Safia Boudra
email: safia.boudra@gmail.com

Itheri Yahiaoui
email: itheri.yahiaoui@univ-reims.fr

Ali Behloul
email: ali.behloul@gmail.com

A Comparison of Multi-Scale Local Binary Pattern Variants for Bark Image Retrieval

Keywords: Plant Identification, Multi-scale LBP, Texture description, Bark species recognition, Image retrieval

With the growing interest in identifying plant species and the availability of digital collections, many automated methods based on bark images have been proposed. Bark identification is often formulated as a texture analysis problem. Among numerous approaches, Local Binary Pattern (LBP) based texture description has achieved good performances. Bark structure appearance is subject to resolution variations which can be due to a number of factors (environment, age, acquisition conditions, etc). Thus it remains a very challenging problem. In this paper, we implement and study the efficiency of different multi-scale LBP descriptors: Multi-resolution LBP (MResLBP), Multi-Block LBP (MBLBP), LBP-Filtering (LBPF), Multi-Scale LBP (MSLBP), and Pyramid based LBP (PLBP). These descriptors are compared on two bark datasets: AFF and Trunk12. The descriptors are evaluated under increasing levels of scale space. The performances are assessed using the Mean Average Precision and Recall\Precision curves. The results show that multi-scale LBP descriptors outperform the basic LBP and MResLBP. In our tests, we observe that the best results of LBPF and PLBP are obtained under low scale space levels. We also observe similar results for MSLBP and MBLBP across the six scales considered.

Introduction

Plants play an essential role in sustaining life on our planet. In addition to providing a natural habitat, they are a constant source of oxygen, food, and medicine. Given the vast diversity and variety of plant species, there is understandably increasing interest in indentifying new and existing species in order to improve agriculture and plant production, while adding to the proof of knowledge available to researchers in the field of botany.

The classical approach to identifying and classifying plant species requires specialist domain knowledge meaning that only a taxonomist or botanist can distinguish between various species. However, ever a domain expert cannot be expected to know of all plant species, and recent years have seen increasing interest in automated plant species identification and classification.

Over the last decade, many automated plant species identification methods based on low-level features extracted from images of organs (leaf, flower, fruit, stem, bark …) have been proposed; [START_REF] Belhumeur | Searching the World's Herbaria: A System for Visual Identification of Plant Species[END_REF][START_REF] Nilsback | An automatic visual flora: Segmentation and classification of flower images[END_REF][START_REF] Chi | Plant species recognition based on bark patterns using novel Gabor filter banks[END_REF][START_REF] Fiel | Automated identification of tree species from images of the bark, leaves and needles[END_REF][START_REF] Goëau | Multi-organ Plant Identification[END_REF]. Mobile applications, Leafsnap and Pl@ntNet, have been developed aiming to achieve accurate real time identification. Recently, many studies based on bark (or stem) images have appeared [START_REF] Chi | Plant species recognition based on bark patterns using novel Gabor filter banks[END_REF][START_REF] Fiel | Automated identification of tree species from images of the bark, leaves and needles[END_REF] [START_REF] Song | Bark classification by combining grayscale and binary texture features[END_REF][START_REF] Wan | Bark texture feature extraction based on statistical texture analysis[END_REF][START_REF] Huang | Bark Classification Based on Contourlet Filter Features Using RBPNN[END_REF][START_REF] Sixta | Image and Video-based Recognition of Natural Objects[END_REF][START_REF] Sulc | Kernel-mapped histograms of multi-scale LBPs for tree bark recognition[END_REF].

The appearance and morphology of the bark are used by foresters and botanists to distinguish between plant species and to estimate plant age [START_REF] Whitmore | Studies in Systematic Bark Morphology. I. Bark Morphology in Dipterocarpaceae[END_REF]. The Bark has the advantage of being the only part of the tree that is available throughout the year and it is present for almost all plant's lifetime. As bark is a rigid 3D object, its 2D image acquisition is straightforward.

Since bark shows texture properties, its automated identification is formally defined as a texture analysis problem, and researchers aim to develop relative methods to extract highly discriminative features for an accurate identification. Nonetheless, it remains a challenging problem in the image processing and computer vision field.

Bark appearance often depends on environmental conditions, tree age and the effects of plant diseases. Additionally, acquisition conditions like rescaling, uncontrolled illumination changes, branch shadow clutter can alter the image quality and the texture properties. The most significant image transformation problem in bark images is scale changes, due to the fact that image samples are taken at distinct distances from the tree trunk: texture structures taken close to the trunk are of high resolution while those far from the trunk are of low resolution. To handle this disparity, many features need to be extracted to capture texture properties at different scale levels.

Several texture descriptors [START_REF] Mirmehdi | Handbook of Texture Analysis[END_REF] have been used for bark image classification and identification. Statistical features such as co-occurrence distribution were used by [START_REF] Wan | Bark texture feature extraction based on statistical texture analysis[END_REF]. Huang et al [START_REF] Huang | Bark Classification Based on Contourlet Filter Features Using RBPNN[END_REF], [START_REF] Huang | Classification Based on Gabor Filter Using RBPNN Classification[END_REF][START_REF] Huang | Bark Classification Using RBPNN Based on Both Color and Texture Feature[END_REF] proposed different approaches, respectively, based on contourlet filter, Gabor filters, and Discrete Wavelet Decomposition (DW). In [START_REF] Fiel | Automated identification of tree species from images of the bark, leaves and needles[END_REF], a bag of words model was constructed with SIFT interest points. Recently, structural features such as LBP variants have been used [START_REF] Sixta | Image and Video-based Recognition of Natural Objects[END_REF][START_REF] Sulc | Kernel-mapped histograms of multi-scale LBPs for tree bark recognition[END_REF], [START_REF] Goëau | LifeCLEF Plant Identification Task 2014[END_REF][START_REF] Švab | Computer-vision-based tree trunk recognition[END_REF].

Sixta et al [START_REF] Sixta | Image and Video-based Recognition of Natural Objects[END_REF], used Multi-Block Local Binary Pattern where mean filter with different sizes is applied to input images. MBLBP was the first multi-scale LBP variant used for bark texture analysis. Sulc et al [START_REF] Sulc | Kernel-mapped histograms of multi-scale LBPs for tree bark recognition[END_REF] proposed a Multi-Scale LBP. Input images are Gaussian Filtered prior to the LBP operator with increasing radii. In both, histograms of all the scales considered are concatenated to form the final texture descriptor.

Motivated by the high performances achieved in the two last studies, we want to focus more closely on multi-scale LBP as efficient texture descriptor for bark texture identification.

Our work aims to quantitatively discuss and compare four different multi scale LBP approaches with filters for bark texture analysis, namely: (1) Multi-Block LBP (MBLBP) [START_REF] Liao | Learning Multi-scale Block Local Binary Patterns for Face Recognition[END_REF]with a mean filter, (2) LBP Filtering (LBPF) [START_REF] Mäenpää | Multi-scale Binary Patterns for Texture Analysis[END_REF] and (3) Multi-Scale LBP (MSLBP) [START_REF] Sulc | Kernel-mapped histograms of multi-scale LBPs for tree bark recognition[END_REF]with a low pass Gaussian filter, and (4) Pyramid-based LBP (PLPB) [START_REF] Qian | PLBP: An effective local binary patterns texture descriptor with pyramid representation[END_REF]with a pyramid transform. These methods are implemented and compared to the conventional Multi Resolution LBP (MResLBP) [START_REF] Ojala | Multiresolution Gray-Scale and Rotation Invariant Texture Classification with Local Binary Patterns[END_REF] where texture information is simply collected from single pixels at different scales rather than using filter's responses.

The remainder of this paper is structured as follows: the LBP operator and its multi-scale variants are presented in Section 2. In Section 3, a detailed description of bark datasets is given. Our bark image retrieval experiments and results are set out and discussed in Section 4. Finally, the conclusion is given in Section 5.

The LBP operator and its Multi-Scale variants

2.1

The LBP operator

Basic LBP [START_REF] Ojala | Multiresolution Gray-Scale and Rotation Invariant Texture Classification with Local Binary Patterns[END_REF] encodes the sign of the local difference between a central pixel p and its P neighbors p , evenly spaced on a circle of radius R. Formally, it is given by:

LBP , = s(p -p )2 (1)
Where s(x) is a step function; s(x) = 1, if x >= 0; 0 otherwise. Once the LBP codes have been computed, a histogram is built to represent the texture image.

Another extension to the basic LBP operator considers uniform patterns; the uniformity measure was first defined by [START_REF] Topi | Robust texture classification by subsets of local binary patterns[END_REF] as "the number of bitwise 0/1 and 1/0 changes when the pattern is considered circular". Based on this definition, a local binary pattern is said to be uniform if its uniformity measure takes that form U≤ 2.

Using this mapping, denoted by LBPu2, every uniform pattern is assigned to a single bin in the histogram and all non uniform patterns are assigned to a unique bin.

It is formally defined by:

LBP , = ∑ s(p -p ), if U LBP , ≤ 2, + 1 ℎ (2)
The uniform patterns are shown to provide fundamental local texture information properties [START_REF] Ojala | Multiresolution Gray-Scale and Rotation Invariant Texture Classification with Local Binary Patterns[END_REF]. Furthermore, it can significantly reduce the histogram length: only 59 bins with 8 samples in the local neighborhood instead of 256.

Multi Resolution LBP (MRes-LBP).

Bark texture images are captured at various scales. Therefore, large-scale structures cannot be defined within the 3×3 space area of the original LBP.

An intuitive and efficient way to capture large-scale structures is to combine different LBP operators with increasing values of (P, R), i.e. (8, 1), (16, 2), (24, 3).

Ojala's [START_REF] Ojala | Multiresolution Gray-Scale and Rotation Invariant Texture Classification with Local Binary Patterns[END_REF] multi resolution LBP (MResLBP) is based on the concatenation of three uniform LBP histograms, LBP , + LBP , + LBP , . Using different LBP operators with increasing radii causes an aliasing effect and leads to noise sensitivity since the texture information is collected from a single pixel at different levels. To overcome this issue, several multi-scale LBP schemes have been proposed [START_REF] Sulc | Kernel-mapped histograms of multi-scale LBPs for tree bark recognition[END_REF], [START_REF] Liao | Learning Multi-scale Block Local Binary Patterns for Face Recognition[END_REF][START_REF] Mäenpää | Multi-scale Binary Patterns for Texture Analysis[END_REF][START_REF] Qian | PLBP: An effective local binary patterns texture descriptor with pyramid representation[END_REF] mainly based on filter responses to collect texture information from large areas at different scales. Therefore, it captures microstructures as well as macrostructures with reduced noise.

2.2

Multi-Scale LBP Multi-Block Local Binary Pattern (MBLBP).

Liao [START_REF] Liao | Learning Multi-scale Block Local Binary Patterns for Face Recognition[END_REF] applied a set of mean filters at different scales to the input image. The simple point to point comparison in basic LBP was extended to a comparison between mean intensity values of square sub-blocks. The size of the filter s×s denotes the scale of the MBLBP operators. Each filter is divided into 9 sub blocks as shown in Fig. 3. Therefore its size must be a multiple of 3. Local Binary Pattern Filtering (LBPF). Following a multi-scale approach, in [START_REF] Mäenpää | Multi-scale Binary Patterns for Texture Analysis[END_REF] large-scale texture patterns are detected by combining exponentially growing neighborhood radii with Gaussian low-pass filtering. Gaussian low-pass filtering is used to collect information from an area larger than a single pixel, named the "effective area". Solid circles in Fig. 4 (a) indicate a constant number of effective areas over different scales. The P circles (P=8) are tangent and have the same size.

