Bianca Jansen Va Rensburg

Student Member, IEEE William Puech
email: william.puech@lirmm.fr

Senior Member, IEEE Jean-Pierre Pedeboy

The First Draco 3D Object Crypto-Compression Scheme

Keywords: compression, 3D security, crypto-compression, AES encryption, draco, compression

3D objects have come to play an essential role in industry. They can also be very large, sometimes containing millions of vertices, and therefore it is vital that they are compressed, particularly when it comes to uploading them to the web and during real time rendering. The Draco 3D object compression system, proposed by Google, is becoming an industry standard for the compression of 3D objects structured as geometric meshes or point clouds. These 3D objects are important assets which also need to be secured. In this paper, we propose the first 3D object crypto-compression method, which integrates an encryption step into Google's Draco compression scheme, by adding an AES encryption step during Draco's entropy encoding step. Our proposed Draco 3D object crypto-compression scheme is format compliant, has no size expansion and does not require additional information such as an auxiliary file. After the entire decoding process (joint decryption and decompression), the reconstructed 3D object obtained is identical to the one after a standard compression by Draco. Experimental results on real 3D objects and a security analysis show our proposed method is efficient.

I. INTRODUCTION

Over the last decade, 3D objects have become an essential part of everyday life. They are used in many different domains such as manufacturing, healthcare and the entertainment industry. 3D objects are often high quality and can be composed of several million vertices. They can therefore occupy a lot of space and need to be compressed during their network transmission and cloud storage. This is especially true when they are uploaded to the web, or need to be rendered in real time.

Over the past few years, many methods for 3D compression have been proposed. In 2017, Dong et al. described a progressive compression algorithm that uses the 3D object's attributes [START_REF] Dong | '3D model progressive compression algorithm using attributes[END_REF]. Recently, in 2021, Que et al. proposed an octree-based deep learning framework for point cloud compression [START_REF] Que | VoxelContext-Net: An octree based framework for point cloud compression[END_REF]. In 2019, Doumanoglou et al. detailed a comparison of real-time 3D compression methods [START_REF] Doumanoglou | Benchmarking open-source static 3D mesh codecs for immersive media interactive live streaming[END_REF]. Then, in 2020, Liu et al. described a comparison of 3D point cloud compression methods [START_REF] Liu | A comprehensive study and comparison of core technologies for MPEG 3-D point cloud compression[END_REF]. Among these proposed methods

The associate editor coordinating the review of this manuscript and approving it for publication was Diana Gratiela Berbecaru .

is the 3D compression method Draco [START_REF]Draco 3D Graphics Compression[END_REF], this has been developed by Google and is quickly becoming the industry standard.

3D objects have become important assets and need to be secured as such, as they are often stored on the cloud or transferred many times during their existence. It is therefore important that they are both compressed and secured jointly. However, 3D object compression first and encryption afterwards is not efficient, because it is not format compliant and the trade off between the compression rate and the distortion is not optimized. This is the reason why over the years, several crypto-compression methods for multimedia have been proposed. These methods are beneficial as they combine the encryption and compression into a single process. This adds an extra layer of security as an additional level of complexity and uncertainty is added, making it more difficult for an attacker to break the system.

During the last twenty years, several JPEG image crypto-compression methods have been proposed where an encryption step is integrated into the JPEG compression method. Van Droogenbroeck and Benedett suggested encrypting only the AC coefficients after the Discrete Cosine Transform (DCT) [START_REF] Van Droogenbroeck | Techniques for a selective encryption of uncompressed and compressed images[END_REF]. Puech and Rodrigues proposed encrypting the DC coefficients and the lowest frequency AC coefficients [START_REF] Puech | Crypto-compression of medical images by selective encryption of DCT[END_REF]. Gmira et al. proposed adding a dynamic Hill-Cipher encryption to the quantization step of JPEG compression [START_REF] Gmira | Securing the architecture of the JPEG compression by an dynamic encryption[END_REF]. Hajji et al. [START_REF] Hajji | Cryptocompression of images based on chaos[END_REF] and Dridi et al. [START_REF] Dridi | Crypto-compression of medical image based on DCT and chaotic system[END_REF] both proposed crypto-compression schemes for images based on chaos.

Crypto-compression methods have also been developed for videos. Dufaux and Ebrahimi described two scrambling methods to hide private data in regions of interest [START_REF] Dufaux | Scrambling for privacy protection in video surveillance systems[END_REF]. In 2011, Shahid et al. proposed an encryption method for H.264/AVC by selectively encrypting Context Adaptive Video Length Encoding (CAVLC) and Context Adaptive Binary Arithmetic Coding (CABAC) for P and I frames [START_REF] Shahid | Fast protection of H.264/AVC by selective encryption of CAVLC and CABAC for I and P frames[END_REF]. Then, in 2017, Hamidouche et al. proposed an encryption scheme based on the chaos system in the scalable extension of High-Efficiency Video Coding (HEVC) [START_REF] Hamidouche | Real-time selective video encryption based on the chaos system in scalable HEVC extension[END_REF].

To the best of our knowledge, we are the first to propose a crypto-compression method for 3D objects. We note that a crypto-compression method based on Draco was requested on Github and was subsequently added by Google to their list of calls for Draco enhancements [START_REF]Please Offer an Option for Encryption[END_REF]. In this paper, we propose integrating an encryption step into Google's compression method Draco. During the range Asymmetric Numeral System (rANS) encoding step of the Draco compression scheme, we propose encrypting the encoded vertex prediction errors. This encryption is performed with the AES encryption scheme where the cipher feedback (CFB) mode is used. The proposed method is format compliant and has no size expansion in the encrypted or clear domain. It has a low complexity and does not require additional information such as an auxiliary file.

This paper is organised as follows. First, in Section II, we detail the proposed Draco 3D object crypto-compression method. Then, in Section III, we describe our experimental results and perform a security analysis. Finally, in Section IV, we conclude this paper.

II. PROPOSED DRACO 3D OBJECT CRYPTO-COMPRESSION METHOD

In this section, we detail the proposed Draco 3D object crypto-compression method. Fig. 1 illustrates an overview of the proposed Draco 3D object crypto-compression method. The encryption step is integrated in the rANS encoding of the prediction errors of the quantized vertices. First, in Section II-A, we give an overview of Google's compression method Draco, as well as the compression method Edgebreaker on which Draco is based. Then, in Section II-B, we describe the encryption step integration in the compression method Draco. Finally, in Section II-C, we describe the Draco decoding phase in which the decryption step is integrated.

A. DRACO 3D OBJECT COMPRESSION OVERVIEW

In Fig. 1 we can see the main steps of Google's compression method for 3D objects, Draco. This compression method relies heavily on the compression method Edgebreaker, proposed by Rossignac in 1999 [START_REF] Rossignac | '3D compression made simple: Edgebreaker with Zipand-Wrap on a corner-table[END_REF]. The Edgebreaker method is used to encode the 3D object's connectivity by encoding each triangle of a manifold 3D object with less than 2 bits.

