MD Amandine Crombé
email: a.crombe@bordeaux.unicancer.fr

Michèle Kind

David Fadli

François Le Loarer

Antoine Italiano

Xavier Buy

Olivier Saut

Intensity Harmonization Techniques Influence Radiomics Features and Radiomics-based Predictions in Sarcoma Patients

Intensity harmonization techniques (IHT) are mandatory to homogenize multicentric

MRIs before any quantitative analysis because signal intensities (SI) do not have standardized units. Radiomics combine quantification of tumors' radiological phenotype with machine-learning to improve predictive models, such as metastasticrelapse-free survival (MFS) for sarcoma patients. We post-processed the initial T2weighted-imaging of 70 sarcoma patients by using 5 IHTs and extracting 45 radiomics features (RFs), namely: classical standardization (IHTstd), standardization per adipose tissue SIs (IHTfat), histogram-matching with a patient histogram (IHTHM.1), with the average histogram of the population (IHTHM.All) and plus ComBat method (IHTHM.All.C), which provided 5 radiomics datasets in addition to the original radiomics dataset without IHT (No-IHT). We found that using IHTs significantly influenced all RFs values (p-values: <0.0001-0.02). Unsupervised clustering performed on each radiomics dataset showed that only clusters from the No-IHT, IHTstd, IHTHM.All, and IHTHM.All.C datasets significantly correlated with MFS in multivariate Cox models (p= 0.02, 0.007, 0.004 and 0.02, respectively). We built radiomics-based supervised models to predict metastatic relapse at 2-years with a training set of 50 patients. The models performances varied markedly depending on the IHT in the validation set (range of AUROC from 0.688 with IHTstd to 0.823 with IHTHM.1). Hence, the use of intensity harmonization and the related technique should be carefully detailed in radiomics post-processing pipelines as it can profoundly affect the reproducibility of analyses.

Introduction

Radiomics has now become an intensive field of research, based on the extraction and mining of several quantitative variables, which are referred to as radiomics features (RFs). RFs enable to screen extensively the shape and texture of objects of interests within medical images of any modality. In oncology, RFs have been used in predictive models based on machine-learning classifiers to discriminate benign and malignant lesions, identify molecular alterations in tumors, predict patients' outcome, and even build radio-genomics signatures [START_REF] Limkin | Promises and challenges for the implementation of computational medical imaging (radiomics) in oncology[END_REF][START_REF] Lambin | Radiomics: the bridge between medical imaging and personalized medicine[END_REF][START_REF] Gillies | Radiomics: Images Are More than Pictures, They Are Data[END_REF] . Regarding sarcomas, radiomics have improved predictions of grading, prognosis and response to chemotherapy/radiotherapy, based on CT-scans, structural MRI alone or combined with positron emission tomography, dynamic-contrast enhanced or diffusion MRI [START_REF] Vallières | A radiomics model from joint FDG-PET and MRI texture features for the prediction of lung metastases in softtissue sarcomas of the extremities[END_REF][START_REF] Peeken | CT-based radiomic features predict tumor grading and have prognostic value in patients with soft tissue sarcomas treated with neoadjuvant radiation therapy[END_REF][START_REF] Peeken | Tumor grading of soft tissue sarcomas using MRI-based radiomics[END_REF][START_REF] Spraker | MRI Radiomic Features Are Independently Associated With Overall Survival in Soft Tissue Sarcoma[END_REF][START_REF] Crombé | T2 -based MRI Delta-radiomics improve response prediction in softtissue sarcomas treated by neoadjuvant chemotherapy[END_REF][START_REF] Corino | Radiomic analysis of soft tissues sarcomas can distinguish intermediate from high-grade lesions[END_REF] .

Though one aim of radiomics is to provide an objective assessment of tumor phenotype, several studies have shown the influence of pre-and post-processing factors on the value of RFs [START_REF] Berenguer | Radiomics of CT Features May Be Nonreproducible and Redundant: Influence of CT Acquisition Parameters[END_REF][START_REF] Crombé | Influence of temporal parameters of DCE-MRI on the quantification of heterogeneity in tumor vascularization[END_REF][START_REF] Bogowicz | Stability of radiomic features in CT perfusion maps[END_REF][START_REF] Buch | Quantitative variations in texture analysis features dependent on MRI scanning parameters: A phantom model[END_REF][START_REF] Caramella | Can we trust the calculation of texture indices of CT images? A phantom study[END_REF][START_REF] Ford | Quantitative Radiomics: Impact of Pulse Sequence Parameter Selection on MRI-Based Textural Features of the Brain[END_REF] . These findings question the validity and reproducibility of inter-site radiomics studies. This issue is even more prominent with MRI because of the absence of standard intensity scale. Therefore, signal intensities (SIs) lack of comparability, even for a given sequence acquired on the same MRscanner. Unlike gray-levels discretization or voxel-size standardization, technical details regarding homogeneization of SIs are frequently missing in materials and methods and, even when performed, assessment of the optimal setting for the MRI dataset of interest is often lacking.

Some intensity harmonization techniques (IHTs) have been proposed in the neuroimaging literature to enable robust analysis of structural and diffusion MRIs across different radiological centers and longitudinally, but most cannot be transposed to sarcomas because of the heterogeneity of tissues surrounding sarcomas, which are ubiquitous tumors. Available IHTs regarding non-brain MRI are scarce. The most frequently encountered are global scaling (e.g. where SIs values are centered by removing the mean and scaled to unit variance, or transformed to range between 0 and 1), ratio with SIs of a healthy tissue that is not affected by the disease (for instance adipose tissue or muscle in musculoskeletal imaging), or histogram-matching (HM, where the intensity histograms are transformed to match a reference intensity histogram) [START_REF] Wang | Correction for variations in MRI scanner sensitivity in brain studies with histogram matching[END_REF][START_REF] Nyúl | On standardizing the MR image intensity scale[END_REF][START_REF] Nyúl | New variants of a method of MRI scale standardization[END_REF] . In addition, Orlhac et al. have recently shown that ComBat harmonization method, which was initially described in genomics to remove batch effect, could correct non biological differences related to the type of scanners [START_REF] Orlhac | Validation of A Method to Compensate Multicenter Effects Affecting CT Radiomics[END_REF] .

Though the authors focused on CT-scanner, ComBat may help reduce unwanted variations in MRI-based radiomics datasets as well.

Thus, our aim was to investigate how the IHT could influence MRI-based radiomics analyses in a uniformly-treated cohort of soft-tissue sarcomas (STS) patients with which the presence of intra-tumor heterogeneity on initial T2-weighted-imaging (-WI) has been previously correlated with metastatic-relapse free survival (MFS) [START_REF] Vallières | A radiomics model from joint FDG-PET and MRI texture features for the prediction of lung metastases in softtissue sarcomas of the extremities[END_REF][START_REF] Peeken | Tumor grading of soft tissue sarcomas using MRI-based radiomics[END_REF][START_REF] Crombé | Soft-Tissue Sarcomas: Assessment of MRI Features Correlating with Histologic Grade and Patient Outcome[END_REF] . To do so, to comprehensively assess the impact of IHT on radiomics analyses, we investigated its influence on: (i) the RFs values; (ii) the prognostic value of radiomics-based unsupervised classifications; and (iii) the performances of supervised classifiers to predict early metastatic relapses.

Methods

Study population

This study was approved by the local Research Ethics Committee of Bergonié Insitute (Bordeaux, France) according to good clinical practices and applicable laws and regulations. All methods were performed in accordance with the relevant guidelines and regulations. The need for written informed consent was waived because of its retrospective nature.

Patients were consecutively recruited as they fulfilled the following inclusion criteria:

MRI acquisition

The baseline MRI examinations were acquired on 3 different 1. After anonymizing MRIs, the postprocessing was performed with R (version 3.5.3, Vienna, Austria) by using the "oro.nifti", "ANTsR" and "extranstr" packages [START_REF] Muschelli | Neuroconductor: an R platform for medical imaging analysis[END_REF] .

First, T2-WIs were converted to nifti format. Voxel size resampling (with b-spline interpolator) and N4 bias field correction were applied to obtain a common spatial resolution of 1 x 1 x 4 mm 3 and to correct non-uniform intensities [START_REF] Tustison | N4ITK: improved N3 bias correction[END_REF] .

Second, a senior radiologist (A.C., with 4 years of experience in sarcoma imaging) manually segmented the whole tumor volume, slice-by-slice, by using LIFEx freeware (version 5.10, Inserm, Orsay, France, www.lifexsoft.org) [START_REF] Nioche | LIFEx: A Freeware for Radiomic Feature Calculation in Multimodality Imaging to Accelerate Advances in the Characterization of Tumor Heterogeneity[END_REF] . The radiologist had access to all the other MRI sequences to adjust the boundary of the segmentation if needed. The volumes of interests were all validated by a second senior radiologist (M.K., with 28 years of experience in sarcoma imaging).

Third, 4 IHTs were applied in parallel to the whole imaging dataset in order to harmonize the SIs of the T2-WI, providing 4 harmonized datasets, i.e.:

(1) IHTfat, which consisted in dividing all the SIs of a given T2-WI by the mean SI of adipose tissue on that T2-WI, as follows:

SI(x, y, z) )*+,-./ = SI(x, y, z) mean(SI(adipose tissue))

Where x, y and z are the coordinates of a voxel. To do so, the first senior radiologist segmented a volume of at least 10 cm 3 of pure normally-appearing adipose tissue on each T2-WI in order to extract the mean SI per patient.

(2) IHTstd, which consisted in normalizing the SIs of a T2-WI according to the minimum and maximum of all voxels included in this T2-WI, as follows: SI(x, y, z) )*+,=/> = SI(x, y, z) -min (@AB) max(@AB) -min (@AB)

(3) IHTHM.

