Romain Saussard
email: romain.saussard@renault.com

Boubker Bouzid
email: boubker.bouzid@renault.com

Marius Vasiliu
email: marius.vasiliu@u-psud.fr

Roger Reynaud
email: roger.reynaud@u-psud.fr

A Robust Methodology for Performance Analysis on Hybrid Embedded Multicore Architectures

Today's vehicles increasingly embed software intelligence in order to be safer for the driver, and to achieve autonomous driving in a close future. To answer the computational needs of these algorithms, system-on-chip (SoC) suppliers propose heterogeneous architectures. With such complex SoCs, embedding applications in vehicle becomes more and more complex for car manufacturers. Indeed, it is not trivial to find the best suited SoC for a given application, and to define load balancing strategies when working with heterogeneous architectures. These difficulties can be overcome by using performance prediction, based on computing architectures models. To build these models, we provide a set of test vectors which automatically extract key characteristics of tested architectures. Our methodology is able to perform a complete computing architecture model, by using 3 different levels of tests, each one characterizing a specific situation representative of real applications. We aim to obtain performance prediction for different applications, for any embedded SoCs based on models performed with this methodology. In this paper, we describe our characterization methodology, and show results obtained with embedded SoCs used for automotive applications.

I. INTRODUCTION

Computational needs for vehicles are increasing with the emergence of advanced driver assistance systems (ADAS) and autonomous driving systems. Indeed, vehicles increasingly use sensors and complex algorithms to sense the environment. Thus, automotive industry uses more and more computational powerful systems-on-chip (SoCs), especially to embed image processing algorithms. Image processing algorithms process high amounts of data, so they need high computational resources. Most of state-of-the-art image processing algorithms for ADAS are designed to be executed on powerful computer, sometimes not in real time. Nevertheless, they often can be easily parallelized, so they can be accelerated by massively parallel architectures. This implies an effort from automotive actors to bridge the gap between prototypes on computer and embedded SoCs on vehicles.

Semiconductor companies are moving into the market of ADAS with heterogeneous SoCs. These systems provide different kind of processors to bring more computational performance and energy efficiency. We can cite Nvidia (Tegra K1 and X1), Texas Instruments (TDA2x), Renesas (R-Car H2 and R-Car H3). In [START_REF] Saussard | The embeddability of lane detection algorithms on heterogeneous architectures[END_REF], we show that computational intensive image processing algorithms, such as lane detection, can be embedded and executed in real time on heterogeneous SoCs.

When embedding software applications on vehicle, two challenges need to be addressed. First, one needs to guess the best suited SoC for a given application, then one needs to find how to partition the computational load on the different processors of the heterogeneous SoC. In [START_REF] Saussard | Towards an automatic prediction of image processing algorithms performances on embedded heterogeneous architectures[END_REF], [START_REF] Saussard | Optimal performance prediction of ADAS algorithms on embedded parallel architectures[END_REF] we present a way to address these challenges, by using performance prediction. However, performance prediction models need architecture characteristics to proceed, and this information is not always provided by suppliers.

In this paper, we propose a generic methodology to automatically extract key features of heterogeneous SoCs. Characteristics extracted show few raw performance indicators for the measured architectures, and can be used in a performance prediction model. First, in section II, we briefly present some heterogeneous SoCs used for ADAS applications. Then, in section III, we present existing work on architecture characterization, followed by our novel approach description in section IV. Finally, we show some results obtained with our methodology in section V, and we discuss about future work and conclude in section VI.

II. HETEROGENEOUS SOCS FOR ADAS

In order to meet automotive industry needs for embedding computational intensive ADAS applications, semiconductor companies such as Nvidia, Renesas, or Texas Instruments propose heterogeneous SoCs. These architectures are often composed of ARM processors, for general processing, and of one or few hardware accelerators to handle computationally intensive operations such as image processing. In this paper, we propose a generic methodology to characterize computing architectures, including modern computers and any of these SoCs. Architectures characteristics are summarized in table I.

A. Nvidia Tegra K1 and X1

Nvidia has released two embedded architectures for ADAS applications: the Tegra K1 and the Tegra X1. Both are composed of ARM processors, GPUs and Image Signal Processors (ISPs). The Tegra K1 consists of a quad-core ARM Cortex A15 CPU providing ARMv7 instruction set and a Kepler GPU, composed of one streaming multiprocessor (SMX) of 192 cores. The development platform is known as Nvidia Jetson TK1. The Tegra X1 is composed of a quad-core ARM Cortex A57, a quad-core ARM Cortex A53 providing ARMv8 ARM processors provide out-of-order speculative issue superscalar execution pipeline. Each core handles SIMD instructions with a NEON unit and has a FPU unit. GPU are well known for accelerating image processing application execution time [START_REF] Castaño-Díez | Performance evaluation of image processing algorithms on the gpu[END_REF]. CUDA framework [START_REF]Cuda C programming guide[END_REF] is used for kernel implementation on the GPU of Tegra K1 and Tegra X1. The ISP provides fast and specific image processing kernels such as delayering, noise reduction, etc. This unit is very fast, but user can only control a limited set of parameters and the chaining order of kernels is restricted.

B. Renesas R-Car

Renesas has released two embedded architectures for ADAS applications: the R-Car H2 and the R-Car H3. Both are composed of ARM processors, programmable hardware accelerators to handle image processing kernels, and ISPs.

The R-Car H2 provides a quad-core ARM A15 and a quadcore ARM A7. It is composed of a programmable hardware accelerator, the high performance real-time image recognition processor (IMP-X4).

C. Texas Instruments TDA2x

The TDA2x [START_REF] Sankaran | TDA2X, a SoC optimized for advanced driver assistance systems[END_REF] is composed of four different types of programmable units. First, it provides a 750 MHz dual-core ARM A15 and a dual-Cortex-M4. These computing units do not bring that much computing capability (A15 core on TDA2x is 4 times less powerful than the one in K1), but they can be used for data management, video acquisition control/rendering, high level decision making, etc.

To handle heavy image processing tasks, TDA2x provides a mix of Texas Instruments fixed and floating point TMS320C66x DSP (Digital Signal Processor) and up to four EVE (Embedded Vision Engine) cores. TMS320C66x is the most recent DSP from Texas Instruments, it can handle up to 32 multiply accumulate operations per cycle. Each EVE is a 650 MHz core, optimized for image processing, composed of one specific RISC processor and one 512-bit vector coprocessor.

D. Software Environment

Each SoCs manufacturer has its own software environment to develop on its platform. For example Nvidia provides the CUDA API for GPU programming, Texas Instruments proposes cl6x (DSP compiler), specific tools to program EVE processors, and TI Vision SDK [START_REF] Chitnis | TI vision SDK, optimized vision libraries for ADAS systems[END_REF]. Thus, a user who wants to work on different platforms has to learn different software API, languages, etc. In addition, porting an algorithm from PC to an embedded SoC, with a specific API, is not trivial.

To facilitate portability and genericity, the Khronos Group has released the OpenVX standard. OpenVX [START_REF] Rainey | Addressing system-level optimization with OpenVX graphs[END_REF] is an open, royalty-free standard for cross platform acceleration of computer vision applications. It enables performance and poweroptimized computer vision processing, it is based on the implementation of image processing kernels designed by SoC manufacturers, beneficing from hardware acceleration of the architecture.

Nvidia, Renesas and Texas Instruments take parts to the OpenVX specification definition. In addition, Nvidia has released an OpenVX implementation to address Tegra K1 and Tegra X1: VisionWorks. To our knowledge, Texas Instruments and Renesas has not released yet an OpenVX implementation for their platforms.

E. Kernel Mapping Optimization

When working with heterogeneous architectures, a challenge needs to be addressed: how to partition the different tasks (or kernels) of the algorithm to embed on the different processors of the heterogeneous architecture. That is what we call the kernel mapping problem, introduced in [1]- [START_REF] Saussard | Optimal performance prediction of ADAS algorithms on embedded parallel architectures[END_REF].

Let P be the vector of the processing units of a given heterogeneous architecture, K be the vector of the kernels of a given algorithm, the matrix M constitutes the mapping of K on P , given by P = M.K. Let ϕ be the spatiotemporal dependency matrix: a kernel instance K i (t) may depends on the execution of another kernel K j (t), and its previous instance K i (t -1); ϕ is used to find possible execution pipelines. Let τ (M ) be the execution function (returning the execution time for each kernel), δ(M ) be the transfer function (returning the transfer delay needed for each kernel), η(M ) be the occupancy function (returning the occupancy for each computing unit) and f (P, K, ϕ, τ (M ), δ(M ), η(M )) be the cost function (returning the global execution time of the algorithm). The aim of the kernel mapping optimization is to find M minimizing f :

arg min M [f (P, K, ϕ, τ (M ), δ(M ), η(M ))] . (1)
As discussed in [START_REF] Saussard | Towards an automatic prediction of image processing algorithms performances on embedded heterogeneous architectures[END_REF], [START_REF] Saussard | Optimal performance prediction of ADAS algorithms on embedded parallel architectures[END_REF], the parameters of the function f can be predicted for different M . In these papers we have presented a methodology to estimate the execution τ (M ) and transfer δ(M ) times with little knowledge of target architectures.

Our performance prediction approach is based on two levels of accuracy. The first one builds an architecture model based on basic information provided by manufacturers; but this level cannot deal with cache effects, compiler optimizations, memory latency, concurrent memory access, resources starvation, etc. Thus the second level overcomes these limitations by using a generic test vector set which automatically extracts features, for any architectures and compilers in order to build a more precise model for the association architecture + compiler. In this paper, we explain our methodology for extracting some features of the tested architectures and their software environment.

III. EXISTING WORK ON ARCHITECTURE CHARACTERIZATION

A. Legacy Metrics

One of the most well-known metrics to characterize architecture performance is the FLOPS (Floating-point Operations Per Second). It only measures floating point operations, unlike the MIPS (Millions of Instruction per second) which measures all type of instruction (moving, computing, comparing, etc.) executed in a second. However, MIPS cannot be used to compare different instruction sets for the same workload (e.g. CISC vs RISC).

The Dhrystone benchmark [START_REF] Weicker | Dhrystone: a synthetic systems programming benchmark[END_REF] was created to be representative of CPU performance. It does not use floating point operations, the output corresponds to the number of Dhrystones per second (the number of iterations of the main code loop per second), measured in D-MIPS.

B. Benchmarks for Computing

The benchmark consists in measuring execution time of workloads for a given computing architecture. Then, benchmark results can be compared for many architectures. However, results are strongly dependent on workloads (parallelism degree, operations used, etc.).