Exponentially growing radii of the LBP operator, , indicated by dotted circles in Fig. 4 (a) at level s, are given by: =

(3)

Multi-Scale Local Binary Pattern (MSLBP).

In contrast to the scale space in [START_REF] Mäenpää | Multi-scale Binary Patterns for Texture Analysis[END_REF] where LBP radii are designed so that the effective areas at different levels are tangent, in MSLBP [START_REF] Sulc | Kernel-mapped histograms of multi-scale LBPs for tree bark recognition[END_REF] a finer scale with a step of √2 is used between LBP radii, i.e.

= √2 = 1 (4)
Pyramid-Based Local Binary Patterns (PLBP).

Qian et al [START_REF] Qian | PLBP: An effective local binary patterns texture descriptor with pyramid representation[END_REF] proposed Pyramid-based LBP. Each image at level s of the pyramid representation is obtained by convolving it with a Gaussian low pass filter, ( , ), followed by down sampling of the s-1 th level image. Formally ( , ) is obtained as follows, where ( , ) is the original image:

(x, y) = ( , ) * + , + , > 1 (5)
Where R , R are the down-sampling ratios in x and y directions respectively, and the Gaussian filter, G(x, y), is given by:

( , ) = (6)
PLBP can be seen as a general case of LBPF and MSLBP differing in that is sampling or no sampling; that the effective areas being tangent or not; and low pass filter types, (more details can be found in [START_REF] Qian | PLBP: An effective local binary patterns texture descriptor with pyramid representation[END_REF]). ent LBP bits at each scale [START_REF] Qian | PLBP: An effective local binary patterns texture descriptor with pyramid representation[END_REF], [START_REF] Sulc | Kernel-mapped histograms of multi-scale LBPs for tree bark recognition[END_REF].

Bark Datasets

Two bark image datasets (AFF1 [START_REF] Fiel | Automated identification of tree species from images of the bark, leaves and needles[END_REF] and Trunk122 [START_REF] Švab | Computer-vision-based tree trunk recognition[END_REF]) were used to evaluate the multi-scale LBP descriptors. These datasets differ with regard to the number of classes, the number of samples per class, image transformation i.e. scale, pose and illumination changes. Fig. 5 shows samples from each class of the two datasets. A challenging bark dataset, ImageClef, was excluded from this comparison study since its bark images do not show only the tree trunk, but also contain natural background. Thus a segmentation preprocessing would be required to extract the bark regions. In addition, unlike AFF and Trunk12, ImageClef image samples are subject to rotation changes, as the bark images are captured at random orientations.

Experimental Results and Evaluation

Bark images in the AFF dataset and the Trunk12 dataset are of high resolution and processing the samples with their original pixel resolution slows down the task. Therefore, all the images are resized to 600×400 px and converted to gray level.

LBP histograms at level s are normalized to unit length, and then concatenated. Thus the final multi-scale histogram length is 2 × where P is set to 8 neighbors for all scales and ∈ {1, … , } where S=6, is the scale space level. Table 1 summarizes the parameter settings for each multi-scale LBP descriptor at each level of the scale space, where σ, and R s denote respectively, the standard deviation of the Gaussian filter and the LBP radius at level s (see [START_REF] Sulc | Kernel-mapped histograms of multi-scale LBPs for tree bark recognition[END_REF][START_REF] Mäenpää | Multi-scale Binary Patterns for Texture Analysis[END_REF] for details). To evaluate the descriptors presented above, we use the Mean Average Precision and the Precision\Recall curves. The Precision (Pre) and the Recall (Rec) are given by:

= # # ; = # # (7)
The Mean Average Precision (MAP) is the mean of the Average Precision (AP) of a set of queries Q, and is defined by:

= ∑ ( )
, where

( ) = ∑ ( )× ( ) # (8)
Where Pre (k) is the precision at a given cut-off, and f (k) is set to 1 if the retrieved image at rank k is relevant; zero otherwise.

In what follows, we highlight the max values of MAP in bold and min values in italics. Table 3 and Table 4 show MAP values for the multi-scale LBP descriptors on the AFF and the Trunk12 datasets respectively with increasing scale space levels. The uniform extension of multi-scale LBP variants, noted u2, as well as the original patterns i.e. all possible patterns (256), noted org, are also considered. Note that for MBLBP, the uniformity measure defined in [START_REF] Liao | Learning Multi-scale Block Local Binary Patterns for Face Recognition[END_REF] is also tested in this study, noted by MBLBPn. Fig 6 illustrates Recall\Precision curves. The multi-scale LBP descriptors are chosen at their best scale according to the highest MAP value in Table 3 and Table 4 for the AFF and Trunk 12 datasets respectively.

The above results suggest that form MResLBP and basic LBP cro-texture information cap value.

Moreover, the information is collected from region single pixels, as is performed in MResLBP. creases performances. One reason why all multi-scale descriptors with only u2 patterns perform slightly lower than org patterns is the part of that is roughly described by the last bin of the non-uniform histogram.

MBLBPn has the lowest MAP value and the worst Recall\Precision curve on the AFF dataset, but not on the Trunk12 dataset. Note, however, that MBLBPn is based on a statistical distribution of patterns and not on fundamental local texture properties. Consequently, the comparison of two histograms can match completely different patterns together. This can explain the AFF results. For the Trunk12 dataset, we suppose that the matching between different patterns coincides with space projection.

MBLBP has the lowest performances on the AFF dataset and the Trunk12 dataset. We believe that this came from low pass filtering used, i.e. mean filter in MBLBP.

For MSLBP, the best MAP values are obtained at scale 6 on both datasets. MSLBP MAP values increase slowly compared to other variants. Indeed, a finer scale with step of √2 is used between LBP radii (see Table 1) and Gaussian smoothing is applied firstly at scale 4 (more details in [START_REF] Sulc | Kernel-mapped histograms of multi-scale LBPs for tree bark recognition[END_REF]). The best results for LBPF are obtained at scale 3 with LBP radius equal to 12.19, which is higher than the MSLBP radius at scale 6 (R 6 =8). Based on these remarks, we believe that MSLBP reaches its optimal performance at scales higher than 6. However, it results in a longer histogram compared to LBPF. The sharp drop in MAP values for the LBPF descriptor on both, AFF and Trunk 12 from scales 3 and 4 respectively can be explained follows: With increasing values of σ over the scales (details in Table 1), images are increasingly smooth, and local texture information is lost and subject to noise sensitivity. Thus the descriptor loses its discriminative power. Fig 7 shows an example of an image request and the first 5 images returned, the LBPF descriptor, cannot distinguish between different classes at scale level 6.

The deterioration in PLBP performances on the two datasets is due to the fact that images at coarse pyramid levels are of very low resolution, as reported in Table 1, and do not provide enough structure information.

Conclusion

This paper reports on the evaluation results of basic LBP, uniform LBP, and five multi-scale LBP descriptors. These descriptors are tested and compared on two bark datasets (AFF and Trunk12).

It is worth noticing that multi-scale LBP provides more discriminative texture features than basic and uniform LBP. Therefore, multi-scale information improves LBP results. LBPF gives the best results over all the descriptors tested on both datasets. MBLBPn produced less satisfying results than we had expected for both datasets. This is due to its uniformity definition. Using a distribution percentage does not take into account the local structure properties, and the uniqueness of the relative patterns.

In this work, we focused on the multi-scale problem. It would be interesting to explore other LBP configurations with different neighborhood topologies in addition to the classic circular one, and to combine other complementary texture information in order to boost performances.

FigFig. 1 .

 1 Fig. 1. Examples of the visual diversity of the surface of bark: (a) lichen, (b) peeled bark, (c) scars, (d) tree age deformation, (e) illumination change, (f) shadow clutters, (g) different texture structures at different scales.

  Fig 2 shows LBP operators with different configurations of (P, R).

Fig. 2 .

 2 Fig. 2. LBP operator with different values of (P, R): (8, 1), (16, 2) and (8, 2).

Fig. 3 .

 3 Fig.3. MBLBP operator of size 9*9[START_REF] Liao | Learning Multi-scale Block Local Binary Patterns for Face Recognition[END_REF]

Fig. 4 .

 4 Effective areas. (a)LBPF, (b)MSLBP Finer scale space, (c) PLBP with differ-

Fig. 5 .

 5 Fig. 5. Bark image samples; Top row, AFF dataset, bottom row, Trunk12 dataset.

Fig. 6 .

 6 Fig. 6. Recall

  ore LBP scales lead to increased MAP values on both datasets. scale descriptors do not behave in a similar way at different ll the multi-scale LBP descriptors on the Trunk12 dataset better than they do for the AFF dataset. One reason for this may be that proper scale outpere LBP descriptors, mas to increasing MAP and not from sensitivity and inboth datasets. at different scales. It Trunk12 dataset behave this may be that Trunk12 classes are more homogenous than those of AFF regarding both imaging conditions and botanical factors.

Fig. 7 .

 7 Fig. 7. LBPF descriptor behavior. Request image highlighted in solid square, false positive in dotted square, from top to bottom; first five returned images at level 3, second row, returned images et level 6; third row: LBP images at level 3, with high inter-class variation; bottom row, LBP images at level 6, high inter-class similarity.

Table 1 .

 1 Multi-scale LBP descriptor parameters over different scales.

		LBPF		MSLBP	PLBP	MBLBP
	s	σ	R s	σ	R s	Image size Filter size
	1 0.38	2.43	0.28 1.41 600×400	3×3
	2 0.85	5.44	0.39 2	300×200	9×9
	3 1.91	12.19	0.55 2.83 150×100	15×15
	4 4.27	27.3	0.78 4	75×50	21×21
	5 9.56	61.16	1.1	5.66 38×25	27×27
	6 21.42 136.98 1.56 8	19×13	33×33

Table 2 .

 2 Mean Average Precision of LBP variants without filtering.

		LBP LBPu2 MResLBP
	AFF	31.46 31.00	32.69
	Trunk12 31.42 29.69	30.03

Table 2

 2 reports the MAP values of LBP, LBPu2, and MResLBP. We can see that the LBP and LBPu2 results are very close. The MResLBP, which is the concatenation of three uniform LBPs slightly, exceeds the uniform LBP performance. One reason for this slight improvement of MResLBP, is the aliasing effect in the second and third scales.

Table 3 .

 3 Mean Average Precision of multi-scale LBP variants on the AFF dataset.

	AFF MBLBP		LBPF		MSLPB	PLBP
	s	org	u2	n	org	u2	org	u2	org	u2
	1	32.12 30.28 26.39 34.1	33.95 32.14 31.66 34.99 33.69
	2	33.86 31.75 29.4	35.62 34.96 33.25 33.08 35.17 34.18
	3	33.40 31.9	29.98 36.6	35.39 34.09 33.74 34.68 34.78
	4	32.74 31.72 30.04 35.5	34.19 34.87 34.53 32.93 32.78
	5	32.17 31.65 30	29.75 28.44 35.33 34.71 27.82 27.91
	6	31.67 31.53 29.93 18.97 19.91 35.8	34.77 22.71 22.98

Table 4 .