Radiomics features extraction

The tumor volumes were then propagated on the 4 post-processed imaging datasets

ComBat compensation

We applied the ComBat-Harmonization function in R (https://github.com/fortin1/ComBatHarmonization) to the 45 RFs that were extracted from the IHTHM.All dataset with a non-parametric setting in order to remove unwanted noise due to technical variations between the 3 MR-systems of the study while preserving biological variability, and notably when there are only a few patients per site [START_REF] Orlhac | Validation of A Method to Compensate Multicenter Effects Affecting CT Radiomics[END_REF][START_REF] Fortin | Harmonization of multi-site diffusion tensor imaging data[END_REF][START_REF] Fortin | Removing inter-subject technical variability in magnetic resonance imaging studies[END_REF] . ComBat-Harmonization is classically applied at the end of the postprocessing pipeline, herein, after the extraction of RFs obtained with the IHT that was hypothesized to be the more relevant and realistic among the 5 IHTs (namely IHTHM.All). This data-driven method identifies the protocol effect assuming that the value of each feature, RF, measured in a volume-of-interest, (x,y,z), with an imaging protocol, i, can be written as: RFi,(x,y,z)= α + γi + δi × εi,(x,y,z) (in which α is the average value for features yij; γi is an additive protocol effect and δi is a multiplicative protocol effect affected by an error term εij). The compensations consists in estimating the model parameters α, γi and δi, and by using a maximum likelihood approach on the basis of the set of available observations: CD E,F(G,H,I)

JKLMNO = P Q + ST U,V(W,X,Y) ,Z [ ,\ [ U ] ^U
, in which

P Q, _ Q E and

Statistical analysis

Statistical analysis was performed with R. All tests were two-tailed. A p-value of less than 0.05 was deemed significant. A 3-steps approach was performed to evaluate the impact of IHTs on each aspect of radiomics studies (Figure 1):

(1) Per-RF analysis: RFs were all normalized in order to range between 0 and 1 and to facilitate direct comparisons. For each RF, the influence of the IHT was evaluated with one-way repeated-measures ANOVA. Post-Hoc comparisons were assessed with Tukey test and Bonferroni corrections. Intraclass correlation coefficients (ICC) were estimated for each RF, with a 2-way random model, agreement between raters and 6 raters ("irr" package)

(2) Unsupervised analysis: A hierarchical clustering analysis with the Ward method was applied on each of the 6 subsets of RFs. RFs were centered and scaled by mean beforehand and the Euclidean distance between each pair of patients was computed.

Visual inspection of the silhouette plot enabled to select 2 clusters of patients for each harmonization technique. We calculated the Baker's gamma coefficient between each pair of dendrograms (dendextend" package), and the Kappa index between each pair of clustering results, which enabled the quantification of their divergence depending on the IHT [START_REF] Galili | dendextend: an R package for visualizing, adjusting and comparing trees of hierarchical clustering[END_REF] .

The correlations between MFS and the clusters yielded by the models were assessed with Kaplan-Meier analysis and multivariable Cox models -after adjustment to the classical confounding covariables for sarcomas, i.e.: the longest baseline diameter (< vs. ≥ 10 cm), performance status (0 vs. 1-2), histological type (undifferentiated sarcomas vs. other), number of chemotherapy cycles (4 vs. 5-6), chemotherapy type (anthracycline-ifosfamide vs doxorubicine), adjuvant radiotherapy, surgical margins (R0 vs. R1-R2) and histological response (goods vs. poor responder to chemotherapy with a cut-off of 10% viable cells on post-chemotherapy surgical specimen).

Prognostic performances of the 6 multivariate models were evaluated and compared through concordance-indices, which estimate the models's ability to provide a reliable ranking of the survival times based on the individual risk scores

(3) Supervised analysis: The same supervised machine-learning approach was applied to the 6 datasets of RFs in order to predict the occurrence of a metastatic relapse within 2 years after curative surgery by using the "caret" and "glmnet" packages [START_REF] Kuhn | Building Predictive Models in R Using the caret Package[END_REF][START_REF] Friedman | Regularization Paths for Generalized Linear Models via Coordinate Descent[END_REF]

Results

Thirty-two of the 70 patients (45.7%) were women with a median age of 58 (range:

19-84) (Table 1). The most frequent histological types were high-grade undifferentiated sarcomas (31/70, 44.3%), with a median size of 116 mm (range 40-273) and mostly deep-seated in the lower limb (35/70, 50%).

Per-RF analysis

The influence of IHT was significant for all RFs (p-values range: <0.0001-0.02, Supplemental Data 4). All significant differences in the RFs comparisons between each pair of post-processing techniques are listed in

Unsupervised analysis

All 6 unsupervised classifications achieved were different. Table 3

Supervised analysis

In total, there were 29/70 (41.4%) metastatic relapses within the first two years of follow-up, which were distributed into 21/50 (42%) events in the training cohort and 8/20 (40%) events in the validation cohort.

The final hyperparameters and performances of the classification models are given in Table 5. The best performances in repeated cross-validation were found with the models based on the RFs from the IHTHM.All and IHTHM.1 datasets (AUROC = 0.71, 95%CI = 0.66 -0.76, and 0.69, 95%CI = 0.64 -0.74, respectively). The lowest AUROC was obtained with the No-IHT dataset (0.57, 95%CI = 0.52 -0.63).

In descending orders, the AUROCs on the testing cohort were 0.82 (95%CI = 0.59 - Regarding the best final model, namely IHTHM.1, the number of selected radiomics features was of 7 out of 48 possible (by including the 3 shape features). Among these features, HISTO_Quartile1 and GLZLM_SZLGE were the most frequently selected (in 5 out of 6 models, and 4 out of 6 models, respectively) (Supplemental Data 5).

Discussion

The post-processing of medical images to perform radiomics studies is mandatory to ensure the comparability of multicentric datasets but it can result in additional bias that may alter the performances of predictive models and preclude the reproducibility of MRI-based radiomics signatures. Because structural MRIs are acquired in arbitrary units, the intensity harmonization is crucial to enable the comparability of examinations acquired with different MR-systems, coils, and acquisition parameters.

We found that all 45 textural features widely used in the literature were significantly influenced by IHT. Furthermore, depending on the IHC used, the results of unsupervised and supervised analyses based on RFs and their clinical correlations were dramatically changed. In addition, using an inappropriate IHT could decrease the performances of radiomics-based predictive models as it was highlighted by the comparative analysis with the models built with the No-IHT imaging dataset.

Our results concur with previous studies that found a significant influence of other post-processing steps on the absolute values of RFs (such as voxel size [START_REF] Zwanenburg | The Image Biomarker Standardization Initiative: Standardized Quantitative Radiomics for High-Throughput Image-based Phenotyping[END_REF] .

Previous studies have already emphasized the influence of IHT on segmentation and tissue classification tasks but they mostly involved brain MRI for inflammatory or degenerative diseases, and not specifically study their influence on radiomics analyses [START_REF] Fortin | Harmonization of multi-site diffusion tensor imaging data[END_REF][START_REF] Fortin | Removing inter-subject technical variability in magnetic resonance imaging studies[END_REF][START_REF] Shinohara | Statistical normalization techniques for magnetic resonance imaging[END_REF][START_REF] Robitaille | Tissue-based MRI intensity standardization: application to multicentric datasets[END_REF] . Moreover, the methods proposed in these studies were not readily transposable to non-brain imaging and/or not available in open source language (for instance, DeepHarmony) [START_REF] Dewey | DeepHarmony: A deep learning approach to contrast harmonization across scanner changes[END_REF] .

In this study, we focused the analyses on techniques previously used in the bodyimaging radiomics literature (i.e. scaling, histogram-matching or ComBat-Harmonization) but further studies should consider translating other popular intensity harmonization algorithms to body MRI. The RAVEL algorithm, which aims at estimating a voxel-specific unwanted variation by using a control region (i.e. brain cerebro-spinal fluid), may be particularly promising if applied to body-MR, with the possible use of healthy adipose tissues as control in the setting of soft tissue sarcomas for example [START_REF] Fortin | Harmonization of multi-site diffusion tensor imaging data[END_REF][START_REF] Fortin | Removing inter-subject technical variability in magnetic resonance imaging studies[END_REF] . Alternatively, instead of a post-processing intensity harmonization, the harmonization of SIs could be achieved since the acquisition step, through the use of standardized T1-mapping or T2-mapping sequence. However, thousands of MRIs have already been stored and, logically, the radiological community expects to pool and include these images in retrospective radiomics studies.

None of the IHTs used in this study demonstrated an unequivocal superiority compared to the others. This observation lets us hypothesize that the "best" technique is not universal but may actually vary depending on the dataset and the study objectives. Our present data does not allow us to validate this hypothesis, as it would require additional datasets to test if the same IHT constantly provides the best models whatever the disease and the outcome. While the unsupervised analysis highlighted the prognostic value of clusters elaborated with RFs from the IHTstd, IHTHM.All and IHTHM.All.C datasets, the supervised analysis emphasized on the other hand the prognostic value of other models elaborated with RFs from the IHTfat and IHTHM.1 in the testing cohort. It is worth noting that our supervised models showed moderately higher performances in the validation cohort than in the training cohort (range of differences: 0.03 -0.13). Although this finding suggests that the models were not overfitted, it also indicates that the training could have been premature (despite the use of repeated cross-validation and exhaustive grid search) and that a sampling bias could have occurred during the data partitioning in our rather small study population (despite the fact that the splits were obtained randomly and were well-balanced regarding the outcome).

Importantly, our unsupervised analysis revealed that using an inappropriate IHT could even lead to a total loss of relevant information from the radiomics data. Indeed, the concordance indices of the reference model (which was elaborated with clinical and radiological variables alone) and the model relying on IHTHM.1 were equivalent, which stresses the lack of prognostic value of the corresponding clusters. Similarly, although the lowest AUROC was reached with the No-IHT dataset in crossvalidation, the performances of this supervised model were not markedly different from those obtained with some of the IHTs in the two cohorts (especially the IHTstd).