1) Serial CPU: The SPEC [START_REF]The Standard Performance Evaluation Corporation (SPEC)[END_REF] benchmark is made of a set of 49 compute-intensive workloads. It can only measure performance for CPU (no parallelism), it is based on integer and floating-points operations [START_REF] Henning | Spec cpu2006 benchmark descriptions[END_REF]. The Embedded Microprocessor Benchamark Consortium (EMBC) [START_REF]Embedded Microprocessor Benchmark Consortium (EMBC)[END_REF] uses the CoreMark benchmark [START_REF] Gal-On | Exploring coremark a benchmark maximizing simplicity and efficacy[END_REF]. This benchmark outputs only one scalar, representing computing architecture capability. It is based on noncontiguous memory operations, matrix operations (to illustrate hardware acceleration like MAC, or SIMD instructions), and state machine processing (to illustrate branch prediction performance).

2) Parallel Computing: Some benchmarks are defined to characterize parallel architecture. For example, SPLASH-2 benchmark [START_REF] Woo | The splash-2 programs: Characterization and methodological considerations[END_REF] aims to characterize multi-processor architecture. For different workloads, it measures computing load repartition between all processors, communication/computing ratio, impact of dataset size, etc.

3) Heterogeneous Computing: The famous Rodinia benchmark [START_REF] Che | Rodinia: A benchmark suite for heterogeneous computing[END_REF] is composed of multi-core CPU and GPU kernels (using OpenMP and CUDA). Workloads are inspired by Berkeley's dwarf taxonomy [START_REF] Asanovic | The landscape of parallel computing research: A view from Berkeley[END_REF]. It characterizes communication between processing units, synchronization techniques, power consumption, etc. Parboil [START_REF] Stratton | Parboil: A revised benchmark suite for scientific and commercial throughput computing[END_REF] is quite similar, but only based on few kernels. Scalable Heterogeneous computing (SHOC) [START_REF] Danalis | The scalable heterogeneous computing (shoc) benchmark suite[END_REF] uses OpenCL and CUDA implementation to target CPU+GPU architectures. It is based on two different types of test: Level zero (low level characteristics of the architecture, e.g. PCIe Bus speed, Memory Bandwith, Kernel Compilation, Peak FLOPS, etc.), and Level One (based on parallel kernels, e.g. FFT, matrix multiplication, etc.).

C. Benchmarks for Memory

Some benchmarks aim to characterize memory performance. For example the STREAM benchmark [START_REF] Mccalpin | Memory bandwidth and machine balance in current high performance computers[END_REF] measures performance for 4 different kernels: Copy

a[i] = b[i], Scale a[i] = q × b[i], Sum a[i] = b[i] + c[i], and Triad a[i] = b[i] + q × c[i].
The Low level architectural characterization benchmark suite (LLCBench) [START_REF] Mucci | Llcbench-low level architectural characterization benchmark suite[END_REF] characterizes architecture with a set of 3 benchmarks: MPBench for MPI messaging, BLASBench for computing performance based on BLAS routines, and CacheBench for memory performance. It only outputs raw data and graphs.

IV. OUR METHODOLOGY

Most of the state-of-the-art benchmarks focus on specific applications, or focus on one type of operation (floating-point or integer). In order to obtain low level characteristics of tested architectures, we developed a novel methodology which is based on a set of performance test vectors. Our approach is generic in the sense that it can target any programmable architectures (software meaning), including PC and any of the heterogeneous SoCs listed in section II. Our methodology is composed of 3 levels: low level, mid level, and high level test vectors. Test vectors are all

A. Low Level Test Vectors

These test vectors aim to extract low level characteristics of the tested architecture. It is divided into two parts computing test vectors (extracting computing capability of the architecture) and memory test vectors (extracting bandwidth and latency).

1) Memory: To start with, let us define memory operation that we want to characterize:

• Read -Read: 2 consecutive reading on the same data.

• Read -Write: 1 reading, then 1 writing on the same data.

• Write -Read: 1 writing, then 1 reading on the same data.

• Write -Write: 2 consecutive writing on the same data.

• Mcpy: memcopy with @src = @dst.

• Trsf : memory transfer from a computing unit to another. The tests consist in measuring time needed to execute one of the six memory operation for different sizes. Two strategies are used: in one test, allocated data size is fixed and we vary the numbers of memory operations; in the other test, we vary the allocated memory size. In all the tests, we use contiguous memory access in order to obtain maximum bandwidth and to be close to image processing use-case. However, it is possible to apply the same methodology with non-contiguous access.

2) Computing: We want to characterize a computing operation (e.g. sum, multiplication, multiply accumulate, bitwise operators, etc.) for different data type (int32, int16, int8, float64, float32). Thus, for a given operator, for each data type, we measure the execution time of a known number of operations while varying the arithmetic intensity (I A ). The I A is the ratio of computing operations to memory operations.

So, we obtain an execution time depending on the I A as described in the Boat Hull Model [START_REF] Nugteren | The boat hull model: adapting the roofline model to enable performance prediction for parallel computing[END_REF]:

• Execution time is constant when the I A is low, performance is limited by memory bandwidth and latency. • Execution time is proportional to the I A when the I A is high enough, memory bandwidth and latency are hidden by computing operations. The slope represents the throughput of the processor for the tested operation and the variable type used. Note that the limit between a low and a high I A is specific for each processor, it depends on its memory bandwidth and computing capabilities. These tests are based on few loops with a known size at compilation time. So they also highlight compiler capabilities, illustrating the auto-vectorization and loop-unrolling performances.

These tests are designed to achieve high parallelism degree, to fully exploit massively parallel processors such as GPU, or multi-core CPU with SIMD instructions. In order to characterize sequential execution, we also run these tests without parallelism acceleration (e.g. for CPU, by using only 1 core without SIMD instructions).

3) Conflict Management: Conflict management ensure isolation of shared data from concurrent threads, while causing performance decrease when two or more thread simultaneously try to operate on the same data. These test vectors study the behavior of these specific mechanisms for different architectures (e.g Mutex for CPU, or Atomic instructions for GPU).

B. Mid Level Test Vectors

Mid level test vectors consist in characterizing concurrency execution on a processor, i.e. the impact of executing few independent tasks at the same time on the same processor. We use the previously defined low level test vectors, running two or more low level tests concurrently (e.g. multiplication and addition, or addition and memory, etc.) in two different configurations on the same processor:

• Concurrent execution on different cores: the tests may only share few cache levels, so it only impacts memory access delay. • Concurrent execution on the same core: the tests share all resources, execution time is fully impacted. These tests highlight some hazards on performance due to concurrency, that are not described in datasheets. Results are integrated in the architecture model, to achieve more accurate performance prediction.

C. High Level Test Vectors

High Level testing uses as vectors real-time programs (e.g. ADAS applications) built from full known source code or using some binary libraries. The last case is the most difficult to evaluate or to predict, because binary blocks must be treated as "black-boxes".

We aim to use characteristics extracted by the low level tests to predict the "black-box" behavior through different architectures. A typical example are applications using the new standard OpenVX. As discussed in section II-D, this new standard enables to execute the same code on different heterogeneous platforms. For example, with VisionWorks (Nvidia implementation of OpenVX), it is possible to compile and run the same code on PC with Nvidia GPU, Jetson and DrivePX platforms without any software adaptation.

V. RESULTS

Our methodology is applicable for any heterogeneous architectures. Nonetheless, in this paper, we focus on three SoCs: K1, X1, and R-Car H2. Software configurations for our tests are summarized in table II.

A. Computing

For each architecture, we present our test results for the ARM processor in 4 different configurations: 1 core, 1 core with handwritten SIMD instructions (NEON), 4 cores using OpenMP, and 4 cores with NEON; plus the results for the massively parallel processors (except for the R-Car H2 SoC due to a NDA).

In this paper, we only show results for int32 addition and multiplication, and float64 multiplication. Results are illustrated in Fig. 1. As predicted by the Boat Hull model [START_REF] Nugteren | The boat hull model: adapting the roofline model to enable performance prediction for parallel computing[END_REF], we observe a constant execution time for low I A , and a linear execution time for high I A . In this linear part, the slope can be directly exploited to obtain throughput for a given configuration (operation and variable type).

In addition, results also highlight some compiler effects: for some ARM configurations there is break in the line (I A =5 for integer), this is due to auto-vectorization and loop-unrolling. Actually, after this threshold, compiler stops auto-vectorizing and loop-unrolling. Some extracted throughputs are given in table III, compared to throughputs given by manufacturers, obtained values are close to those provided by datasheets. The gaps between measurements and datasheets for some throughputs can be explained by our test design. In fact in our tests, the operation that we want to characterize is followed by some data transfer instructions. So the instruction pipeline is not fully exploited, but it is more representative of what happened in reality.

Then, in Fig. 2, we show results of concurrent executions on ARM relative to single threaded execution (Fig. 1): in one case we run two processes concurrently on different cores, in the other case we run two processes concurrently on the same core. Running two instances of the same test on different cores on the ARM seems to have no impact on the execution time. However, the execution time of two tasks executed on the same core is 2 times greater than single execution. About K1, the execution time on the same core is bigger than 2 times for I A ≤ 1, where performance is limited by memory bandwidth and latency. So we deduce it is due to memory/cache management.

To strengthen the K1 model, we take into account this behavior when working with concurrent operations on different cores.

B. Memory

In this paper, we choose to focus on transfer (CPU to GPU, GPU to CPU), and memcopy operations. In Fig. 3, we give the delay needed to transfer different data size from one processor to another. Note that for all measures, data size allocated in memory is fixed to 4096 kB. Transfer delay is piecewise linear, non-linearities are due to cache effects. X1 transfer bandwidth seems to be about 1.7 times faster than K1 transfer bandwidths.

In Fig. 4, we give characterization of memcopy operations for K1, X1, and R-Car SoCs. Two consecutive operations on the same data do not have the same behavior, the second one being faster than the first one. Regarding GPU results, there is a static delay due to the latency of kernel execution on GPU; this delay depends on different parameters (e.g. size of kernel).

In Fig. 5, we show behaviors of concurrent memcopy operations on ARM using 2, 3 or 4 concurrent processes on different cores relative to single threaded execution (Fig. 4). In the 4 cores configuration, both X1 and K1 have a relative execution time lower than ×4, whereas we operate 4 times more memory operations than single core test. It means that, in single core configuration, performance is limited by cache bandwidth, while in 2 or more cores configuration, performance is limited by memory bandwidth. According to these results, K1 memory bandwidth is about 1.33 times greater than cache bandwidth, and X1 memory bandwidth is about 2 times greater than cache bandwidth.

C. OpenVX / VisionWorks

One of the high level test vectors we choose to analyze in this paper is a feature tracker algorithm. Its VisionWorks implementation is composed of 4 kernels: color to gray conversion, Gaussian pyramid construction, Lukas Kanade optical flow, and Harris feature tracker. We focus on color to gray conversion and Harris feature tracker kernels for three different architectures: K1, X1 and a PC equipped with a GTX 970M Nvidia GPU.