The Edgebreaker method consists of traversing the connectivity of the 3D object step-by-step by means of a depth-first spiraling triangle spanning tree. At each step, a new triangle is visited and encoded according to which of its neighbouring triangles have already been visited. The current triangle is then encoded with a single character C, L, E, R or S. These characters serve to describe how the current triangle can be reattached to set of already reconstructed triangles during the reconstruction. triangle is labeled 'C' and we move to the right. If the vertex is visited, then there are four possibilities. If the left triangle is visited, the current triangle is labeled 'L' and we move to the right. If the right triangle is visited, the current triangle is labeled 'R' and we move to the left. If neither are visited, the current triangle is labeled 'S' and we move to the right first and then recursively to the left. If both are visited, the current triangle is labeled 'E' and we end the current loop.

The Draco compression method has two main parameters which are used to compress a 3D object (Fig. 1). The quantization parameter qp, where qp ∈ [0, 30], corresponds to the number of bits conserved per coordinate, except for qp = 0, which signifies that there is no quantization. The parameter cl corresponds to the compression level, where cl ∈ [0, 10]. The value cl = 0 corresponds to no compression, and cl = 10 to the highest level of compression. The vertex prediction step relies on this parameter. The value of qp is a trade-off between the compression rate and quality, whereas the value of cl is a trade-off between the compression rate and processing time. A vertex prediction step is then performed in order to transmit only the prediction errors. Depending on the compression level cl, the vertex prediction method used is either a delta prediction, a parallelogram prediction, or a constrained multi-parallelogram prediction.

Asymmetric Numeral System (ANS) encoding is an entropy encoding scheme proposed by Duda et al. in 2015 [START_REF] Duda | The use of asymmetric numeral systems as an accurate replacement for Huffman coding[END_REF]. A range Asymmetric Numeral System (rANS) encoding is performed separately after the connectivity encoding and the quantized vertex prediction. A compressed 3D object is then obtained.

B. ENCRYPTION PHASE

In this paper, we propose integrating an encryption step during the rANS encoding of the prediction errors of the quantized vertices. As the proposed 3D object crypto-compression method must be format compliant we decide not to encrypt the CLERS string data. Otherwise this would make the 3D object crypto-compression illegible for the Edgebreaker decoder. Therefore the 3D object's connectivity is not modified.

As we propose only encrypting the prediction errors, then only the geometry is encrypted (Fig. 1). In order to compress the geometry, the vertices of the 3D object are then predicted according to a prediction scheme. This prediction scheme is determined according to the Draco compression level parameter cl, as detailed in Section II-A. The prediction errors, along with other information needed to decode the vertices, are encoded with the rANS encoding scheme, and then stored in the Draco output buffer. The rANS encoded prediction errors are then substituted with their encryption. We note that since the encryption takes place after the rANS entropy encoding, there is no size expansion and therefore Draco's original compression rate is maintained. This is because encryption eliminates redundancy and therefore increases the entropy.

To encrypt the prediction errors, we use the Advanced Encryption Standard (AES) algorithm, proposed by Daemen and Rijmen [START_REF] Daemen | The Design of Rijndael[END_REF] in 1999. The AES encryption function consists of a set of processing operations which are performed iteratively on a block of 128 bits. The number of iterations, called rounds, depends on the size of the key. A 128 bit key has 10 rounds, and a 256 bit key has 14 rounds. In this paper, we use a 256 bit key. For each round, a round key is generated according to the original 256 bit key. Each processing operation depends on its corresponding round key. The AES algorithm supports many different block encryption modes such as Cipher Block Chaining (CBC), Cipher Feedback (CFB), Counter (CTR), ECB (Electronic Code Book), or Output Feedback (OFB). In the context of our application, the ECB mode should be avoided, because when two identical blocks are encrypted, their encryption is also identical. This is the reason why, as illustrated in Fig. 3 which represents the prediction error encryption step, in our method we use the CFB mode. In this case, only the AES encryption function, and not the decryption function, is used.

In addition to prediction errors, the prediction data contains other information needed to correctly decode the vertices. Markers are necessary to locate the prediction errors in the Draco output buffer (Fig. 3). The structure of the prediction data and therefore the location of the prediction errors depend on several parameters such as qp and cl, but also on the characteristics of the 3D object. From these markers, we are then able to encrypt the correct segment of information after the rANS encoding.

C. DECODING PHASE

In order to successfully decode the 3D object, the decryption is done jointly during the decompression. Fig 4 presents the vertex decoding, decryption and reconstruction process. In order to avoid adding to the output buffer and therefore increasing its size, decryption is performed jointly with the rANS decoding step. The AES decryption in CFB mode is carried out before prediction errors are decoded by rANS. During the rANS decoding step, the decoder is first initialised using prediction error data that remains in the clear domain.

Once the decoder has extracted the prediction errors, they are decrypted using the AES algorithm using the CFB mode. The decrypted prediction errors can then be decoded by the rANS decoder in order to reconstruct the 3D object's vertices.

III. EXPERIMENTAL RESULTS

In this section, we detail our experimental results. In Section III-A, we describe our results when our proposed method is applied to the Stanford 3D dataset [START_REF] Levoy | The Stanford 3D Scanning Repository[END_REF]. Then in Section III-B, we perform a security analysis on our proposed method by performing a differential analysis, comparing the correlation between the Draco compressed 3D object and the crypto-compressed 3D object and analysing the entropy.

A. CRYPTO-COMPRESSION RESULTS

Our experimentation was performed on the Stanford 3D dataset [START_REF] Levoy | The Stanford 3D Scanning Repository[END_REF]. Each combination of cl and qp is applied to the 11 objects, resulting in a dataset of 3630 different 3D objects. Each 3D object is encrypted with a different pseudo randomly generated key. Our proposed method is fully reversible. There is no size expansion or data loss. The root mean squared error (RMSE) between a decoded standard Draco compressed 3D object O and its corresponding decoded decrypted Draco cryptocompressed 3D object O e is always 0. This means that these obtained 3D objects are identical and our proposed crypto-compression method is fully reversible in relation to the Draco compression scheme. Therefore, we note both the decoded standard Draco compressed 3D object and its corresponding decoded decrypted Draco crypto-compressed 3D object O . Table 1 presents compression rates and hausdorff distances (HD) when comparing the original 3D objects of the Stanford dataset and their corresponding decoded standard Draco compressed O and decoded Draco crypto-compressed O e 3D objects. We define the compression rate as the ratio between the size of the original 3D object and the size of the crypto-compressed 3D object. We note that our proposed Draco crypto-compression scheme has no size expansion in relation to the standard Draco compression scheme. Therefore the compression rate remains constant for O and O e . The HD between O and O remains low with an order of 10 -4 .

We note that the proposed encryption method is efficient, as the AES encryption scheme is linear. The average time 1 of the standard Draco compression encoding process of the 11 1 Algorithms were tested on a 6-core work station with 32 GB of RAM and a Windows based operating system. 3D objects is 157.455 ms, while that of the proposed Draco crypto-compression method is 157.545 ms. The average time of the standard Draco decoding process is 33.636 ms, while the average decoding and decryption time of the proposed Draco crypto-compression method is 34.818 ms. Therefore we conclude that the time added by the AES encryption and decryption is negligible.

Fig. 6 illustrates a full example of the compression rate according to the quantization level qp for each compression level cl for the 3D object Venus. The curve represents the decoded standard Draco compressed 3D object O , while the points represent the decoded Draco crypto-compressed 3D object. We observe that there are two major trends according to cl. This is explained by the type of encoding method used during Edgebreaker. For the parameters cl ∈ [1 -5] where the compression rate starts at about 75, the standard Edgebreaker encoding is used, while for parameters cl ∈ [6 -10], a valence encoding is used and the compression rate starts at about 150. We can observe that our proposed crypto-compression method has absolutely no size expansion, which means that the compression rate is preserved. We observe that apart from the low quantization levels where the 3D object is unrecognizable, the average RMSE remains similar around 1.25 when qp increases. We note that the RMSE does not vary with the compression level cl.