These findings also suggest that radiomics studies should investigate all the available IHTs in an exploratory subset of the cohort, as well as no use of IHT, and subsequently select the one that optimizes the predictions. For instance, the extraction of RFs according to various voxel sizes and/or numbers of gray levels is commonly performed in radiomics studies. By analogy, one could consider extracting the RFs according to different IHTs and select the most robust and predictive RFs at univariable level. Hence, the intensity harmonization techniques could be considered as a "hyperparameter" of the post-processing pipeline. Interestingly, IHTHM. Our results also deepened that intra-tumoral heterogeneous SIs on T2-WI is predictive of MFS in a quantitative manner and other studies have also correlated this parameter with overall and/or metastatic-relapse free survivals in STS patients with relatively close and similar performances to ours [START_REF] Peeken | Tumor grading of soft tissue sarcomas using MRI-based radiomics[END_REF][START_REF] Spraker | MRI Radiomic Features Are Independently Associated With Overall Survival in Soft Tissue Sarcoma[END_REF][START_REF] Crombé | Soft-Tissue Sarcomas: Assessment of MRI Features Correlating with Histologic Grade and Patient Outcome[END_REF] . Indeed, Peeken et al. used an equivalent of IHTstd and applied ComBat to correct for multicenter effect. They also provided the sarcoma histological type as a biological covariable (which slightly improved the performances) [START_REF] Peeken | Tumor grading of soft tissue sarcomas using MRI-based radiomics[END_REF] . Their best model relied on radiomics features from Fat Sat T2 weighted imaging and showed a concordance-index of 0.74 in the validation cohort.

On the other hand, Spraker et al did not explicitly use an intensity harmonization technique, neither ComBat 7 . Interestingly, their best clinical and radiological prognostic models for the overall survival showed a concordance-index of 0.78 in the validation cohort.

Our study has limits. First, the study population was relatively small although this is the largest study investigating IHT and radiomics. It should be noted sarcoma radiological studies rarely exceed our population number. Second, we focused this proof-of-concept methodological study on T2-WI sequences but further investigations should be performed on other MRI sequences, such as T1-WI, contrast-enhanced T1-WI, DCE-MRI and diffusion imaging. We purposely chose this sequence because it is commonly reported as the most informative morphological sequence for sarcomas [START_REF] Crombé | T2 -based MRI Delta-radiomics improve response prediction in softtissue sarcomas treated by neoadjuvant chemotherapy[END_REF][START_REF] Crombé | Soft-Tissue Sarcomas: Assessment of MRI Features Correlating with Histologic Grade and Patient Outcome[END_REF] .

Third, our study design could be criticized. Indeed, judging which of the IHTs is the best by using the performances of predictive models (AUROC or concordance-index)

as judgment criteria can only be valid if the intrinsic prognostic value of MRI-based radiomics features is certain. In this case, lowering these performances with a particular IHT would mean that this IHT caused noise and inappropriate deviation in the data. However, as already stated, prior studies converged towards same results regarding the relationship between MRI-based radiomics features, heterogeneity on T2-WI and outcomes of sarcoma patients [START_REF] Peeken | Tumor grading of soft tissue sarcomas using MRI-based radiomics[END_REF][START_REF] Spraker | MRI Radiomic Features Are Independently Associated With Overall Survival in Soft Tissue Sarcoma[END_REF][START_REF] Crombé | Soft-Tissue Sarcomas: Assessment of MRI Features Correlating with Histologic Grade and Patient Outcome[END_REF][START_REF] Crombé | High-Grade Soft-Tissue Sarcomas: Can Optimizing Dynamic Contrast-Enhanced MRI Postprocessing Improve Prognostic Radiomics Models?[END_REF] . Furthermore, adding more potential radiomics predictors in our multivariate analyses would have increased the multidimensionality of our dataset and the risk of overfitted results regarding the limited number of patients.

To conclude, through the example of sarcomas, our study highlights that the IHT can directly influence the values of MRI-based RFs, subsequently leading to dramatical changes in the predictions of both unsupervised and supervised models. Therefore, IHTs need to be deepened regarding non-brain MRI and should be carefully explored and detailed when building radiomics models to ensure the robustness and reproducibility of radiomics signatures.

  newly-diagnosed, non-metastatic (according to chest CT-scan), histologically-proven high-grade STS of trunk wall or extremities (n=163), treated with 4-6 cycles of anthracycline-based neoadjuvant chemotherapy and curative surgery at our sarcoma reference center from June 2006 to November 2016 (n=133), available baseline MRI (n=95) with axial spin-echo T2-WI without artefacts (n=72), and available clinical and radiological follow-ups for at least 2 years after the surgery (n=70). Follow-ups consisted in a clinical examination and chest radiograph every 3 months for 2 years, every 6 months for 5 years and annually until 10 years after surgery, which were complemented by chest CT-scans and MRIs in case of doubtful findings. All relapses were histopathologically confirmed. MFS was defined as the time since curative surgery to metastatic relapse.

5 -

 5 Tesla MR-systems (Philips Signa [17/70, 24.3%], Siemens MAGNETOM Aera [41/70, 58.5%], General Electrics Healthcare Optima Jem MR450w [12/70, 17.1%]) with adjustment of coils, field-of-view and matrix depending on tumor size, location and depth. Regarding T2-WI, the range of repetition and echo times were 2400-4500msec and 70-130 msec, respectively. Slice thickness ranged from 3 to 5 mm. The protocol also systematically included 2D or 3D T1-WI after intra-venous gadolinium-chelates injection (with or without fat-suppression) MRI post-processing (Figure 1)

  `aE are estimators of α, γi and δi. Parametric and non-parametric forms of ComBat-Harmonization have been developed. The non-parametric form does not assume law followed by the parameters and has been used in the present study. The resulting RFs were labelled IHTHM.All.C. In total, six paired datasets of 45 RFs were obtained, namely: No-IHT, IHTfat, IHTstd, IHTHM.1, IHTHM.All and IHTHM.All.C.

  . The total population of 70 patients with available clinical and radiological follow-up was randomly subdivided into one training cohort of 50 patients and one testing cohort of 20 patients with the same proportion of metastatic relapses by using the createDataPartition function. The training cohort was used to train a binomial logistic regression with combination of least absolute shrinkage and selection operator (LASSO) and ridge penalizations (elasticnet-LR). This algorithm consists of reducing the number and the importance of explanatory variables in order to optimize the performances of the classification model. The coefficients of the less contributive variables are shrunken towards 0 (: ridge regression) or even set to 0 (: LASSO). The amount of ridge and LASSO penalization was investigated by using a manual grid search with two hyperparamètres: α (mixing percentage) and λ (regularization parameter) and 10-fold cross validation, repeated 5 times. The same partitioning of patients was used for the 6 datasets. The same clinical and pathological covariables as in the unsupervised analysis were included, in addition to the same 3 shape RFs (volume, compacity and sphericity -which are independent from the IHT).The performances of supervised models were evaluated through cross-validated accuracy and area under the ROC curves (AUROC) with 95% confidence interval (95%CI). To do so, we extracted the 5 × 10 = 50 estimations of the accuracy and AUROC from the 50 distinct test sub-cohorts of 5 patients from the training cohort, and we applied the CI function from the Rmisc package to these vectors. Finally, for each RFs dataset, the final model with the highest AUROC in cross-validation was used on the testing cohort to estimate the AUROC and accuracy.

Figure 2

 2 Figure 2 shows the 45 ICCs in descending order. The highest ICCs were reached with GLRLM_RLMNU, GLRLM_GLNU and GLCM_Correlation (≥ 0.95). The lowest ICCs were reached with GLZLM_ZLNU, GLZLM_LZE, HISTO_maximum, GLZLM_LZLGE and HISTO_minimum (<0.20).

4 .

 4 shows the correlation matrices for Kappa indices and Baker coefficients. The pair of clustering with the highest positive correlation was obtained with IHTHM.All versus IHTHM.All.C (Kappa = 0.75, Baker coefficient = 0.55). The lowest correlated pair was obtained with No-IHT versus IHTHM.1 (Kappa = 0.18, Baker coefficient = 0.05). Both correlated dendrograms are displayed in Figure 3. Regarding the prognostic value of the clusters, our univariate analysis showed that significantly different survivals were found with the clusters obtained with the IHTHM.All radiomics dataset (Log-rang p-value = 0.03) but not with the other IHTs. Kaplan Meier curves for the 6 clustering analyses are given in Figure To assess the prognostic values in presence of confounding variables, we elaborated multivariate models demonstrating that the clusters obtained with RFs from the No-IHT, IHTstd, IHTHM.All and IHTHM.All.C were independently associated with MFS in the multivariate modeling (p = 0.02, 0.007, 0.004 and 0.02, respectively -Table 4) but not the clusters obtained with RFs from the IHTfat and IHTHM.1. Concordance-indices of the 6 prognostic models ranged from 0.71 (95%CI = 0.67-0.75) for IHTHM.1 to 0.75 (95%CI = 0.70-0.79) for No-IHT, IHTHMstd and IHTHM.All. The concordance-index of a reference prognostic model taking into account the clinical and pathological confounding co-variables alone was of 0.71 (95%CI = 0.67 -0.75).

1 )Figure 5 .

 15 Figure 5. The number of radiomics features included in the final models ranged from 3 (with No-IHT and IHTHM.AllC) to 21 (with IHTfat). Regarding the best final

  All.C yielded moderately good performances in both unsupervised and supervised analyses (with similar results in training and testing cohorts), which suggests that this method may provide the more realistic radiomics data in the setting of our study. It should be emphasized that the co-variable arguments given to the ComBat function may/might be incomplete in the setting of sarcomas. In any case, the clinical outcome of the study should not be included among the ComBat covariables because it should not depend on the MR-system or acquisition parameters of the sequences. A distinctive feature of sarcomas over other cancers is their anatomical ubiquity, hence, requiring adjusting several other acquisition parameters depending on the tumor location (for instance thoracic wall, thigh or wrist). Further studies should investigate the best covariables for ComBat for non-brain MRI. In addition, ComBat could have been used with the No-IHT, IHTfat, IHTstd, IHTHM.1 radiomics features. We purposely decided to limit the application of ComBat to only one dataset (IHTHM.All) to avoid multiplying the post-hoc analyses, performances measurements, or superposing ROC curves, while our current results already enables us to stress the strong impact of IHT on radiomics-features and radiomics-based classifications and predicitions.