In Fig. 6, we give execution time of the two kernels versus the number of Mpixels to process, for K1, X1, and PC architectures. Fig. 7 shows histograms of execution times for K1. As far as we know, VisionWorks mainly uses GPU for image processing kernels. We observe that execution time increases linearly with image size, with an offset due to kernel launch latency, like what we obtained with memory low level test vectors on GPU (Fig. 4).

As seen in the results for computing test vectors (Fig. 1), GPU needs a very high I A to be computing bound, so we assume performance is limited by memory bandwidth. Thus, for architecture a, and kernel k, execution time is given by:

t k,a = α a • γ k,a • x + β k,a . (2)
Where β k,a denotes the kernel launch latency, α a the memory bandwidth (in µs/Byte) obtained with our low level tests, x the number of pixels, and γ k,a the number of memory access for each pixels. By deriving the previous equation, we obtain:

dt k,a dx /α a = γ k,a . (3)
As the source code is identical for each architectures (only the VisionWorks library binary is specific for each architecture), each implementation should have the same amount of memory access, so γ k should be constant. With measured

dt k,a
dx , and α a obtained from our low level tests, we have for:

• Color kernel: γ 1,P C = 3.2; γ 1,X1 = 8.6; γ 1,K1 = 8.7.

• Track kernel: γ 2,P C = 5.3; γ 2,X1 = 15.3; γ 2,K1 = 15.9. For K1 and X1, γ k are close enough to consider them as similar. Thus, a known execution time on K1 can be directly extrapolated on X1 and vice versa. However, γ k for PC is not equal but roughly proportional for different kernels. This can be explained by different memory access strategies, specific compiler optimizations, etc.

VI. CONCLUSION AND FUTURE WORK

In this paper, we have introduced a novel methodology for characterizing computing architectures. Our test vectors are based on 3 levels. Low level vectors extract some key features of the tested architecture, mid level vectors study behaviors in concurrency conditions, and high level vectors analyze performances of real applications.

We are currently working on applying our methodology for other architectures, like TDA2x, R-Car H3, or the hardware accelerator of the R-Car H2 (IMP-X4). We are also studying behaviors of other "black box" kernels, in order to validate our approach with the high level test vectors (e.g. OpenVX / VisionWorks) and performance prediction.

The characteristics extracted with our approach can be directly used to strengthen a model of a computing architecture, in order to be applied for performance prediction. Actually, our main goal is to define a global methodology to help in finding the best suited SoC for a given application, and defining load balancing strategies for heterogeneous architectures, by using performance prediction.

  gpu Second cpu to gpu First gpu to cpu Second gpu to cpu (b) X1 Transfer operation.

Fig. 3 :

 3 Fig. 3: Transfer CPU-GPU characterization, given for K1 and X1 SoCs. Allocated size is fixed to 4096 kB for all measures.

  R-Car memcpy operation.

Fig. 4 :

 4 Fig. 4: Memcpy characterization, given for K1, X1 and R-Car H2 SoCs. Allocated size is fixed to 4096 kB for all measures.

Fig. 5 :

 5 Fig.5: Concurrent memcpy operations on ARM, using 2, 3 or 4 cores. Allocated size is fixed to 4096 kB for all measures.

  Harris feature tracker kernel.

Fig. 6 :Fig. 7 :

 67 Fig.6: Results of OpenVX/VisionWorks tests for two kernels, given for three different architectures. Execution time is proportional to the number of pixels, with a static offset due to kernel launch latency on GPU.

TABLE I :

 I Summary of hardware configurations.

	SoC	Processors	Parallel Units	Classification	Parallel Degree	Memory Bandwidth	Tools
	Tegra K1	4×A15 with NEON	1 SMX Kepler GPU	SIMT	192 CUDA cores	17 GB/s	GCC, (OpenVX) CUDA,	Visionworks
	Tegra X1	4×A57, 4×A53 with NEON	2 SMX Maxwell GPU	SIMT	2×128 CUDA cores	26.5 GB/s	GCC, (OpenVX) CUDA,	Visionworks
	R-Car H2	4×A15, 4×A7 with NEON	IMP-X4	MIMD	Under NDA	6.4 GB/s	GCC
	TDA2x	2×A15 with NEON, 2×C66x DSPs	4×EVE	SIMD	512 bits vector size	n.a.	GCC, cl6x, TI Vision SDK
	instruction set, and a Maxwell GPU composed of two SMX
	of 128 cores. The development platform for autonomous cars,
	DrivePX, provides 2 Tegra X1.

TABLE II :

 II Configurations of tested architectures.

	SoC	GCC	Compiler flags	CUDA
	K1	4.8	-O3 -mtune=cortex-a15 -mfpu=neon-vfpv4 -funroll-loops -fopenmp	7.0
	X1	4.9	-O3 -mtune=cortex-a57 -funroll-loops -fopenmp	7.5
	R-Car	4.8	-O3 -mtune=cortex-a15 -mfpu=neon-vfpv4 -funroll-loops -fopenmp	/

TABLE III :

 III Computing throughputs extracted from our test vectors compared to theoretical values. Throughputs are given in operation per cycle for ARM-A15 1 core, the GPU of the K1, and the GPU of the X1. The " * " denotes multiple instructions. Computing characterization examples, given for K1, X1 and R-Car H2 SoCs. We only show here a small sample of our results (integer and double variables). Note that we managed to have the same amount of memory access for all variable types. Concurrent operations characterization on ARM, given for K1, X1 and R-Car H2 SoCs. Even if two ARM cores share L2 cache, running two tests concurrently on different cores seems to have no impact on the execution time. However, if the tests are run on the same core, execution time is about 2 times greater.

	Integer add	Integer add	Integer add
	Different cores	Different cores	Different cores
	Same core	Same core	Same core
	Throughput→ Operation↓ int8 add int16 add int32 add float32 add float64 add int8 mult int16 mult int32 mult float32 mult float64 mult 2 4 8 Arithmetic Intensity in ops/byte A15 (datasheet) n.a. n.a. 2 0.25 0.25 n.a. n.a. 0.5 0.2 0.2 16 32 64 128 Integer add 1 core 1 core neon 1 4 cores 4 cores neon GPU (a) K1 additions on integers. 0.5 0.5 1 2 4 8 16 32 64 128 Arithmetic Intensity in ops/byte Integer mult 1 core 1 core neon 4 cores 4 cores neon GPU (d) K1 multiplications on integers. 10 100 1000 10000 100000 1x10 6 10 100 1000 10000 100000 1x10 6 10 100 1000 10000 100000 1x10 6 0.5 1 2 4 8 16 32 64 128 Arithmetic Intensity in ops/byte Double mult 1 core 4 cores GPU (g) K1 multiplications on doubles. ×2 ×3 0.5 1 2 4 8 16 32 64 128 Relative execution time Arithmetic Intensity in ops/byte (a) K1 concurrent additions on integers. 500 1000 1500 Fig. 1: ×1 Time in µs Time in µs Time in µs 500 1000 1500 2000 2500 3500 4000 Time in µs First cpu to gpu Second cpu to gpu First gpu to cpu Fig. 2: 0 3000 Second gpu to cpu	A15 (measured) 1 1 2 0.22 0.22 0.22 0.22 0.4 0.18 0.18 10 100 1000 10000 100000 1x10 6 0.5 1 1 core neon GPU (datasheet) K1 n.a. n.a. 160 192 8 n.a. n.a. 32 192 8 2 4 8 16 Arithmetic Intensity in ops/byte GPU (measured) K1 124 124 128 128 8 30 30 32 8 32 64 128 Integer add 1 core 4 cores 4 cores neon GPU (b) X1 additions on integers. 10 100 1000 10000 100000 1x10 6 0.5 1 2 4 8 16 32 64 128 Arithmetic Intensity in ops/byte Integer mult 1 core 1 core neon 4 cores 4 cores neon GPU (e) X1 multiplications on integers. 10 100 1000 10000 100000 1x10 6 0.5 1 2 4 8 16 32 64 128 Arithmetic Intensity in ops/byte Double mult 1 core 4 cores GPU (h) X1 multiplications on doubles. ×1 ×2 ×3 0.5 1 2 4 8 16 32 64 128 Relative execution time Arithmetic Intensity in ops/byte (b) X1 concurrent additions on integers. (c) R-Car concurrent additions on integers. GPU X1 (datasheet) GPU X1 (measured) n.a. 200 n.a. 200 256 225 256 225 8 8 n.a. 60 n.a. 60 * 84 256 225 8 8 10 100 1000 10000 100000 1x10 6 0.5 1 2 4 8 16 32 64 Time in µs Arithmetic Intensity in ops/byte Integer add 1 core 1 core neon 4 cores 4 cores neon (c) R-Car H2 additions on integers. 10 100 1000 10000 100000 1x10 6 0.5 1 2 4 8 16 32 64 Time in µs Arithmetic Intensity in ops/byte Integer mult 1 core 1 core neon 4 cores 4 cores neon (f) R-Car H2 multiplications on integers. 128 128 10 100 1000 10000 100000 1x10 6 0.5 1 2 4 8 16 32 64 128 Time in µs Arithmetic Intensity in ops/byte Double mult 1 core 4 cores (i) R-Car H2 multiplications on doubles. ×1 ×2 ×3 0.5 1 2 4 8 16 32 64 128 Relative execution time Arithmetic Intensity in ops/byte 2000 Time in µs Time in µs Time in µs 2500 3000 3500 4000 Size in kB cpu-gpu Trsf


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Laurence Croguennec

Strong Impact of the Oxygen Content in Na 3 V 2 (PO 4 ) 2 F 3-y O y (0  y  0.5) on its Structural and Electrochemical Properties

Polyanionic materials such as Na3V2(PO4)2F3-yOy (0 ≤ y ≤ 2) are of high interest as positive electrode for Na-ion batteries since they offer competitive electrochemical performances compared to sodiated transition metal oxides. The composition Na3V2(PO4)2F3 (y = 0) has the highest theoretical energy density among the series but surprisingly a lot of discrepancies are reported throughout the literature considering its structure and its electrochemical properties. We will show that most of the compounds reported as being Na3V III 2(PO4)2F3 are in fact slightly oxidized due to synthesis conditions resulting in a partial oxygen substitution for fluorine. In order to get an in-depth understanding of this system, a series of compositions Na3V2(PO4)2F3-yOy (0 ≤ y ≤ 0.5, i.e. near the fluorine-rich composition) was synthesized and characterized combining synchrotron X-ray diffraction, X-ray absorption spectroscopy, solid state nuclear magnetic resonance spectroscopy and galvanostatic electrochemical tests. The structural features and electrochemical signatures of these oxidized compounds will be carefully compared to those recently obtained for Na3V III 2(PO4)2F3 by Bianchini et al.

