overhangs, thin walls, and overall height demand consistent rheological behavior, particularly a high yield stress, to prevent filament collapse during both extrusion and drying. Its geometry, with slightly staggered filament layers as seen in Fig.2.e). These shifts are particularly pronounced in tall and thin structures like the radome, where cumulative deviations
can impact both strength and stability. This form serves as an excellent test for the
suspension's ability to support such a delicate and extended structure. Achieving successful
prints of this demanding shape requires a suspension of exceptional quality (free from
agglomerates and bubbles, with proper binding properties) to prevent the structure from
collapsing. The complexity of this overhanging structure underscores the need for precise
material preparation and process control. All printed parts were left to dry for at least one night
at room temperature to ensure stability before further processing.

2.1.4 *Debinding and sintering*

Contrary to other technologies [34,35], the suspension of DIW can be aqueous and
contain low quantity of organics (< 2wt%) . This advantage allows to debind parts quickly with
relatively low risk of generating cracks. A simple debinding cycle is used, drawing on the work
of Marie and al. [34]. Pyrolysis is favoured by conducting the thermal cycle in nitrogen from
room temperature to 600°C to protect the sample from exothermicity and thermal runaway.
However, an O₂ flux is introduced for a short time (1h30) at 600°C to ensure that all the residual
carbon is removed after pyrolysis. The heating continues up to 1250 °C with a 1 hour dwell
time to pre-sinter the material. The cycle (Fig.3) depicts the final heating cycle selected.

<figure><img src="image_5.png" /><figcaption>Fig. 3. Debinding and pre-sintering program</figcaption></figure>

The sintering of green parts was carried out in N₂ atmosphere at 1850°C during 2h with
40 MPa. As the entire sintering cycle belongs to our industrial partner, Solcera, this information
is confidential. However, to be more specific, the temperature rate is usually a few °C/h, 1 or
2 °C/h up to the high-temperature dwell sintering temperature [36]. It is important to work under
high N₂ pressure to avoid the decomposition of Si₃N₄ in gaseous elements which is happening
at the sintering temperature [37].
## 2.3. Materials characterization

### 2.3.1. Powders and suspensions characterizations

The particle size distribution of the powders was analyzed by laser granulometry (Mastersizer 2000, Malvern, UK) and observed by scanning electron microscope (SEM) (JSM-7200F, JEOL, Japan).

The rheological properties of suspensions was measured with a rotational rheometer (AR1000, TA instruments, USA). The measurements were done by measuring the viscosity at various shear rates, ranging from 0.1 - 100 (1/s) and 10-100 (1/s). These shear rate ranges are similar to those used during printing, using a plate-plate configuration at room temperature. Additionally, a shear rate loop test was performed, consisting of a ramp-up from 0 to 100 s⁻¹ followed by a ramp-down from 100 to 0 s⁻¹, to evaluate both the static and dynamic yield stress of the suspension by plotting the shear stress in function of shear rate. Subsequently, oscillatory stress measurements were carried out at a constant angular frequency of 1 rad/s to determine the complex modulus components, G' and G", providing valuable insights into the viscoelastic behavior of the formulated suspension. Finally, the printability of the suspension was assessed using the figure of merit (Ø) proposed by Del Mazo-Barbara and Ginebra [23], which links key rheological parameters to the performance requirements of extrusion-based additive manufacturing.

### 2.3.3. Sintered parts

Coupled with the SEM, an energy dispersive spectrometer (EDS) (X-Flash 6-60, Bruker, Germany) was used to collect X-ray mapping and analyze the composition of the parts. The crystalline phases of the initial powders and the sintered parts were analyzed using X-ray diffraction (D8 advance Vario 1, Bruker), with Cu kα (λ=1.5406 Å) with a monochromator Ge (111) (type Johansson) and a detector Lynx Eye. The parameters setup were 2θ ranging from 10° to 90°, with an angular step of 0.01°. The crystalline phases were identified by comparing the experimental diffractograms to those in the X'pert Highscore database. The hardness of parts were characterized by Vickers micro-indentation (MMT-X7B, Matsuzawa, Japan) using 1kgf. About 9 hardness measurements were made at the core of parts.

The fracture strength (σ<sub>f</sub>) was measured by the three-point bending method (Material Testing Systems MTS 1/M) on specimens with the dimensions 2 × 2 × 15 mm³. The span between the two supporting pins was equal to 13 mm. Cross-head speed was fixed at 0.1 mm/min.