Figure 1 .Figure 2 .

 12 Figure 1. Study pipeline. Abbreviations: HM: histogram matching, IHT: intensity harmonization technique, No-IHT: no use of IHT before extracting radiomics features, RF: radiomics features, WI: weighted imaging

Figure 3 .

 3 Figure 3. Comparisons of the hierarchical clustering results based on radiomics features from different datasets depending on the intensity harmonization technique (IHT) with: (a) the highest divergence, and (b) the lowest divergence. The dendrograms were obtained according to the following IHTs: histogram matching (HM) with a randomly-chosen normalized histogram of a patient (IHTHM1) versus no use of harmonization technique (No-IHT); and HM with the average normalized histogram of the study population (IHTHM.All) versus IHTHM.All combined with ComBat harmonization method (IHTHM.All.C). By convention, cluster-1 (in blue) corresponds to the group of patients with the best prognosis regarding metastaticrelapse free survival.

Figure 4 .

 4 Figure 4. Kaplan-Meier curves for metastatic-relapse free survival depending on unsupervised clustering results based on radiomics features obtained with the different intensity harmonization techniques (IHT) or no use of harmonization technique (No-IHT).

Figure 5 .

 5 Figure 5. ROC curves for the best and worse supervised models to predict metastatic relapse within 2 years after the end of initial treatment in the testing cohort (built on the radiomics features from the IHTHM.1 and IHTstd datasets, respectively). The ROC curve of the final model without using harmonization technique (No-IHT) is also shown for comparison.

Table 2 .

 2 The highest and lowest amounts of differences were obtained for post-hoc comparisons between IHTHM-All and IHTfat (31 statistically different RFs out of 45, 68.9%) and IHTHM.All and IHTHM.1 (6/45, 13.3%), respectively.

Table 3 .

 3 Comparisons of the different dendrograms obtained by hierarchical clustering of the radiomics features with the 6 datasets depending on the intensity harmonization technique (IHT). (a) Corresponds to the Cohen's Kappa index ranging from 0 (completely different clustering assignements) to 1 (exactly the same clustering assignements). (b) Corresponds to the the Baker's gamma coefficient ranging from 0 (completely different dendrograms) to 1 (exactly the same two dendrograms).

	(a)	IHTfat	IHTstd IHTHM.1 IHTHM.All IHTHM.All.C	(b)	IHTfat IHTstd IHTHM.1 IHTHM.All IHTHM.All.C
	No-IHT	0.40	0.33	0.18	0.39	0.35	No-IHT	0.19	0.11	0.05	0.05	0.07
		IHTfat	0.33	0.23	0.36	0.43		IHTfat	0.14	0.15	0.17	0.18
			IHTstd	0.25	0.51	0.67			IHTstd	0.11	0.30	0.42
				IHTHM.1	0.40	0.44				IHTHM.1	0.26	0.29
					IHTHM.All	0.75					IHTHM.All	0.55

Table 4 .

 4 Unsupervised analysis based on radiomics features (RFs) -Prognostic value of the clustering results depending on the intensity harmonization technique (IHT).NOTE. Results for 2-years survival probability, hazard ratio and concordance-index are given with 95% confidence interval.[START_REF] Limkin | Promises and challenges for the implementation of computational medical imaging (radiomics) in oncology[END_REF] Multivariate Cox modeling were adjusted for the following clinical and pathological covariables: performance status, histotype, initial longest diameter of the tumor, type of neoadjuvant chemotherapy, number of cycles of chemotherapy, surgical margins, histological response and adjuvant Radiotherapy, Abbreviations: HM: histogram matching, HR: hazard ratio, No: number. *: p<0.05, **: p<0.005, ***: p<0.001

	Intensity harmonization technique	Clustering result	No. Of patients	No. Of events	2-years survival probability	Univariate analysis Log-rank p-value Concordance-index	HR	Multivariate Cox Modeling 1 Concordance-p-value index
	No-IHT	Cluster-1 Cluster-2	51 19	22 10	64.7 (52.8-79.3) 52.6 (34.4-80.6)	0.3	0.55 (0.50-0.59)	-2.64 (1.15-6.04)	-0.02*	0.75 (0.71-0.79)
	IHTfat	Cluster-1 Cluster-2	53 17	23 9	62.3 (50.5-76.8) 58.8 (39.5-87.6)	0.6	0.51 (0.47-0.55)	-1.65 (0.70-3.89)	-0.3	0.72 (0.67-0.76)
	IHTstd	Cluster-1 Cluster-2	30 40	11 21	70 (55.4-88.5) 55 (41.6-72.8)	0.1	0.55 (0.50-0.60)	-3.26 (1.48-7.71)	-0.007*	0.75 (0.72-0.79)
	IHTHM.1	Cluster-1 Cluster-2	50 20	22 10	64 (52-78.8) 55 (37-81.8)	0.6	0.52 (0.48-0.56)	-1.52 (0.66-3.49)	-0.3	0.71 (0.67-0.75)
	IHTHM.All	Cluster-1 Cluster-2	20 50	5 27	80 (64.3-99.6) 54 (41.8-69.7)	0.03*	0.58 (0.54-0.62)	-4.72 (1.64-13.56)	-0.004**	0.75 (0.70-0.79)
	IHTHM.All.C	Cluster-1 Cluster-2	28 42	10 22	67.9 (52.6-87.6) 57.1 (44-74.3)	0.3	0.53 (0.51-0.55)	-2.89 (1.19-7.05)	-0.02*	0.73 (0.68-0.77)

Table 5 .

 5 Accuracy and area under the ROC curves (AUROC) of the supervised models in repeated cross validation (training cohort) and in the testing/validation independent cohort, depending on the 5 intensity harmonization techniques (IHTs) or the lack of IHT (named No-IHT).

	Intensity harmonization	Best hyperparameter	Training cohort (results in repeated cross-validation)	Testing cohort
	technique	tuning	Accuracy	AUROC	Accuracy	AUROC
	No-IHT	alpha=0.883 lambda=0.114	0.56 (0.52 -0.64)	0.57 (0.52 -0.60)	0.75 (0.51 -0.89)	0.76 (0.50 -1.)
	IHTfat	alpha=0.226, lambda=0.048	0.60 (0.64 -0.55)	0.68 (0.63-0.73)	0.75 (0.51 -0.91)	0.80 (0.56 -1.)
	IHTstd	alpha=0.384, lambda=0.086.	0.63 (0.59 -0.55)	0.64 (0.59-0.69)	0.70 (0.46 -0.88)	0.69 (0.41 -0.89)
	IHTHM.1	alpha=0.394, lambda=0.200	0.62 (0.66 0.59)	0.69 (0.64-0.74)	0.75 (0.51 -0.91)	0.82 (0.59 -1)
	IHTHM.All	alpha=0.338, lambda=0.384	0.61 (0.63 -0.58)	0.71 (0.66-0.76)	0.60 (0.36 -0.81)	0.77 (0.52 -1)
	IHTHM.All.C	alpha=0.166 lambda=0.840	0.58 (0.57 -0.59)	0.68 (0.63-0.73)	0.60 (0.36 -0.81)	0.71 (0.44 -0.97)

NOTE.-Results are giving with 95% confidence interval.

Acknowledgements

The authors would like to thank Mrs. Camille Martinerie for medical writing services.

Data Availability

The datasets generated during and/or analyzed during the current study are not publicly available due to the clinical and confidential nature of the material but can be made available from the corresponding author on reasonable request.

Competing interests

This study did not receive any funding. The authors declare no competing interests.


Liyuan Liu

Yih-Chyng Wu

Patrick Rozier

Pierre-Louis Taberna

Patrice Simon
email: simon@chimie.ups-tlse.fr

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible

Recently, multivalent aqueous calcium-ion batteries (CIBs) have attracted considerable attention as a possible alternative to Li-ion batteries. However, traditional Ca-ion storage materials show either limited rate capabilities and poor cycle life or insufficient specific capacity. Here, we tackle these limitations by exploring materials having a large interlayer distance to achieve decent specific capacities and one-dimensional architecture with adequate Ca-ion passages that enable rapid reversible (de)intercalation processes. In this work, we report the high-yield, rapid, and low-cost synthesis of 1D metal oxides MV 3 O 8 (M = Li, K), CaV 2 O 6 , and CaV 6 O 16 •7H 2 O (CVO) via a molten salt method. Firstly, using 1D CVO as electrode materials, we show high capacity 205 mA h g -1 , long cycle life (>97% capacity retention after 200 cycles at 3.0 C), and high-rate performance (117 mA h g -1 at 12 C) for Ca-ion (de)intercalation. This work represents a step forward for the development of the molten salt method to synthesize nanomaterials and to help pave the way for the future growth of Ca-ion batteries.

