A gravity-driven sintering method to fabricate geometrically complex compact piezoceramics

Highly compact and geometrically complex piezoceramics are required by a variety of electromechanical devices owing to their outstanding piezoelectricity, mechanical stability and extended application scenarios. 3D printing is currently the mainstream technology for fabricating geometrically complex piezoceramic components. However, it is hard to print piezoceramics in a curve shape while also keeping its compactness due to restrictions on the ceramic loading and the viscosity of feedstocks. Here, we report a gravity-driven sintering (GDS) process to directly fabricate curved and compact piezoceramics by exploiting gravitational force and high-temperature viscous behavior of sintering ceramic specimens. The sintered lead zirconate titanate (PZT) ceramics possess curve geometries that can be facilely tuned via the initial mechanical boundary design, and exhibit high piezoelectric properties comparable to those of conventional-sintered compact PZT (d33 = 595 pC/N). In contrast to 3D printing technology, our GDS process is suitable for scale-up production and low-cost production of piezoceramics with diverse curved surfaces. Our GDS strategy is an universal and facile route to fabricate curved piezoceramics and other functional ceramics with no compromise of their functionalities.


Supplementary Note 2 | Explanation of the tuneability
In the simplified model shown in Fig. 3d, the gravitational force Fg is balanced by the equivalent resistance force Fr, and the equilibrium can be written as: For the three tuning regions, we consider a small deformation where the slight change of configuration has a negligible effect on θ (cosθ). To further study the tuning abilities of the three regions, we consider the configuration evaluation from the view of forming new equilibrium, which is determined by Fg, Fr and θ. The range of θ for each tuning region is shown in Fig. 3b and the corresponding value of cosθ is listed in Supplementary Figure 6. We first discuss the tunability of the two LT regions. As illustrated in the main text, in region B (Fig. 3b), the small variation of Fg requires a large change of Fr due to low cosθ (Supplementary Figure 6). This means that a slight modification of the configuration comes with a dramatic change of the designing parameter (effective length le). For region D, the value of 2cosθ range from 0.584 to 1.06, which indicates that the configuration is highly sensitive to the designing parameter. In the OT region, the moderate value of 2cosθ enables a relatively stable tuning of the configuration. Table 1 Scalability for scale-up production. In practical 3D printing ceramic process, the printer normally produces only one specimen within one processing cycle. This means that to fabricate N piezoceramic green bodies, one printer has to run N times processing cycle. Furthermore, the high resolution of 3D printing processes usually requires low printing speed, which predestines them to exhibit low scalability in scale-up production.

Supplementary Note 3 | Explanation of parameters with * superscipt in
In CTE-based methods, the curvatures of fabricated specimens are tuned via modifying the thickness of each layer and heating setup (e.g. heating rate and temperature). This fabrication characteristic allows users simultaneously process several specimens with similar laminate structures under the same heating setup. In the pre-stressed method, the curvatures of post-processing piezoceramics are strongly dependent on the particular laminate structures of the specimens. Similarly, only specimens that have the same laminate design can be simultaneously strained by one fabrication device. The discussion above illustrates that a given laminate structure corresponds to a particular processing setup (heating and loading setup) that is fixed during one processing cycle. Therefore, the two post-processing methods are not available for scalable production of curved piezoceramics with diverse geometries. We demonstrated the potential of the GDS process for massive production in the main text and the corresponding schematic is shown in Fig. 4a. As a demonstration of this scalability, we fabricated 24 PZT ceramics with 3 different configurations in one GDS processing cycle. Our GDS process exhibits a good feasibility for large-scaled production without any restrictions on the geometrical similarity of the processing specimens. Based on the elaboration above, we confirm that our GDS process is superior than 3D-printing techniques and post-processing methods currently available from the view of scale-up production.

Compactness [piezoceramic ratio in green bodies].
Compactness is defined as the ratio of piezoceramic constituent in the green body. For example, in the GDS process, the commercial PZT powders are mixed with PVA binder and then they are pressed to a rectangle shape. Hence the compactness of the PZT green body used in our GDS process is measured as 99 vol%.
For slurry-based 3D-printing technologies, the high ratio of piezoceramic constituent in the ceramic/polymer mixture usually results in a high viscosity of feedstock, which deteriorates their ability to print complex-geometry piezoceramic green bodies. For bulk solid-based methods, the composite filaments are prepared by loading piezoceramic particles into thermoplastic binders. Similar to slurry-based methods, the fused piezoceramic/polymer filaments comprised a high ratio of piezoceramic particles that undermines the processibility of feedstock. Powder-based ceramic 3D printing technologies are mainly used for processing porous ceramic components as the powder beds containing loose ceramic particles work as feedstock. It should be noted that the compactness listed in Table 1 are the highest ratio mentioned among the reference works that focus on studying 3D printing of piezoelectric materials.
Geometrical limits. The GDS method are not suitable for fabricating piezoceramics in over than halfround arches and close-loop shapes as the main driven force using in this method is gravitational force. In addition, the GDS method take advantage of the thermal-induced creep effect for shaping, so the final geometry of the GDS-fabricated piezoceramic is limited by the surface tension of the liquid-like semifinal specimen for example square and cone shapes.

Piezoelectricity [d33 pC/N].
Piezoelectricity is an important feature of piezoceramics, which enables conversion between electrical and mechanical signals. We use the piezoelectric coefficient d33 to characterize the piezoelectricity of the piezoceramics discussed in Table 1. The post processing methods directly process compact piezoceramic sintered bodies, therefore, the value of d33 is mainly determined by the piezoelectricity of the used piezoceramic layer. The differences in d33 between the GDS-fabricated and post-processing curved ceramics originate from the material composition of the purchased PZT material. However, for 3D printing methods, low volume of piezoceramic constituents in the printed green bodies predestine the as-sintered piezoceramics in porous bodies and thus compromised piezoelectricity (small value of d33) compared with the other two kinds of methods.

Supplementary Figures
Supplementary Figure 1