 4 Mean Average Precision of multi-scale LBP variants on the Trunk12 dataset.

	Trunk12 MBLBP		LBPF		MSLPB	PLBP
	s	org	u2	n	org	u2	org	u2	org	u2
	1	32.34 28.32 24.76 32.85 31.11 31.3	28.75 36.23 34.74
	2	34.43 29.16 28.75 37.44 35.51 31.62 29.43 40.93 39.67
	3	35.8	29.84 31.22 42.8	40.14 32.68 30.59 45.05 44.29
	4	36.46 30.74 32.58 47.66 44.28 35.09 33.15 47.1	46.74
	5	36.66 31.22 33.32 39.07 36.64 37.38 35.01 37.6	38.27
	6	36.57 31.79 33.77 17.38 18.2	39.59 36.66 23.45 24.85

We are grateful to the computer vision Lab, TU, Vienna for allowing us access to the AFF dataset for scientific use.

http://www.vicos.si/Downloads/TRUNK12


Weiwei Cao

Xiaoyan Yang

Cécile Genevois

Mathieu Allix
email: mathieu.allix@cnrs-orleans.fr

Xiaojun Kuang
email: kuangxj@glut.edu.cn

Extended B-Site Vacancy Content Range and Cation Ordering in Twinned Hexagonal Perovskites Ba 8 Cr 4- x Ta 4+0.6x O 24

-layer hexagonal perovskite superstructure within 2.4  x  3.0. The later shows expanded a and b axes by times compared to the simple 8-layer hexagonal perovskite structure owing to the partial face-sharing octahedral (FSO) B cation ordering along the ab plane. The B-cation and vacancy distributions in the tripled superstructure were characterized by neutron and X-ray powder diffraction and further confirmed by scanning transmission electron microscopy-high angle annular dark field imaging and intensity profile analysis. The formation of 8-layer twinned hexagonal perovskites Ba 8 Cr 4-x Ta 4+0.6x O 24 in an extended solid solution range can be attributed to the presence of both covalent B-B and B-O-B bonding and B-site vacancies in the FSO sites. This work provides an effective way of combining covalent B-B and B-O-B bonding and vacancy creation as well as the cationic ordering in the FSO sites to reduce electrostatic repulsion which could further enable the stabilization of new hexagonal perovskite compounds.

• INTRODUCTION

Hexagonal perovskite oxides with mixed cubic (c) and hexagonal (h) stacking of AO 3 layers have received considerable interest owing to their structural diversity and technologically important physical properties such as high dielectric constant [START_REF] Kuang | Crystal structure, microwave dielectric properties and AC conductivity of Bcation defficient hexagonal perovskite La 5 M x Ti 4-x O 15 (x = 0.5[END_REF][START_REF] Moussa | Ba 8 ZnTa 6 O 24 : a high-Q microwave dielectric from a potentially diverse homologous series[END_REF][START_REF] Keith | Synthesis, crystal structure, and characterization of Ba(Ti 1/2 Mn 1/2 )O 3 : a high pernittivity 12R-type hexagonal perovskite[END_REF][START_REF] Kuang | Internal barrier layer capacitance effect in hexagonal perovskite Ba 4 YMn 3 O 11.5[END_REF] , ionic mobility [START_REF] Kuang | Oxygen vacancy ordering phenomena in the mixed-conducting hexagonal perovskite Ba 7 Y 2 Mn 3 Ti 2 O 20[END_REF][START_REF] Fop | Oxide ion conductivity in the hexagonal perovskite derivative Ba 3 MoNbO 8.5[END_REF] , photocatalytic activity, [START_REF] Tao | First 14-layer twinned hexagonal perovskite Ba 14 Mn 1.75 Ta 10.5 O 42 : atomic-scale imaging of cation ordering[END_REF][START_REF] Xu | Monomolecular-layer Ba 5 Ta 4 O 15 nanosheets: synthesis and investigation of photocatalytic properties[END_REF][START_REF] Yugo | Water spliting into H 2 and O 2 over niobate and titanate photocatalysts with (111) plane-type layered perovskite structure[END_REF] etc. The hexagonal stacking introduces face sharing octahedral (FSO) units with shorter B-B contacts compared with those in corner-sharing octahedral (CSO) block. This may result in significant electrostatic repulsion between the FSO B cations, which could destabilize the hexagonal perovskite structure. Therefore hexagonal perovskites usually form B-site deficient compositions with FSO B-site vacancies, favorable for reducing the FSO B-B electrostatic repulsion [START_REF] Tao | First 14-layer twinned hexagonal perovskite Ba 14 Mn 1.75 Ta 10.5 O 42 : atomic-scale imaging of cation ordering[END_REF][START_REF] Trolliard | TEM study of cation-deficientperovskite related A n B n-1 O 3n compounds: the twin-shift option[END_REF] . B-site fully occupied hexagonal perovskites are less but often observed in transitional metal containing oxides since the semimetal BB bonding form in the FSO sites to relieve the BB electrostatic repulsion such as in manganates. [START_REF] Kuroda | The crystal structure of α-SrMnO 3[END_REF] Recently, the 8-layer B-site deficient twinned hexagonal tantalate perovskites Ba 8 MTa 6 O 24 (M = Zn, Ni, Co) [START_REF] Moussa | Ba 8 ZnTa 6 O 24 : a high-Q microwave dielectric from a potentially diverse homologous series[END_REF][START_REF] Thirumal | Ba 8 ZnTa 6 O 24 : a new high Q dielectric perovskite[END_REF][START_REF] Kan | Microwave dielectric properties of perovskitelike structure Ba 8 Ta 6 (Ni 1-x M x )O 24 (M = Co, Cu and Zn) solid solution[END_REF][START_REF] Kawaguchi | Microwave dielectric properties of Ba 8 Ta 6 (Ni 1-x M x )O 24 (M = Zn and Mg) ceramics[END_REF] have drawn much attention owing to their high quality factors, showing potential application as microwave dielectric resonators, on which there are great demand particularly for the development of new 5G mobile communication technology 15,[START_REF] Guo | Design of a high-efficiency and -gain untenna using novel low-loss, temperature-stable Li 2 Ti 1-x (Cu 1/3 Nb 2/3 ) x O 3 microwave dielectric ceramics[END_REF] . This stimulated further synthesis of new analogues through changing the M 2+ cations e.g. on Ba 8 CuTa 6 O 24 [START_REF] Kan | Microwave dielectric properties of perovskitelike structure Ba 8 Ta 6 (Ni 1-x M x )O 24 (M = Co, Cu and Zn) solid solution[END_REF] and Ba 8 MnTa 6 O 24 [START_REF] Tao | First 14-layer twinned hexagonal perovskite Ba 14 Mn 1.75 Ta 10.5 O 42 : atomic-scale imaging of cation ordering[END_REF] compositions or introducing trivalent cations, leading to the formation of Ba 8 Ga 4-x Ta 4+0.6x O 24 [START_REF] Cao | New 8-layer twinned hexagonal perovskite microwave dielectric ceramics Ba 8 Ga 4x Ta 4+0.6x O 24[END_REF] compounds with variable B-site vacancy content covering from 10% to 16%, in contrast with the fixed vacancy content at 12.5% in Ba 8 MTa 6 O 24 and a narrow range of 12.5-14.5% vacancy content in Ba 8 Ti 3-x Ta 4+0.8x O 24 [START_REF] Baranov | Microwave frequency dielectric properties of hexagonal perovskite in the Ba 5 Ta 4 O 15 -BaTiO 3 system[END_REF] . So far Ba 8 Ga 4-x Ta 4+0.6x O 24 possesses the widest B-site vacancy content range, which is the only one example of 8-layer twinned hexagonal perovskite displaying B-site vacancy content below 12.5%. [START_REF] Cao | New 8-layer twinned hexagonal perovskite microwave dielectric ceramics Ba 8 Ga 4x Ta 4+0.6x O 24[END_REF] However, the 8-layer twinned structure does not extend to the Ga-rich end member Ba 2 GaTaO 6 presumably with pure Ga 2 O 9 FSO dimer in Ba 8 Ga 4-x Ta 4+0.6x O 24 , revealing that FSO Ga-Ga dimer is an unstable configuration.

Ba 2 CrTaO 6 [START_REF] Choy | Crystal structure and the role of covalency in eightlayered hexagonal Ba 2 CrTaO 6[END_REF] has been known as a line phase for more than 25 (99.99%, Aladdin) were weighed according to the correct stoichiometries and mixed with ethanol in an agate mortar for ~ 45 min to reach homogeneousness. The mixtures were pressed uniaxially into pellets, which were calcined at 750 C for 1 h using heating and cooling rates of 5 C/min, then were ball-milled for 9 h and repressed into pellets with a thickness ~ 7 mm in height and  10 mm in diameter by a cold-isostatic pressing facility under pressure 250 MPa for 20 min. The pellets were sintered at 1525 C for 6 h to get dense ceramic for electrical characterizations and microwave dielectric performance measurements. The densities of the pellets were calculated using their weights and dimension sizes.

Characterization. Phase assemblage was investigated by X-ray powder diffraction (XRPD), which was performed using a Panalytical X'Pert PRO diffractometer running with Cu K radiation. High-quality XRPD data for Rietveld analysis were collected on a Bragg-Brentano D8

Advance Bruker laboratory diffractometer equipped with a LynxEye XE detector. Neutron powder diffraction (NPD) data were collected at the 3T2 station using a step size of 0.05 and wavelength of λ = 1.225 Å at the LLB laboratory (Saclay, France). The XRD and NPD data were analyzed by the Rietveld method [START_REF] Rietveld | A profile refinement method for nuclear and magnetic structures[END_REF] , which was performed using TOPAS-Academic (V5) software [START_REF] Coelho | Topas academic V5; coelho software[END_REF] . Bond valance sums (BVS) were calculated by the method of Brown and Altermatt [START_REF] Brown | Bond-valence parameters obtained from a systematic analysis of the inorganic crystal structure database[END_REF] .

Selected area electron diffractions (SAED) were performed on a Philips CM20 transmission electron microscopy (TEM) operating at 200 kV. The fine sample powders were homogeneously dispersed in ethanol and deposited on a carbon-coated molybdenum grid before the TEM measurement. High resolution scanning transmission electron microscopy-high angle annular dark field (STEM-HAADF) imaging and X-ray energy dispersive spectroscopy (EDS) elemental mapping were performed at 200 kV using a JEOL-ARM200 Cold FEG microscope equipped with a double spherical aberration correctors and fitted with a JEOL SDD CENTURIO EDS system. The STEM-HAADF images and EDS maps were acquired with a 1 Å and 1.3 Å probe size respectively. The morphology examination for the ceramic samples were performed on ZEISS Gemini SEM 300 scanning electron microscope (SEM, Germany), equipped with also performed during the SEM experiments.

The oxidation state of Cr was measured by X-ray Photoelectron Spectroscopy (XPS) using a Thermo Fisher Scientific ESCALAB 250xi X-ray Photoelectron Spectrometer with a monochromatic Al Kα (1486.6 eV) X-ray beam. The binding energies are corrected based on the C 1s peak (284.6 eV). The peak deconvolutions were carried out using the XPSPEAK software based on a combination of Gaussian-Lorentzian peak function and Shirley background subtraction method.

Microwave dielectric properties were measured with Hakki-Coleman dielectric resonator method [START_REF] Hakki | A dielectric resonator method of measuring inductive capacities in the millimeter range[END_REF] with the TE 011 mode using Agilent network analyzer N5230A. Temperature coefficients of resonance frequency  f were measured from RT up to 85 C. AC impedance spectroscopy measurement was implemented by a Solartron 1260A impedance/gain-phase analyzer over the frequency range from 10 -1 to 10 7 Hz on the pellets, which were painted with platinum paste on both front and back surfaces and heated at 700 C for 30 min to remove organic component and form electrodes.