Ultrafast Synthesis of Calcium Vanadate for Superior Aqueous Calcium-Ion Battery

Introduction

To satisfy the demand for portable electronics and the electric vehicle market, the development of rechargeable battery technique plays a significant role. In the past decades, considerable efforts have been devoted to monovalent ion batteries such as Li + , Na + , and K + intercalation materials [START_REF] Rozier | Cation-disordered Li 3 VO 4 : reversible Li insertion/deinsertion mechanism for quasi Li-rich layered Li 1+x [V 1/2 Li 1/2 ]O 2 (x = 0-1)[END_REF][START_REF] Beda | Hard carbons derived from green phenolic resins for Na-ion batteries[END_REF][START_REF] Liu | 3D rGO aerogel with superior electrochemical per-formance for K -Ion battery[END_REF]. Recently, researchers have started to pay more attention to multivalent charge carriers [START_REF] Gheytani | An aqueous Ca-ion battery[END_REF][START_REF] Liang | Interlayer-expanded molybdenum disulfide nanocomposites for electrochemical magnesium storage[END_REF][START_REF] Xia | Rechargeable aqueous zinc-ion battery based on porous framework zinc pyrovanadate intercalation cathode[END_REF][START_REF] Jayaprakash | The rechargeable aluminum-ion battery[END_REF][START_REF] Gummow | Calcium-ion batteries: current state-of-the-art and future perspectives[END_REF][START_REF] Ponrouch | On the road toward calciumbased batteries[END_REF]. Among them, various divalent metal ions have been proposed as alternatives to monovalent ions, including Ca 2+ [START_REF] Gheytani | An aqueous Ca-ion battery[END_REF], Mg 2+ [START_REF] Liang | Interlayer-expanded molybdenum disulfide nanocomposites for electrochemical magnesium storage[END_REF], or Zn 2+ [START_REF] Xia | Rechargeable aqueous zinc-ion battery based on porous framework zinc pyrovanadate intercalation cathode[END_REF]. The adoption of divalent ions results in a potential improvement in the specific capacity and hence a significant boost in the energy density of cells compared to monovalent ion cells (2F (1F = 96500C mol -1 ) exchanged per mole of divalent metal ion intercalated instead of 1F for monovalent, for instance). Furthermore, the abundance of these divalent elements largely reduces the cost of storage systems and relieves the stress of the lack of lithium resources [START_REF] Gheytani | An aqueous Ca-ion battery[END_REF].

Nevertheless, multivalent-ion electrodes suffer from slow cation diffusion because of the strong binding between the multivalent ions and the negatively charged active materials [START_REF] Gheytani | An aqueous Ca-ion battery[END_REF][START_REF] Liang | Interlayer-expanded molybdenum disulfide nanocomposites for electrochemical magnesium storage[END_REF]. Thanks to the low charge density of Ca-ion (see Table S1), this problem has been effectively alleviated in Ca-ion intercalation electrodes compared to the other multivalent-ion materials [START_REF] Gheytani | An aqueous Ca-ion battery[END_REF][START_REF] Liang | Interlayer-expanded molybdenum disulfide nanocomposites for electrochemical magnesium storage[END_REF]. Besides, the standard reduction potential of Ca/Ca 2+ (-2.9 V vs. normal hydrogen electrode, NHE) is 0.5 V lower than Mg 2+ /Mg (-2.4 V vs. NHE), 1.2 V lower than Al 3+ /Al (-1.6 V vs. NHE), and only 0.1 V higher than Li + /Li (-3.0 V vs. NHE) [START_REF] Gheytani | An aqueous Ca-ion battery[END_REF][START_REF] Liang | Interlayer-expanded molybdenum disulfide nanocomposites for electrochemical magnesium storage[END_REF][START_REF] Jayaprakash | The rechargeable aluminum-ion battery[END_REF]. According to Gummow et al., the theoretical volumetric capacity of Ca 2+ (2073 mA h ml -1 ) is higher than Na + (1128 mA h ml -1 ) and K + (591 mA h ml -1 ), similar to Li + (2062 mA h ml -1 ) [START_REF] Gummow | Calcium-ion batteries: current state-of-the-art and future perspectives[END_REF]. As reported by Monti et al., the hypothetical energy density of a graphite/Ca 3 Co 2 O 6 Ca-ion battery (120 Wh l -1 and 50 Wh kg -1 ) is higher than both LFP/graphite and NVPF/HC configurations [START_REF] Monti | Multivalent batteries-prospects for high energy density: Ca batteries[END_REF].

However, research activities on Ca-metal battery are still at preliminary stages due to the incompatibility between the metal Ca anode and the conventional organic electrolyte [START_REF] Ponrouch | On the road toward calciumbased batteries[END_REF]: Ca plating reaction is difficult to achieve at room temperature in organic Ca-ion batteries since Ca 2+ is difficult to transport through the solid electrolyte interphase film when Ca metal is used as an anode [START_REF] Wang | Reversible calcium alloying enables a practical room-temperature rechargeable calcium-ion battery with a high discharge voltage[END_REF]. This problem remained unsolved until very recently when Wang et al. used Ca 7 Sn 6 alloy to replace Ca metal as anode, but the cycling stability and coulombic efficiency are still waiting to be improved [START_REF] Wang | Reversible calcium alloying enables a practical room-temperature rechargeable calcium-ion battery with a high discharge voltage[END_REF]. Differently from organic Ca-metal batteries, there is more success on the development of Ca-ion batteries where host materials such as organic polyimide can be used as the anode [START_REF] Gheytani | An aqueous Ca-ion battery[END_REF]; also, several materials such as K 0.31 MnO 2 •0.25H 2 O [START_REF] Hyoung | Investigation of electrochemical calcium-ion energy storage mechanism in potassium birnessite[END_REF], Prussian blue analog copper hexacyanoferrate [START_REF] Padigi | Potassium barium hexacyanoferrate -a potential cathode material for rechargeable calcium ion batteries[END_REF], or CaCo 2 O 4 [START_REF] Cabello | Advancing towards a veritable calcium-ion battery: CaCo 2 O 4 positive electrode material[END_REF] have been proposed as cathodes for reversible Ca 2+ (de)intercalation for aqueous Ca-ion batteries. We believe that the development of Ca-ion batteries would play a critical role in pushing the Ca-metal batteries forward.

Recently, Zn-ion batteries have won a lot of attention [START_REF] Verma | Batteries: progress in rechargeable aqueous zinc-and aluminum-ion battery electrodes: challenges and outlook[END_REF]. Among the cathode materials, many vanadiumbased oxides have been reported such as Zn 0.25 [START_REF] He | High-performance aqueous zincion battery based on layered H 2 V 3 O 8 Nanowire cathode[END_REF], LiV 3 O 8 [START_REF] Alfaruqi | Electrochemical zinc intercalation in lithium vanadium oxide: a high-capacity zincion battery cathode[END_REF], and Na 2 V 6 O 16 •1.63H 2 O nanoribbon [START_REF] Soundharrajan | Na 2 V 6 O 16 •3H 2 barnesite nanorod: an open door to display a stable and high energy for aqueous rechargeable Zn-ion batteries as cathodes[END_REF]. These vanadium-based oxides show excellent electrochemical performance in Zn-ion batteries thanks to their open-framework crystal structure and the existence of multiple oxidation states of vanadium. So far, no vanadate has been reported in aqueous Ca-ion batteries, which indicates that there might be a lot of interesting vanadium-based electrode materials remaining to be discovered for Ca-ion batteries. For organic Ca-ion batteries, only V 2 O 5 has been reported as the cathode material, but the reversible capacity drops down to only 20% after only 4 cycles [START_REF] Hayashi | Electrochemical characteristics of calcium in organic electrolyte solutions and vanadium oxides as calcium hosts[END_REF][START_REF] Murata | Effect of water in electrolyte on the Ca 2+ insertion/extraction properties of V 2 O 5[END_REF]. Among the vanadium-based oxides, metahewettite-type CaV 6 O 16 •3H 2 O has been reported as a possible cathode material for Li-ion [START_REF] Zhang | Ultralong metahewettite CaV 6 O 16 •3H 2 O nanoribbons as novel host materials for lithium storage: Towards high-rate and excellent long-term cyclability[END_REF] and Zn-ion batteries [START_REF] Liu | Calcium vanadate submicrofibers as highly reversible host cathode material for aqueous zinc-ion batteries[END_REF]. It exhibits a layered structure composed by the stacking of V 6 O 16 layers linked together by Ca 2+ and H 2 O, which lying in the interlayer spaces, lead to a large interlayer distance which favors the intercalation of ions [START_REF] Liu | Calcium vanadate submicrofibers as highly reversible host cathode material for aqueous zinc-ion batteries[END_REF].

V 2 O 5 •2H 2 O [16], Fe 5 V 15 O 39 (OH) 9 •9H 2 O [17], Zn 3 V 2 O 7 (OH) 2 •2H 2 O [6], H 2 V 3 O 8
In this work, 1-dimensional CaV 6 O 16 •7H 2 O (CVO) samples were successfully prepared by using an ultrafast (synthesis time of only a few minutes) and high-yield (several grams can be easily prepared in one pot at lab scale) molten salt method (MSM). This compound was then characterized to assess its use as an electrode material in an aqueous Ca-ion battery. Interestingly, the MSM synthesis method can be extended to the preparation of a large variety (Li + and K + besides Ca 2+ ) of ion intercalated vanadium oxides all with large interlayer distance, making this method promising to prepare nanomaterials for energy storage applications.

Results and Discussion

2.1. Material Characterization. Low-temperature molten salts are achieved using inorganic salts such as nitrates, sulfates, or chloride. Since salt is in the liquid state, ion diffusion is faster during reaction compared to the conventional solidstate chemistry route-for which high temperature is thus required-resulting in an improvement of the reaction kinetics and homogeneous mixing of reactants. In our experiments, the nitrate was first heated in the air in a 450 °C muffle furnace (the furnace was firstly heated to 450 °C and then kept at this temperature before adding the nitrates inside) to reach molten state before adding the precursors into it (Figure 1(a)). The precursor was then added inside, and the reaction time was kept to only a few minutes, leading to the formation of a brownish solid well dispersed in the colorless molten salt (Figure 1(b)). After that, the crucible with the product was taken out of the furnace. Once cooled down to room temperature, the recrystallized salt was solubilized in water and the solid product recovered by filtration (Figure 1(c)). More synthesis details have been given in Material Synthesis.

1D CVO (Figure 2(a)) compounds were prepared in a mixture of calcium nitrate and sodium nitrate (to decrease the melting point) used as molten salt. SEM image in Figure 2(a) shows the 1D nanoribbon morphology of the prepared CVO with lengths from 2 μm to 10 μm. These nanoribbon structures were highly ordered with uniform shapes and flat surfaces. TEM (Figure 2(a)) studies confirm that the CVO sample adopts a ribbon-like morphology with diameters of 50-200 nm. [START_REF] Zhang | Ultralong metahewettite CaV 6 O 16 •3H 2 O nanoribbons as novel host materials for lithium storage: Towards high-rate and excellent long-term cyclability[END_REF], and some other vanadium bronzes incorporating alkali metals.