B. SECURITY ANALYSIS

In this Section, we examine the security of the proposed crypto-compression scheme in terms of confidentiality. We first perform a differential analysis and measure the 3D object's correlation. Then we study the entropy of the decoded standard Draco compressed 3D object O and the decoded Draco crypto-compressed 3D object O e . Fig. 9 illustrates the differential analysis for the 3D object Venus with the default parameters cl = 7 and qp = 11. A Key 2 test is performed, where the 3D object is decrypted using keys where only a single bit of the correct 256 bit private key is flipped. The x axis represents the index of the flipped bit in the private key, and the y axis represents the RMSE between the resulting 3D object and the decoded standard Draco compressed 3D object. We note that the key used in position 128 is the correct private key.

We observe from Fig. 9 that while the correct key results in an RMSE of 0, and therefore a perfect decryption, any incorrect key results in an encrypted 3D object with an RMSE of around 1.65. This stable value means that an attacker cannot try to converge to the correct value. Therefore an incorrect key which has only a single false bit does not reveal any information about the 3D object. This is to be expected, since the AES encryption scheme is used. We note that the default Draco parameters of cl = 7 and qp = 11 were used. The correlation was performed between pairs of neighbouring vertices, where the neighbours are defined by the Edgebreaker scheme and are separated into two groups u and v. We note that this division into groups was performed in the same manner for both the decoded standard Draco compressed 3D object O and the decoded Draco crypto-compressed 3D object O e .

We observe that there is a strong correlation between neighbouring vertices in the decoded standard Draco compressed 3D object O . However, we can also note that there is a large portion of uncorrelated data. This can be explained by the vertex order defined by the the Edgebreaker scheme. Once a loop is completed, there can be a jump to the start of the next loop. In comparison, we observe that when the 3D object is crypto-compressed, the neighbouring vertices are no longer correlated.

The Pearson correlation coefficient between the vertices of O and O e is 0.004 for Venus, 0.043 for Cow, and 0.510 for Bunny. These results show that the Draco crypto-compressed 3D objects O e is not correlated with its corresponding 3D object O in the clear domain. We observe in Fig. 13.b and Fig. 14.b that after the 3D object has been encrypted, we obtain a histogram which is uniform within intervals of powers of 2. The entropy between the interval 2 8 + 1 and 2 9 is 7.79 bits/prediction error for the standard Draco compressed 3D object Venus and 7.90 for Bunny, and a near maximum value of 7.99 bits/prediction error for the Draco crypto-compressed 3D object Venus and 7.97 for Bunny.

From this security analysis, we can conclude that our proposed Draco crypto-compression method is secure in terms of confidentiality.

IV. CONCLUSION

In this paper, we propose a format compliant cryptocompression method for 3D objects based on Google's compression method Draco. We have integrated an AES encryption step using the CFB mode during the rANS encoding step, where we encrypted the vertex prediction errors. This encryption step is performed jointly with the 3D object compression. The proposed crypto-compression scheme has no size expansion and is completely reversible. To the best of our knowlege, we are the first to propose a crypto-compression method for 3D objects. We have shown with our experimental results that the proposed method is efficient in terms of time and compression rate. Based on an AES encryption with a 256 bit key, we have also shown with a security analysis that the proposed method is secure in terms of confidentiality. In future work, we want to develop a selective crypto-compression based on Draco.

FIGURE 1 .

 1 FIGURE 1. Overview of the proposed Draco 3D object crypto-compression method.

FIGURE 2 .

 2 FIGURE 2. The CLERS string allocation for the Edgebreaker compression method.

Fig. 2

 2 illustrates the CLERS string allocation, where the triangles or vertices in blue are not yet visited, while those in red have been visited, and the arrow indicates the next triangle to visit. If the vertex is not yet visited, then the VOLUME 10, 2022

FIGURE 3 .

 3 FIGURE 3. Encryption of prediction errors using the AES in CFB mode.

FIGURE 4 .

 4 FIGURE 4. The vertex reconstruction process.

FIGURE 5 .

 5 FIGURE 5. Illustrations of the Draco 3D object crypto-compression scheme: a) The original 3D object O, b) the decoded standard Draco compressed 3D object O , c) the decoded Draco crypto-compressed 3D object O e without a key, and d) the decoded decrypted 3D object O . The default Draco parameters cl = 7 and qp = 11 are used.

Fig. 5

 5 illustrates three examples of our proposed method, Venus (100, 759 vertices), Bunny (35, 947 vertices) and Cow (2,904 vertices). Fig 5.a shows the original 3D object O, then the decoded standard Draco compressed 3D object O is shown in Fig 5.b, followed by the decoded Draco cryptocompressed 3D object O e without a key in Fig 5.c. Then, the decoded decrypted Draco crypto-compressed 3D object O is shown in Fig 5.d. For these examples, the default parameters provided by Google for Draco are used: cl = 7 and qp = 11.

TABLE 1 .

 1 Compression rates and hausdorff distances (HD) between the original 3D objects of the Stanford dataset O and their decoded standard Draco compression O and decoded Draco crypto-compression O e .

FIGURE 6 .

 6 FIGURE 6. Compression rate according to the quantization parameter qp for each compression level cl for both the decoded standard Draco compression and the decoded Draco crypto-compression of the 3D object Venus.

FIGURE 7 .

 7 FIGURE 7. Average RMSE between the decoded standard Draco compressed 3D objects of the Stanford datset O and their corresponding decoded crypto-compression O e according the quantization level qp.

FIGURE 8 .

 8 FIGURE 8. Results of the proposed Draco crypto-compression method applied to a manufactured object Shoe (Provided by STRATEGIES (https://www.romans-cad.com/)): a) The original manufactured 3D object O, b) The decoded standard Draco compressed 3D object O , c) The decoded Draco crypto-compressed 3D object O e , d) The decoded decrypted Draco crypto-compressed 3D object O .

FIGURE 9 .

 9 FIGURE 9. Differential analysis of the 3D object Venus.

Fig. 7

 7 Fig.7illustrates the average RMSE between the Draco compressed 3D objects O of the Stanford dataset and their corresponding crypto-compression O e according to the quantization level qp. We observe that apart from the low quantization levels where the 3D object is unrecognizable, the average RMSE remains similar around 1.25 when qp increases. We note that the RMSE does not vary with the compression level cl. Fig. 8 illustrates the results of the proposed Draco crypto-compression method on a manufactured 3D object Shoe 2 composed of 976, 943 vertices. Fig. 8.a presents the original manufactured 3D object and Fig. 8.b the decoded standard Draco compressed 3D object O . Fig. 8.c illustrates the decoded Draco crypto-compressed 3D object O e and Fig. 8.d the decoded decrypted Draco crypto-compressed 3D object O . There is a compression rate of 34.75 and the RMSE between O and O e is 273.817.

