A bioinspired surface tension-driven route toward programmed cellular ceramics

The intriguing biomineralization process in nature endows the mineralized biological materials with intricate microarchitected structures in a facile and orderly way, which provides an inspiration for processing ceramics. Here, we propose a simple and efficient manufacturing process to fabricate cellular ceramics in programmed cell-based 3D configurations, inspired by the biomineralization process of the diatom frustule. Our approach separates the ingredient synthesis from architecture building, enabling the programmable manufacturing of cellular ceramics with various cell sizes, geometries, densities, metastructures, and constituent elements. Our approach exploits surface tension to capture precursor solutions in the architected cellular lattices, allowing us to control the liquid geometry and manufacture cellular ceramics with high precision. We investigate the geometry parameters for the architected lattices assembled by unit cells and unit columns, both theoretically and experimentally, to guide the 3D fluid interface creation in arranged configurations. We manufacture a series of globally cellular and locally compact piezoceramics, obtaining an enhanced piezoelectric constant and a designed piezoelectric anisotropy. This bioinspired, surface tension-assisted approach has the potential to revolutionize the design and processing of multifarious ceramic materials for structural and functional applications in energy, electronics and biomedicine.


REVIEWER COMMENTS
Reviewer #1 (Remarks to the Author): The manuscript presents a novel and intriguing way of additive manufacturing of cellular ceramics.A 3D printed organic cellular structure is used as a scaffold and via a variation of the surface tension of the pre-cursor solution the structure of the final cellular ceramics can be tuned in a certain range, the balance between surface tension and gravity is another physical constraint determining the accessible range of structural specifications.Overall, the processing route is described quite well and as far as I understand the final result is an open cellular ceramic object consisting of densely sintered struts.The paper may be considered for publication in Nature Communications, but requires significant revision.
1) The presented cellular ceramic structures (see Fig. 4 or Suppl.Fig. 8) could also be produced in a simpler and faster way using direct ink writing (DIW).There is a plethora of literature about that, and e.g. the groups of Jennifer Lewis (Harvard University), Andre Studart (ETH Zürich) or Willenbacher (KIT) have published significant work in that title and the authors should benchmark their new approach against well-established DIW in terms of fabrication speed or accessible feature size.Furthermore, the first paragraph of the Results section should be moved to the Introduction.
2) The wording in the section about the design principle on page 5 could be clearer e.g. in line 211 it should read "…increasing precursor solution concentration…" and the term "capillary length" is not clearly defined (line 224).
3) The authors have varied the precursor solution concentration in order to change the wetting angle.This may have an effect on drying time, gel-structure, sintering conditions and also the properties of the final ceramics.Alternatively, the wetting angle could be changed in a wide range by adding trace amounts of appropriate surfactants to a precursor solution with fixed concentration, also the surface properties of the 3D printed organic scaffold may be varied (e.g.plasma treatment) to tune the wetting behavior, these aspects should be discussed carefully.

4) Caption of Fig. 3 is incomplete:
The insert in Fig. 3d is not visible (not even when enlarged on the computer screen), the meaning of the different lines in Fig. 3d is unclear.The colors of the lines in Fig. 3e are not explained, correlation to frame radius?Meaning of blue regions in Fig. 3h is not explained, meaning of subfigures i), ii), iii, and iv) in Fig. 3h is not explained.
5) The section about the piezoelectric performance of the cellular ceramic metamaterials is the weakest part of the manuscript.It is not clear what could be achieved here beyond the state of the art regarding piezoelectric properties, e.g. in David Menne et al., ACS Applied Materials and interfaces 14 (2), 3027-3037 (2022) cellular piezoceramic structures are described with higher d33 values and it is demonstrated in Fig. S1 of that paper, that strut diameters as small as 70 µm can be achieved using DIW.The manuscript discusses a novel approach for manufacturing cellular ceramics inspired by the biomineralization process found in nature.This approach involves separating ingredient synthesis from architecture building to create programmable 3D configurations of cellular ceramics.The technique utilizes surface tension to capture precursor solutions in architected cellular lattices, allowing for precise control of liquid geometry.The authors investigate the geometry parameters of these lattices theoretically and experimentally to guide 3D fluid interface creation.They successfully manufacture various cellular ceramics, including piezoceramics with enhanced properties, such as a higher piezoelectric constant and designed anisotropy.
The proposed approach possesses similarities to the negative replica approach used for foams as well as for printed sacrificial structures (see for example: https://doi.org/10.1111/j.1151-2916.1997.tb02993.x);nevertheless, the theoretical approach proposed here allows to predict and design structures specifically to fit the process requirements and is certainly novel.I would recommend to further characterize the cellular structures produce to understand how they fit in the current state of the art; in particular: -microCT scan and defect assessment; -mechanical properties (not only piezoelectric ones) I would also better address the role of the usage of sol-gel precursors in achieving the proposed results: what happens if conventional powder-based suspensions are used instead?