The hydrated calcium vanadate mineral CaV 6 O 16 •nH 2 O has three distinct phases containing 9-, 7-, and 3H 2 O, respectively [START_REF] Geological | The crystal structure of hewettite[END_REF]. The water content in our CVO material was determined using TGA technique in argon atmosphere such as shown in Figure 2(c). The plot reveals a total weight loss of 20.5% from room temperature to 400 °C. Two peaks can be clearly observed in the derivative thermos gravimetric (DTG) curve shown in Figure 2(c). As a result, the TG curve can be divided into two parts: from room temperature to 100 °C, a smaller weight variation 3.7% weight loss corresponds to physisorbed water, whereas above 100 °C, the weight loss of 16.8 wt% is due to the crystal water. This value matches well with the theoretical content in the formula CaV 6 O 16 •7H 2 O (17 wt%). Therefore, the final product can be classified as CaV 6 O 16 •7H 2 O. Several reasons could be explained as the source of the crystal water; the crystal water might be inserted inside the CVO layer during the reaction process or cooling process from moisture or even the washing process [START_REF] Hu | Rapid mass production of twodimensional metal oxides and hydroxides via the molten salts method[END_REF]. This high content of crystal water might explain the large interlayer spacing of the CVO sample since the interlayer distance of CaV 6 O 16 •7H 2 O (10.4 Å) is larger than that of the partial dehydrated CaV 6 O 16 •3H 2 O (8.08 Å) as reported in [START_REF] Liu | Calcium vanadate submicrofibers as highly reversible host cathode material for aqueous zinc-ion batteries[END_REF].

EDX analysis was also achieved to confirm the composition of the CVO particles. As shown in Figure 2(d), peaks located at 0.34 keV, 3.69 keV, and 4.01 keV evidence the presence of Ca, the peaks centered at 0.51 keV, 4.95 keV, and 5.43 keV show the presence of V element while the peak located at 0.53 keV is proof of the existence of the O element. Ca atomic percentage in the sample was estimated at 4:5 ± 0:6%, V content was 26:3 ± 1:1% while O was 69:2 ± 11:6%, leading to a ratio of 1 : 6 : 16 between Ca, V, and O atoms, respectively, which well agrees with the CVO formula. The composition was also verified using X-ray fluorescence spectrometry. As shown in Figure S1, a similar Ca : V ratio of 1 : 6 was obtained.

Electrochemical Characterizations.

The prepared CVO samples were electrochemically tested in three-electrode Swagelok cells, where an overcapacitive activated carbon electrode was used as a counter electrode and a saturated calomel electrode (SCE) as a reference electrode. The electrolyte was 4.5 M aqueous Ca(NO 3 ) 2 since Lee et al. reported an improved cycling performance of CuHCF in a superconcentrated aqueous electrolyte [START_REF] Lee | A novel superconcentrated aqueous electrolyte to improve the electrochemical performance of calcium-ion batteries[END_REF]. However, the low pH value of the 4.5 M aqueous Ca(NO 3 ) 2 , measured at 2.3 could result in the partial dissolution of CVO as well as proton (de)intercalation. To tackle these issues, pH was adjusted to 10 by adding Ca(OH) 2 while additional Ca(NO 3 ) 2 •4H 2 O was used to maintain the Ca(NO 3 ) 2 at 4.5 M. A working potential window of ~1.3 V (from -0.7 V to 0.6 V vs. SCE (2.44 to 3.74 V vs. Ca/Ca 2+ ) which falls within the H 2 O stability potential window) was obtained during cyclic voltammetry (CV) experiments, achieved at 0.2 mV s -1 (Figure S2).

The electrochemical characterizations of CVO as the electrode for Ca-ion batteries in the aqueous electrolytes are presented in Figure 3. As shown in Figure 3(a), the initial three charge/discharge galvanostatic plots were almost totally overlapped, suggesting a high reversibility of the Ca 2+ insertion/extraction process. The initial charge and discharge specific capacities are 203 mA h g -1 and 208 mA h g -1 , Interestingly, the molten salt synthesis route was extended to the family of 1D MV 3 O 8 (M = Li, K) (Figure S4) which also shows nanoribbon morphology and own excellent electrochemical performance. For example, nonhydrated LiV 3 O 8 (JCPDS card number: 35-0437) synthesized by MSM was used as a cathode material for the Li-ion battery. High capacity of 310 mA h g -1 at 100 mA g -1 and 170 mA h g -1 at 2 A g -1 could be achieved without any optimization in a nonaqueous electrolyte (Figure S5). These performances compare positively with those of LiV 3 O 8 nanoribbons synthesized by electrospinning method [START_REF] Chen | High rate, long lifespan LiV 3 O 8 Nanorods as a cathode material for lithium-ion batteries[END_REF]. 1D CaV 2 O 6 (Figure S6) was also first proposed as an electrode material for the aqueous Ca-ion battery, with a capacity of 153 mA h g -1 , long cycle life (>95% capacity retention after 700 cycles at a 5C rate), and high-rate performance (58 mA h g -1 at 50C) during Ca-ion (de)intercalation reactions (Figure S7). By playing with the nature of the precursor, the reaction time, and the heating temperature, K 3 V 5 O 14 and Ca 2 V 2 O 7 were also successfully prepared by MSM with high yield as well as CaMoO 4 (Figure S8). As can be seen, all the synthesized compounds (CaV 6 O 16 •7H 2 O, CaV 2 O 6 , LiV 3 O 8 , and KV 3 O 8 ) own similar layered structures where ions intercalated between the layers. The main difference lies in the bonds between the different species (ionocovalent V-O, ionic Ca-O, and van der Walls interaction for H 2 O) as well as the way the different VO 6 octahedra and VO 5 square pyramids are connected to build the V 3 O 8 layers inducing anisotropy in the growing kinetic. In genreal, layered structure can easily form 2D morphologies. However, in the case of these Vbased compounds, 1D nanoribbon morphology forms are due to preferential, fast growth of the V 3 O 8 or V 2 O 6 layer in one specific direction. For example, 1D nanoribbon morphology is obtained for CaV 6 O 16 •7H 2 O because of the rapid growth in the [100] direction of the alternate strings of V 4 O 11 and V 2 O 6 , with a poor connection between each other. The short time of the molten salt synthesis process with exacerbated kinetic differences is assumed to be at the origin of the nanoribbon-like morphology observed from different samples by favoring one-direction growth mechanism.

To sum up, the present molten salt route offers clear advantages over previous preparation procedures in terms of time and offers new opportunities to design electrode materials for energy storage applications. Furthermore, the high synthesis yield of the molten salt-based method is compatible with large-scale preparation.

Charge Storage Mechanism.

Differently from nonaqueous systems, the charge storage mechanism in the aqueous electrolyte is more complex because of the possible contribution of proton or hydronium ions. For instance, Sun et al. report the simultaneous H + and Zn 2+ insertion/deinsertion reactions at the positive electrode of an aqueous Zn-MnO 2 battery [START_REF] Sun | Zn/MnO 2 battery chemistry with H + and Zn 2+ coinsertion[END_REF]. Hyoung et al. studied K 0.31 MnO 2 •0.25H 2 O as a cathode material in aqueous Ca-ion batteries [START_REF] Hyoung | Investigation of electrochemical calcium-ion energy storage mechanism in potassium birnessite[END_REF]. They confirmed that Ca 2+ was the main contributor to the electrochemical reaction while hydronium ions were also proposed to cointercalate during the reaction [START_REF] Hyoung | Investigation of electrochemical calcium-ion energy storage mechanism in potassium birnessite[END_REF]. respectively, at a current density of 0.25C (1C rate corresponds to a full discharge in one hour that is a current density of 50 mA g -1 , see Figure S3), corresponding to a 5.5 electron redox process per CaV 6 O 16 •7H 2 O unit. A potential plateau is observed at -0.48 V vs. Ref. during discharge, shifted down to -0.25 V vs. Ref. during charge, resulting in a voltage hysteresis of about -0.23 V, consistent with the CV curves shown in Figure S2. Figure 3(b) shows the charge/discharge galvanostatic plots at various current densities. The voltage hysteresis was only slightly increased when the C rate was 40 times increased, indicating a relatively low activation and concentration polarizations [START_REF] Chen | High rate, long lifespan LiV 3 O 8 Nanorods as a cathode material for lithium-ion batteries[END_REF]. The electrode rate performance is summarized in Figure 3(c), where the current density was increased stepwise from 0.3C to 12C and then returned to 0.3C. Upon continuous cycling under various current densities, the specific capacities dropped only marginally on doubling/quadrupling the rates and immediately recovered with their reversal. The initial discharge capacity of 205 mA h g -1 at 0.3C had only a small decrease of 15% (178 mA h g -1 ) at 1.2C, and 117 mA h g -1 was still delivered at 12C rate, thus demonstrating the good power capability of the CVO electrode. This can be explained by the nanoribbon morphology, which increases the active material/electrolyte interface area as well as shortens diffusion distances. The cycle life of a CVO electrode was evaluated at the 3C rate for 200 cycles (Figure 3(d)). The electrode delivers a reversible capacity of 141 mA h g -1 with 97% capacity retention after 200 cycles. During the initial 12 cycles, the battery exhibits gradually increasing capacity until reaching a maximum capacity of 157 mA h g - 1 and then declines slowly for the next 188 cycles. Moreover, high initial coulombic efficiency (98%) was observed, and nearly 100% coulombic efficiency can be achieved after just 8 cycles, which further proves the superior performance of CVO in aqueous Ca-ion batteries. The long cycling stability might be explained in that the volume expansion/contraction during charge/discharge cycles and the associated material fading can be effectively avoided with 1D-nanostructured architecture and that this raises the cycling stability [START_REF] Jin | 1D nanomaterials: design, synthesis, and applications in sodium-ion batteries[END_REF]. Besides, the crystal water between the CVO layers might also play a significant role in affecting the electrochemical performances. First of all, the interlayer spacing can be further expanded by the intercalation of water molecules, providing an increased Ca 2+ diffusion rate [START_REF] Chen | High Rate, Long Lifespan LiV 3 O 8 Nanorods as a Cathode Material for Lithium-Ion Batteries[END_REF]. Besides, according to Zhang et al. [START_REF] Zhang | Ultralong metahewettite CaV 6 O 16 •3H 2 O nanoribbons as novel host materials for lithium storage: Towards high-rate and excellent long-term cyclability[END_REF], the interlayer water molecules form O-O bonds with the V 6 O 16 layers. In other words, interlayer water molecules could be taken as pillars to alleviate the structural strain thus maintaining substantial architectural stability providing a higher cyclability. Additionally, interlayer water molecules could effectively screen the electrostatic interactions between Ca 2+ and the host framework or the CVO layers to facilitate Ca 2+ diffusion [START_REF] Chen | High Rate, Long Lifespan LiV 3 O 8 Nanorods as a Cathode Material for Lithium-Ion Batteries[END_REF].