Fig. 8

 8 Fig.7illustrates the average RMSE between the Draco compressed 3D objects O of the Stanford dataset and their corresponding crypto-compression O e according to the quantization level qp. We observe that apart from the low quantization levels where the 3D object is unrecognizable, the average RMSE remains similar around 1.25 when qp increases. We note that the RMSE does not vary with the compression level cl. Fig. 8 illustrates the results of the proposed Draco crypto-compression method on a manufactured 3D object Shoe 2 composed of 976, 943 vertices. Fig. 8.a presents the original manufactured 3D object and Fig. 8.b the decoded standard Draco compressed 3D object O . Fig. 8.c illustrates the decoded Draco crypto-compressed 3D object O e and Fig. 8.d the decoded decrypted Draco crypto-compressed 3D object O . There is a compression rate of 34.75 and the RMSE between O and O e is 273.817.

FIGURE 10 .

 10 FIGURE 10. Correlation of the decoded standard Draco compressed 3D object Venus (red), and the correlation of the corresponding decoded Draco crypto-compressed 3D object (blue) with the parameters cl = 7 and qp = 11.

FIGURE 11 .

 11 FIGURE 11. Correlation of the decoded standard Draco compressed 3D object Cow (red), and the correlation of the corresponding decoded Draco crypto-compressed 3D object (blue) with the parameters cl = 7 and qp = 11.

FIGURE 12 .

 12 FIGURE 12. Correlation of the decoded standard Draco compressed 3D object Bunny (red), and the correlation of the corresponding decoded Draco crypto-compressed 3D object (blue) with the parameters cl = 7 and qp = 11.

FIGURE 13 .

 13 FIGURE 13. Prediction error distribution for: a) The decoded standard Draco compressed 3D object Venus O , b) The corresponding crypto-compressed 3D object O e (parameters cl = 7 and qp = 16).

Fig. 10

 10 illustrates the correlation of the euclidean norms of vertices belonging to the decoded standard Draco compressed 3D object Venus in red, and the correlation of the euclidean norms of the vertices belonging to the decoded Draco cryptocompressed 3D object Venus in blue. Fig.11presents the same for the 3D object Cow and Fig.12the same for Bunny.

FIGURE 14 .

 14 FIGURE 14. Prediction error distribution for: a) The decoded standard Draco compressed 3D object Bunny O , b) The corresponding crypto-compressed 3D object O e (parameters cl = 7 and qp = 16).

Fig. 13 .

 13 a presents the prediction error distribution of the decoded standard Draco compressed 3D object Venus while Fig. 13.b presents the prediction error distribution of the decoded Draco crypto-compressed 3D object Venus, where the parameters are cl = 7 and qp = 16. Fig. 14.a shows the prediction error distribution of the decoded standard Draco compressed 3D object Bunny and Fig. 14.b shows the prediction error distribution of the decoded Draco cryptocompressed 3D object Bunny, where the parameters are cl = 7 and qp = 16.

Provided by STRATEGIES (https://www.romans-cad.com/)VOLUME 10, 2022

 VOLUME 10, 2022


Dr Pierre Gibot
email: pierre.gibot@isl.eu

Fabien Schnell
email: fabien.schnell@isl.eu

Denis Spitzer
email: denis.spitzer@isl.eu

Synthesis of Nb 2 O 5 and Ta 2 O 5 nanopowders by means of an endo-biotemplating method

Keywords: Hard-templating approach, Template, Niobium (V) oxide, Tantalum (V) oxide, Tricalcium phosphate Hard-templating approach, Biotemplate, Niobium (V) oxide, Tantalum (V) oxide, Tricalcium phosphate

Finding efficient templates for the nanostructuring of materials is a key point. Here, the niobium (V) -and tantalum (V) oxide ceramics nanopowders have been synthesized by a hard-templating approach by using the tricalcium phosphate biomaterial (Ca3(PO4)2.xH2O) as template agent. The oxide ceramics were investigated by X-ray Diffraction (XRD), Fourier Transform Infrared (FTIR) spectroscopy, nitrogen physisorption and Scanning Electron Microscopy (SEM). It was observed that the surface properties (specific surface areas, pore volumes) of the Nb2O5 and Ta2O5 powders were strongly dependent of the amount of the Ca3(PO4)2.xH2O template previously used in the preparation of the [oxide ceramics/template] composites. For instance, with a Ca3(PO4)2.xH2O/ceramic salt weight ratio ranging from 0 to 1, the specific surface areas of Nb2O5 and Ta2O5 were gradually enhanced of 48 to 166 m2/g and 5 to 84 m2/g, respectively. The pore volumes were increased as well. The use of the eco-friendly tricalcium phosphate material (Ca3(PO4)2.xH2O) as template in the hard-templating approach may be suitable and efficient in the aim of synthesizing materials with enhanced surface properties.

Introduction

Niobium (Nb) and tantalum (Ta) pentoxides, ceramics made of two major group V transition metals, exhibit some interesting properties such as good chemical stabilities in particular in acidic environments, high melting points (T Nb2O5 = 1512 °C, T Ta2O5 = 1784 °C), high refractive indexes (n Nb2O5 = 2.33, n Ta2O5 = 2.27) and wide energy band gaps (Eg Nb2O5 = 3.4 eV, Eg Ta2O5 = 3.8 eV). Since few years, these ceramics attract growing interest thanks to some of these properties making them promising candidates for numerous potential applications. For instance, Nb 2 O 5 niobium (V) oxide and Ta 2 O 5 tantalum (V) oxide can be used in the fields of catalysis (selective oxidation of hydrocarbons, aldol condensation of ketone…) [START_REF] Ushikubo | Recent topics of research and development of catalysis by niobium and tantalum oxides[END_REF][START_REF] Paulis | Preparation and characterization of niobium oxide for the catalytic aldol condensation of acetone[END_REF][START_REF] Guo | Preparation of mesoporous tantalum oxide and its enhanced photocatalytic activity[END_REF][START_REF] Sreethawonga | Facile surfactant-aided sol-gel synthesis of mesoporous-assembled Ta 2 O 5 nanoparticles with enhanced photocatalytic H 2 production[END_REF], of hydrogen storage [START_REF] Bhat | High surface area niobium oxides as catalysts for improved hydrogen sorption properties of ball milled MgH 2[END_REF], of electrochromism (lithium insertion/extraction process) [START_REF] Ozer | Preparation and properties of spin-coated Nb 2 O 5 films by the sol-gel, process for electrochromic applications[END_REF] and as sensors (oxygen, humidity) [START_REF] Ohtaki | Oxygen sensing properties of Ti-doped Nb 2 O 5[END_REF][START_REF] Gimon-Kinsel | Pulsed laser deposition of mesoporous niobium oxide thin films and application as chemical sensors[END_REF], domains where the structuring of the material at nanoscale and the development of its porosity are essential to achieve optimal performance. Among the different physical or chemical approaches addressed to assign such properties to materials, the use of templates is seen as a successful strategy. Two kinds of templates can be used; the soft templates (polymers, surfactants) and the hard exo-templates (mesoporous silicas and carbons, alumina membranes, zeolithes…) or endo-templates (colloidal silica dispersions, polystyrene and polymethylmethacrylate beads…) which can be removed by means of a specific treatment to release porosity and thus evolve into complex architectures exhibiting unique surface properties.