• RESULTS

Ba 8 Cr 4-x Ta 4+0.6x O 24 solid solution. Figure 1a and Figure S1 show the XRPD data of Ba 8 Cr 4-

x Ta 4+0.6x O 24 (x = 0.0-4.0) fired at 1525 C for 6 h, which indicate that compositions x = 0.0-3.0 form an 8-layer twinned hexagonal perovskite solid solution. Careful examination of XRPD data (Figure 1a) reveals that compositions within the 0.0  x < 2.4 range formed simple 8H phases; while the 2.4  x  3.0 compositions form a tripled superstructure of the simple 8H phase, as indicated by the appearance of several extra weak reflections highlighted in the rectangles in Figure 1a. The relatively weak but obvious peak of the x = 2.4 composition in 20.7-22 2Theta range witnesses the transition process from simple to tripled 8H phase. The tripled 8H phase has an enlarged ab plane, 3 times of that in the simple 8H phase, similar to Ba 8 Ga 4-x Ta 4+0.6x O 24 [START_REF] Cao | New 8-layer twinned hexagonal perovskite microwave dielectric ceramics Ba 8 Ga 4x Ta 4+0.6x O 24[END_REF] and Ba 8 MTa 6 O 24 (M= Zn, Ni) cases. [START_REF] Moussa | Ba 8 ZnTa 6 O 24 : a high-Q microwave dielectric from a potentially diverse homologous series[END_REF][START_REF] Abakumov | The crystal ctructue of Ba 8 Ta 6 NiO 26 : cation ordering in hexagonal perovskite[END_REF] The compositions within 3.2  x  3.8 form a mixture of tripled 8H phase and Ba 5 Ta 4 O 15 phase and the end-member composition (x = 4.0) forms a 5-layer shifted hexagonal perovskite phase, namely Ba 5 Ta 4 O 15 (Figure S1). The refined cell parameters of Ba 8 Cr 4-x Ta 4+0.6x O 24 (Figure 1b) linearly increase with x within the 0.0  x  3.0 region, obeying the Vegard's law [START_REF] Denton | s law[END_REF] and consistent with the Ta 5+ (0.64 Å) substitution for the smaller Cr 3+ (0.615 Å). [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF] Beyond point x = 3.0, the cell parameters remain almost constant, confirming the solid solution limit close to x  3.0. x Ta 4+0.6x O 24 [START_REF] Cao | New 8-layer twinned hexagonal perovskite microwave dielectric ceramics Ba 8 Ga 4x Ta 4+0.6x O 24[END_REF] cases. The refinements confirm that the B-site vacancies are confined only on the FSO B sites. However, as there are four crystallographically distinct FSO B sites (B1-3 and B6 sites in Figure 4a) in the P6 3 cm model, refinement of the occupancies of two cations in these partially occupied FSO sites is challenging. Thus similarly to the Ba 8 Ga 4-x Ta 4+0.6x O 24 case 17 , all B site occupancies (including the CSO B4 and B5 sites in Figure 4a) were refined with a simulated annealing approach and under the compositional constrain according to the nominal compositions. The compositional constraint was applied by placing a penalty function on the calculated and nominal overall contents of Cr and Ta based on the sums of atom contents for each type on all of the B sites with the site occupancies and multiplicity taken into consideration.

The final refinement shows that the CSO B4 and B5 sites are fully occupied by Ta atoms; the FSO B1 and B2 sites (Figure 4c) comprise respectively 0.62(2) Ta/0. XPS data. The oxidation states of chromium in the as-made and low-temperature annealed (800 C in air for 6 h) Ba 8 Cr 4-x Ta 4+0.6x O 24 (x = 0, 2.8) powders were examined by XPS measurements. Although no difference from the XRPD patterns between the as-made and airannealed samples (Figure S4) could be detected, their XPS spectra (Figure 6) exhibit different features. For the as-made samples, the 2p Impedance data. AC impedance spectroscopy measurements were performed under N 2 atmosphere for minimizing the oxidation from Cr 3+ to Cr 6+ . Figure 7a shows a typical complex impedance plot measured on the tripled 8H sample x = 2.8 at 250 °C. The small and large semicircular arcs have associated capacitances with a magnitude of ~ 3 pF/cm and ~ 10 -9 F/cm (Figure S5), corresponding to bulk and grain boundary responses, respectively. [START_REF] Irvine | Electroceramics: characterization by impedance spectroscopy[END_REF] The bulk and grain boundary response arcs remain well-resolved until the temperature was elevated to 800 °C.

The Arrhenius plots of conductivities of Ba 8 Cr 4-x Ta 4+0.6x O 24 (Figure 7b and S6) show that the are ~ 2-3 orders of magnitude lower than those of Ba 2 CrTaO 6 . 0 Arrhenius plots of bulk conductivities for Ba 8 Cr 4-x Ta 4+0.6x O 24 (x = 0.0, 2.0 and 2.8) ceramics.

Microwave dielectric properties. Table 3 shows the microwave dielectric properties and relative densities of the Ba 8 Cr 4-x Ta 4+0.6x O 24 (x = 0.0-3.0) pellets with relative densities ~ 89-96%.

The pellets for the compositions x = 0.0 and 1.0 did not show resonant peaks, indicating high dielectric loss, and the other pellets display modest dielectric permittivity  r ~ 25, low Qf values from 4424 to 15985 GHz and large temperature coefficient of resonant frequencies  f ~ 14-25 ppm/C. Microstructure. The surface morphology images recorded by SEM on pellets of x = 0.0-3.0 compositions show that the pellets contain plate-shaped grains with thickness ~ 2 m which are tightly packed (Figure 8). The grain sizes (width and length) in the compositions x = 0.0 and 2.0 have broad distribution up to ~ 10 m. While the Ta-rich compositions display some extraordinary long grains (> 40 m). x Ta 4+0.6x O 24 [START_REF] Cao | New 8-layer twinned hexagonal perovskite microwave dielectric ceramics Ba 8 Ga 4x Ta 4+0.6x O 24[END_REF] and Ba 8 Ta 4+0.8x Ti 3-x O 24 [START_REF] Baranov | Microwave frequency dielectric properties of hexagonal perovskite in the Ba 5 Ta 4 O 15 -BaTiO 3 system[END_REF] showing variable B-site vacancy contents as ~ 10-16% and 12.5-14.5%, respectively. The Ba ions have also partially filled d orbits and unpaired electrons.

Regarding the inhomogeneous microstructure, it is interesting to compare the Ta-rich composition Ba 8 Cr 1.2 Ta 5.68 O 24 with Ba 8 CuTa 6 O 24 [START_REF] Yu | Conductivity, dielectric loss, and electrical heterogeneous microstrcuture of eight-layer twinned hexagonal perovskite ceramics Ba 8 CuTa 6 O 24-[END_REF] regarding their comparable Qf values as well as their more insulating grain boundary regions than grains. In Ba 8 CuTa 6 O 24 , there is partial reduction from Cu 2+ to Cu + during the firing procedure and limited reoxidation along the grain boundary region on cooling, therefore enhancing the resistivity for the grain boundary. In Ba 8 Cr 4-x Ta 4+0.6x O 24 , as revealed by XPS measurements, partial oxidation of Cr 3+ into Cr 6+ could take place unavoidably on cooling. This is expected to induce p type conduction, which was confirmed by the bulk conductivity measured as a function of partial oxygen pressure in Ba 2 CrTaO 6 (x = 0.0) (Figure S7). Therefore, if partial oxidation of Cr 3+ into Cr 6+ took place along the grain boundary, smaller resistivity would be measured for the grain boundary regions compared to the grains. However, this is in contradiction with experimental observations. As the XPS technique detects only the surface, the partial oxidation of Cr 3+ to Cr 6+ could not take place as bulk property. Careful SEM-EDS elemental mapping at higher magnification on the Ba 8 Cr 1.2 Ta 5.68 O 24 pellet revealed the existence of small amount of Ta-rich oxide phases different from the main phase along the boundary regions (Figure S8), which could explain the more insulating grain boundary compared to the grains. The electrically and compositional inhomogeneous (along grain boundary regions) microstructure in Ba 8 Cr 4-x Ta 4+0.6x O 24 pellets could also contribute to their high microwave dielectric losses.

• CONCLUSION

Aliovalent substitution of Ta 5+ for Cr 3+ in the B-site fully occupied hexagonal perovskite

For Table of Content Only

The covalent Cr-Cr and Cr-O-Cr bonding, the B-site vacancies and cationic ordering in the FSO sites relieving electrostatic repulsion stabilize the 8-layer twinned hexagonal perovskites Ba 8 Cr 4-

x Ta 4+0.6x O 24 with an extended range of B-site vacancy content and partial cation ordering among the FSO sites.

For Table of Content only

  years, and adopts an 8-layer twinned hexagonal structure with FSO and CSO B sites respectively fully occupied by Cr and Ta cations. In this B-site fully-occupied structure, chromium atoms in the FSO dimers form semimetal covalent Cr-Cr and 90 Cr-O-Cr bonding, which decreases the FSO B-B electrostatic repulsion. However, there was no attention on whether this structure is able to accommodate vacancies on the FSO B-sites. In this study, through aliovalent substitution of Ta 5+ for Cr 3+ in Ba 2 CrTaO 6 an 8-layer twinned hexagonal solid solution Ba 8 Cr 4-x Ta 4+0.6x O 24 (x = 0.0-3.0) was successfully isolated, showing the widest range of FSO B-site vacancy content among the 8-layer twinned hexagonal perovskites. The B-cation and vacancy distributions were characterized by neutron and X-ray powder diffraction and further confirmed by scanning transmission electron microscopy-high angle annular dark field imaging and intensity profile analysis.

3 )Figure 1 .

 31 Figure 1. (a) XRPD patterns and (b) refined cell parameters of Ba 8 Cr 4-x Ta 4+0.6x O 24 . The indices

Figure 2 .

 2 Figure 2. SAED patterns of the Ba 8 Cr 1.2 Ta 5.68 O 24 composition recorded along (a) [010] and (b)

Figure 3 .

 3 Figure 3. Rietveld refinement plots of (a) XRPD data and (b) NPD data of Ba 8 Cr 1.2 Ta 5.68 O 24 .

Figure 4 .

 4 Figure 4. Crystal structure plots of (a) the tripled 8H Ba 8 Cr 1.2 Ta 5.68 O 24 with six B sites B1, B2,

2 Å

 2 O 24 was observed by STEM-HAADF imaging at the atomic resolution level. Since the contrast in STEM-HAADF images is proportional to the sample density and the atomic number Z of the elements, for the observed thin area (several tens of nanometers thick), an analytical expression of the Z dependence of the image intensity can be approximated by with n in the range 1.6 -2. At the atomic scale, for an atomic column composed of several elements (i) with a ratio m i and Z i (the atomic number of the element i), this formula becomes . Consequently, intensity profiles can be used to analyze the elemental atomic distribution by indexing the atomic columns from the brightest to the darkest contrasts in relation with the heaviest to the lightest atom sites: B4-B5: Ta (Z = 73) > Ba (Z = 56) > B 1 :Ta 1 (≈ 49) > B 2 :Ta 2 (≈ 29). Figure 5a shows STEM-HAADF image recorded along the [010] direction to obtain the atomic information along all the atomic columns, and the intensity profiles of three typical strips from the STEM-HAADF image for Ba 8 Cr 1.2 Ta 5.68 O 24 . The probe with the smallest size was used considering the short distances of Ba-Ba (2.4 Å) and Ba-Ta1/Ta2 (11.) along the c axis in the projected plane. Variation of local cation distribution in the sample may be indirectly demonstrated by the intensity profiles (Figure 5b) within one cell along the stacking direction of the BaO 3 layer, i.e. the c axis. The intensity dropping on B sites located at the same layer along the c axis (highlighted by the red arrows in Figure 5b) indicates that the corresponding B sites are co-occupied with Cr or vacancies. Accordingly, the intensity from site to site of the same B-cation layer may vary along the c axis, depending on the local distribution of Cr and vacancy along the b axis. The EDS atomic maps of Ba/Ta (Figure S3) was also attempted to confirm the cationic distribution proposed from the intensity profiles. The resolution of the EDS mapping does not enable atomic resolution given the short distances between the atomic columns (Ba-Ba (2.4 Å) and Ba-Ta1/Ta2 (11.2 Å) along the c axis), and the sample drift caused by the electron discharging process. Although Cr atoms cannot be detected due to their low content and relatively low atomic number, fortunately, Ba atoms can be clearly distinguished and the Ta distribution can be discerned. Two areas can be identified: the CSO Ta4-Ta5 blocks and the FSO blocks with less Ta distribution marked in blue and red region, respectively in Figure S3, confirming the existence of B-site vacancy and Cr atoms within the FSO sites.