To the best of our knowledge, the high reversible specific capacity, rate capacity, and cycling stability of these CVO nanoribbons compare positively with previously reported materials for aqueous Ca-ion batteries (see Table S3) such as K 0.31 MnO 2 •0.25H 2 O [START_REF] Hyoung | Investigation of electrochemical calcium-ion energy storage mechanism in potassium birnessite[END_REF] and K 0.3 CuHCF [START_REF] Padigi | Potassium barium hexacyanoferrate -a potential cathode material for rechargeable calcium ion batteries[END_REF].

Besides, the capacity of CVO in the pH 10 electrolyte was found to be slightly higher, where the proton or hydronium ion concentration is negligible. Figure 4(b) compares the discharge capacity in both electrolytes at various current densities, showing better capacity retention in the pH 10 electrolyte than in pH 2.3 (59% and 38%, respectively) from 50 mA g -1 to 2000 mA g -1 . All these features support the Ca-ion intercalation as the main charge storage mechanism during the charge/discharge processes of the CVO electrode in Ca 2+ -containing aqueous electrolyte at pH 10.

An EQCM study was achieved using the CVO electrode in the two electrolytes (pH = 2:3 and pH = 10), to get further information on the charge storage mechanism (see Figure S9). Results confirmed that a heavier ion was intercalated in the pH = 10 electrolyte compared with the acidic one (pH = 2:3). As a result, the heavier molar weight obtained for the pH = 10 electrolyte would support the intercalation of a heavier Ca 2+ ion with one water molecule, while the intercalation of hydronium ions would explain the charge storage mechanism in the acidic electrolyte. Those results also exclude the possibility for CVO dissolution since the frequencies at the starting and ending points of the CV are roughly the same (see Figure S9a).

Reaction Kinetics.

To further understand the electrochemical kinetics of CVO in Ca-ion batteries, CVO electrodes were tested at various potential scan rates from 0.1 to 5 mV s -1 in a pH 10 electrolyte. There is mainly one set of redox peaks observed at -0.25/-0.48 V at a 0.2 mV s -1 scan rate (Figure 5(a)), representing the dominant electrochemical processes assumed to involve the V 5+ /V 4+ redox couple. Even though the characteristic peaks turn broader and the peak separation increases with increasing potential scan rate, the CV curves show similar signatures even at 5 mV s -1 corresponding to discharge in 260 s, equivalent to 14C (Figure 5(a)). The kinetic analysis has been made following the method proposed by Wang et al. [START_REF] Wang | Pseudocapacitive contributions to electrochemical energy storage in TiO 2 (anatase) nanoparticles[END_REF], where the peak current is plotted versus the potential scan rate to calculate the b value:

i = av b , ð2Þ
where i is the peak current of various scan rates and v is the scan rate. The b value is the slope of the fitting line with peak current versus scan rate in the log scale. The b value is between 0.5 and 1; a b value of 1 represents a charge storage dominated by surface processes whereas the diffusioncontrolled process gives a minimum b value (b = 0:5) [START_REF] Lindström | Li + ion insertion in TiO 2 (anatase). 2. voltammetry on nanoporous films[END_REF]. As seen in Figure 5(b), the average b value is 0.70 for the cathodic peak and 0.71 for the anodic peak, which likely indicates that both contributions (surface and bulk) are present. The surface (changing with v) and bulk (changing with v 1/2 ) contributions to the total current were calculated using the following equation, proposed by Wang's group [START_REF] Wang | Pseudocapacitive contributions to electrochemical energy storage in TiO 2 (anatase) nanoparticles[END_REF]: 0.2 mV s -1 . While the electrochemical storage in CVO is mainly controlled by the solid-state diffusion process at a low scan rate (62%), the surface process accounts for about 38% of the total current. Figure 5(d) shows the change of the surface and bulk contributions at various potential scan rates. As expected, the capacitive charge contribution increases with increasing potential sweep rate, reaching a maximum value of 77% at 5 mV s -1 . The above data shows that the surface intercalation redox process (not diffusion-limited) plays a significant role in the electrochemical reaction, which accounts for the excellent rate capability of the present CVO electrode since the bulk intercalation process is diffusion-limited at high current density. Electrochemical impedance spectroscopy (EIS) measurements were also done to get a further understanding of the reaction process. The CVO electrode was discharged stepwise from OCV to -0.6 V vs. Ref. and then charged back to 0.2 V vs. Ref.. This process was repeated twice following the same procedure before achieving EIS measurements. The Nyquist plots recorded at various constant potentials during discharge (reduction) are shown in Figure 6(a); Figure S10 shows the Nyquist plots recorded during the charge (oxidation) step. In the high-frequency region, the Nyquist plots normally show two different behaviors depending on the applied potential. At 0.2 V vs. Ref., the impedance plot shows a typical blocking electrode behavior; this is consistent with the "double layer-like" signature observed in the CV of Figure 5 above. At -0.6 V vs. Ref., the increase of the impedance in the low-frequency region evidences a diffusion-limited process [START_REF] Li | A polyaniline-coated sulfur/carbon composite with an enhanced high-rate capability as a cathode material for lithium/sulfur batteries[END_REF], in agreement with the redox reaction visible on the CV in Figure 5.

i v ð Þ = k 1 v + k 2 v 1/2 : ð3Þ
Ca-ion diffusion coefficient into the structure was calculated from the impedance measured at -0.6 V. The linear change of the impedance vs. ω -1/2 in the lowfrequency region results from the diffusion-controlled electrochemical reaction kinetics [START_REF] Mertens | Quantitative analysis of time-domain supported electrochemical impedance spectroscopy data of Li-ion batteries: reliable activation energy determination at low frequencies[END_REF]. The diffusion coefficient can be calculated according to the following equation [START_REF] Mertens | Quantitative analysis of time-domain supported electrochemical impedance spectroscopy data of Li-ion batteries: reliable activation energy determination at low frequencies[END_REF]:

D = 1 2 RT ACσz 2 F 2 2 , ð4Þ
where A is the surface area of the electrode, z is the valence of the ion, F is the Faraday constant, C is the concentration of Ca 2+ in the CVO electrode, R is the gas constant, T is the room temperature in our experiment, and σ is the slope of the line Z′∼ω -1/2 in the low-frequency region, which is obtained from Figure 6(b). Ca-ion diffusion coefficient is calculated to be 1:8 * 10 -10 cm 2 s -1 at -0.6 V, which is similar to that obtained for Ca 0.25 V 2 O 5 used as the cathode in a Zn-ion battery [START_REF] Liu | Calcium vanadate submicrofibers as highly reversible host cathode material for aqueous zinc-ion batteries[END_REF]. This large value can be explained by the 1D morphology and the large interlayer distance of our CVO material. It is two decades higher than the Li + diffusion in LiV 3 O 8 [START_REF] Chen | High rate, long lifespan LiV 3 O 8 Nanorods as a cathode material for lithium-ion batteries[END_REF], TiO 2 [START_REF] Reddy | Metal oxides and oxysalts as anode materials for Li ion batteries[END_REF], and LiCoO 2 [START_REF] Okubo | Nanosize effect on highrate Li-ion intercalation in LiCoO 2 electrode[END_REF] in organic or aqueous cells, which shows that the diffusion of Ca ion in the solid CVO electrode might not be the rate-limiting step of the mass transport.

Finally, the set of results presented here highlights the high performance of CaV 6 O 16 •7H 2 O (CVO) with 1D morphology as an electrode material for Ca-ion aqueous battery application, prepared from the molten salt method synthesis route. Beyond CVO, this method allows for the preparation of other 1D materials with high electrochemical performance, which highlights the opportunities offered by such a method to prepare materials with improved performance for energy storage applications.

Conclusions

In this paper, we proposed a general and rapid molten salt synthesis route (MSM) to prepare various 1D cationintercalated vanadium-based ternary metal oxides. Nanoribbons LiV 3 O 8 , CaV 2 O 6 and CVO have also been prepared and used as electrode materials and excellent electrochemical performances were observed. As a novel electrode material for aqueous Ca-ion batteries, the electrochemical performance and storage mechanism of CVO were studied in detail. Favorable structural features and nanoscale morphology act in concert to enable high specific capacities (205 mA h g -1 ), high-rate kinetics (117 mA h g -1 at 12C), and long-term cyclability (97% capacity retention after 200 cycles at 3.0C). Additionally, 1D CaV 2 O 6 was also first proposed as the electrode material for the aqueous Ca-ion battery, with a capacity of 153 mA h g -1 , long cycle life (>95% capacity retention after 700 cycles at a 5C rate) and high-rate performance (58 mA h g -1 at 50C) during Ca-ion (de)intercalation reactions.

Materials and Methods

4.1. Material Synthesis. Ca(NO 3 ) 2 •4H 2 O (99%), LiNO 3 (99%), NaNO 3 (99%), and KNO 3 (99%) were obtained from Sigma-Aldrich and V 2 O 5 (99.6%) from Aldrich and VCl 3 (97%) from Alfa Aesar.