For instance, regarding the soft-templated synthesis, niobium (V) and tantalum (V) oxide ceramics may be prepared by using different organic structure-directing agents such as (i) poly(alkylene oxide) symmetric triblock copolymers (PEO-PPO-PEO as P-123, F-127) [START_REF] Yang | Generalized syntheses of large-pore mesoporous metal oxides with semicrystalline frameworks[END_REF][START_REF] Katou | Synthesis of 2D-hexagonally ordered mesoporous niobium and tantalum mixed oxide[END_REF][START_REF] Guo | In situ carbonization of a soft-template to directly synthesize crystalline mesoporous metal oxides with high surface areas[END_REF][START_REF] Ismail | Synthesis of mesoporous sulfur-doped Ta 2 O 5 nanocomposites and their photocatalytic activities[END_REF][START_REF] Shirokura | Synthesis of crystallized mesoporous transition metal oxides by silicone treatment of the oxide precursor[END_REF][START_REF] Noda | Synthesis of crystallized mesoporous tantalum oxide and its photocatalytic activity for overall water splitting under ultraviolet light irradiation[END_REF], (ii) a poly(styrene-b-2-vinyl-1-methylpyridinium iodide-b-ethylene oxide) asymmetric triblock copolymer (PS-b-PVMP-b-PEO) [START_REF] Liu | Synthesis of hollow metal oxide nanospheres by templating polymeric micelles with core-shell-corona architecture[END_REF], (iii) poly(isoprene-block-b-ethylene oxide) (PI-b-PEO) and poly(ethylene-cobutylene-b-poly ethylene oxide) (PEB-b-PEO as KLE) diblock copolymers [START_REF] Lee | Direct access to thermally stable and highly crystalline mesoporous transition-metal oxides with uniform pores[END_REF][START_REF] Brezesinski | Pseudo capacitive contributions to charge storage in highly ordered mesoporous group V transition metal oxides with iso-oriented layered nanocrystalline domains[END_REF], (iv) a poly(ethylene glycol) stearyl ether copolymer (Brij-76) [START_REF] Macıas | Electrospun mesoporous metal oxide fibers[END_REF], (vi) a quaternary ammonium surfactant (cetyltrimethylammonium bromide or CTAB) [START_REF] Guo | Preparation of mesoporous tantalum oxide and its enhanced photocatalytic activity[END_REF] and (vii) primary amines molecules (1,12-diaminododecane, lauryl-amine, octadecyl-amine…) [START_REF] Sun | Synthesis of microporous transition metal oxide molecular sieves with bifunctional templating molecules[END_REF][START_REF] Sreethawong | Facile surfactant-aided sol-gel synthesis of mesoporous-assembled Ta 2 O 5 nanoparticles with enhanced photocatalytic H 2 production[END_REF][START_REF] Takahara | Mesoporous tantalum oxide -characterization and photocatalytic activity for the overall water decomposition[END_REF]. In most cases, Nb 2 O 5 and Ta 2 O 5 materials with significant surface properties are obtained. However, the materials exhibit amorphous pore walls and low thermal stabilities thus limiting their applicative potential. A post heat treatment is then need to crystallize the pore walls thus leading to a significant decrease of the surface properties.

Concerning the hard-templated route, less developed than the previous one for the current case, the synthesis of niobium (V) and tantalum (V) oxide ceramics may be synthesized by using (i) threedimensionally (ordered or not) macroporous architectures made of self-assembly of polystyrene beads [START_REF] Orilall | Highly crystalline inverse opal transition metal oxides via a combined assembly of soft and hard chemistries[END_REF][START_REF] Li | Fabrication and characterization of three-dimensionally ordered macroporous niobium oxide[END_REF][START_REF] Xin | Fabrication of three-dimensionally ordered macroporous Ta 2 O 5 films through aqueous organic gel process[END_REF][START_REF] Huang | Layer-by-layer assembly of TaO 3 nanosheet/polycation composite nanostructures: multilayer film, hollow sphere, and its photocatalytic activity for hydrogen evolution[END_REF], (ii) activated carbon [START_REF] Grewe | Activated-carbon-templated crystalline tantalates for photocatalytic water splitting[END_REF] and (iii) ordered mesoporous silica materials such as SBA-15 and FDU-1 [START_REF] Nowak | Hard'' vs. ''Soft'' templating synthesis of mesoporous Nb 2 O 5 catalysts for oxidation reactions[END_REF]. From this hard-template approach, the pore walls of the as-prepared Nb 2 O 5 and Ta 2 O 5 materials are well-crystallized since higher temperatures may be reached during the process without risking of losing the nanodimensions and the porous character of the materials. However, if with exotemplates, ordered porous materials can be prepared, the low yield and the high cost of the templates are real drawbacks for an up-scaling. These last facts may be reasonably avoided with the use of endotemplates such as, for example, marketed cheap silica colloidal suspensions [START_REF] Gibot | Porous WS 2 and W 2 N powders by hard templating with colloidal silica[END_REF][START_REF] Gibot | Synthesis of WO 3 nanoparticles for superthermites by the template method from silica spheres[END_REF].

Herein, an efficient route is reported for the synthesis of niobium (V) and tantalum (V) oxide materials exhibiting tunable surface properties. The synthetic route is a so called endo-hard-templating approach where alkoxydes are selected as ceramic reagents and the role of the hard template carried out by the tricalcium phosphate biomaterial. For us, the commercial availability of the template in different sizes, at low cost, its readily removal and its environmentally friendly trait, make of its use a promising and competitive alternative in the constant research of new templates for the synthesis of large surface areas materials.

Experimental section

The syntheses were performed with commercially available reagents without further purification. Niobium (+V) ethoxide (Nb(OCH 2 CH 3 ) 5 , 99.95%), tantalum (+V) ethoxide (Ta(OC 2 H 5 ) 5 , 99.98%), tricalcium phosphate hydrate (Ca 3 (PO 4 ) 2 .xH 2 O, < 200 nm, reagent grade) and ethyl alcohol (C 2 H 5 OH, reagent grade) were all purchased from Sigma Aldrich. Hydrochloric acid (HCl, 37%) was obtained from Prolabo.

The typical synthesis procedure inspired by [START_REF] Gibot | Ca 3 (PO 4 ) 2 biomaterial: A non-toxic template to prepare highly porous Cr 2 O 3[END_REF] was as follows: 200 µL of Nb(OCH 2 CH 3 ) 5 and Ta(OCH 2 CH 3 ) 5 starting materials were added to 25 mL of ethyl alcohol and stirred for 10 min. Precise amounts of non-porous spherical Ca 3 (PO 4 ) 2 .xH 2 O template particles (Supporting Information S1) were added to each solution to adjust the template/alkoxyde weight ratio to 1/3, 2/3 and 1. The suspensions were homogenised by magnetic stirring for 1 hour before to be stored under a fume hood overnight.

After room temperature ethyl alcohol removal, the obtained composites were grounded in a mortar and heat treated at 500 °C (2.5 °C/min) in air atmosphere for 2 hours, minimal thermal conditions for synthesizing crystallized materials, in particular for niobium-based ceramics, without formation of calcium niobate (Ca x Nb y O z ) or calcium tantalate (Ca x Ta y O z ). The resulting powders were washed with hydrochloric acid (1 M) overnight to remove the template particles. The products were isolated by centrifugation, washed with water and acetone before dried at 80 °C. Subsequent calcination at higher temperature (750 °C, 2h, 2.5 °C/min) was performed on the tantalum-based products to lead to their crystallisation. Finally, the samples were denoted Nb 2 O 5 -CaP X or Ta 2 O 5 -CaP X where CaP and X refer to the calcium phosphate biotemplate and X the Ca 3 (PO 4 ) 2 .xH 2 O/ceramic salt weight ratio (X = 1/3, 2/3 and 1). Reference samples (Nb 2 O 5 and Ta 2 O 5 ) were prepared following the same experimental procedure except with the use of calcium-based template particles (X = 0).