Figure 5 .

 5 Figure 5. (a) STEM-HAADF image for Ba 8 Cr 1.2 Ta 5.68 O 24 along the [010] orientation and (b)

Figure 6 .

 6 Figure 6. XPS spectra of (a) Ba 2 CrTaO 6 and (b) Ba 8 Cr 1.2 Ta 5.68 O 24 . (i) and (ii) are respectively

Figure 7 .

 7 Figure 7. (a) Complex impedance plot of Ba 8 Cr 1.2 Ta 5.68 O 24 pellet collected at 250 C. The

Figure 8 .

 8 Figure 8. SEM images of Ba 8 Cr 4-x Ta 4+0.6x O 24 (x = 0.0-3.0) compositions.

Ba 2

 2 CrTaO 6 led to an 8-layer twinned hexagonal solid solution Ba 8 Cr 4-x Ta 4+0.6x O 24 showing the widest B-site vacancy content range reported to date (0-15%). Ba 8 Cr 4-x Ta 4+0.6x O 24 form a simple 8-layer hexagonal perovskite structure within 0.0  x < 2.4, and a tripled 8-layer hexagonal perovskite superstructure within 2.4  x  3.0 owing to the partial FSO B cation ordering in the ab plane. Complementary techniques including neutron and X-ray powder diffractions as well as and Centre-Val de Loire region with the European regional development fund (ERDF) which are co-funded by Europe Union. The authors acknowledge the ICMN laboratory (Orléans, France) for TEM (CM20) access. Prof. Liang Fang and Prof. Huanfu Zhou are acknowledged for access to the microwave dielectric measurements.

Table 1 .

 1 Final refined structural parameters of tripled 8H Ba 8 Cr 1.2 Ta 5.68 O 24 * in P6 3 cm space group from a Rietveld refinement combining XPRD and NPD data.

	ato	Site x	y	z	occupancy	U iso (Å 2 )
	m Ba1 2a	0	0	0.25	1	0.34(1)
	Ba2 4b	1/3	2/3	0.2350(2)	1	0.34(1)
	Ba3 6c	0.6594(5)	0	0.6034(2)	1	0.34(1)
	Ba4 6c	0.3100(3)	0	0.8819(3)	1	0.34(1)
	Ba5 6c	0.3348(7)	0	0.4897(3)	1	0.34(1)
	B1	4b	1/3	2/3	0.4271(3)	0.62(2) Ta/0.16(5) Cr 0.030(5)
	B2	4b	1/3	2/3	0.0563(4)	0.16(4) Ta/0.73(8) Cr 0.030(5)
	B3	2a	0	0	0.0528(1)	0.95(1) Ta/0.05(1) Cr 0.030(5)
	B4	6c	0.3301(3)	0	0.6786(1)	0.998(6) Ta	0.030(5)

* Space group P6 3 cm (No. 185), a = 10.01521(2) Å, c = 18.88022(9) Å, and V = 1640.05(1) Å 3 , Z = 3.

Table 2 .

 2 Bond lengths and Bond Valence Sums (BVSs) for the tripled 8H Ba 8 C 1.2 Ta 5.68 O 24

	structure.
	Bond	length (Å)	Bond	length (Å)	bond	length (Å)
	Ba1 -O2 (×3)	2.853(4)	Ba4 -O2 (×2)	2.728(4)	B1 -O4 (×3)	1.979(4)
	Ba1 -O5 (×6)	2.905(2)	Ba4 -O4 (×2)	2.847(5)	B1 -O8 (×3)	2.053(4)
	Ba1 -O7 (×3)	2.861(4)	Ba4 -O3 (×1)	2.792(6)	(BVS) Cr/Ta at B1	2.74/4.65
	(BVS) Ba1	2.38	Ba4 -O8 (×2)	3.015(3)	B2 -O4 (×3)	1.949(6)
	Ba2 -O8 (×3)	2.901(4)	Ba4 -O8 (×2)	3.031(3)	B2 -O6 (×3)	2.166(5)
	Ba2 -O6 (×3)	2.783(4)	Ba4 -O5 (×2)	3.047(5)	(BVS) Cr/Ta at B2	2.54/4.32
	Ba2 -O5 (×3)	2.885(2)	Ba4 -O1 (×1)	3.228(6)	B3 -O3 (×3)	1.851(3)
	Ba2 -O1 (×3)	2.895(3)	(BVS) Ba4	2.17	B3 -O7 (×3)	2.177(4)
	(BVS) Ba2	2.52	Ba5 -O2 (×1)	2.796(7)	(BVS) Cr/Ta at B3	3.01/5.11
	Ba3 -O3 (×1)	2.522(5)	Ba5 -O3 (×2)	2.925 (7)	B4 -O7 (×1)	1.907(5)
	Ba3 -O4 (×2)	2.731(4)	Ba5 -O4 (×2)	2.881(2)	B4 -O6 (×2)	1.907(3)
	Ba3 -O6 (×2)	2.863(3)	Ba5 -O4 (×2)	2.896(7)	B4 -O5 (×2)	2.083(3)

a The site occupancies of Cr/Ta at B sites were considered in the BVS calculation for oxygen atoms.

STEM-HAADF imaging of Ba

8 Cr 1.2 Ta 5.68 O 24 . Local B-site cationic distribution in Ba 8 Cr 1.2 Ta 5.68

  3/2 and 2p 1/2 peaks centered at 575.3 eV and 584.8 eV for the x = 0 composition, and at 576.7 eV and 586.6 eV for the x = 2.8 composition are assigned to Cr 3+ . Apart from these two peaks, there are additional peaks around 578.8 eV for Ba 2 CrTaO 6 or 579.6 eV for Ba 8 Cr 1.2 Ta 5.68 O 24 , belonging to Cr 6+ 2p 3/2 line[START_REF] Contarini | Decomposition of chromate salts stimulated by and electron irradiation[END_REF][START_REF] Naumkin | NIST x-ray photoelectron spectroscopy database[END_REF][START_REF] Aronniemi | Chemical state quantification of iron and chromium oxides using XPS: the effect of the background sustraction method[END_REF] , of which intensities increased after the annealing process. This indicates that oxidation from Cr 3+ to Cr 6+ took place slightly in the as-made samples during the cooling procedure, which was enhanced significantly upon the low temperature air annealing.

		(a) x = 0.0					(b) x = 2.8
	Intensity (a. u.)	peak 1 575.3 eV (ii) 2p 3/2 (Cr 3+ )	peak 2 578.8 eV 2p 3/2 (Cr 6+ )	peak 3 584.8 eV 2p 1/2 (Cr 3+ )	Intensity (a.u.)	(ii)	peak 1 576.7 eV 2p 3/2 (Cr 3+ )	peak 2 579.6 eV 2p 3/2 (Cr 6+ )	peak 3 586.6 eV 2p 1/2 (Cr 3+ )
								(i)
		(i)
		570	575	580	585	590		570	575	580	585	590
			Binding energy (eV)				Binding energy (eV)

Table 3 .

 3 Microwave dielectric properties and relative densities of Ba 8 Cr 4-x Ta 4+0.6x O 24 (x = 0.0-3.0)

	pellets.
	composition (x)	ɛ r	Qf (GHz)	 f (ppm/C)	relative density (%)
	0.0	--	--	--	91
	1.0	--	--	--	92
	2.0	25	4424	14	96
	2.4	25	15985	25	96
	2.6	25	5816	18	92
	2.8	25	7698	20	89
	3.0	25	10947	15	91

  8 Cr 4-x Ta 4+0.6x O 24 solid solution reported here shows the widest B-site vacancy content range (0-15%) among the 8-layer twinned hexagonal perovskites. The end member Ba 2 CrTaO 6 19, 31 , containing two distinguished occupation blocks for Cr (in FSO dimers) and Ta (in CSO dimers), features covalent Cr-Cr and 90 Cr-O-Cr bonding in the FSO dimers. According to Goodenough 32 , the covalency of these metal-metal and metal-anionmetal bonding are enhanced via respectively forming σ bonds between the t 2g orbits of transitional metal cations and σπ bonds between the t 2g orbits of transitional metal cations and the 2p orbits of oxide anions. The certain Cr/Ta atomic ratio and bonding solution therefore are deemed to be the main reason for the stabilization of the B-site fully occupied 8-layer twinned hexagonal structure. In Ba 8 Cr 4-x Ta 4+0.6x O 24 (x ≠ 0), the aliovalent substitution of Ta 5+ for Cr 3+ induces B-site vacancies, therefore both Cr-Cr and Cr-O-Cr bonding, and B-site vacancies as well as cation ordering in the FSO sites could contribute together to the stabilization of the Ba 8 Cr 4-x Ta 4+0.6x O 24 twinned hexagonal perovskite structure. The FSO Cr-Cr and Cr-O-Cr bonding still takes place in Ta-rich compositions as there are still ~ 16% FSO CrCr dimers in the Ba 8 Cr 1.2 Ta 5.68 O 24 composition among the FSO B1-B2 dimers (the rest are ~ 33% Ta/Cr, ~ Ta atoms and vacancies are required to minimize the FSO electrostatic repulsion through avoiding formation of the Ta 5+ -Ta 5+ dimers. The accommodation of partial ordered vacancies and cations in the FSO B sites is helpful to relieve the FSO BB repulsion, which is common in twinned hexagonal perovskite structures, i.e. 8-layer Ba 8 ZnTa 6 O 24 12 and Ba 8 Ti 3 Ta 4 O 24 33 , 10-layer Ba 10 Ti 1.2 Ta 7.04 O 30 33 and Ba 8 Zr 0.4 Ti 2.6 Ta 4 O 24 34 , and 14-layer Ba 14 Mn 1.75 Ta 10.5 O 42 7 as well as the shifted hexagonal structures with completely ordered vacant octahedral layer between two successive h layers. Similarly to the Ba 8 Ga 4-x Ta 4+0.6x O 24 case, a tendency of the less Cr content or the higher B-site vacancy content, the higher Qf values 18 was observed for Ba 8 Cr 4-x Ta 4+0.6x O 24 compositions. It is interesting to note there is an exception for x = 2.4 at the critical point of disorder-order transition showing the highest Qf value among Ba 8 Cr 4-x Ta 4+0.6x O 24 , which is not well understood and awaits further investigation. Compared with Ba 4 LiTa 3 O 24 35 , Ba 8 Ga 4- x Ta 4+0.6x O 24 17 , Ba 8 Ti 3-x Ta 4+0.8x O 24 18 and Ba 8 MTa 6 O 24 (M = Co, Ni, Zn) 2, 12-14 cases, Ba 8 Cr 4- x Ta 4+0.6x O 24 pellets possess much lower Qf values. Such high dielectric loss of Ba 8 Cr 4-x Ta 4+0.6x O 24 could be attributed to the existence of Cr 3+ with partially filled d shells and cationic disorder in the structure as well as inhomogeneous microstructure. The resonant spin excitation induced by the unpaired d electrons in transition metal atoms can be attributed to the microwave dielectric loss, which could explain the high microwave dielectric loss of Ba(Zn 1/3 Ta 2/3 )O 3 36 and Ba 8 MnNb 6 O 24 37 , as well as the materials in this work. On the other hand, owing to the smaller charge and size differences between Cr 3+ (0.615 Å) and Ta 5+ (0.64 Å) 26 compared with those between M 2+ (M = Ni, Mg, Cu, Co, Zn, 0.69-0.72 Å) and Ta 5+ , the distribution of Cr/Ta atoms and vacancies in the FSO sites is much more disordered than in Ba 8 MTa 6 O 24 . This could be the main reason of the higher Qf values for Ba 8 MTa 6 O 24 (M = Co, Ni, Zn) although Co 2+ and Ni 2+