Introduction

Up to now, Li-ion batteries have been shown to be the most efficient technology for the electrochemical energy storage developed for portable and automotive applications. [START_REF] Armand | Building better batteries[END_REF] In order to overcome drawbacks associated to the availability and prize of lithium resources, [START_REF] Tarascon | Is lithium the new gold?[END_REF] and thus to develop alternatives to Li-ion batteries for targeted applications, the Na-ion technology appears to be a short term reasonable option given that it is similar in terms of materials used and industrial processing. [START_REF] Palomares | Naion batteries, recent advances and present challenges to become low cost energy storage systems[END_REF] Despite several advantages including lower price and very large earth-abundance of sodium important drawbacks must be overcome to ensure a possible future for the Na-ion technology: a less negative standard reduction potential (-2.7

V vs SHE for the Na + aq/Na against -3.04 V for the Li + aq/Li one) and a higher molecular mass both contributing to reduce the energy density compared to Li-ion material with the same composition.

Among several polyanionic-based electrode materials, [START_REF] Jian | Superior Electrochemical Performance and Storage Mechanism of Na3V2(PO4)3 Cathode for Room-Temperature Sodium-Ion Batteries[END_REF][START_REF] Sauvage | Crystal structure and electrochemical properties vs. Na + of the sodium fluorophosphate Na1.5VOPO4F0.5[END_REF][START_REF] Shakoor | A combined first principles and experimental study on Na3V2(PO4)2F3 for rechargeable Na batteries[END_REF][START_REF] Liu | Preparation of NaV1-xAlxPO4F cathode materials for application of sodium-ion battery[END_REF][START_REF] Chihara | Cathode properties of Na3M2(PO4)2F3 [M= Ti, Fe, V] for sodium-ion batteries[END_REF][START_REF] Kim | Na2FeP2O7 as a Promising Iron-Based Pyrophosphate Cathode for Sodium Rechargeable Batteries: A Combined Experimental and Theoretical Study[END_REF][START_REF] Masquelier | Polyanionic (phosphates, silicates, sulfates) frameworks as electrode materials for rechargeable Li (or Na) batteries[END_REF] one of the most promising family turns out to be the sodium-vanadium fluorophosphate compounds Na3V2(PO4)2F3-yOy (also called NVPF3-yOy in this paper) where y can vary from 0 to 2 [START_REF] Serras | High voltage cathode materials for Na-ion batteries of general formula Na3V2O2x(PO4)2F3-2x[END_REF][START_REF] Serras | Electrochemical performance of mixed valence Na3V2O2x(PO4)2F3-2x/C as cathode for sodium-ion batteries[END_REF][START_REF] Park | A new high-energy cathode for a Na-ion battery with ultrahigh stability[END_REF][START_REF] Park | A Family of High-Performance Cathode Materials for Na-ion Batteries, Na3(VO1-xPO4)2F1+2x (0≤ x≤ 1): Combined First-Principles and Experimental Study[END_REF][START_REF] Bianchini | Comprehensive Investigation of the Na3V2(PO4)2F3 -NaV2(PO4)2F3 System by Operando High Resolution Synchrotron X-ray Diffraction[END_REF][START_REF] Bianchini | Na3V2(PO4)2F3 revisited: a high-resolution diffraction study[END_REF][START_REF] Tsirlin | Phase separation and frustrated square lattice magnetism of Na1.5VOPO4F0.5[END_REF][START_REF] Gover | The electrochemical insertion properties of sodium vanadium fluorophosphate, Na3V2(PO4)2F3[END_REF][START_REF] Song | Multifunctional dual Na3V2(PO4)2F3 cathode for both lithium-ion and sodium-ion batteries[END_REF] also reported as Na3V2O2y(PO4)2F3-2y [START_REF] Serras | High voltage cathode materials for Na-ion batteries of general formula Na3V2O2x(PO4)2F3-2x[END_REF][START_REF] Serras | Electrochemical performance of mixed valence Na3V2O2x(PO4)2F3-2x/C as cathode for sodium-ion batteries[END_REF] and Na3(VO1-yPO4)2F1+2y [START_REF] Park | A Family of High-Performance Cathode Materials for Na-ion Batteries, Na3(VO1-xPO4)2F1+2x (0≤ x≤ 1): Combined First-Principles and Experimental Study[END_REF] where y can vary from 0 to 1. For instance in Na3V2(PO4)2F3 (y = 0, NVPF3) the extraction of 2 Na + ions has been experimentally demonstrated with two main voltage-composition plateaus at around 3.7 and 4.2 V vs Na + /Na and a theoretical energy density of 507 Wh/kg [START_REF] Gover | The electrochemical insertion properties of sodium vanadium fluorophosphate, Na3V2(PO4)2F3[END_REF][START_REF] Barker | Hybrid-ion a lithium-ion cell based on a sodium insertion material[END_REF][START_REF] Barker | Li4∕3Ti5∕3O4 ‖ Na3V2(PO4)2F3: An Example of a Hybrid-Ion Cell Using a Non-graphitic Anode[END_REF] (128 Ah/kg at an average potential of 3.95 V) competitive with that delivered by LiFePO4 in Li-ion batteries. Several studies have been performed recently which revealed significant discrepancies in the structural description and electrochemical properties of NVPF3. For instance, unit cell volumes ranging from 871 to 878 Å [START_REF] Palomares | Naion batteries, recent advances and present challenges to become low cost energy storage systems[END_REF] were reported [START_REF] Gover | The electrochemical insertion properties of sodium vanadium fluorophosphate, Na3V2(PO4)2F3[END_REF][START_REF] Barker | Hybrid-ion a lithium-ion cell based on a sodium insertion material[END_REF] whereas the phase diagram observed upon cycling was described either as complex with a series of two-phase reactions and solid solution [START_REF] Bianchini | Comprehensive Investigation of the Na3V2(PO4)2F3 -NaV2(PO4)2F3 System by Operando High Resolution Synchrotron X-ray Diffraction[END_REF] or only as a solid solution. [START_REF] Liu | Local Structure and Dynamics in the Na Ion Battery Positive Electrode Material Na3V2(PO4)2F3[END_REF] It clearly stands out that some subtle differences in as-prepared compositions have to be clarified considering especially the effect on the structural and electrochemical features of a possible partial substitution of oxygen for fluorine and thus of a mixed valence state for vanadium (V 3+,4+ ) induced by synthesis conditions.

More precisely, the structure of NVPF3-yOy (0 ≤ y ≤ 2) consists of a tridimensional framework of V2O8F3-yOy bi-octahedra which are connected by PO4 tetrahedra. When y > 0 the substitution of oxygen for fluorine occurs at the apex of the V2O8F3-yOy bi-octahedra, inducing the formation of shorter covalent vanadyl-type bonds as terminal bonds and thus the contraction of the bi-octahedra. Regardless the F/O ratio, the framework of NVPF3-yOy (0 ≤ y ≤ 2) is characterized by large tunnels where Na + ions are mobile upon the intercalation and deintercalation reactions. To date, two space groups have been used to describe the crystal structure at 298 K of the whole series NVPF3-yOy (0 ≤ y ≤ 2): P42/mnm and Amam.

Recently it has been evidenced by Bianchini et al. [START_REF] Bianchini | Na3V2(PO4)2F3 revisited: a high-resolution diffraction study[END_REF] that the well-known structure of NVPF3 described by Le Meins et al. in the tetragonal space group P42/mnm [START_REF] Meins | Phase transitions in the Na3M2(PO4)2F3family (M= Al 3+, V 3+, Cr 3+, Fe 3+, Ga 3+): synthesis, thermal, structural, and magnetic studies[END_REF] turned out to be not appropriate since a subtle orthorhombic distortion had to be considered. As shown in Figure 1 this distortion is linked to the sodium distribution only, and does not affect significantly the framework. Three sodium sites (one in 4c and two in 8f Wyckoff positions) are observed in the Amam space group, and only two sites (in 8i Wyckoff positions) in the P42/mnm space group. Since all NVPF3-yOy compositions (i.e. with a different F/O ratio) are reported to be tetragonal [START_REF] Serras | Electrochemical performance of mixed valence Na3V2O2x(PO4)2F3-2x/C as cathode for sodium-ion batteries[END_REF][START_REF] Park | A Family of High-Performance Cathode Materials for Na-ion Batteries, Na3(VO1-xPO4)2F1+2x (0≤ x≤ 1): Combined First-Principles and Experimental Study[END_REF][START_REF] Serras | Electrochemical Na Extraction/Insertion of Na3V2O2x(PO4)2F3-2x[END_REF] it is crucial to determine if this distortion subsists in oxidized compounds, its impact on the sodium distribution, but also more extensively the relationship between composition, structure and electrochemical properties. Furthermore, the creation of a more covalent bond within the transition metal environment induces a decrease in the average operating voltage which is important regarding electrochemical performance. In other words, a deviation from the "ideal" y = 0 composition is expected to be associated to a loss of performance hence the importance of studying this feature for Na3V2(PO4)2F3.

Here a series of six partially oxidized Na3V2(PO4)2F3-yOy compositions with y ranging from 0 (NVPF3) to 0.5 (NVPF2.5O0.5) has been prepared through a two-step solid state synthesis method in order to control the F/O ratio that governs the vanadium initial oxidation state: from +3 for y = 0 to +3.25 for y = 0.5.

This study gives new insights into slightly oxidized NVPF3-yOy compositions and helps conciliating all the discrepancies observed in the literature and arising in fact from a partial oxidation of the as-prepared material.

Experimental

Na3V2(PO4)2F3-yOy (0 ≤ y ≤ 0.5) powders were prepared by a two-step solid-state reaction using stoichiometric amounts of V V OPO4, V III PO4, NaF (Sigma-Aldrich; ≥ 99 %), and Na2CO3 (Riedel-de Haën; 99.8 %) as precursors. V V OPO4 and V III PO4 were prepared using stoichiometric amounts of V2O5 (Sigma-Aldrich; ≥ 99.6 %) and NH4H2PO4 (Sigma-Aldrich; ≥ 99.99 %), according to one and two-step solid-state reactions respectively.

High resolution Synchrotron powder X-ray diffraction (SXRD) data were collected using the MSPD diffractometer at ALBA (Barcelona, Spain). The powders were placed in a 0.5 mm diameter capillary and data recorded in Debye-Scherrer geometry with a wavelength of 0.9540 Å in the 2θ angular range of 1 -70 ° with a 0.005 ° step and an accumulation time of 6 minutes. As already reported by Bianchini et al. [START_REF] Bianchini | Na3V2(PO4)2F3 revisited: a high-resolution diffraction study[END_REF] for the structural determination of Na3V III 2(PO4)2F3 (y = 0), the use of very high angular resolution techniques is essential as a very small orthorhombic distortion exists. Their detection is important to reveal significant changes in the distribution of sodium ions within the 3D framework and thus in the interpretation of electrochemical processes.