## 3. Results & discussion
## 3.1. Powders analysis

The graphic (Fig.4) presents the particle size distribution of the three inorganic powders. The Si₃N₄ powder exhibits a primary particle size distribution with a peak at 1.1 µm, Y₂O₃ peaks at 1.44 µm, and alumina at 0.55 µm. The SEM observations confirm the grain sizes measured by optical granulometry (Fig.4.a),b),c)). Si₃N₄ grains are faceted with a slightly acicular shape, which is typical for this material. Yttria grains are composed of nanometric grains that form hexagonal platelets, while alumina grains are equiaxed. Many small holes are observed on the yttria platelet grains, which may affect the total specific surface area of this powder. From the point of view of sintering, the shape of the inorganic additive compound grains, such as yttria and alumina, is not crucial, as these phases are known to react at high temperatures during sintering to form a glassy phase. They act as sintering additives. However, when preparing suspensions for direct ink writing, the grain shape may influence the effect of the organics, as they interact with the inorganic grains from their surface. This means that changing the grain size and morphology may impact the dispersant quantity. This point must be kept in mind when optimizing the suspension composition for DIW.
<figure><img src="image_6.png" /><figcaption>Fig. 4. Particle size distribution and SEM images of particle size: a) Si₃N₄, b) Y₂O₃, c) Al₂O₃</figcaption></figure>

## 3.2 Rheology of the slurries

The optimal amount of dispersant required to obtain a stable suspension was first investigated. This was carried out by measuring the viscosity versus the shear rate of a 40 vol% solid loading suspension with different amounts of dispersants (0 to 0.7 wt%). In Fig. 5.a), the lowest viscosity was obtained for 0.4 and 0.5 wt% of Dolapix. As explained before, the optimal quantity of dispersant is determined when the viscosity reaches its minimum value. This condition is met for a dispersant concentration between 0.4 and 0.5 wt%. Fig. 5.b) shows the plot of viscosity versus dispersant concentration for different shear rates. The shear rates of 10 and 100 s⁻¹ correspond to the extremes of the printability range, while 30 s⁻¹ corresponds to the in-layer shear rate in the 1.2 mm diameter nozzle used in our study. It is to be noted the
in-layer shear rate is not referring to the shear rate inside the nozzle but to the shear rate in the deposited layer which is close to the planar shear rate [38]. In this model, the shear rate $\dot{\gamma}$ is given by eq(1)

$$ \dot{\gamma} = \frac{\nu}{h} \qquad (1) $$

where $\nu$ is the printing speed and $h$ is the layer height. Following the recommendations of Chartier et al. [32] who advise using a layer height equal to or less than 70% of the nozzle diameter, we selected a layer height of 0.6 mm (50% of a 1.2 mm nozzle diameter) and a printing speed of 20 mm/s. This yields a shear rate around $30 \text{ s}^{-1}$. These curves show that the minimal viscosity is achieved with 0.45 wt% of dispersant, regardless of the shear rate value (Fig.5.b)).

<figure><img src="image_7.png" /><figcaption>Fig. 5. Determination of the optimal concentration of dispersant: a) Viscosity versus shear rate, b) viscosity versus dispersant concentration</figcaption></figure>

Fig.6.a) shows the viscosity versus the shear rate for suspensions with different solid loadings, while the dispersant concentration is fixed at 0.45 wt%. The viscosity increases with higher solid loading. The 50 vol% solid loading yields rheological properties closest to those of reference clay, but it was not homogeneous enough. Therefore, the formulation was optimized with 47 vol%. To achieve the desired viscosity, a compromise must be found between the amount of solid loading and the CMC content. As shown in Fig.6.b), the viscosity increases with the amount of CMC. However, an increase in viscosity may be accompanied by a degradation in paste homogeneity. A more viscous paste may need to be mixed for a longer time. Indeed, in Fig.6.c), the mixing time was increased by 30 minutes, which significantly improved the homogeneity of the mixture while reducing the viscosity at high shear rates. This pronounced shear thinning behaviour, is highly favourable for the extrusion process. In
summary, the suspension should have a loading concentration slightly lower than 50 vol% to avoid excessive sensitivity to drying heterogeneity. This issue can be addressed by increasing the content of viscosifying agent (CMC content) and extending the milling time. The latter adjustment of Si₃N₄ paste is mandatory to enable the printing of high height parts, similar to what is done with reference clay.

<figure><img src="image_8.png" /><figcaption>Fig. 6. Influence of different parameters on the viscosity: a) the solid loading, b) the amount of CMC, c) the mixing time</figcaption></figure>

The final composition of the Si₃N₄ paste, suitable for DIW with 1.64 vol% of organic content, is presented in **table 1**, with a milling time of 1,5 hours by ball milling.