Crystal structures of the pristine materials were investigated by using a Bruker D8 Advance diffractometer (Cu K radiation) operating at 40 kV -40 mA. A step size of 0.01° was applied to record the diffraction patterns in the 2 range of 10-80°. The surface properties of the niobium-and tantalum-based powders were determined from nitrogen sorption measurements conducted at -196 °C on outgassed samples (200 °C, 6 hours) by means of a Micromeritics ASAP 2020 device. The Specific Surface Areas (SSA) were determined according to the Brunauer-Emmet-Teller (BET) method in the 0.05 -0.25 relative pressure range and the total pore volumes (V p ) were estimated from the quantity of nitrogen gas adsorbed at a relative pressure of 0.99. The microstructures of the powders were examined using a FEI Nova NanoSEM 450 scanning electron microscope operating at 15 kV. Prior to the examination, the samples were coated with a thin layer of gold with a Desk II TSC Denton Vacuum spray apparatus.

Results and Discussion

The crystal structures of the hard-biotemplated niobium (V) and tantalum (V) oxide ceramics, in particular, those synthesized with a Ca 3 (PO 4 ) 2 .xH 2 O/ceramic salt weight ratio (X) of 1, are shown in Figures 1B and2B, respectively. The XRD patterns of the reference samples (X = 0) were also presented for comparison (Figure 1A and2A). The pristine materials were identified as Nb 2 O 5 niobium (V) oxide and Ta 2 O 5 tantalum (V) oxide, respectively. The diffraction peaks were indexed in a pseudo-hexagonal system for the Nb 2 O 5 material and in an orthorhombic structure with a Pmm2 space group for the Ta 2 O 5 material, as described in the international crystallographic cards No 28-0317 and No. 25-0922, respectively. As the X value increases, the diffraction peaks are less intense and broader with the presence of an amorphous phase (nonlinear baseline) than for niobium (V)-and tantalum (V) oxides synthesized free of template (X = 0, Figure 1A and2A). This observation suggests the formation of material less crystallized and made of particles with smaller crystallites or coherent diffraction domains. This lower crystallinity may be explained by a confinement effect induced by the calcium phosphate template, characterized by a low thermal conductivity, leading the niobium and tantalum salts to be less exposed to the heating treatment need to their decompositions and the crystallisation of the reaction products. The Nb-and Ta-salt are less exposed to the heating when they are mixed with a high amount of Ca 3 (PO 4 ) 2 nanoparticles (X = 1) than with no template (X = 0). As the crystallinity depends on the heating temperature, the more the amount of Ca 3 (PO 4 ) 2 is, the less the crystallinity of the Nb 2 O 5 and Ta 2 O 5 materials is. Consequently, to totally crystallize the niobium-and tantalum-based products, the powders were subsequently calcined at higher temperatures while maintaining an oxidizing atmosphere. The corresponding X-ray diffraction patterns are presented in Figure 1C 3 and4, respectively. For the free templated-synthesized ceramics (Figures 3A and4A), the isotherms may be identified as type-IV isotherms coupled to a H2 hysteresis loop supporting the idea that materials exhibit a mesoporosity with a complex pore structure. For samples prepared with template and achieved by means of different heat treatments, the corresponding isotherms are shown on Figures 3B, 3C andFigures 4B, 4C. The different curves can be described as type-IV isotherms with H3 hysteresis loops. The presence of larger pores (> 50 nm, macroporosity), suggested by capillary condensation at relatively high relative pressure coupled to a saturation not clearly visible, was confirmed by pore size distribution (PSD) calculated by means of the Brunauer-Jarrett-Halenda (BJH) model applied to the desorption branches of the nitrogen isotherms. The PSD curves of the Nb 2 O 5 and Ta 2 O 5 materials prepared with X = 1 at 650°C and 850°C, respectively were inserted in Figure 3 and4. The PSD profiles are very wide with pores sizes ranged from 10 to 100 nm in both cases. As it can also be seen, the hysteresis loops, originated by the superposition/difference of the adsorption and desorption branches, for both oxides increases with the amount of tricalcium phosphate hydrate template used (Figures 3B and4B) illustrating a gain of porosity for the materials. The different properties data of the Nb 2 O 5 and Ta 2 O 5 , namely the specific surface areas and pore volumes, are gathered in Table 1.

Table 1:

Surface properties of the (semi-)crystalline Nb 2 O 5 and Ta 2 O 5 ceramics synthesized by means of a hard-biotemplated approach and after the tricalcium phosphate template removal. * determined from the BJH method for pores below 100 nm. The error on the measurements of the S BET and V p is of ± 5 and ± 10 %, respectively. With a Ca 3 (PO 4 ) 2 .xH 2 O/ceramic precursor weight ratio ranging from 1/3 to 1, the specific surface areas were gradually increased from 106 to 166 m 2 /g and 30 to 84 m 2 /g for Nb 2 O 5 and Ta 2 O 5 ceramics, respectively while values of 49 and 5 m 2 /g characterize the powders synthesized without the use of templates. Same trend was also observed for the pore volumes were the highest values of 0.86 and 0.72 cm 3 /g were obtained for Nb 2 O 5 and Ta 2 O 5 powders elaborated at 500°C and 750°C with a Ca 3 (PO 4 ) 2 .xH 2 O/ceramic precursor weight ratio of one. No porosity were determined for both oxides synthesized free of calcium-based template. For pure crystalline niobium and tantalum oxide ceramic phases, i.e. after heat treatment at 650 °C and 850 °C respectively, the surface properties are lower but remains clearly superior to these determined for their counterparts synthesized without template at 500°C and 750°C as mentioned in the Table 1 and clearly visible in the Figure 3C and4C, respectively. These lower values of specific surface areas and pore volumes can be explained by a growth of the particles and a pore filling originating from a classical diffusion phenomenon of the matter with the temperature raising. To remember, the porosity of the materials was released by the calcium-based template particles removal. Everything points out to the fact that the Ca 3 (PO 4 ) 2 mineral as template efficiently acts to modulate the surface properties of oxides ceramics materials prepared by a hard-templated approach.