Reviewer Comments (and change made in accordance)
Reviewer #1 (Remarks to the Author): The manuscript presents a novel and intriguing way of additive manufacturing of cellular ceramics.
A 3D printed organic cellular structure is used as a scaffold and via a variation of the surface tension of the pre-cursor solution the structure of the final cellular ceramics can be tuned in a certain range, the balance between surface tension and gravity is another physical constraint determining the accessible range of structural specifications.Overall, the processing route is described quite well and as far as I understand the final result is an open cellular ceramic object consisting of densely sintered struts.The paper may be considered for publication in Nature Communications, but requires significant revision.

Response:
We thank the referee for the recommendation of the publication in Nature Communications.Following the referee's comments and suggestions, we have revised our manuscript with the most seriousness (the revised portions are marked in Red Color in the manuscript) and our detailed responses are listed below.

Questions and comments:
1.The presented cellular ceramic structures (see Fig. 4 or Suppl.Fig. 8) could also be produced in a simpler and faster way using direct ink writing (DIW).There is a plethora of literature about that, and e.g. the groups of Jennifer Lewis (Harvard University), Andre Studart Response: We thank the referee very much for the constructive suggestions.For comment 1: Yes, we fully agree with you.Ceramic additive manufacturing using direct ink writing (DIW) has been extensively studied, and many research groups have significant contributions including the groups of Jennifer Lewis, Andre Studart, and Willenbacher.We fully respect these inspiring studies.In the revised manuscript, we have referred to these published significant works about ceramic additive manufacturing using DIW, and compared our new STATS approach with the well-established DIW, SLA/DLP, and SLS in terms of effective constituent loading, fabrication speed, and accessible feature size, as shown in Supplementary Table 1 [1][2][3][4][5][6][7][8][9][10][11][12] .All these references have been cited in the revised manuscript.
The slurry extrusion-based DIW has the advantage of high effective constituent loading regardless of its limited fabrication speed and feature size.As a comparison, the photosensitive resin-based SLA/DLP possesses an increasing fabrication speed and decreasing feature size, with limited effective constituent loading.The proposed STATS approach combines the advantages of DIW in effective constituent loading and SLA/DLP in fabrication speed and accessible feature size.Our approach utilizes SLA/DLP to process high-resolution organic lattices, and we prepare the feedstock suspensions with highly effective ceramic constituent loading, which is usually used in DIW.Moreover, the exposure time of common resin is usually 2-3 s per layer in DLP, while it increases over one time (5-7 s) for the curing of DLP processed ceramic-resin mixture.In the proposed STATS approach, the organic lattices with designed architectures are processed by the additive manufacturing of common resin, greatly increasing the printing speed.Therefore, the separation of ingredient synthesis from architecture building in the STATS manufacturing process dramatically simplifies and speeds up the manufacturing process of cellular ceramics.The following sentences are added to the revised manuscript (page 4): "Supplementary Table 1 summarizes the parameters in terms of effective constituent loading, fabrication speed, and accessible feature size for the well-established DIW, SLA/DLP, and SLS [31][32][33][34][35][36][37][38][39][40][41][42] .The slurry extrusion-based DIW has the advantage of high effective constituent loading regardless of its limited fabrication speed and feature size, while the photosensitive resin-based SLA/DLP possesses an increasing fabrication speed and decreasing feature size, with limited effective constituent loading.
In comparison, the philosophy of the STATS process is different.It avoids an engineering trade-off by separating the steps of architecture building and ingredient synthesis.The proposed STATS approach combines the advantages of DIW in effective constituent loading and SLA/DLP in fabrication speed and accessible feature size.We utilize SLA/DLP to process high-resolution organic lattices, and we prepare the feedstock suspensions, similar to the DIW process, with high effective ceramic constituent loading.Moreover, the exposure time of common resin is usually 2-3 s per layer in DLP, while it increases over one time (5-7 s) for the curing of DLP processed ceramic-resin mixture 40 .In the proposed STATS approach, the organic lattices with designed architectures are processed by the additive manufacturing of common resin, greatly increasing the printing speed.Therefore, the separation of ingredient synthesis from architecture building in the STATS manufacturing process dramatically simplifies and accelerates the cellular ceramic manufacturing." For comment 2: The first paragraph of the Results section has been moved to the Introduction section.Thank you for your suggestion.
2. The wording in the section about the design principle on page 5 could be clearer e.g. in line 211 it should read "…increasing precursor solution concentration…" (comment 1) and the term "capillary length" is not clearly defined (line 224) (comment 2).