The chemical composition of NVPF3-yOy in Na, V and P was confirmed by inductively coupled plasmaoptical emission spectroscopy (ICP-OES) using a Varian Model 720-ES spectrometer after complete dissolution of the powder into a hydrochloric acid (HCl) solution.

Vanadium K-edge X-ray absorption spectra were collected at room temperature in transmission mode using three ionization chambers mounted in series for simultaneous measurements of the sample and reference at the beamline CLAESS at ALBA (Barcelona, Spain). The synchrotron radiation emitted by the CLAESS multipole wiggler was first vertically collimated and then monochromatised by a Si(111) double-crystal monochromator. The monochromatised beam was then focused down to 100 x 200 μm 2 at the sample position by a toroidal focusing mirror. Higher harmonic contributions to the selected energy were suppressed by setting the coating and the rejecting angle of the two mirrors. Powder samples were mixed uniformly in boron nitride matrix and pressed into pellets of 13 mm diameter, for obtaining the vanadium K-edge step close to 1. Several X-ray absorption scans were collected to ensure the reproducibility of the spectra and to obtain high signal to noise ratio. [START_REF] Meins | Phase transitions in the Na3M2(PO4)2F3family (M= Al 3+, V 3+, Cr 3+, Fe 3+, Ga 3+): synthesis, thermal, structural, and magnetic studies[END_REF] Na MAS NMR spectra were recorded on a Bruker Avance 500 MHz spectrometer (132.3 MHz resonance frequency for 23 Na) using a standard Bruker 2.5 mm MAS probe with a 30 kHz typical spinning frequency. A short pulse length of 1 µs corresponding to a selective π/12 pulse determined using an aqueous 0.1 mol/L NaCl solution was employed. The spectral width was set to 1 MHz and the recycle time to D0 = 0.5 s, long enough to avoid T1 saturation effects. The baseline distortions resulting from the spectrometer dead time (5-10 µs) were removed computationally using a polynomial baseline correction routine. The 0 ppm external reference was a 0.1M NaCl aqueous solution. [START_REF] Poumellec | Experimental and theoretical studies of dipole and quadrupole contributions to the vanadium K-edge XANES for VOPO4⋅2H2O xerogel[END_REF] P MAS NMR spectra were recorded on a Bruker Avance III 100 MHz spectrometer (40.6 MHz resonance frequency for 31 P), using a standard Bruker 2.5 mm MAS probe with a 30 kHz typical spinning frequency. A Hahn echo sequence was used with a 90 ° pulse of 1.1 µs. A recycle delay of 1 s was typically used. The 0 ppm external reference was H3PO4 85 % sigma Aldrich.

Scanning electron microscopy (SEM) analysis of metallized samples (Pd-deposited) was performed using a Hitachi Model S-4500 microscope.

Electrochemical tests were performed in CR2032-type coin cells. The positive electrodes were prepared from a slurry made of 80 wt% Na3V2(PO4)2F3-yOy (0 ≤ y ≤ 0.5), 10 wt% carbon black, and 10 wt% polyvinylidene fluoride (PVDF) dispersed in N-methyl-2-pyrrolidone (NMP), casted on an Al foil and dried at 80 °C overnight. The loading of the active material on the electrodes was around 2.5 mg/cm². The negative electrode was sodium metal, whereas the electrolyte was home-made from a 1 M solution of NaPF6 (Strem Chemical; 99%) in ethylene carbonate and dimethyl carbonate (EC:DMC = 1:1) with 3 wt% of fluoroethylene carbonate (FEC) as additive. The electrochemical cells were charged and discharged in galvanostatic mode, at a C/20 between 2.5 and 4.3 V vs Na + /Na corresponding to the exchange of 0.1 mol of sodium ions/electrons per hour.

Results and discussion

Syntheses of the series of Na3V2(PO4)2F3-yOy (0 ≤ y ≤ 0.5) compositions

The synthesis of Na3V2(PO4)2F3-yOy (0 ≤ y ≤ 0.5) was performed in two steps using conditions similar to those reported by Park et al. [START_REF] Park | A Family of High-Performance Cathode Materials for Na-ion Batteries, Na3(VO1-xPO4)2F1+2x (0≤ x≤ 1): Combined First-Principles and Experimental Study[END_REF] with V V OPO4 and V III PO4 used as intermediate precursors. The V III phosphate precursor was prepared by mixing stoichiometric amounts of V V 2O5 and NH4H2PO4 in a high energy ball mill for 90 min. This mixture was then continuously heated under pure H2 to ensure a complete reduction of V V to V III at 300 °C for 5 h (with a heating ramp of 0.5 °C/min) and at 800 °C for 5 h (with a heating ramp of 2 °C/min), before being cooled down to room temperature at 3 °C/min. VPO4 is obtained without any carbon coating, contrary to that prepared by Park et al. using carbothermal reduction conditions. V V OPO4 was obtained by the oxidation of V III PO4 in air by a thermal treatment at 700 °C for 5 h (heating/cooling rate of 3 °C/min). Na3V2(PO4)2F3-yOy compounds were finally obtained according to the following reaction, mixing stoichiometric amounts of V III and V V precursors in order to control the average oxidation state of vanadium with NaF and Na2CO3 in in order to control the F/O ratio in a high energy ball mill for 90 min, and then sintering this mixture under argon at 750 °C for 2 h (heating/cooling rate of 3 °C/min):

(3-y)NaF + y/2Na2CO3 + (2-y)V III PO4 + yV V OPO4  Na3V III 2-y(V IV O)y(PO4)2F3-y + y/2CO2 + y/4O2
As previously reported by Bianchini et al. [START_REF] Bianchini | Na3V2(PO4)2F3 revisited: a high-resolution diffraction study[END_REF] the powders were washed for around 24 h under stirring in water in order to eliminate minor impurities soluble in water such as Na3VF6 and Na5P3O10. The resulting powders were then dried under vacuum for 24 h at 80 °C. The color of the resulting powders gradually varies from dark green for the y = 0 compound to light green for y = 0.5 which is consistent with previous observations. [START_REF] Park | Tailoring a fluorophosphate as a novel 4 V cathode for lithium-ion batteries[END_REF] The SXRD patterns of the six samples thus obtained are compared in Figure 2. All the main diffraction lines can be indexed in unit cells described in the Amam space group similar to that determined by Bianchini et al. for Na3V2(PO4)2F3. [START_REF] Bianchini | Na3V2(PO4)2F3 revisited: a high-resolution diffraction study[END_REF] No superstructure peaks are observed suggesting neither anionic nor electronic order. Close inspection of the SXRD data especially for the angular ranges [9.9 -10.4°] and [24.15 -24.55°] highlights a continuous decrease of the c cell parameter with increasing y, as the (002) line shifts to higher 2 angles. In addition, the (400) and (040) reflections tend to merge as a unique peak from y = 0.4 suggesting a decrease/disappearance of the orthorhombic distortion with increasing y. The cell parameters determined for the six NVPF3-yOy samples from the profile matching refinement of their SXRD data are reported in Figure 3 and in Table 1. As expected, the y = 0 end member has similar cell parameters to those already reported by Bianchini et al. [START_REF] Bianchini | Na3V2(PO4)2F3 revisited: a high-resolution diffraction study[END_REF] for Na3V2(PO4)2F3 (a = 9.02847(3) Å, b = 9.04444(3) Å and c = 10.74666(6) Å) and once again the orthorhombic distortion with a b/a ratio of 1.002 is confirmed. The c cell parameter and unit cell volume V of Na3V2(PO4)2F3-yOy are decreasing from 10.7538 to 10.6863 Å and from 878.393 to 872.604 Å 3 respectively, in good agreement with a partial oxidation of V III to V IV due to an increasing substitution of oxygen (O 2-) for fluorine (F -). As expecting from the continuous merging of the (040) and (400) lines with increasing y, the b/a ratio decreases from 1.002 for y = 0 to 1.0002 for y = 0.5 questioning the validity of the orthorhombic distortion for the most oxidized composition (y = 0.5). It is interesting to compare these unit cell parameters to the large panel of units cells reported in the literature for compositions announced to be Na3V2(PO4)2F3, whereas they are most probably (slightly) oxidized. [START_REF] Shakoor | A combined first principles and experimental study on Na3V2(PO4)2F3 for rechargeable Na batteries[END_REF][START_REF] Chihara | Cathode properties of Na3M2(PO4)2F3 [M= Ti, Fe, V] for sodium-ion batteries[END_REF][START_REF] Bianchini | Na3V2(PO4)2F3 revisited: a high-resolution diffraction study[END_REF][START_REF] Tsirlin | Phase separation and frustrated square lattice magnetism of Na1.5VOPO4F0.5[END_REF][START_REF] Gover | The electrochemical insertion properties of sodium vanadium fluorophosphate, Na3V2(PO4)2F3[END_REF][START_REF] Song | Multifunctional dual Na3V2(PO4)2F3 cathode for both lithium-ion and sodium-ion batteries[END_REF][START_REF] Barker | Hybrid-ion a lithium-ion cell based on a sodium insertion material[END_REF][START_REF] Meins | Phase transitions in the Na3M2(PO4)2F3family (M= Al 3+, V 3+, Cr 3+, Fe 3+, Ga 3+): synthesis, thermal, structural, and magnetic studies[END_REF] The SXRD patterns exhibit narrower diffraction peaks with increasing y (0.03387(5) °  FWHM(002)  0.02853(4)° for y increasing from 0 to 0.5) and reveal thus a higher crystallinity of the powder obtained in the presence of a larger amount of sodium carbonate Na2CO3 used as sodium precursor which might act as a flux for crystalline growth. Indeed, considering the SEM micrographs given as supplementary information (see figure S1) a growth of the primary particles is observed as y is increasing from 1 to 5 µm approximatively. Careful inspection of these SXRD data reveals also the presence of negligible amounts of remaining impurities in some samples. The small intensity peak observed at 2θ = 20 ° is attributed to Na3VF6 and those observed at 2θ = 15 ° and 22 ° to Na5P3O10 (highlighted by ¤ and * respectively in Figure 2). Molar ratios of Na/V/P determined by chemical analyses carried out with ICP-OES are in good agreement with the expected chemical formula Na3V2(PO4)2F3-yOy (i.e. with 1.5Na:1V:1P as reported in Table 1). The obtained results of ICP are not affected by the small amount of impurity considering uncertainty intrinsic to the measurement.

In the following, in-depth structural characterization using synchrotron X-ray diffraction is detailed for the series of compounds Na3V2(PO4)2F3-yOy (0  y  0.5).