Compared to similar hard-templated methods, mentioned in the literature, our method is very competitive since values of specific surface areas of 10 to 51 m 2 /g and 90 m 2 /g coupled to pore volumes of 0.05 to 0.20 cm 3 /g and 0.32 cm 3 /g were obtained for crystallized Nb 2 O 5 and Ta 2 O 5 samples, respectively, synthesized from SBA-15, FDU-1 mesoporous silica matrices [START_REF] Nowak | Hard'' vs. ''Soft'' templating synthesis of mesoporous Nb 2 O 5 catalysts for oxidation reactions[END_REF] and activated carbon [START_REF] Grewe | Activated-carbon-templated crystalline tantalates for photocatalytic water splitting[END_REF]. Moreover, our process exhibit some advantages compared to the previously quoted methods as higher yields in term of nanostructured powder and also that the tricalcium phosphate template is cheaper than some of the suggested templates in particular the mesoporous silica materials. Now regarding the different experimental procedures evolved in the literature according to a softtemplated approach which is considered more performing in the synthesis of large surface properties materials, our results can be qualified as intermediate or higher in particular in the case of the pore volumes (V p ). In fact, the data given in the literature for the Nb 2 O 5 are ranged from 125 to 196 m 2 /g and 0.25 to 0.50 cm 3 /g [START_REF] Yang | Generalized syntheses of large-pore mesoporous metal oxides with semicrystalline frameworks[END_REF][START_REF] Guo | In situ carbonization of a soft-template to directly synthesize crystalline mesoporous metal oxides with high surface areas[END_REF][START_REF] Lee | Direct access to thermally stable and highly crystalline mesoporous transition-metal oxides with uniform pores[END_REF] and for Ta 2 O 5 between 13 to 117 m 2 /g and 0.1 to 0.18 cm 3 /g [START_REF] Guo | In situ carbonization of a soft-template to directly synthesize crystalline mesoporous metal oxides with high surface areas[END_REF][START_REF] Ismail | Synthesis of mesoporous sulfur-doped Ta 2 O 5 nanocomposites and their photocatalytic activities[END_REF][START_REF] Shirokura | Synthesis of crystallized mesoporous transition metal oxides by silicone treatment of the oxide precursor[END_REF][START_REF] Guo | Preparation of mesoporous tantalum oxide and its enhanced photocatalytic activity[END_REF][START_REF] Sun | Synthesis of microporous transition metal oxide molecular sieves with bifunctional templating molecules[END_REF][START_REF] Sreethawong | Facile surfactant-aided sol-gel synthesis of mesoporous-assembled Ta 2 O 5 nanoparticles with enhanced photocatalytic H 2 production[END_REF][START_REF] Takahara | Mesoporous tantalum oxide -characterization and photocatalytic activity for the overall water decomposition[END_REF] for the specific surface areas and pore volumes, respectively. As a remind, the highest values of the surface properties obtained in the present work for the niobium (V) oxide and tantalum (V) oxides are 166 m 2 /g -0.86 cm 3 /g and 84 m 2 /g -0.72 cm 3 /g, respectively. Furthermore in our case, the niobium and tantalum pentoxides are semi-crystalline as shown by the X-ray diffraction analysis (Figure 1B and2B) while amorphous samples are prepared as per the corresponding literature which may be a drawback for specific applications as in catalysis. At last, the soft-templated pathways are more time-consuming (until several days in some cases) [START_REF] Yang | Generalized syntheses of large-pore mesoporous metal oxides with semicrystalline frameworks[END_REF][START_REF] Katou | Synthesis of 2D-hexagonally ordered mesoporous niobium and tantalum mixed oxide[END_REF][START_REF] Guo | In situ carbonization of a soft-template to directly synthesize crystalline mesoporous metal oxides with high surface areas[END_REF][START_REF] Brezesinski | Pseudo capacitive contributions to charge storage in highly ordered mesoporous group V transition metal oxides with iso-oriented layered nanocrystalline domains[END_REF][START_REF] Guo | Preparation of mesoporous tantalum oxide and its enhanced photocatalytic activity[END_REF][START_REF] Sun | Synthesis of microporous transition metal oxide molecular sieves with bifunctional templating molecules[END_REF] than our hard-templated one.

In rare cases, crystalline Nb 2 O 5 material can be synthesized from a soft-template route with specific surface areas and pore volumes ranged from 54 to 150 m 2 /g and 0.05 to 0.20 cm 3 /g as established by Lee's [START_REF] Lee | Direct access to thermally stable and highly crystalline mesoporous transition-metal oxides with uniform pores[END_REF] and Brezesinski's works [START_REF] Brezesinski | Pseudo capacitive contributions to charge storage in highly ordered mesoporous group V transition metal oxides with iso-oriented layered nanocrystalline domains[END_REF]. Compared to these data, our results remain interesting with values of 68 m 2 /g and 0.63 cm 3 /g (heating temperature of 650°C). Finally, Yang et al. [START_REF] Yang | Generalized syntheses of large-pore mesoporous metal oxides with semicrystalline frameworks[END_REF] described a soft-templated amorphous Ta 2 O 5 material able to develop a specific surface area of 165 m 2 /g coupled to a pore volume of 0.50 cm 3 /g. In our case, for an amorphous Ta 2 O 5 material prepared at 500°C (Supporting Information S2), the specific surface area and pore volume were determined as equal to 135 m 2 /g and 0.72 cm 3 /g, respectively. The fact that the pore volumes exhibited by our as-synthesized oxide materials were systematically higher than those of the literature's samples can be related to the existence of pores of wider diameters [START_REF] Charpin | Caractérisation de la texture poreuse des matériaux[END_REF]. This parameter is verified since our Nb 2 O 5 and Ta 2 O 5 materials exhibit pore size distributions of 10 -100 nm (inserts of Figures 3 and4) while the literature reveals pore size distributions of 3 -15 nm and 3 -40 nm for both oxides synthesized from soft and hard template ways, respectively [9-16, 19,27].

The morphology and the microstructure of the niobium-and tantalum oxide materials synthesized with or without the use of Ca 3 (PO 4 ) 2 .xH 2 O sacrificial biotemplate are displayed in Figure 5 and6, respectively. The Nb 2 O 5 and Ta 2 O 5 materials synthesized free of template (X = 0) are made of micronsized particles with a spherical morphology for the former (Figure 5A) and a much more faceted undefined morphology for the latter (Figure 6A). At higher magnifications (Figure 5B and 6B), the surfaces of the particles appear rough and might be described as made of sintered smaller particles. These observations are consistent with the surface properties of these materials since these Nb 2 O 5 and Ta 2 O 5 as-prepared samples (X = 0) exhibit the lowest specific surface areas associated to a non-porosity. As regards the oxide ceramics synthesized with the use of calcium-based template (X = 1), the microstructure and morphologies radically change as shown in Figure 5C and Figure 6C. The agglomerates are featured by microstructures made of smaller agglomerated particles that adopt nanometric dimensions. The Nb 2 O 5 (Figure 5D) and the Ta 2 O 5 (Figure 6D) nanoparticles show a quasi-sphere like shape whose size is approximately ranged around 50 nm. In some places in the pictures, hollow spheres may be noticed for both oxide ceramics, suggesting the elaboration of Ca 3 (PO 4 ) 2 .xH 2 O/Nb 2 O 5 and Ca 3 (PO 4 ) 2 .xH 2 O/Ta 2 O 5 composites with a core/shell structure before the removal of the calcium template by the acidic etching. All these characteristics are in good agreement with the nitrogen physisorption measurements carried out on these samples for which improved surface properties have been determined (specific surfaces and pore volumes).