Response:
We thank the referee for this comment.For comment 1: The following sentence is revised in the manuscript (page 6): "The contact angle increases, accompanied by the increasing concentration of the precursor solution, but all within 90° (Fig. 3b and Supplementary Fig. 13)." For comment 2: Capillary length is a characteristic length scale for fluid subject to a body force from gravity and a surface force due to surface tension 13 , which is most commonly given by λ=√σ/∆ρg (R1) where λ is the surface tension of the fluid interface, g is the gravitational acceleration and Δρ is the mass density difference of the fluids.
The following sentence is revised in the manuscript (page 6): "Besides, the size of the created fluid interface (a -2r) must be within the capillary length √ σ 12 /∆ρ 12 g, where σ12 is the interfacial tension of fluid 1-fluid 2, Δρ12 is the density difference between fluid 1 and fluid 2, and g is the gravitational acceleration 25 ." The following sentence is revised in Supporting Information (page 6): "In addition, the size of the created fluid interface must be within the capillary length, a characteristic length scale for the fluid subject to a body force from gravity and a surface force due to surface tension 25 , which means where Δρ12 is the density difference between fluid 1 and fluid 2, and g is the gravitational acceleration." 3. The authors have varied the precursor solution concentration in order to change the wetting angle.This may have an effect on drying time, gel-structure, sintering conditions and also the properties of the final ceramics.(comment 1) Alternatively, the wetting angle could be changed in a wide range by adding trace amounts of appropriate surfactants to a precursor solution with fixed concentration, also the surface properties of the 3D printed organic scaffold may be varied (e.g.plasma treatment) to tune the wetting behavior, these aspects should be discussed carefully.(comment 2) Response: We thank the referee very much for the constructive suggestions.For comment 1: Yes, we fully agree with you.The precursor solution concentration does have an effect on drying time, gel-structure, sintering conditions and also the properties of the final ceramics.
For instance, the reduced precursor solution concentration leads to an increasing drying time during the sol-gel transition, as well as a reduced shell thickness for the sintered cellular ceramics, which decreases from 187 μm to 100 μm as the concentration decreases from 5 mM to 1 mM (Fig. 2e and Supplementary Fig. 7).
The following sentence is added in Supporting Information (page 5): "The shell thickness is significantly influenced by the concentration of the precursor solution, which increases from 100 μm to 187 μm as the concentration increases from 1 mM to 5 mM (Fig. 2e and Supplementary Fig. 7)." For comment 2: The addition of surfactants in the precursor solution and the plasma treatment on the organic lattices also benefit the decrease of contact angle to some extent.For instance, under the condition of 2 mM concentration of the precursor solution, the contact angle is 20° while the addition of 1 wt.% surfactants in the precursor solution reduces the contact angle to 13° and a plasma treatment (2 min) on the organic lattices reduces it to 15°.Considering that a contact angle of 20° is enough to form a solution-philic condition (α is 0.98 at the contact angle of 20°, close to its maximum), these factors are not considered in the following experiments from the perspective of simplification of experimental procedure.