<table><caption>Table 1. Final composition of Si₃N₄ suspension</caption><thead><tr><td>Materials</td><td>Compositions (vol%)</td></tr></thead><tbody><tr><td>Mix ceramics Si₃N₄ (89.3wt%)/ Y₂O₃ (7wt%)/ Al₂O₃ (3.7wt%)</td><td>45,90</td></tr><tr><td>Water</td><td>52,46</td></tr><tr><td>Dolapix A88</td><td>0,72</td></tr><tr><td>PEI</td><td>0,26</td></tr><tr><td>CMC</td><td>0,66</td></tr></tbody></table>
For the final composition, a shear stress-shear rate loop test (Figure 7.a)) was conducted. This measurement allows to evaluated the static yield stress $\sigma_y^{Stat}$, which correspond to the minimum stress required to initiate extrusion, and the dynamic yield stress $\sigma_y^{Dyn}$, measured after the relaxation, which represents the maximum stress a unrecovered printed layer can withstand without collapsing.

The maximum printable height ($h_{max}$) was estimated using the following relationship eq(2):

$$h_{max} = \frac{\sigma_y^{Dyn}}{\rho g} \qquad (2)$$

This equation links the dynamic yield stress to the gravitational acceleration ($g=9.81m.s^{-2}$) and material volumetric mass ($\rho$) supported by the printed structure. A dynamic yield stress of 600 Pa was determined from the shear stress-rate loop. Using Equation (1), this corresponds to a maximum printable height of approximately 3 cm for the final suspension. Since printing a 3 cm high structure takes some time, this allows the material to recover its structure during deposition. Consequently, the maximum printable height can be estimated using the static yield stress of 1500 Pa, leading to a theoretical height of 7.4 cm. This supports the successful printing of a self-supported structure such as the radome, which reaches approximately 6 cm in height. Additionally, the 30 mm height allows sufficient time for partial drying, which increases the viscosity of the bottom layers and further enhances self-supporting capability.

The Fig.7.b) shown that the elastic component (G') dominates over the viscous component (G") up to 5000 Pa, indicating a predominantly solid-like behavior in this area. Notably, this solid-like behavior remains stable under increasing oscillatory stress, confirming a wide linear viscoelastic region (LVR) [18,39]. Del-Mazo-Barbara and Ginebra [23] provide an elastic modulus-based figure of merit (Ø) showing that most printable suspensions have values over 20 (Ø>20). In our case (Fig.7.c), we obtain the elastic modulus of G'_{eq}=4.57E6 Pa and a flow stress of $\tau_f=6310$ Pa giving a figure of merit of Ø = 742, which is far above 20 confirming the printability of the suspension.
<figure><img src="image_9.png" /><figcaption>Fig. 7. Rheological characterization: a) shear stress vs. shear rate loop test, b) viscoelastic behavior analysis, and c) elastic modulus and flow stress assessment.</figcaption></figure>

### 3.3. Printing conditions

As shown in Fig. 8, the optimal pressure test was conducted by printing a filled square. This test is used to adjust the dispensing pressure and the correct layer width which cannot be determined easily by single-walled printing tests. During the test, the pressure was adjusted until optimal extrusion was achieved, resulting in a homogeneous, continuous, and well-formed filament (zone 2). In contrast, in zone 3, the filament was discontinuous due to insufficient pressure, while in zone 1, sub-extrusion occurred, making the filament indistinguishable.
<figure><img src="image_10.png" /><figcaption>Fig. 8. Extrusion speed adjustment tests</figcaption></figure>

The final composition was printed two different types of parts. Floral geometry green part is illustrated in Fig.9.a). As seen, the filament is homogenous, continuous and accurate, as well as the superposition of filaments. The same observation can be done for the green radome, whose printing is illustrated in Fig.9.b), and the final part in Fig.9.c). This printing success validates the formulation of our paste, as the printed parts are of high quality and stability. However, the printing process can become more challenging when bubbles or agglomerates are present in the syringe and are expelled through the nozzle. This can lead to the collapse of the parts. After printing, the green parts are dried for at least one night at room temperature. Once dried, the parts show no signs of cracking.
<figure><img src="image_11.png" /><figcaption>Fig. 9. Green part: a) Floral geometry, b) radome printing, c) radome</figcaption></figure>

**3.4 Si₃N₄ sintering and characterization**

The sintering of green parts is carried out at 1850°C for 2 hours in a N₂ atmosphere under a pressure of 40 bars. The sintered radome is presented in Fig.10.b) and is compared to the green parts (Fig.10.a)). The shrinkage can be noticed in these pictures, and the parts show no signs of cracking. The green radome initially measures 60 mm in height and 25 mm at the base. After sintering, their dimensions are 48 mm in height and 20 mm at the base, corresponding to around 20% shrinkage in both height and width.
<figure><img src="image_12.png" /><figcaption>Fig. 10. a) Green radome, b) Sintered radome</figcaption></figure>