Structural study

The structural descriptions used in the following for Rietveld refinements derive from those reported by Le Meins et al. [START_REF] Meins | Phase transitions in the Na3M2(PO4)2F3family (M= Al 3+, V 3+, Cr 3+, Fe 3+, Ga 3+): synthesis, thermal, structural, and magnetic studies[END_REF] and Bianchini et al. [START_REF] Bianchini | Na3V2(PO4)2F3 revisited: a high-resolution diffraction study[END_REF] for the y = 0 composition and already described in Figure 1. The analysis of the y = 0.5 sample is presented in details in the following. As depicted in Figure 4 the full pattern matching refinements (limited to the determination of the profile and unit cell parameters), considering the unit cell description of NVPF2.5O0.5 either in P42/mnm or Amam space groups lead to similar agreement factors: χ² = 4.14 and 4.33 respectively. In order to reach the best structural description, systematic Rietveld refinements combined with Fourier difference map calculations were carried out to assert how the F/O ratio affects the structure.

In a first step, only the framework V2(PO4)3F3-yOy was considered in order to localize from scratch the Na + ions by the analysis of the Fourier difference maps. As expected, major residues were observed that correspond to Na + ions as presented in Figure 5. A rather good minimization of the residues is achieved considering the two structural descriptions already reported for NVPF3 in Amam [START_REF] Bianchini | Na3V2(PO4)2F3 revisited: a high-resolution diffraction study[END_REF] and P42/mnm [START_REF] Meins | Phase transitions in the Na3M2(PO4)2F3family (M= Al 3+, V 3+, Cr 3+, Fe 3+, Ga 3+): synthesis, thermal, structural, and magnetic studies[END_REF] space groups. However, significant residues are still observed between crystallographic Na sites indicating a lack of accuracy in our structural model. A further decrease of the residue accompanied with an increase of the refinement quality is achieved adding one additional site in both cases (see Figure 5). Even if there are still some small residues in the Fourier difference maps, adding additional sites did not lead to a significant improvement of the refinement quality. Note that the resulting Na + ions distributions displayed in Figure 5 are close to each other as sodium ions are located within the whole torus provided by the polyanionic framework similarly to what has been reported before for the high temperature structure of NVPF3. [START_REF] Bianchini | Na3V2(PO4)2F3 revisited: a high-resolution diffraction study[END_REF] Considering the quality of the refinement and the chemical bonds associated to the framework, the orthorhombic unit cell appears to be the most relevant to describe the structure of the y = 0.5 oxidized compound. First, the agreement factors are better for a similar number of refined parameters: χ² = 9.07 and RBragg = 5.94 in the Amam space group compared to 10.8 and 6.68 respectively in the P42/mnm space group. Besides, careful analysis of the structural parameters obtained for the two structural descriptions (gathered in Tables S1, S2 and S3) reveals that for the structure described in the tetragonal symmetry the P-O interatomic distances are significantly out the range expected for highly covalent bonds in phosphate groups (i.e. Å] and the apical ones around 1.82 Å for the shortest and 2.03 Å for the longest. These features led us to conclude that the Amam space group describes also better the structure of NVPF2.5O0.5.

As illustrated in Figure 5, the Na + ions are distributed among four sites in NVPF2.5O0.5. Na( 1) is localized at the center of a pyramid with an occupancy around 85 %, whereas the three others are in pyramidal (Na(2) and Na(4)) or in capped prismatic (Na(3)) sites but not at their center. Because of their vicinity, to minimize the electrostatic repulsions, neighboring Na(2), Na(3) and Na(4) positions cannot be occupied simultaneously. Besides, for the same reason, the more distant a Na site is from its equivalent position, the more occupied it is.

In conclusion, crystal structure Rietveld refinements of the whole series of compositions Na3V2(PO4)2F3-yOy (0  y  0.5) have been carried out in the Amam space group based on the structure proposed by Bianchini et al. [START_REF] Bianchini | Na3V2(PO4)2F3 revisited: a high-resolution diffraction study[END_REF] with one additional sodium site, Na(4). In every studied compositions it turns out that this additional site increases significantly the quality of the refinement, with its occupancy increasing up to 16 % for y = 0.5.

Oxygen substitution for fluorine is associated to a decrease of the c cell parameter. As shown in the inset of Figure 3, the c parameter is composed of two components (c = 2h + d), that are the height of the bioctahedra (h) and the distance between the two terminal fluorine (or oxygen) anions (d). [START_REF] Park | A Family of High-Performance Cathode Materials for Na-ion Batteries, Na3(VO1-xPO4)2F1+2x (0≤ x≤ 1): Combined First-Principles and Experimental Study[END_REF] From y = 0 to 0.5, 2h varies from 7.883(2) Å to 7.687(3) Å whereas d varies from 2.871(2) Å to 2.999(3) Å. Partial oxygen substitution for fluorine is compensated by a partial oxidation of V 3+ to V 4+ and thus by the formation of covalent vanadyl-type bonds (V IV O) 2+ at the apex of the bi-octahedra, shorter than the ionic bonds V III -F: this evolution explains the decrease of the h and c parameters (evolution of interatomic distances within vanadium environment are given in Figure S2 andS3). The increase of the d parameter is explained by the increase of the distances between the Na + ions and the apex of the bi-octahedra as displayed in Figure 1, in average from 2.42 to 2.50 Å. That increase is coming from the antagonist effect: the more covalent (i.e. the shorter) the bond V-(O,F)apex the more ionic (i.e. the longer) the bond Na-(O,F) is. Nevertheless, based on this structural characterization only, no conclusion can be made concerning possible impact of oxygen substitution for fluorine on the sodium mobility within this framework. Indeed, no major changes in the sodium sites occupancy and in the isotopic thermal displacement parameters (Biso) are observed.

Spectroscopic study X-ray absorption near edge structure (XANES):

X-ray absorption spectra were recorded at the vanadium K-edge in order to probe changes on the vanadium oxidation state and local structure as function of the partial oxygen substitution for fluorine in the Na3V2(PO4)2F3-yOy (0  y  0.5) series of compounds. Figure 6 displays the spectra recorded for y = 0, 0.1, 0.3, 0.4 and 0.5 in which the pre-edge and the main peak are localized at 5470 and 5485 eV respectively. The pre-edge features arise from 1s to 3d forbidden transitions that become allowed by orbital 3d-p hybridizations [START_REF] Wong | K-edge absorption spectra of selected vanadium compounds[END_REF] while their energy positions and intensities distributions are linked to the electronic structure and the local structural environment of the probed element. The strong main-peak arises from the 1s → 4p dipole allowed transition whereas the features at higher energies are strongly influenced by the local geometry around the absorber mainly determined by multiple scattering contributions. [START_REF] Stizza | Structure of oriented V2O5 gel studied by polarized x-ray-absorption spectroscopy at the vanadium K edge[END_REF][START_REF] Šipr | Geometric and electronic structure effects in polarized V K-edge absorption near-edge structure spectra of V2O5[END_REF][START_REF] Mansour | In situ XAS investigation of the oxidation state and local structure of vanadium in discharged and charged V2O5 aerogel cathodes[END_REF] While there is a continuous shift towards higher energy for the rising edge which is in good agreement with the oxidation of vanadium, significant changes are also observed in the pre-edge. From the insets given in Figure 6, one can observe that at y = 0 the pre-peak is composed by three features located at 5466, 5468, and 5469.5 eV characteristic of the V 3+ state. [START_REF] Serras | Electrochemical Na Extraction/Insertion of Na3V2O2x(PO4)2F3-2x[END_REF] By increasing y, a feature observed at higher energy (5469.5 eV) arises which is characteristic of a V 4+ state. [START_REF] Serras | Electrochemical Na Extraction/Insertion of Na3V2O2x(PO4)2F3-2x[END_REF] Moreover, a constant growth of the global intensity of the pre-edge is observed as a function of y, in good agreement with an increase of the vanadium oxidation state and especially with the distortion of the local symmetry around the absorber [START_REF] Wong | K-edge absorption spectra of selected vanadium compounds[END_REF] that leads to an increasing 3d-4p orbital mixing, and thus to a larger overlap of the 3d vanadium orbital with the 2p oxygen orbitals. These spectroscopic signatures are fully consistent with previous observations made for highly oxidized compositions such as Na3V2(PO4)2F3-yOy (where y = 1.6 [START_REF] Park | A new high-energy cathode for a Na-ion battery with ultrahigh stability[END_REF][START_REF] Serras | Electrochemical Na Extraction/Insertion of Na3V2O2x(PO4)2F3-2x[END_REF] and y = 2.0 [START_REF] Park | A Family of High-Performance Cathode Materials for Na-ion Batteries, Na3(VO1-xPO4)2F1+2x (0≤ x≤ 1): Combined First-Principles and Experimental Study[END_REF] ) and also with related compounds such as VOPO4•2H2O. [START_REF] Poumellec | Experimental and theoretical studies of dipole and quadrupole contributions to the vanadium K-edge XANES for VOPO4⋅2H2O xerogel[END_REF][START_REF] Chauvel | In Spectroscopic Study of VOPO4⋅2H2O Intercalation Compounds[END_REF] NMR Figure 7 illustrates the [START_REF] Meins | Phase transitions in the Na3M2(PO4)2F3family (M= Al 3+, V 3+, Cr 3+, Fe 3+, Ga 3+): synthesis, thermal, structural, and magnetic studies[END_REF] Na MAS NMR spectrum of NVPF3 recorded at 132.3 MHz under a 11.75 T field. Both nuclear dipolar and first order quadrupolar interactions are partially suppressed by MAS.

However for nuclei with a strong quadrupolar constant like [START_REF] Meins | Phase transitions in the Na3M2(PO4)2F3family (M= Al 3+, V 3+, Cr 3+, Fe 3+, Ga 3+): synthesis, thermal, structural, and magnetic studies[END_REF] Na (I = 3/2) located in a non-symmetrical site the second order quadrupolar interaction is affected but not suppressed by MAS, possibly causing some residual broadening to the central transition. The isotropic shift of the [START_REF] Meins | Phase transitions in the Na3M2(PO4)2F3family (M= Al 3+, V 3+, Cr 3+, Fe 3+, Ga 3+): synthesis, thermal, structural, and magnetic studies[END_REF] Na signal is mainly governed by the Fermi contact interaction in such paramagnetic phases; i.e. it depends on the electronic spin density at the [START_REF] Meins | Phase transitions in the Na3M2(PO4)2F3family (M= Al 3+, V 3+, Cr 3+, Fe 3+, Ga 3+): synthesis, thermal, structural, and magnetic studies[END_REF] Na nucleus.