The following sentence is added in the manuscript (page 6): "Besides, the addition of surfactants in the precursor solution and the plasma treatment on the organic lattices also benefit the decrease of contact angle to some extent (Supplementary Fig. 14).Considering that a contact angle of 20° is enough to form a solution-philic condition, these factors are not considered in the following experiments from the perspective of simplification of experimental procedures." The following sentence is added in Supporting Information (page 2): "The addition of surfactants in the precursor solution and the plasma treatment on the organic lattices also benefit the decrease of contact angle to some extent.Under the condition of 2 mM concentration of the precursor solution, the contact angle is 20° while the addition of 1 wt.% surfactants in the precursor solution reduces the contact angle to 13° and a plasma treatment obtained result (a -2r < 1.64 mm) is shown as Area II below the red solid line in Figure 3d, and the intersection between Area I and Area II (blue region) represents the safe area with the appropriate frame length and radius to successfully create a stable liquid interface.
When considering the whole architected lattice, in which the precursor solution is assembled with a programmed arrangement, both of the successful capture in parts of the unit cells and the failed capture in other parts are required.Taking the architected lattices depicted in Fig. 3g for example, the unit cells with a length of a should be filled with the precursor solution while it is the opposite for the cells with a length of i) 2a.As a result, the constrains, shown as the yellow region in Fig. 3d, consisting of 7.15 < a/r < 14.3 (blue dash line and blue solid line) and 0.82 mm < a -2r < 1.64 mm (red dash line and red solid line), are required to form a programmed arrangement with an interval length of i) 2a depicted in Fig. 3g.
The following sentences are revised in the manuscript (page 6): "Combining Equation 1 and the geometry requirement (a > 2r), we obtain 2.0 < a/r < 14.3, shown as Area I between the blue solid line and black solid line in Fig. 3d." "The obtained result (a -2r < 1.64 mm) is shown as Area II below the red solid line in Figure 3d, and the intersection between Area I and Area II (blue region) represents the safe area with the appropriate frame length and radius to successfully create a stable liquid interface." The following sentence is revised in Supporting Information (page 7): "As a result, the constrains, shown as the yellow region in Fig. 3d, consisting of 7.15 < a/r < 14.3 (blue dash line and blue solid line) and 0.82 mm < a -2r < 1.64 mm (red dash line and red solid line), are required to form a programmed arrangement with an interval length of i) 2a depicted in Fig. 3g." For comment 3: The colors of the lines in Fig. 3e correlate with frame radius, namely, the red, blue, green and purple line corresponds to a radius of 0.1 mm, 0.15 mm, 0.2 mm, 0.25 mm, respectively.
Fig. 3e summarizes the relation between liquid height and the maximum contact perimeter in a unit column as the radius increases from 0.1 mm (red dash line) to 0.25 mm (purple dash line) (detailed in Supplementary Fig. 17c).A relation between the liquid height h and the contact perimeter s with corresponding radii from the gravitational force is also given as the solid line in Fig. 3e (e.g., red solid line corresponds to a radius of 0.1 mm) according to Equation 2.
The following sentences are revised in the manuscript (page 7): "A relation between the liquid height h and the contact perimeter s with corresponding radii from the gravitational force is also given as the solid line in Fig. 3e (e.g., red solid line corresponds to a radius of 0.1 mm) according to Equation 2." For comment 4: The blue region in Fig. 3h represents the fraction of precursor solution in the FE analysis, in which a darker color means a higher proportion.And the subfigures i), ii), iii, and iv) in Fig. 3h represent the formation of the programmed liquid arrangement from i) to iv) under gravity for the architected lattice with an interval length of 3a.