Fig. 11 shows the XRD patterns of both the initial mixture powder and the sintered sample. The Si₃N₄ powder used predominantly contains α-Si₃N₄ with a minor presence of β-Si₃N₄. To enhance clarity and avoid overcrowding, only the major peaks have been indexed in the figure. In the sintered sample (Fig. 11.b)), the silicon, yttrium and alumina elements are present in other crystalline phases such as AlN·7OSi₅ and AlN₀.₈SiY₄. These phases indicate that the secondary phases are crystallized rather than purely glassy, which can enhance the mechanical properties [40]. The phase transition of α-Si₃N₄ into β-Si₃N₄ is expected for the sintering of this ceramic [41].

<figure><img src="image_13.png" /><figcaption>Fig. 11. X-ray diffraction profile of: a) Powder mixture and b) Sintered sample</figcaption></figure>
The SEM micrographs of sintered Si₃N₄ parts are presented in Fig.12.a,b). The non-equiaxed Si₃N₄ grains (needles) of Si₃N₄ are visible, along with the white phase associated with additives (Y₂O₃/Al₂O₃), as confirmed by the EDS mapping shown in Fig.12.c). In Fig.12.b), the focus is on the Si₃N₄ needles, which are made up of hexagonal crystals randomly oriented. The microstructure and the hardness value of 1505 HV are comparable to Si₃N₄ ceramics fabricated through conventional processing, which typically have hardness values ranging from 1400 to 1600 HV [42,43]. The graph presented in Fig. 13.a) compares our hardness results with those from other studies using additive manufacturing, Faria et al for direct ink writing [1], Marie et al for stereolithography [34], as well as conventional methods such as CIP [44,45] and hot pressing [46]). Regarding the flexural strength, a value of 374 MPa was obtained, which falls within the typical range of 300–550 MPa reported in other studies on Si₃N₄ fabricated by both additive manufacturing and conventional methods. Faria et al. [1] and Yang et al. [47] reported flexural strengths of 430 MPa and 348 MPa, respectively, for parts produced via direct ink writing. Zhao et al. [3], who combined direct ink writing with hot isostatic pressing (HIP), achieved a higher value of 552 MPa. These results are compared with ours in the graph shown in Fig.13.b), along with the flexural strength reported by Marie et al. [34] for Si₃N₄ fabricated by stereolithography and by Lukianova [45] for Si₃N₄ produced using cold isostatic pressing (CIP). Our results are therefore consistent with the literature. Our printed, debound and sintered ceramic retains the properties achieved through conventional processes.
<figure><img src="image_14.png" /><figcaption>Fig. 12. Characterization of sintered sample: a) SEM image of global structure, b) zoom on the complex crystals structure inside a porosity c) SEM image of Si₃N₄ needles, d) EDS mapping</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 13. Histogram: a) Vickers hardness, b) Flexural strength</figcaption></figure>
## 4. Conclusion

In this article, a Si₃N₄ suspension with low organic content (<2% vol of CMC binder and dispersants) has been successfully developed to enable the rapid printing of large, thin shapes by direct ink writing. The procedure is simple and fast, as a single ball-milling step is used to ensure the desagglomeration of the powders while homogenizing the suspension. The successful printing of radome shapes, which feature tall and thin walls, clearly demonstrates that the suspension supports a high weight while resisting buckling and warping during the stage when the shapes are still wet and highly deformable. Regarding the microstructure of the sintered ceramics, they exhibit a fully dense microstructure with the typical beta grain needle structure developed. The mechanical properties give a hardness of 1505 HV and a flexural strength of 374 MPa, these values fall in the expected range of conventionally produced silicon nitride parts. The comparison with those published in the literature on additive manufacturing shows that our material is well positioned. These results show that direct ink writing is a promising additive manufacturing technology for producing complex-shaped Si₃N₄ structural ceramics.

## ACKNOWLEDGMENTS

The authors thank Solcera® compagny for providing the materials used in this work and for conducting the sintering experiments. The authors also grateful to Ms. Gaelle Riou for collecting the XRD patterns and to Mr. Lucas Le-Gars for his contribution to XRD analysis. The authors also appreciate the technical support provided by Eazao.

## Funding:

This work as been funded by UNICAEN PhD funding number: "Allocations Etablissements 2023 (2023) 2023050211502900001220000257"

## Data

All data are given in the graph of the article

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