	51% TaCr dimers for minimizing the B-B repulsion) according to the structure refinement (Table 1). Although there are large amount of ~ 51% TaCr in the FSO B1-B2 dimers, the average B1-B2 distance (~ 2.46 Å) in Ba 8 Cr 1.2 Ta 5.68 O 24 is essentially identical to the Cr-Cr distance (~ 2.49 Å) in Ba 2 CrTaO 6 . This could be mainly ascribed to the existence of vacancies in the FSO B1-B2 dimers. As indicated by the formation of simple and tripled 8H structures respectively within 0 ≤ x < 2.4, and 2.4 ≤ x ≤ 3.0 ranges, the covalent Cr-Cr and Cr-O-Cr bonding could play a dominant role within 0.0 ≤ x < 2.4, while the B-site vacancies and cation ordering could take over the Cr-Cr and Cr-O-Cr bonding in the Ta-rich range 2.4 ≤ x ≤ 3.0. High dilution of Cr atoms, ordering of Cr/Dielectric loss.

STEM-HAADF imaging and intensity profile analysis confirm the distribution of vacancies in the FSO blocks in the tripled superstructure. The 8-layer twinned hexagonal perovskites Ba 8 Cr 4-

x Ta 4+0.6x O 24 with a broad solid solution range reported here highlight the roles of the covalent Cr-Cr and Cr-O-Cr bonding and the B-site vacancies as well as the cation ordering in the FSO dimers on relieving the electrostatic repulsion and therefore stabilizing the twinned hexagonal perovskite structures.

Supporting information: XRPD patterns of Ba


Yongchang Guo

Ying Zhang

Mathieu Allix
email: mathieu.allix@cnrs-orleans.fr

Shaowei Feng

Hong Sun

Cécile Genevois

Emmanuel Véron

Jianqiang Li
email: jqli@ipe.ac.cn

7 pyrochlore-based glass-ceramics for the immobilization of high-level wastes

Keywords: Melt solidification, Pyrochlore glass-ceramics, Actinide immobilization, High-level wastes, Metastable crystalline phase

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

High-level wastes (HLWs) generated by the reprocessing of spent nuclear fuels (SNFs) from nuclear facilities contain a large amount of radioactive elements. Transuranium minor actinides based nuclear wastes have long half-life and it is urgent to find suitable ways to store them in a stable and durable form [START_REF]Radioactive waste management[END_REF][START_REF] Ojovan | An introduction to nuclear waste immobilisation[END_REF][START_REF] Weber | Materials science of high-level nuclear waste immobilization[END_REF]. At present, a variety of materials and techniques are available for the immobilization of high-level wastes (HLWs), including vitrification, crystallization into ceramics and the combination of both in a glass-ceramics system [START_REF] Boccaccini | Hot-pressed glass matrix composites containing pyrochlore phase particles for nuclear waste encapsulation[END_REF][START_REF] Wang | Ceramics for high level radioactive waste solidification[END_REF][START_REF] Mcmaster | Radionuclide disposal using the pyrochlore supergroup of minerals as a host matrix-a review[END_REF]. Glass possesses extraordinary loading capacity for various wasted nuclides and has the advantage of relatively simple and mature preparation process, which is the mainstream method of the immobilization of high-level wastes in industry [START_REF] Lee | Immobilisation of radioactive waste in glasses, glass composite materials and ceramics[END_REF]. However, confined by the poor chemical stability and radiation tolerance owing to its metastable nature, coupled with the low solubility of minor actinides, glass immobilization remains challenging for long-term and stable HLWs storage [START_REF] Chartier | Radiation effects in lanthanum pyrozirconate[END_REF]. In comparison, ceramics exhibit long-term chemical stability and high minor actinides loading due to the localization of actinides in specific crystallographic sites in lattices [START_REF] Jafar | Preparation and structure of uranium-incorporated Gd 2 Zr 2 O 7 compounds and their thermodynamic stabilities under oxidizing and reducing conditions[END_REF]. Nevertheless, the rigorous selection of elements and limitation of ceramic crystal structures result in difficulties of ceramics immobilization to practical application [START_REF] Xu | Electron energy-loss spectroscopy (EELS) study of oxidation states of Ce and U in pyrochlore and uraninite-natural analogues for Pu-and U-bearing waste forms[END_REF][START_REF] Gieré | Element partitioning in a pyrochlore based ceramic nuclear waste form[END_REF]. Therefore, in recent years, glass-ceramics are attracting much attention as a promising host material for minor actinide immobilization because it can combine the advantages of glass and ceramics, meanwhile, supplement their shortcomings [START_REF] Taurines | Microstructure of powellite-rich glass-ceramics: a model system for high level waste immobilization[END_REF][START_REF] Ringwood | Immobilisation of high level nuclear reactor wastes in synroc[END_REF][START_REF] Loiseau | Glass-ceramic nuclear waste forms obtained by crystallization of SiO 2 -Al 2 O 3 -CaO-ZrO 2 -TiO 2 , glasses containing lanthanides (Ce, Nd, Eu, Gd, Yb) and actinides (Th): Study of the crystallization from the surface[END_REF].

Currently, glass-ceramics with various crystalline structures have been investigated for the immobilization of high-level wastes (HLWs), including perovskite [START_REF] De | Development of glass-ceramics for the incorporation of fission products[END_REF], pyrochlore [START_REF] Zhang | Pyrochlore based glass-ceramics for the immobilization of actinide-rich nuclear wastes: from concept to reality[END_REF][START_REF] Carter | HIPed tailored pyrochlore-rich glass-ceramic waste forms for the immobilization of nuclear waste[END_REF][START_REF] Zhang | Development of brannerite glass-ceramics for the immobilization of actinide-rich radioactive wastes[END_REF][START_REF] Zhang | Phase evolution from Ln 2 Ti 2 O 7 (Ln=Y and Gd) pyrochlores to brannerites in glass with uranium incorporation[END_REF][START_REF] Wei | Hot isostatically pressed Y 2 Ti 2 O 7 and Gd 2 Ti 2 O 7 pyrochlore glass-ceramics as potential waste forms for actinide immobilization[END_REF][START_REF] Kong | A new method for production of glass Ln 2 Ti 2 O 7 pyrochlore (Ln=Gd, Tb, Er, Yb)[END_REF][START_REF] Kong | Preparation of Y 2 Ti 2 O 7 pyrochlore glass-ceramics as potential waste forms for actinides: the effects of processing conditions[END_REF],

zirconolite [START_REF] Loiseau | Glass-ceramic nuclear waste forms obtained by crystallization of SiO 2 -Al 2 O 3 -CaO-ZrO 2 -TiO 2 , glasses containing lanthanides (Ce, Nd, Eu, Gd, Yb) and actinides (Th): Study of the crystallization from the surface[END_REF][START_REF] Loiseau | Glass-ceramic nuclear waste forms obtained from SiO 2 -Al 2 O 3 -CaO-ZrO 2 -TiO 2 glasses containing lanthanides (Ce, Nd, Eu, Gd, Yb) and actinides (Th): study of internal crystallization[END_REF][START_REF] Caurant | Crystallization of neodymium-rich phases in silicate glasses developed for nuclear waste immobilization[END_REF] and brannerite [START_REF] Zhang | Development of brannerite glass-ceramics for the immobilization of actinide-rich radioactive wastes[END_REF][START_REF] Zhang | Phase evolution from Ln 2 Ti 2 O 7 (Ln=Y and Gd) pyrochlores to brannerites in glass with uranium incorporation[END_REF][START_REF] Zhang | Structural and spectroscopic studies on the crystallization of uranium brannerite phases in glass[END_REF]. Among these, the pyrochlore structure offers a wide range of possibilities for the immobilization of actinide nuclides due to the flexibility of the A 2 B 2 O 7 structure, in which A, B and O are 8-, 6-and 4-coordinated cation sites, respectively [START_REF] Jafar | Preparation and structure of uranium-incorporated Gd 2 Zr 2 O 7 compounds and their thermodynamic stabilities under oxidizing and reducing conditions[END_REF][START_REF] Jafar | X-ray diffraction and Raman spectroscopic investigations on CaZrTi 2 O 7 -Y 2 Ti 2 O 7 system: delineation of phase fields consisting of potential ceramic host materials[END_REF][START_REF] Jafar | Phase evolution and microstructural studies in CaZrTi 2 O 7 -Nd 2 Ti 2 O 7 system[END_REF][START_REF] Mandal | Gd 2 Zr 2 O 7 pyrochlore: potential host matrix for some constituents of thoria based reactor's waste[END_REF][START_REF] Kutty | Actinide immobilization in crystalline matrix: a study of uranium incorporation in gadolinium zirconate[END_REF]. Additionally, reports on radiation damage have revealed that the chemical stability of the pyrochlore structure is sustained even in the completely amorphous states [START_REF] Icenhower | Dissolution kinetics of pyrochlore ceramics for the disposition of plutonium[END_REF][START_REF] Strachan | Radiation damage effects in candidate titanates for Pu disposition: Pyrochlore[END_REF]. Current research on pyrochlore-based glass-ceramics are mainly focused on compositions considering a single element on the B site, such as titanate pyrochlore (A 2 Ti 2 O 7 ) and zirconite pyrochlore (A 2 Zr 2 O 7 ) [START_REF] Boccaccini | Hot-pressed glass matrix composites containing pyrochlore phase particles for nuclear waste encapsulation[END_REF][START_REF] Jafar | Preparation and structure of uranium-incorporated Gd 2 Zr 2 O 7 compounds and their thermodynamic stabilities under oxidizing and reducing conditions[END_REF][START_REF] James | Crystal chemistry and structures of (Ca, U) titanate pyrochlores[END_REF][START_REF] Carter | Titanate ceramics for immobilization of uranium-rich radioactive wastes arising from 99Mo production[END_REF]. Previous reports showed that the A 2 B 2 O 7 pyrochlore structure is stable only when the A/B ionic radii ratio is in the range of 1.46-1.78, otherwise the defect fluorite structure or monoclinic structure are likely to be stabilized [START_REF] Subramanian | Oxide pyrochlores-a review[END_REF]. The current consideration of B-site occupation by a single element is limiting the application of pyrochlore-structured glass-ceramics to immobilize diverse actinide nuclides. Therefore, binary, or even multiple elements occupation on the B-site of pyrochlore-based glass-ceramics with subtle differences in ionic radii are expected to improve the loading flexibility of actinide nuclides, while sustained high loading capacity. In this work, possibility and feasibility of synthesizing binary substituted (La,Y) 2 (Zr,Ti) 2 O 7 pyrochlore-based glass-ceramics were investigated.