The following sentence is revised in the manuscript (page 14): "Finite element analysis of the formation of the programmed liquid arrangement from i) to iv) under gravity for the architected lattice with an interval length of 3a." Response: We thank the referee very much for these constructive comments.For comment 1: The value of effective d33 significantly depends on the porosity of the cellular piezoceramics.
In our work, we prepare two types of PZT piezoceramics through the STATS manufacturing process, with solid and cellular structures, respectively.The as-prepared solid piezoceramic plates exhibit a piezoelectric constant (d33) around 500 pC N -1 , close to commercial PZT (Fig. 4a).To further demonstrate the advantages of the STATS approach in manufacturing cellular piezoceramics, we fabricate a series of cellular PZT ceramics with various relative densities (relative to the density of solid ceramics) and characterize their piezoelectric properties.The relative density of 0.13, 0.21, 0.27, and 0.34 corresponds to a porosity of 0.980, 0.963, 0.951 and 0.931, respectively (Supplementary Fig. 21a).Owing to the similar configuration and porosity, the cellular PZT ceramics exhibit a close d33 (~ 200 pC N -1 ) regardless of the changing relative density (Supplementary Fig. 21b).Compared with the solid piezoceramic plates, the decreased d33 is attributed to the significantly increased porosity.
Generally speaking, a lower porosity leads to a higher d33.In the work reported by David Menne et al., the highest d33 (330 pC N -1 ) is achieved at a porosity of 0.58.This porosity is obviously lower than that in our work (> 0.9), and the d33 is larger than that in our work (~ 200 pC N -1 ).However, as the porosity increases to 0.63, the d33 value dramatically reduces to 101 pC N -1 , obviously lower than that in our work.This occurs due to the significantly increased strut porosity.As a comparison, the locally compact structure of the cellular piezoceramics from the STATS process in our work ensures an extremely low strut porosity, finally resulting a high d33 (~ 200 pC N -1 ) even at a relatively high porosity (> 0.9).
The advantage of the STATS process proposed in our work lies in the manufacturing of globally porous but locally compact structure, endowing the cellular piezoceramics with a relatively low density and a higher piezoelectric constant than a variety of piezoelectric ceramics/composites.As a result, the locally compact structure in our work ensures a dense strut with low strut porosity, which allows the cellular piezoceramics to possess a relatively high d33 (~ 200 pC N -1 ) even at a very high overall porosity (> 0.9).
The following sentences are revised in the manuscript (page 14): "The piezoelectric performance of the prepared cellular PZT ceramics is demonstrated by characterizing their d33 and piezoelectric voltage coefficient (g33).Owing to the similar configuration and porosity (from 93.1% to 98.0%), the cellular PZT ceramics exhibit a close d33 (~ 200 pC N -1 ) regardless of the changing relative density (Supplementary Fig. 21).
Compared with the solid piezoceramic plates, the decreased d33 is attributed to the high porosity.Nevertheless, the locally compact structure ensures that the STATS manufactured cellular piezoceramics possess a relatively high d33 even at a very high overall porosity (> 90%)."For comment 2: In the work reported by David Menne et al., they utilize DIW to print with a strut/pore diameter of approx.1:6 (70 μm strut and 440 μm pore diameter).In our work, the shell thickness and chamber length depend on the feature size of organic lattice and the precursor solution concentration.The shell thickness is significantly influenced by the concentration of the precursor solution, which increases from 100 μm to 187 μm as the concentration increases from 1 mM to 5 mM (Fig. 2e and Supplementary Fig. 7).Besides the concentration of the precursor solution, the shell