The NVPF3 spectrum exhibits two major signals at 91 and 138 ppm with very different magnitude and a set of spinning side bands for each. Liu et al. [START_REF] Liu | Local Structure and Dynamics in the Na Ion Battery Positive Electrode Material Na3V2(PO4)2F3[END_REF] reported a similar spectrum and assigned these peaks to the partially filled Na(2) site and to the fully occupied Na(1) site respectively based on the tetragonal structure described in the space group P42/mnm and reported by Le Meins et al. [START_REF] Meins | Phase transitions in the Na3M2(PO4)2F3family (M= Al 3+, V 3+, Cr 3+, Fe 3+, Ga 3+): synthesis, thermal, structural, and magnetic studies[END_REF] As discussed in the following a different assignment for these signals is proposed.

Figure 7 shows the [START_REF] Meins | Phase transitions in the Na3M2(PO4)2F3family (M= Al 3+, V 3+, Cr 3+, Fe 3+, Ga 3+): synthesis, thermal, structural, and magnetic studies[END_REF] Na MAS NMR spectra of the complete series of NVPF3-yOy compounds from y = 0 (NVPF3) to y = 0.5 (NVPF2.5O0.5). In addition to the 138 and 91 ppm signals, a third signal grows around 50 ppm when the amount of oxygen increases. In the meantime, the 138 ppm signal decreases in intensity and broadens (and slightly shifts toward higher values corresponding to more paramagnetic shifts) and the peak at 91 ppm increases and also shifts towards more paramagnetic shifts. The increase of oxygen content in the lattice induces the formation of V 4+ ions. Since the V 4+ (t2g 1 ) ion generally causes a weaker Fermi contact shift than V 3+ (t2g 2 ) as it is less paramagnetic, the signals observed at 138, 91 and 50 ppm are respectively assigned to Na interacting with two V 3+ , with one V 3+ and one V 4+ , and with two V 4+ (all Na sites being surrounded by two V ions). In our study these pairs are respectively depicted as peak 1, peak 2 and peak 3 in Figure 7. Note that the effect of one V 4+ in the environment of Na instead of one V 3+ is a decrease of the shift by around 45 ppm each time. This assignment is in agreement with the one reported by Serras et al. [START_REF] Serras | Electrochemical Na Extraction/Insertion of Na3V2O2x(PO4)2F3-2x[END_REF] for the mixed F/O composition Na3V2(PO4)2F1.4O1.6 (y = 1.6). Therefore, our series of spectra strongly suggests that the signal observed at 91 ppm in NVPF3 actually denotes already the presence of small amount of unexpected oxygen defects in the pristine compound induced either by an incomplete reduction of V III PO4 during the synthesis of the precursor or a partial oxidation of the vanadium (or a lack of fluorine) during the annealing of NVPF3. Thus, the isotropic signals recorded for the sodium sites would lead to the single broad signal observed around 138 ppm. Indeed, all sodium sites have a very similar environment in terms of V 3+ cations (V-Na interatomic distances are in the range [3.17 -3.69 Å]), suggesting that they all exhibit very close Fermi contact shifts (see Figure S8 in supplementary information). This is actually confirmed by DFT calculations of the Fermi contact shift of each sodium in the structure using the VASP code with both GGA and GGA+U methods (see Table S4 in supplementary information). The actual quantity of oxygen defect present in the pristine NVPF3 material cannot be determined accurately from [START_REF] Meins | Phase transitions in the Na3M2(PO4)2F3family (M= Al 3+, V 3+, Cr 3+, Fe 3+, Ga 3+): synthesis, thermal, structural, and magnetic studies[END_REF] Na MAS NMR since one should take into account the intensities in all spinning sidebands that are widely spread around the isotropic signals. to what has been observed in [START_REF] Meins | Phase transitions in the Na3M2(PO4)2F3family (M= Al 3+, V 3+, Cr 3+, Fe 3+, Ga 3+): synthesis, thermal, structural, and magnetic studies[END_REF] Na MAS NMR, two signals (at 5983 and 4500 ppm) are observed in the spectrum of NVPF3. These two signals were also reported by Liu et al. [START_REF] Liu | Local Structure and Dynamics in the Na Ion Battery Positive Electrode Material Na3V2(PO4)2F3[END_REF] who assigned the resonance at 5932 ppm to one phosphorous site (again in the assumed P42/mnm space group), and the resonance centered at 4500 ppm to the other phosphorous site. In fact, in the actual structure (described in the Amam space group), there is only one phosphorous site which shares corners with four VO4F2 polyhedra (see Figure 1 and Figure S9 in supplementary information). Again, based on the analysis of the NVPF3-yOy (0 ≤ y ≤ 0.5) series another assignment of the 31 P MAS NMR signals is proposed: the five peaks observed at 6097, 4583, 3058, 1565, and ~ 0 ppm are assigned respectively to phosphorous environments with only adjacent V 3+ ions (peak 1), one V 4+ and three V 3+ ions (peak 2), two V 4+ and two V 3+ ions (peak 3), three V 4+ and one V 3+ ions (peak 4), and only adjacent V 4+ ions (peak 5). Indeed, the effect of one V 4+ in the environment of phosphorous instead of one V 3+ leads to a decrease of the shift by around 1500 ppm each time. In very good agreement with the additional [START_REF] Meins | Phase transitions in the Na3M2(PO4)2F3family (M= Al 3+, V 3+, Cr 3+, Fe 3+, Ga 3+): synthesis, thermal, structural, and magnetic studies[END_REF] Na NMR signal discussed above, our series of spectra then strongly suggests that NVPF3 already exhibits some unexpected oxygen defects in the pristine material.

Figure 8 represents the experimental relative amount of the 5 possible [START_REF] Poumellec | Experimental and theoretical studies of dipole and quadrupole contributions to the vanadium K-edge XANES for VOPO4⋅2H2O xerogel[END_REF] P environments (see Figures S4 to S7 in supplementary information for the corresponding fit of spectra into individual components using the DMFit code), compared with those expected based on a statistical distribution of V 4+ ions in NVPF3-yOy (0 ≤ y ≤ 0.5). The theoretical probabilities were calculated using the binominal distribution (cf. Equation 1) which gives the probability for having k occurrences among n possibilities (k = 0, 1, 2, 3, or 4), the probability of each occurrence being p. Here, each phosphorus is surrounded by 4 V (n = 4). Each V has a probability p of being V 4+ . For each compound the probability p is calculated by p = y/z, where y is the oxygen content in NVPF3-yOy (y = 0.1, 0.2, 0.3, 0.4, and 0.5) and z = 2 (the total number of vanadium in the unit cell). Equation 1As shown in Figure 8, the experimental intensities distribution does not follow the theoretical one if the repartition of V 3+ and V 4+ ions would have been statistical around each phosphorous: phosphorous nuclei appear to be experimentally surrounded by more V 4+ than expected. A possible explanation could be that locally a rapid electronic hopping occurs between V n+ ions. So in average the P nuclei would see more V 4+ ions that theoretically expected.

Electrochemical properties

Figure 9 shows the voltage-composition and the associated derivative curves obtained for Na3-xV2(PO4)2F3-yOy (0 < y < 0.5) during their second cycle in Na batteries at the rate of C/20. These electrochemical data are similar to each other with two main voltage domains around 3.65 and 4.15 V vs Na + /Na and a voltage jump around x = 2 which suggests the presence of a stable intermediate phase for this composition regardless the y value.

Previous studies 11-12, 14, 24 of Na3-xV2(PO4)2F3-yOy (0 < y < 2) focused on more oxidized compositions (y > 1.5) have demonstrated that the reversible capacity is around 125 mAh/g whatever the fluorine content: as supported by first-principles calculations the extraction of only two Na + ions is possible within the voltage range 2 -4.5 V vs Na + /Na, imposed by the limited stability of electrolytes such as NaPF6 (1M) in EC:DMC (1:1) (3wt% FEC). [START_REF] Park | A Family of High-Performance Cathode Materials for Na-ion Batteries, Na3(VO1-xPO4)2F1+2x (0≤ x≤ 1): Combined First-Principles and Experimental Study[END_REF] Parasitic reactions induced by the degradation of the electrolyte during the first cycles (see Figure S10 for more detailed information), and especially the modification of the Na metal counter electrode's operating voltage due to the formation of unstable passivation layers at its surface [START_REF] Rudola | A new phenomenon in sodium batteries: Voltage step due to solvent interaction[END_REF][START_REF] Dugas | Optimization of Na-Ion Battery Systems Based on Polyanionic or Layered Positive Electrodes and Carbon Anodes[END_REF] lead to a lack of accuracy in the quantitative evaluation of the reversible capacity delivered by Na//NVPF3-yOy half cells. On the contrary, studies performed in full Na-ion cells for NVPF3 vs hard carbon have already demonstrated truly excellent reversibility and cyclability. [START_REF] Dugas | Optimization of Na-Ion Battery Systems Based on Polyanionic or Layered Positive Electrodes and Carbon Anodes[END_REF][START_REF] Ponrouch | Towards high energy density sodium ion batteries through electrolyte optimization[END_REF] It is now well established that, on the contrary to what is true for the lithium technology, electrochemical tests are required in full Na-ion cells to obtain confident evaluation of the electrochemical performance associated to a given active material. [START_REF] Rudola | A new phenomenon in sodium batteries: Voltage step due to solvent interaction[END_REF][START_REF] Dugas | Optimization of Na-Ion Battery Systems Based on Polyanionic or Layered Positive Electrodes and Carbon Anodes[END_REF] To address these performances studies in full cells versus hard carbon are currently in progress for NVPF3-yOy with y > 0 and will be discussed in a forthcoming paper.

Here, the discussion of the electrochemical signatures will be limited to their relationship with the materials' compositions and structures in order to reconcile all the apparent discrepancies reported in literature.

𝐶 (𝑛, 𝑘) 𝑝 𝑘 (1 -𝑝) (𝑛-𝑘) = ( 𝑛! 𝑘!(𝑛-𝑘)! ) 𝑝 𝑘 (1 -𝑝) (𝑛-𝑘) As y increases (i.e. as the fluorine content decreases) the average potential of the cell continuously decreases, as highlighted by the shift of the derivative peaks to lower voltages on Figure 9. The average voltage of the cell varies from 3.89 V for y = 0 to 3.83 V for y = 0.5. It is ascribed to the formation of highly covalent vanadyl-type bonds (V=O) 2+ at the apex of the bi-octahedra V2O8F3-yOy that "continuously" replace the more ionic V-F bonds as y increases. In fact, a more covalent environment for the transition metal ion raises the energy of its antibonding levels closer to the Fermi energy of sodium and thus induces a decrease in voltage for the involved redox couple vs Na + /Na. Even if the redox couples involved in the electrochemical processes are different since oxygen substitution for fluorine induces a partial oxidation of vanadium from the trivalent state to the tetravalent state, the voltage of the whole series of compounds remains quite similar. Indeed, as already observed for the Tavorite phases LiV III PO4F and LiV IV PO4O [START_REF] Ateba Mba | Synthesis and crystallographic study of homeotypic LiVPO4F and LiVPO4O[END_REF] the impact of the vanadyl-type bond is major and makes that the redox couple V 3+ /V 4+ apparently operates at higher voltage (+ 0.3 V) in LiVPO4F than the "redox couple" V 4+ /V 5+ in LiVPO4O. In fact, V 4+ /V 5+ is actually (V=O) 2+ /(V=O) 3+ in the case of this oxyphosphate.