The possibility of industrial production of materials ensuring the immobilization of high-level wastes (HLWs) depends not only on the nature of the host materials but also on the complexity of the process. Currently, there are two primary processes to synthesize pyrochlore-based glass-ceramics. The first approach consists in sintering a mixture of borosilicate glass and crystalline pyrochlore powders, in which the glass powder is obtained by classic melt-quenching process followed by fine grinding while the crystalline pyrochlore powder is usually prepared by solid-state reaction process or sol-gel route [START_REF] Boccaccini | Borosilicate and lead silicate glass matrix composites containing pyrochlore phases for nuclear waste encapsulation[END_REF][START_REF] Aluri | A study of the electronic structure and structural stability of Gd 2 Ti 2 O 7 based glass-ceramic composites[END_REF][START_REF] Zhou | High-entropy A 2 B 2 O 7 -type oxide ceramics: A potential immobilising matrix for high-level radioactive waste[END_REF]. The second approach to synthesis pyrochlore-based glass-ceramics is based on the controlled crystallization of a glass precursor bulk [START_REF] Loiseau | Glass-ceramic nuclear waste forms obtained by crystallization of SiO 2 -Al 2 O 3 -CaO-ZrO 2 -TiO 2 , glasses containing lanthanides (Ce, Nd, Eu, Gd, Yb) and actinides (Th): Study of the crystallization from the surface[END_REF][START_REF] Zhang | Pyrochlore based glass-ceramics for the immobilization of actinide-rich nuclear wastes: from concept to reality[END_REF][START_REF] Kong | Preparation of Y 2 Ti 2 O 7 pyrochlore glass-ceramics as potential waste forms for actinides: the effects of processing conditions[END_REF]. Both the sintering and crystallization methods were widely studied and show various advantages in the immobilization of high-level wastes (HLWs). However, the complexity of the processes has limited their development at the industrial application. Recently, Xirui Lu et al. reported a method of rapid in situ synthesis of Gd 2 Zr 2 O 7 glass-ceramics using spark plasma sintering [START_REF] Shu | Rapid synthesis of Gd 2 Zr 2 O 7 glass-ceramics using spark plasma sintering[END_REF], which greatly simplifies the synthesis process while increasing the preparation speed compared with the conventional sintering method and crystallization methods.

However, the pressure required (30 MPa) during the sintering process and the existence of cracks at the surface of the obtained Gd 2 Zr 2 O 7 glass-ceramics also limit the industrial application and still require further improvement. Melt solidification is widely used in the synthesis of metals and alloys, which exhibits the advantages of brief and rapid process. Additionally, dense and crack-free solids are expected to be obtained during solidification owing to the good fluidity of the sample melts, and there may be novel glass-ceramic structures discovered due to the rapid melt solidification and crystal growth. However, the preparation of pyrochlore-based glass-ceramics for the immobilization of high-level wastes in this way has never been reported so far.

Aerodynamic levitation (ADL) was extensively used in the fabrication of novel/metastable materials [START_REF] Guo | High-entropy R 2 O 3 -Y 2 O 3 -TiO 2 -ZrO 2 -Al 2 O 3 glasses with ultrahigh hardness, Young's modulus, and indentation fracture toughness[END_REF][START_REF] Li | Upconversion 32Nb 2 O 5 -10La 2 O 3 -16ZrO 2 glass activated with Er 3+ /Yb 3+ and dye sensitized solar cell application[END_REF][START_REF] Fan | La 2 Ga 3 O 7.5 : a metastable ternary melilite with a super-excess of inter-stitial oxide ions synthesized by direct crystallization of the melt[END_REF]. This synthesis process possesses the advantages of high heating power, no contact and no heterogeneous crystallization, high quenching rate which provides access to metastable phases. Additionally, the samples are levitated and the whole process avoids any contact with the wall of container, which confirm with the simple and the pollution-free demand of the immobilization of high-level wastes (HLWs glass-ceramics appears as a promising alternative for the immobilization of HLWs, with simplified preparation process and easier industrial production.

Material and Methods

Sample preparation

Samples were elaborated by aerodynamic levitator (ADL). The high purity oxide powders La 2 O 3 , TiO 2 , Y 2 O 3 and ZrO 2 , Al 2 O 3 in 99.99% purity were purchased from Sinopharm chemical reagent co. ltd and Aladdin chemical reagent co. ltd, respectively. All raw material powders were heated at 1000 ˚C in a muffle furnace for at least 2 h to remove adsorbed water. Then the raw materials were weighed and mixed stoichiometrically with the nominal composition of

La 2 O 3 -Y 2 O 3 -2TiO 2 -2ZrO 2 -Al 2 O
3 in molar ratio. The mixed powders were subsequently ground with ethanol and dry thoroughly in the oven. The obtained dried precursor was then pressed into pellets and crumbled into small pieces. Prior to melts, all pieces were pre-sintered at 600 ˚C for 2 h in air to obtain higher strength. Pieces of ~60-200 mg were then levitated on the nozzle of an ADL with oxygen flow and heated to melt (~2200 ˚C) by three CO 2 lasers. Keeping the molten state of samples for 10~20 s to ensure that the components were homogeneously distributed, then adjusting the laser power to solidify the melt via different cooling rates and the white and spherical samples were obtained. The ADL and the solidification process of samples are presented in Figure 1.

Characterization

The solidification cooling curves were obtained from the data acquisition system of aerodynamic levitator with infrared pyrometer (FTK9S-P400A-20S11-0549, JAPANSENSOR Corporation, Tokyo, Japan). The structure of the obtained (La,Y) 2 (Zr,Ti

Results and discussion

The solidification cooling curves of the as-synthesized (La,Y) 2 (Zr,Ti) 2 O 7 pyrochlore-based glass-ceramics at different cooling rates were shown in Figure 2(a), the method used to calculated the cooling rate is presented in Figure 2(b) and the inset picture showed the resulting bead samples.

The cooling rates refer to the cooling from the melt (~2200 ˚C) down to melt solidification (~1500 ˚C), which could be set and automatically controlled by the temperature control system of the aerodynamic levitator via adjustment of the laser power. The cooling rates were set to 100 ˚C/s, 130 ˚C/s, 200 ˚C/s, 300 ˚C/s and 500 ˚C/s (free cooling), respectively. In Figure 2(a), all samples were first heated up to melting (~2200 ˚C) and the recalescence peaks were observed during the cooling process, which indicated that the melt crystallized during solidification. The observed recalescence peaks at about 1500 ˚C are related to the main phase crystallization. Additionally, the recalescence peak temperatures vary with the cooling rate. Very tiny peaks were observed at about 1500 ˚C when the cooling rate was 500 ˚C/s (free cooling), 300 ˚C/s and 200 ˚C/s, respectively.

With the decrease of the cooling rate to 130 ˚C/s and 100 ˚C/s, the recalescence peaks became stronger and show a slightly up shift. The enhancement of recalescence peaks with the decrease of cooling rate was due to the higher crystallinity of the main crystal phase under the lower solidification cooling rates. The slightly down shifted recalescence peaks with the increased cooling rate could be owing to the solidification point depression caused by deep supercooling.

Particularly, the second recalescence peaks were observed when the cooling rate was ≤ 138 ˚C/s, which was related to the secondary crystallization of residual amorphous phase. Additionally, the two phases are tightly mixed and no cracks can be observed, which is interesting for further use in immobilization of high-level wastes (HLWs). Compared with previous works on pyrochlore-based glass-ceramics [START_REF] Zhang | Pyrochlore based glass-ceramics for the immobilization of actinide-rich nuclear wastes: from concept to reality[END_REF][START_REF] Wei | Hot isostatically pressed Y 2 Ti 2 O 7 and Gd 2 Ti 2 O 7 pyrochlore glass-ceramics as potential waste forms for actinide immobilization[END_REF][START_REF] Kong | A new method for production of glass Ln 2 Ti 2 O 7 pyrochlore (Ln=Gd, Tb, Er, Yb)[END_REF], the great difference in distribution between the crystalline pyrochlore phase and the amorphous phase in (La,Y) 2 (Zr,Ti) 2 O 7 glass-ceramics can mainly be attributed to the preparation methods. For conventional preparation methods, ample time was available for nucleation and crystal growth of pyrochlore and therefore to form the thermodynamically stable cubic structure. For rapid levitated melts solidification process, as shown in Figure 2, the sample melts solidified within 1.5 s when the cooling rate is 500 ˚C/s and the pyrochlore dendritic crystals are obtained by rapid crystal growth from the edge of the bead towards the center, which results in the curved stripe structure of pyrochlore [START_REF] Wisniewski | Y 2 O 3 -Al 2 O 3 microsphere crystallization analyzed by electron backscatter diffraction[END_REF]. where Zr, Y are concentrated in the bright phase and Al is concentrated in the dark phase. For the formation of pyrochlore structures, the ionic radius and valence state of elements are the most important two factors. The ionic radius of La 3+ , Y 3+ in 8-coordination and Zr 4+ , Ti 4+ in 6-coordination are 1.16 Å, 1.019 Å and 0.72 Å, 0.605 Å respectively [START_REF] Shannon | Effective ionic radii in oxides and fluorides[END_REF]. The calculated average ratio of r A /r B is 1.64, which is comply with the radius requirements of 1.46-1.78 for the stable existence of pyrochlore [START_REF] Subramanian | Oxide pyrochlores-a review[END_REF]. Although Al in its trivalent state could meet the substitution requirement of A 2 B 2 O 7 in A site, the small atomic radius (0.39-0.535 Å [START_REF] Shannon | Effective ionic radii in oxides and fluorides[END_REF]) makes it remain challenging to form a stable pyrochlore phase. Consequently, Zr and Y elements appear preferably located in the bright region and form a pyrochlore structure whereas Al is preferably located in the dark region in the amorphous phase. The element distribution at the micro-scale of (La,Y) 2 (Zr,Ti) 2 O 7 pyrochlore-based glass-ceramic materials was previously characterized by EDS mappings (Figure 4). The results

showed that all elements are present both in the pyrochlore and amorphous phases but their contents vary. However, due to a tightly intertwined nanometric microstructure between pyrochlore and amorphous phases, the accuracy of the EDS maps obtained by scanning electron microscopy appears limited. The quantitative analysis of the elemental distribution is challenging as some subtle composition contrasts could be hidden. Therefore, in order to quantify the The heat release generated by the decay of radionuclides is one of the major challenges in the immobilization of high-level wastes. Therefore, waste forms with good thermal stability are seek with great interest. Figure 7 shows the comparison of glass transition temperatures (T g ) between (La,Y) [START_REF] Kong | A new method for production of glass Ln 2 Ti 2 O 7 pyrochlore (Ln=Gd, Tb, Er, Yb)[END_REF][START_REF] Kong | Preparation of Y 2 Ti 2 O 7 pyrochlore glass-ceramics as potential waste forms for actinides: the effects of processing conditions[END_REF][START_REF] Makishima | Direct calculation of Young's modulus of glass[END_REF]. In contrast, the La 2 O 3 -TiO 2 -Al 2 O 3 amorphous phase possesses a higher dissociation energy. Therefore, the higher glass transition temperatures may be mainly attributed to the different glass compositions and dissociation energies. Additionally, the glass transition temperature is also related to the thermal history of the material. In this work, the glass-ceramic samples were solidified from a molten state at a relatively fast cooling rate (500 ˚C/s), which increases the glass transition temperature and thus improve the thermal stability of the amorphous phase.