thickness and chamber length of the sintered cellular ceramics also depend on the feature size of organic lattice (i.e., frame length and radius).For a lattice assembled by cube cell (a frame length of 1 mm and a frame radius of 0.1 mm) and a 1 mM precursor solution concentration, the sintered ceramics possess a shell thickness of 0.1 mm and chamber length of 0.76 mm, with a length/thickness ratio of 7.6.As the frame length increases to 1.25 mm and 1.5 mm with a frame radius of 100 µm, a chamber length of 0.83 mm and 0.99 mm with a shell thickness of 90 µm are obtained in the sintered cellular ceramics, achieving a larger length/thickness ratio of 9.2 and 11, respectively (Supplementary Fig. 8a&b).As the frame radius decreases to 75 µm with a frame length of 1 mm, a chamber length of 0.65 mm and a shell thickness of 65 µm are obtained in the sintered cellular ceramics, with a larger length/thickness ratio of 10 (Supplementary Fig. 8c).
Moreover, in the work reported by David Menne et al., the printed strut possesses a high porosity from 0.3 to 0.5, which adversely affects the mechanical and piezoelectric properties of the printed cellular piezoceramics.As the overall porosity increases to 0.63, the d33 value dramatically reduces to 101 pC N -1 , lower than 200 pC N -1 even at a higher overall porosity (> 90%) in our work.The locally compact structure in our work ensures a dense strut with low strut porosity, which allows the cellular piezoceramics to possess a relatively high d33 at a very high overall porosity.
The following sentences are revised in the manuscript (page 5): "The shell thickness is significantly influenced by the concentration of the precursor solution, which increases from 100 μm to 187 μm as the concentration increases from 1 mM to 5 mM (Fig. 2e and Supplementary Fig. 7).Besides the concentration of the precursor solution, the shell thickness and chamber length of the sintered cellular ceramics also depend on the feature size of organic lattice (i.e., frame length and radius).Once the frame radius of the organic lattice is reduced from 100 μm to 75 μm, a minimum shell thickness of 65 µm is achieved with a length/thickness ratio of 10 (Supplementary Fig. 8)." "Nevertheless, the locally compact structure ensures that the STATS manufactured cellular piezoceramics possess a relatively high d33 even at a very high overall porosity (> 90%)."Response: We thank the referee very much for the insightful suggestions.Here, to prepare the conventional powder-binder-water based suspensions, the PZT powders are dispersed in deionized water to form a suspension with solid loading level of 40 vol%, with polyvinyl alcohol (PVA) and polyacrylic acid which serve as the binder and dispersant respectively.The prepared suspension is ball-milled for 24 hours in zirconia media to create a homogeneous and fine suspension, which is used in the following surface-tension-assisted twostep (STATS) manufacturing process.Compared to the cellular ceramics from sol-powder suspensions, the sample prepared from the conventional powder-water based suspensions shows a lower quality with more defects (Supplementary Fig. 5).
The following sentences is added in the manuscript (page 5): "As a comparison, the sample prepared from conventional powder-binder-water based suspensions shows a lower quality with more defects (Supplementary Fig. 5)." The following sentences are added in Supporting Information (page 3): "To prepare the conventional powder-binder-water based suspensions, the PZT powders are dispersed in deionized water to form a suspension with solid loading level of 40 vol%, with polyvinyl alcohol (PVA) and polyacrylic acid which serve as the binder and dispersant respectively.The prepared suspension is ball-milled for 24 hours in zirconia media to create a homogeneous and fine suspension, which is used in the following STATS manufacturing process."