The electrochemical voltage-composition data differ significantly in their shape depending on the composition in oxygen: the more oxidized the compound, the "smoother" their cycling profiles. In the low voltage domain (between 3.5 and 3.8 V vs Na + /Na), for y = 0 and 0.1 two sharp peaks are clearly observed around 3.7 V in the derivative data whereas for the more oxidized compounds only one broader and asymmetric peak is observed. In the high voltage domain (between 3.9 and 4.3 V), a similar behavior is observed with an evolution from sharp peaks around 4.2 V for y = 0 to broader peaks for more oxidized compositions. This emphasizes that a small change in their initial compositions and thus in their vanadium average oxidation states has a major impact on the phase diagram stabilized upon cycling. It evolves from a complex series of biphasic domains and solid solutions for y = 0, as determined for NVPF3 by Bianchini et al. [START_REF] Bianchini | Comprehensive Investigation of the Na3V2(PO4)2F3 -NaV2(PO4)2F3 System by Operando High Resolution Synchrotron X-ray Diffraction[END_REF] to an extended solid solution for y > 0.2. Complementary in situ and operando experiments are in progress in order to get more in-depth insights in the phase diagrams stabilized upon cycling as function of y (i.e. the oxygen substitution ratio for fluorine).

Another noteworthy feature of the electrochemical performances is the decrease of the hysteresis between charge and discharge as y increases. This could be qualitatively attributed to better transport properties (ionic and electronic) favored by mixed valence V III /V IV in the pristine material that might favor electronic transfer.

To conclude, this study of a series of partially oxidized compositions Na3-xV2(PO4)2F3-yOy (0 < y < 0.5) allows to get a better insight in the incoherency reported throughout the literature. For example, Liu et al. [START_REF] Liu | Local Structure and Dynamics in the Na Ion Battery Positive Electrode Material Na3V2(PO4)2F3[END_REF] reported, for a composition announced to be NVPF3 a solid solution mechanism all along the electrochemical process. However, the cell parameters a = b = 9.04 Å and c = 10.735 Å given suggest a y = 0.15 composition, in good agreement with a solid solution reaction upon electrochemical cycling, according to the results we obtained. Another example is that of Song et al. [START_REF] Song | Multifunctional dual Na3V2(PO4)2F3 cathode for both lithium-ion and sodium-ion batteries[END_REF] who reported NVPF3 with cell parameters of a = b = 9.05 Å and c = 10.679 Å. According to our results this material is strongly oxidized and such as y > 0.5; this explains why the average voltages are as low as 4 and 3.5 V vs Na + /Na for the two composition domains.

Conclusion

A series of Na3V2(PO4)2F3-yOy compositions with 0 ≤ y ≤ 0.5 has been successfully synthesized by controlling the oxidation state of the VPO4 and VOPO4 precursors, as well as the F/O ratio using the stoichiometric mixture (3-y)NaF/(y/2)Na2CO3. An in-depth structural characterization has revealed that all of them are isostructural and crystallize in the orthorhombic space group Amam with an increasing disorder in the Na + ions distribution. Indeed, an additional crystallographic site with a significant occupancy (up to 16 % for y = 0.5) is required to fully describe the localization of the Na + ions within the channels of this three-dimensional framework of the oxidized compound. When Na3V2(PO4)2F3-yOy is partially oxidized the sodium distribution become "mid-way" between those obtained at room temperature and at high temperature for Na3V2(PO4)2F3 (y = 0) by Bianchini et al. [START_REF] Bianchini | Na3V2(PO4)2F3 revisited: a high-resolution diffraction study[END_REF] Combination of XANES and NMR spectroscopies has confirmed the charge compensation of oxygen substitution for fluorine is achieved by the continuous oxidation of vanadium and the continuous formation of vanadyltype bonds, but it has also revealed a tendency to adopt a non-statistical V 4+ distribution within the framework, as well as the presence of a few V 4+ -type defects already in the compound considered to be "non-oxidized". As already shown for other materials of interest for batteries such as LiCoO2 [START_REF] Levasseur | Oxygen vacancies and intermediate spin trivalent cobalt ions in lithiumoverstoichiometric LiCoO2[END_REF] and LiVPO4F [START_REF] Messinger | Revealing Defects in Crystalline Lithium-Ion Battery Electrodes by Solid-State NMR: Applications to LiVPO4F[END_REF] NMR spectroscopy as a local probe of the bulk appears often as the technique of choice to identify the presence of defects. Indeed, single [START_REF] Meins | Phase transitions in the Na3M2(PO4)2F3family (M= Al 3+, V 3+, Cr 3+, Fe 3+, Ga 3+): synthesis, thermal, structural, and magnetic studies[END_REF] Na and 31 P MAS NMR signals are in fact associated to the different crystallographic sites observed for Na and P in the structure of Na3V2(PO4)2F3 (y = 0), the additional signals at 91 ppm (for [START_REF] Meins | Phase transitions in the Na3M2(PO4)2F3family (M= Al 3+, V 3+, Cr 3+, Fe 3+, Ga 3+): synthesis, thermal, structural, and magnetic studies[END_REF] Na) and at 5983 ppm (for 31 P) being due to V 4+ defects in their close environments. Finally, this study has allowed, considering a partial oxygen substitution for fluorine, to understand all the apparent discrepancies reported in the literature for Na3V2(PO4)2F3 (y = 0). With an increase of oxygen content, the electrochemical signature of Na3V2(PO4)2F3-yOy with 0 ≤ y ≤ 0.5 evolves from a complex phase diagram with two voltage plateaus for y = 0 to solid solution type reactions with a "S-shape" for the two voltage domains for y = 0.5. In fact, most of the materials reported as Na3V2(PO4)2F3 in the literature are in fact partially oxidized, with a decrease of the average voltage and thus of the theoretical energy density.

Table caption

Table 1: Cell parameters determined from the profile matching of SXRD data considering a unit cell described in the orthorhombic Amam space group. The corresponding chemical analyses performed by ICP-OES are also given for information.

Figure captions

  [1.5 -1.6 Å]): this result supports strongly the description in the orthorhombic symmetry. Indeed, in the P42/mnm unit cell two PO4 groups are present, the first one being fully isotropic with a single P(1)-O(1) interatomic distance of 1.521(5) Å and the second one being highly distorted with two short P(2)-O(2) interatomic distances of 1.459(5) Å and two long P(2)-O(3) interatomic distances of 1.642(6) Å. For comparison, in the Amam unit cell a single PO4 group is observed with two interatomic distances P(1)-O(1) of 1.534(4) Å and P(1)-O(2) of 1.528(4) Å, consistent with the formation of a highly covalent anionic group. The vanadium environment is very similar in the two structural descriptions, with the equatorial interatomic distances V-O in the typical range of [1.97 -2.02

Figure 8

 8 Figure 8 shows the 31 P MAS NMR spectra of NVPF3-yOy at 40.6 MHz under a 2.35 T field. Similarly

Figure 1 :

 1 Figure 1: Top: Three dimensional framework of NVPF3-yOy where the dark blue atoms emphasize the substitution site of oxygen for fluorine. In red are highlighted the (a,b) planes where the Na + ions are contained -Bottom: two possible Na distributions depending on the space group considered to describe the structure, the fraction of filling in red of the Na atom highlights the partial occupancy of the crystallographic site.

Figure 2 :

 2 Figure 2: Top: comparison of the experimental synchrotron XRD patterns recorded for the six samples Na3V2(PO4)2F3-yOy (0 < y < 0.5) -Bottom angular ranges [9.8 -10.4°] and [24.15 -24.55°] are given for easier comparison. The indexation of the diffraction lines is given in the Amam space group reported for Na3V2(PO4)2F3 by Bianchini et al.

Figure 3 :

 3 Figure 3: Changes in the structural parameters as function of the oxygen substitution for fluorine in NVPF3-yOy considering the description of the structure in the orthorhombic unit cell (Amam).

Figure 4 :

 4 Figure 4: Profile matching of SXRD data obtained for the y = 0.5 compound using P42/mnm and Amam space groups.

Figure 5 :Figure 6 :

 56 Figure 5: Fourier difference maps and associated sodium distribution in the y= 0.5 sample obtained with P42/mnm (top) and Amam (bottom) space groups

Figure 7 :Figure 8 :

 78 Figure 7: Top: 23 Na MAS spectra NMR of Na3V2(PO4)2F3 recorded with a 30 kHz spinning rate and a 11.75 T magnetic field -Bottom: comparison of 23 Na MAS NMR spectra for Na3V2(PO4)2F3-xOx (0 < y < 0.5)

Figure 9 :

 9 Figure 9: Top: second voltage-composition curve of Na3-xV2(PO4)2F3-yOy (0 < y < 0.5) cycled at C/20 between 2.5 and 4.3 V -Bottom: associated derivative curves

Table 1 .

 1 Cell parameters determined from the profile matching of SXRD data considering a unit cell described in the orthorhombic Amam space group. The corresponding chemical analyses performed by ICP-OES are also given for information.

Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8

 12345678 Figure 1

Figure 9

 9 Figure 9

Corresponding author (L. Croguennec): Laurence.Croguennec@icmcb.cnrs.fr

Acknowledgments

The authors thank Philippe Dagault, Cathy Denage and Laetitia Etienne at ICMCB for technical assistance, Rénald David at LRCS for the preparation of the electrolyte, as well as ALBA (Barcelona, Spain) for Synchrotron X-ray diffraction and absorption experiments on MSPD and CLAESS beamlines. The authors also acknowledge RS2E for the funding of TB's postdoctoral fellowship. This project has received funding from Région Aquitaine, the French National Research Agency (STORE-EX Labex Project ANR-10-LABX-76-01 and SODIUM Descartes project ANR-13-RESC-0001-02), and the European Union's Horizon 2020 research and innovation programme under grant agreement No 646433-NAIADES. The Mésocentre de Calcul Intensif Aquitain (MCIA) and the modelling center of ISM are acknowledged for computing facilities.

Supporting Information

Additional information on the powder morphology, structure (SXRD and NMR) and electrochemical characterization. This material is available free of charge via the Internet at http://pubs.acs.org/.