  Rapid solidification synthesis of novel (La,Y)2(Zr,Ti)2O7 pyrochlore-based glass-ceramics for the immobilization of high-level wastes Yongchang Guo, Ying Zhang, Mathieu Allix, Shaowei Feng, Hong Sun, Cécile Genevois, Emmanuel Véron, Jianqiang Li To cite this version: Yongchang Guo, Ying Zhang, Mathieu Allix, Shaowei Feng, Hong Sun, et al.. Rapid solidification synthesis of novel (La,Y)2(Zr,Ti)2O7 pyrochlore-based glass-ceramics for the immobilization of high-level wastes. Journal of the European Ceramic Society, 2021, 41 (14), pp.7253-7260. 10.1016/j.jeurceramsoc.2021.07.051. hal-03438650

Figure 1 .

 1 Figure 1. Schematic diagram of the aerodynamic levitator (ADL) with laser heating and the insert showed the (La,Y) 2 (Zr,Ti) 2 O 7 pyrochlore-based glass-ceramics melt.

  ) 2 O 7 pyrochlore-based glass-ceramics were identified by X-ray powder diffraction (XRPD, Smartlab 9, Rigaku Corporation, Tokyo, Japan). The surface morphology and elements distribution of samples were analyzed by the Field Emission Scanning Electron Microscope (FE-SEM, JSM-7610F, Tokyo, Japan) with energy dispersive spectroscopy (EDS). Prior to SEM observation, the bead samples were pre-processing in advance such as polishing and ion thinning treatment. The accelerating voltage and probe current of SEM were 15 kV and 8, respectively. The nanostructure of (La,Y) 2 (Zr,Ti) 2 O 7 pyrochlore-based glass-ceramics were observed by Transmission Electron Microscopy (TEM), using a JEOL ARM 200F (JEOL Ltd.) Cold FEG microscope operating at 200kV, equipped with a double spherical aberration correctors and fitted with a JEOL SDD CENTURIO EDS system. Bright-field (BF) and High Resolution TEM (HRTEM) images were recorded with a parallel beam. In addition, Scanning TEM -High Angle Annular Dark Field (STEM-HAADF) imaging, with a 68-174.5 mrad inner-outer collection angles, and STEM-EDS elemental mapping were performed with a probe size of 0.13nm. Prior TEM observations, the sample was crushed in ethanol, and a drop of the solution containing a small amount of material in suspension was deposited onto a carbon-coated copper grid. The glass transition temperature T g was measured by a differential scanning calorimeter (Differential thermal analysis (DTA), STA499F3, NETZSCH, Selb, Germany) from room temperature to 1200 ˚C at a heating rate of 10 ˚C/min in Ar atmosphere.

Figure 2 .

 2 Figure 2. Cooling curves of samples during melt solidification. (a) Temperature-time profiles of

Figure 3 .

 3 Figure 3. XRPD patterns of the as-synthesized (La,Y) 2 (Zr,Ti) 2 O 7 pyrochlore-based glass-ceramics at different cooling rates (a) and the enlargement of XRPD patterns in 30°~36° revealing the secondary crystallization evolution (b). The average cooling rates were 100 ˚C/s, 130 ˚C/s, 200 ˚C/s, 300 ˚C/s and 500 ˚C/s (free cooling), respectively.

Figure 4 (

 4 b) to 4(e) shows the microstructure of samples with diameters of ~2 mm, ~3 mm, ~4mm and ~5 mm, respectively. The typical curved stripe structure of pyrochlore were observed for all sizes of samples and the two phases was homogeneity distributed. For samples with larger diameter, the stripe width of pyrochlore phase increased gradually, which is owing to the decreased solidification rate with the increase of sample size, and thus the pyrochlore phase has more time for crystal growth.The (La,Y) 2 (Zr,Ti) 2 O 7 pyrochlore-based glass-ceramics elaborated using a cooling rate of 500 ˚C/s (free cooling) were further studied using EDS mapping. The EDS maps of (La,Y) 2 (Zr,Ti) 2 O 7 pyrochlore-based glass-ceramics are performed to analyze the distribution of Ti, La, Zr, Y and Al at a micrometer scale, as shown in Figure4(f). The Ti and La are homogenously distributed in the two phases. Meanwhile, the enrichment of elements occurs for Zr, Y and Al,

Figure 4 .

 4 Figure 4. SEM images and corresponding EDS elemental maps of the as-synthesized (La,Y) 2 (Zr,Ti) 2 O 7 pyrochlore-based glass-ceramics. (a) Back scattering images of the polished sample with a cooling rate of 500 ˚C/s. (b-e) Back scattering images of the polished sample with

Figure 5

 5 (a) confirms the coexistence of two phases, which appear interweaved with each other and tightly mixed at the nanometer scale. According to the different contrasts, two typical regions with different atom arrangements can be distinguished in the samples using high-resolution TEM mode. Some areas present a disordered atomic distribution and this amorphous character is confirmed by typical diffraction ring patterns on the FFT (Fast Fourier Transform), as shown in Figure5(b). On the other hand, other areas show crystallographic plans characteristic of crystallized grains and the corresponding FFT patterns can be indexed with the pyrochlore structure, as shown Figure5(c).

Figure 5 (

 5 Figure 5(d) shows an enlarged FFT pattern, indexed with the Y 2 Zr 2 O 7 pyrochlore structure along the [0 2] zone axis, showing the (242) weak reflection and the (400) strong reflection. The combination of the microstructural analyses mentioned above makes possible to define that the bright and dark regions of the as-synthesized samples correspond to pyrochlore crystalline and amorphous areas, respectively. This is in accordance with the XRPD results and suggests that (La,Y) 2 (Zr,Ti) 2 O 7 pyrochlore-based glass-ceramics are successfully synthesized in a rapid melts solidification way using aerodynamic levitator (ADL). They possess high density, i.e. no porosity, and therefore may exhibit good mechanical properties.

Figure 5 .

 5 Figure 5. Transmission Electron Microscope (TEM) images and corresponding FFT patterns of the as-synthesized (La,Y) 2 (Zr,Ti) 2 O 7 pyrochlore-based glass-ceramics using a cooling rate of 500 ˚C/s. (a) Bright field image of the mixed crystalline and amorphous phases at nanoscale, (b) HRTEM image of an amorphous region (glass) with the corresponding diffraction ring FFT pattern inserted in the left corner, (c) HRTEM image of a crystalline region with the corresponding FFT pattern inserted in the left corner and (d) the previous FFT pattern enlarged and indexed by the Y 2 Zr 2 O 7 pyrochlore structure along the [0 2] zone axis.

  composition and distribution of Al, La, Y, Zr and Ti elements, STEM-HAADF image and corresponding EDS elemental maps were acquired on the as-synthesized (La,Y) 2 (Zr,Ti) 2 O 7 pyrochlore-based glass-ceramics, as shown in Figure6. STEM-HAADF is a Z-contrast imaging mode where the intensity is proportional to the density or to the average atomic number (≈ Z²) of the phase, consequently heavier is a phase brighter it appears. The STEM-HAADF images exhibit two different phases with different contrasts, the crystalline one is brighter and the amorphous one darker. The STEM-EDS elemental maps clearly demonstrate that aluminum is present in the amorphous areas whereas Y and Zr which are located in the pyrochlore areas. Meanwhile, Ti and La appear present in both phases (amorphous and pyrochlore). Combined with the substitution requirement of A and B site in A 2 B 2 O 7 , they suggest that the formed pyrochlore by rapid melts solidification is composed of La, Ti, Zr and Y, where La and Y occupy the A site and Ti and Zr are located on the B site. Aluminum and the remaining La and Ti contents are homogeneously distributed in the residual amorphous phase.

Figure 6 .

 6 Figure 6. STEM-HAADF image and corresponding STEM-EDS cationic elemental maps of the as-synthesized (La,Y) 2 (Zr,Ti) 2 O 7 pyrochlore-based glass-ceramics at the cooling rate of 500 ˚C/s. The corresponding TEM image and the overlaid EDS maps of Al (glass) and Zr (pyrochlore).

Figure 7 .Figure 8 .Figure 2 (

 782 Figure 7. Comparison of glass transition temperature T g of (La,Y) 2 (Zr,Ti) 2 O 7 pyrochlore-based glass-ceramics at the cooling rate of 500 ˚C/s and some typical borosilicate glasses used for the immobilization of HLWs [44]. The insert showed DTA curve of the as-synthesized glass-ceramics.

Figure 8 .

 8 Figure 8. Pressure demand versus consolidating time during the synthesis of (La,Y) 2 (Zr,Ti) 2 O 7 pyrochlore-based glass-ceramics at the cooling rate of 500 ˚C/s via melting method together with some typical sintering and crystallization methods of the preparation of pyrochlore-based glass-ceramics waste form.

30 

 30 ,Y) 2 (Zr,Ti) 2 O 7 pyrochlore-based glass-ceramics were designed and successfully prepared by melt solidification process with foreseen applications for the immobilization of HLWs.The structure of the obtained glass-ceramic samples were characterized using XRPD, SEM, EDS, HRTEM and STEM-HAADF. The prepared (La,Y) 2 (Zr,Ti) 2 O 7 pyrochlore-based glass-ceramics appear dense and crack-free. The typical curved and striped structure of the glass-ceramics was owed to the rapid crystal growth from the outside towards the center of the bead during the solidification process. The thermal properties of the samples were measured by DTA. The high glass transition temperature T g (863 ˚C) demonstrates that the obtained samples possess outstanding thermal stability compared with the conventional borosilicate glass. In summary, the rapid solidification synthesis of (La,Y) 2 (Zr,Ti) 2 O 7 pyrochlore-based glass-ceramics propose a promising path towards the immobilization of HLWs, and show great potential applications for future's nuclear waste disposal. glass precursors needed # pyrochlore precursors needed

Table 1 ,

 1 2 (Zr,Ti) 2 O 7 pyrochlore-based glass-ceramics and some typical borosilicate glasses used for the immobilization of HLWs. The glass transition temperature of the La 2 O 3 -TiO 2 -Al 2 O 3 (LaTiAlO) the amorphous phase of the prepared glass-ceramic samples consist of La 2 O 3 , TiO 2 and

	amorphous phase is 863 ˚C, which is much higher than the values of the glasses currently used for
	actinide immobilization, such as borosilicate glasses (BSG, ~540 ˚C), alumina borosilicate glass
	(AlBSG, ~547 ˚C), barium borosilicate glass (BaBSG, ~512 ˚C) and lead borosilicate glass
	(PdBSG, ~476 ˚C) [44]. Therefore the prepared (La,Y) 2 (Zr,Ti) 2 O 7 pyrochlore-based
	glass-ceramics demonstrate much better thermal stability for practical applications. As shown in
	Al 2 O 3 , whose molar dissociation energy is 193.9 kJ/mole, 103.9 kJ/mole and 192.0 kJ/mole,
	respectively. The amorphous phase of conventional glass-ceramics for nuclear waste solidification
	mainly consist of alkali metal oxides (˂71.6 kJ/mole), SiO 2 (101.3 kJ/mole) and B 2 O 3 (170.0
	kJ/mole)

Acknowledgements

This work was financially supported by The National Key Research and Development  1.5 s   # # # Program of China (No.2017YFC0703205), National Natural Science Foundation of China (No.51972304, No.51971208), The Project of Scientific Experiment on Chinese Manned Space Station, Chinese Academy of Sciences President's International Fellowship Initiative for 2021 (No.2021VEA0012), Innovation Academy for Green Manufacture, Chinese Academy of Sciences (No. IAGM2020C25). TEM results were realized through the project of Région-Centre Val de Loire and the French minister of research (MESRI-DRRT) and Centre-Val de Loire region with the European regional development fund (ERDF) which are cofunded by the European Union.

Author contributions

Declaration of interests

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