6 )
Fig. 4 is confusing, in Fig. 4a a d33 value of about 500 pC/N is claimed (red bar) but in Fig. 4b d33 values are only about 200 pC/N which is clearly lower then the value of 350 pC/N reported by David Menne et al. (see above) On page 7, line 287 a pressure sensitivity of 3.2 mV/kPa is mentioned (slope of Fig 4c) the authors should explain how this quantity is related to the extensively discussed g33 data.Reviewer #2 (Remarks to the Author):

(
ETH Zürich) or Willenbacher (KIT) have published significant work in that title and the authors should benchmark their new approach against well-established DIW in terms of fabrication speed or accessible feature size.(comment 1) Furthermore, the first paragraph of the Results section should be moved to the Introduction.(comment 2)

( 2 Fig. 2e .Supplementary Fig. 7 .
Fig. 2e.The variation of shell thickness of the sintered cellular ceramics along with the precursor solution concentration, at a 1 mm frame length and 0.1 mm frame radius of the organic lattice.Insets show the SEM images of the cellular ceramics with shell structure and layer-by-layer characteristic.Scale bar, 200 μm.

Fig. 3c .Fig. 3h , 5 .
Fig. 3c.FE results of the dependence of α on the contact angle θ123 for precursor solution in air.Insets show the liquid distribution at the contact angle of 20° and 60°.

Fig. 4a .
Fig. 4a.Comparison of the piezoelectric charge coefficient d33 between the STATS manufactured piezoceramics including solid piezoceramic plates and cellular piezoceramics with high porosity and the previously reported architected piezoelectric composites and ceramics.

Supplementary Fig. 8 .For comment 3 :
a, SEM image of the sintered cellular ceramics with a chamber length of 0.99 mm and a shell thickness of 90 µm, at a frame length of 1.5 mm and a frame radius of 100 µm of the organic lattice.b, SEM image of the sintered cellular ceramics with a chamber length of 0.83 mm and a shell thickness of 90 µm, at a frame length of 1.25 mm and a frame radius of 100 µm of the organic lattice.c, SEM image of the sintered cellular ceramics with a chamber length of 0.65 mm and a shell thickness of 65 µm, at a frame length of 1 mm and a frame radius of 75 µm of the organic lattice.The concentration of precursor solution is 1 mM.Scale bar, 200 μm.The electrical responses of the piezoelectric materials under mechanical deformation originate from the direct piezoelectric effect.Under compressive pressure, the d33 constants of the cellular PZT ceramics are quantified by the ratio of the applied load FN and the generated charge Q, which is given by d 33 = Q F N ⁄ .And the g33 constants are further quantified by the ratio of electric permittivity 33 and d33 constant (g 33 = d 33 ε 33 ⁄ ).The effective permittivity 33 can be calculated by ε 33 = Cl A ⁄ , where C is the capacitance of the cellular PZT ceramics, l is the distance between the electrodes and A is the cross-section area of the cellular PZT ceramics.In addition, the generated charge Q can be expressed by Q=CV out , and the applied load FN can be expressed by F N =PA, where Vout is the open-circuit output voltage and P is the applied pressure.Combining these equations, the open-circuit output voltage can be given by , the open-circuit output voltage is linearly correlated with the applied pressure, and a larger g33 constant leads to an increasing output voltage.

For comment 1 :
To further characterize the cellular structure of the STATS manufactured ceramics, X-ray computed microtomography (micro-CT) is conducted.As shown in Supplementary Fig.9, the micro-CT images clearly show the globally cellular shell structure of the sintered ceramics with a high quality.There are mainly two types of defects, including the cracks existing in the interface between the ceramic shell and the removed organic lattices, and the extra ceramic walls between the unit cells.These defects have little influence on the overall performance of the sintered cellular ceramics.The following sentences are added in the manuscript (page 5): "To further characterize the cellular structure of the STATS manufactured ceramics, X-ray computed microtomography (micro-CT) is conducted.As shown in Supplementary Fig.9, the micro-CT images clearly show the globally cellular shell structure of the sintered ceramics with a high quality.There are mainly two types of defects, including the cracks existing in the interface between the ceramic shell and the removed organic lattices, and the extra ceramic walls between the unit cells.These defects have little influence on the overall performance of the sintered cellular ceramics."2. I would also better address the role of the usage of sol-gel precursors in achieving the proposed results: what happens if conventional powder-based suspensions are used instead?Response: We thank the referee for the useful suggestion.As a comparison, we prepared the cellular ceramics based on the conventional powder-binder-water based suspensions.Usually, the conventional powder-binder-water based suspensions are developed by combining the fine ceramic powder particles with the binder materials in deionized water in the presence of suitable additives (e.g., surfactant).
the cellular PZT ceramics, l is the distance between the electrodes and A is the cross-section area of the cellular PZT ceramics.In addition, the generated charge Q can be expressed by Q=CV out , and the applied load FN can be expressed by F N =PA, where Vout is the open-circuit output voltage and P is the applied pressure.Combining these equations, the opencircuit output voltage can be given by charge Q, which is given by d 33 = Q F N ⁄ .And the g33 constants are further quantified by g 33 = d 33 ε 33 ⁄ .The effective permittivity 33 can be calculated by ε 33 = Cl A ⁄ , where C is the capacitance of