Conclusion

To sum up, the present work claims the successful endo-templated synthesis of niobium (V) and tantalum (V) ceramics by means of a mineral such as the tricalcium phosphate as template. The surface properties, i.e. the specific surface areas and pore volumes, of the oxide materials are strongly dependent on the amount of biotemplate used. Values as high as 166 m 2 /g, 0.86 cm 3 /g and 84 m 2 /g, 0.72 cm 3 /g were thus obtained for semi-crystalline Nb 2 O 5 and Ta 2 O 5 synthesized following the most optimized experimental parameters. By comparison, their counterparts prepared free of template are no porous and exhibit specific surface areas of 48 and 5 m 2 /g, respectively. The fact that Ca 3 (PO 4 ) 2 .xH 2 O, which is an eco-compatible material, can be purchased from chemical manufacturers in different sizes (µmnm), made in laboratories in various morphologies (spheres, fibres, rods) and porous structures (3-D) should strengthen the interest to set up the hard-templated approach in the designing of large surface materials. of a hard-biotemplated approach and after the tricalcium phosphate template removal. * determined from the BJH method for pores below 100 nm. The error on the measurements of the S BET and V p is of ± 5 and ± 10 %, respectively. Supporting information 1

Figure captions

Figure 1 :

 1 Figure 1: XRD patterns of niobium oxide ceramics synthesized by a hard-templated approach with different Ca 3 (PO 4 ) 2 .xH 2 O/ceramic salt weight ratios (X) and at different temperatures: X = 0 and 500°C (A), X = 1 and 500°C (B) and X = 1 and 650°C (C).

Figure 2 :

 2 Figure 2: XRD patterns of tantalum oxide ceramics synthesized by a hard-templated approach with different Ca 3 (PO 4 ) 2 .xH 2 O/ceramic salt weight ratios (X) and at different temperatures: X = 0 and 750°C (A), X = 1 and 750°C (B) and X = 1 and 850°C (C).

  and 2C, respectively. Heating up to 650 °C and 850 °C were need to achieve a single and pure crystallized phase for Nb 2 O 5 and Ta 2 O 5 since the peaks are symmetric and the baselines are relatively linear. At last, for all diffraction patterns, no additional peaks were collected discarding any impurities in the Nb-and Ta-oxide ceramics. The crystallites sizes or crystal coherence lengths (L) of the niobium (V) and tantalum (V) oxides synthesized with X = 1 were determined from the Scherrer equation given below L hkl = 0.9. / (.cosƟ hkl ) where λ is the X-ray wavelength of the radiation ( Cu = 0.15406 nm),  the line broadening at half the maximum intensity (FWHM) corrected by the instrumental line broadening and Ɵ the Bragg angle characteristic of the investigated (h,k,l) Miller plane. The calculations were performed on the (001) diffraction peaks from the diffractograms corresponding to the oxide ceramics synthesized at 650 °C and 850 °C, respectively. Values around 20 nm and 22 nm were thus calculated for Nb 2 O 5 and Ta 2 O 5 materials, respectively. The nitrogen adsorption/desorption isotherms of the niobium (V) and tantalum (V) oxide materials synthesized with different Ca 3 (PO 4 ) 2 .xH 2 O/ceramic salt weight ratios and calcination temperatures are shown in Figures

Figure 3 :

 3 Figure 3: Nitrogen adsorption/desorption isotherms of Nb 2 O 5 oxide ceramics synthesized at 500°C and 650°C by a hard-templated approach with different Ca 3 (PO 4 ) 2 .xH 2 O/ceramic salt weight ratios (X). In insert, the pore size distribution of the Nb 2 O 5 sample synthesized with X = 1 and calcined at 650°C.

Figure 4 :

 4 Figure 4: Nitrogen adsorption/desorption isotherms of Ta 2 O 5 oxide ceramics synthesized at 750°C and 850°C by a hard-templated approach with different Ca 3 (PO 4 ) 2 .xH 2 O/ceramic salt weight ratios (X). In insert, the pore size distribution of the Ta 2 O 5 sample synthesized with X = 1 and calcined at 850°C.

Figure 5 :

 5 Figure 5: SEM images of Nb 2 O 5 ceramics synthesized at 500°C by a hard-templated approach with different Ca 3 (PO 4 ) 2 .xH 2 O/ceramic salt weight ratios (X). X = 0 (A, B) and X = 1 (C, D).

Figure 6 :

 6 Figure 6: SEM images of Ta 2 O 5 ceramics synthesized at 750°C by a hard-templated approach with different Ca 3 (PO 4 ) 2 .xH 2 O/ceramic salt weight ratios (X). X = 0 (A, B) and X = 1 (C, D).

Figure 1 :

 1 Figure1: XRD patterns of niobium oxide ceramics synthesized by a hard-templated approach with different Ca 3 (PO 4 ) 2 .xH 2 O/ceramic salt weight ratios (X) and at different temperatures: X = 0 and 500°C (A), X = 1 and 500°C (B) and X = 1 and 650°C (C).

Figure 2 :

 2 Figure 2: XRD patterns of tantalum oxide ceramics synthesized by a hard-templated approach with different Ca 3 (PO 4 ) 2 .xH 2 O/ceramic salt weight ratios (X) and at different temperatures: X = 0 and 750°C (A), X = 1 and 750°C (B) and X = 1 and 850°C (C).

Figure 3 :

 3 Figure 3: Nitrogen adsorption/desorption isotherms of Nb 2 O 5 oxide ceramics synthesized at 500°C and 650°C by a hard-templated approach with different Ca 3 (PO 4 ) 2 .xH 2 O/ceramic salt weight ratios (X). In insert, the pore size distribution of the Nb 2 O 5 sample synthesized with X = 1 and calcined at 650°C.

Figure 4 :

 4 Figure 4: Nitrogen adsorption/desorption isotherms of Ta 2 O 5 oxide ceramics synthesized at 750°C and 850°C by a hard-templated approach with different Ca 3 (PO 4 ) 2 .xH 2 O/ceramic salt weight ratios (X). In insert, the pore size distribution of the Ta 2 O 5 sample synthesized with X = 1 and calcined at 850°C.

Figure 5 :

 5 Figure 5: SEM images of Nb 2 O 5 ceramics synthesized at 500°C by a hard-templated approach with different Ca 3 (PO 4 ) 2 .xH 2 O/ceramic salt weight ratios (X). X = 0 (A, B) and X = 1 (C, D).

Figure 6 :

 6 Figure 6: SEM images of Ta 2 O 5 ceramics synthesized at 750°C by a hard-templated approach with different Ca 3 (PO 4 ) 2 .xH 2 O/ceramic salt weight ratios (X). X = 0 (A, B) and X = 1 (C, D).

  Figure 1 Click here to download high resolution image

Figure

  Figure S1 -A: SEM picture of the Ca 3 (PO 4 ) 2 .xH 2 O template (Sigma Aldrich). The powder is made of sphere like shape particles with a size distribution ranging from 20 to 200 nm.

Figure

  Figure S1 -B: Nitrogen isotherm of the Ca 3 (PO 4 ) 2 .xH 2 O template (Sigma Aldrich). The isotherm is characteristic of a non-porous material. The specific surface area was determined, according to the Brunauer-Emmett-Teller model, equal to 30 m 2 /g.

Table caption Table 1 :

 caption1 Surface properties of the (semi-)crystalline Nb 2 O 5 and Ta 2 O 5 ceramics synthesized by means

Table caption Table 1

 caption1

	Samples	Temperature (°C)	X	S BET (m 2 /g)	V p (cm 3 /g)*
			0	48	/
	Nb 2 O 5	500	1/3 2/3	106 134	0.46 0.57
			1	166	0.86
		650	1	68	0.63
			0	5	/
	Ta 2 O 5	750	1/3 2/3	30 68	0.32 0.56
			1	84	0.72
		850	1	27	0.33

Table 1

 1

Supporting Information S1

Samples