In a typical procedure, 6 g of nitrate powder (Ca(NO 3 ) 2 •4H 2 O : NaNO 3 = 1 : 1 in weight ratio) mixed in a quartz crucible is transferred into the furnace at a temperature of 450 °C in the air to get colorless molten salt. 0.2 g of V 2 O 5 powder is then added in the molten salt. After 3.5 minutes of holding time, the product inside the crucible is

Figure 1 :

 1 Figure 1: Realistic and schematic representation of the molten salt method synthesis process. (a) The precursor was added when salts were heated to the molten state. (b) The sample was removed from the furnace after reacting for a few minutes. (c) The samples were obtained after washing with DI water.

Figure 2 (

 2 Figure 2(b) shows the X-ray diffraction pattern, where all peaks are well indexed with the CaV 6 O 16 •7H 2 O (JCPDS card number: 01-084-2134); additionally, the weak intensity and broad peak feature evidence a typical nanocrystalline structure of the prepared CVO. The refinement of lattice parameters (a = 11:96 Å, b = 3:56 Å, and c = 10:47 Å) leads to an interlayer spacing of 10.4 Å, which is larger than that of LiV 3 O 8 (6.36 Å), V 2 O 5 (4.37 Å)[START_REF] Zhang | Ultralong metahewettite CaV 6 O 16 •3H 2 O nanoribbons as novel host materials for lithium storage: Towards high-rate and excellent long-term cyclability[END_REF], and some other vanadium bronzes incorporating alkali metals.The hydrated calcium vanadate mineral CaV 6 O 16 •nH 2 O has three distinct phases containing 9-, 7-, and 3H 2 O, respectively[START_REF] Geological | The crystal structure of hewettite[END_REF]. The water content in our CVO material was determined using TGA technique in argon atmosphere such as shown in Figure2(c). The plot reveals a total weight loss of 20.5% from room temperature to 400 °C. Two peaks can be clearly observed in the derivative thermos gravimetric (DTG) curve shown in Figure2(c). As a result, the TG curve can be divided into two parts: from room temperature to 100 °C, a smaller weight variation 3.7% weight loss corresponds to physisorbed water, whereas above 100 °C, the weight loss of 16.8 wt% is due to the crystal water. This value

Figure 2 :

 2 Figure 2: Characterization of CaV 6 O 16 •7H 2 O (CVO) nanomaterial. (a) SEM image and TEM image, (b) X-ray diffraction pattern, (c) TGA result, and (d) EDX image and atom ration of calcium and vanadium element.

Figure 3 :

 3 Figure 3: Electrochemical performance of CaV 6 O 16 •7H 2 O (CVO). (a) Galvanostatic charge/discharge profiles at a current density of 0.3 C. (b) Galvanostatic charge/discharge profiles at different current densities. (c) Rate capability at varying C rates. (d) Cycling performance at a current density of 3 C.

  In this work, to clear out the role of hydronium ions, CaV 6 O 16 •7H 2 O electrodes were tested in various electrolytes with the same Ca(NO 3 ) 2 concentration but at different pH, by increasing the pH with Ca(OH) 2 . The similar electrochemical signatures of the CV (Figure4(a)) in pH 2.3 and pH 10 electrolytes support a redox reaction where the main process is the intercalation of the Ca ion in the CVO host structure, according to CaV 6 O 16 • 7H 2 O + 2:75 Ca 2+ + 5:5 e -↔ Ca 3:75 V 6 O 16 • 7H 2 O

Figure 5 (

 5 Figure 5(c) shows the contribution of surface vs. bulk processes obtained from equation (3) during the CV achieved at

Figure 4 :

 4 Figure 4: Electrochemical behavior of a CaV 6 O 16 •7H 2 O (CVO) electrode in pH = 2:3 (4.5 M Ca(NO 3 ) 2 ) and pH = 10 (4.5 M Ca(NO 3 ) 2 +Ca(OH) 2 ) electrolytes, with (a) CV plots recorded at a potential scan rate of 2 mV s -1 and (b) comparison of the discharged (reduction process) specific capacity versus various current density of the CVO electrode in the two different electrolytes.

  Figure 6(b) shows the change of the real part of the impedance with ω -1/2 .

Figure 5 :

 5 Figure 5: Reaction kinetic analysis of CaV 6 O 16 •7H 2 O (CVO). (a) Cyclic voltammetry curves at various scan rates from 0.05 to 5 mV s -1 in 4.5 M Ca(NO 3 ) 2 at pH 10 electrolyte. (b) The b-coefficient calculated from the peak current and scan rate. (c) Separation of the surface (nondiffusion-limited) and bulk (diffusion-limited) processes of charge storage at 0.2 mV s -1 . (d) Surface and bulk current contributions to the total charge versus the scan rates from 0.05 to 5 mVs -1 .

Figure 6 :

 6 Figure 6: Electrochemical impedance spectroscopy measurements of a CaV 6 O 16 •7H 2 O (CVO) electrode in 4.5 M Ca(NO 3 ) 2 at pH 10 electrolyte. (a) EIS analysis at different potentials at the 3 rd discharge (reduction) cycle. (b) Change of the real part of the impedance Z′ versus the square root of the reverse of the pulsation ω -1/2 in the low-frequency region (from 10 to 32 mHz) recorded at -0.6 V during the 3 rd discharge cycle.

: range using 0.0099 °steps in 1 hour. The patterns are refined using the profile matching method implemented in the Jana2006 software.

The composition of the samples was examined by an Xray fluorescence spectrometer BRUKER S2 Ranger. The morphology and composition of the sample were observed with a Scanning Electron Microscope (SEM) JSM 7100F (JEOL, Japan) at an accelerating voltage of 20 kV with energydispersive X-ray spectroscopy (EDX) capabilities. Transmission Electron Microscopy (TEM) and High-Resolution Transmission Electron Microscopy (HTEM) images were performed using a JEM-2100F microscope working at an acceleration voltage of 200 kV. Thermo gravimetric analysis (TGA) was performed in an alumina crucible using an ATG-ATD Setaram TGDTA 92 in nitrogen using a ramping rate of 10 °C min -1 .

Electrochemical Measurements.

For the electrochemical performance evaluation, 3-electrode Swagelok© cells were assembled in ambient conditions. In this setup, the counter electrode was YP-50 (Kuraray, Japan) and the reference electrode was the saturated calomel electrode (SCE). The R-XR110 type SCE reference electrode was purchased from Bio-Logic Science Instruments. To prepare the electrolyte, 4.5 M Ca(NO 3 ) 2 was dissolved in deionized water firstly and then saturated Ca(OH) 2 was added inside to increase the pH until 10. Finally, additional Ca(NO 3 ) 2 •4H 2 O was added to ensure that the concentration of Ca(NO 3 ) 2 was still kept at 4.5 M. The electrolytes were purged with argon gas before use. The separator was two layers of 260 μm thick porous borosilicate glass fibers (Whatman GF/A). To prepare the working electrode, 70 wt% active material and 20 wt% conductive carbon (Super-P) were mixed homogeneously first and then added inside a bottle containing 10 wt% of polyvinylidene fluoride binder in N-methyl-2-pyrrolidone. The active material mass loading is around 2-4 mg cm -2 . A multichannel VMP3 electrochemical working station (Bio-Logic, S.A.) has been applied for all the electrochemical tests. The electrochemical impedance spectroscopy measurement was scanned from 1 MHz to 0.01 Hz.

For sample preparation of the electrochemical quartz crystal microbalance (EQCM), Bio-Logic 1 in. diameter Au-coated quartz crystals (oscillating frequency, f0, 5 MHz) were coated using a precise pipette (Gilson PIPET-MAN Classic P20) with a slurry containing 70 wt% of active material CVO powder, 20 wt% of conducting carbon (Super-P), and 10 wt% of polyvinylidene fluoride (Arkema, CAS #24937-79-9) binder in N-methyl-2-pyrrolidone (Sigma-Aldrich, CAS #872-50-4). The coated quartz crystal was placed on a PTFE holder in which the coated side is orientated toward the reference and the counter electrode served as the working electrode in a 3-electrode electrochemical cell. The counter electrode is a platinum-coated titanium mesh. The SCE was used as a reference electrode placed between working and counter electrodes. Three electrodes were set in glassware and immersed in 4.5 M Ca(NO 3 ) 2 (pH = 2:3) or a mixture of Ca(NO 3 ) 2 and Ca(OH) 2 (pH = 10) aqueous electrolytes. All the EQCM electrochemical measurements were carried out by a Maxtek EQCM system combined with an Autolab PGSTAT101 which was used for simultaneous EQCM and electrochemical measurements.

The EQCM data was treated based on the Sauerbrey equation: Δm = -Cf * Δf , where Δm is the change of mass of the coating and Cf is the sensitivity factor of the crystal. The sensitivity factor of the coated quartz was obtained by performing a copper deposition experiment conducted in 0.1 M CuSO 4 mixed with 1 M H 2 SO 4 by applying a constant current of 5 mA for 120 seconds. In this experiment, the Cf was calculated to be 5.08 ng•Hz -1 (or 4.05 ng•Hz -1 cm -2 taking into account the Au crystal electrode surface of 1.27 cm 2 ). For consistent results, few cycles were run before starting EQCM measurements, to start from stable, reproducible electrochemical signatures.

Conflicts of Interest

The authors declare no competing financial interests. All of the authors participated in the preparation of the manuscript. The authors thank J. Yao for simplifying the data processing method to separate the capacitive and diffusion contributions.

Authors' Contributions

Acknowledgments

This work was supported by the French Agence Nationale de la Recherche (Labex STOREX program); L. Liu is supported by the China Scholarship Council (CSC).

quenched in the air. The as-synthesized product was thoroughly washed with distilled water to remove excess nitrate powder and finally freeze-dried. MV 3 O 8 (M = Li, K) was prepared following the same molten salt process but using 5 g of LiNO 3 or 5 g of KNO 3 . The molten salt is obtained by heating at 380 °C. 0.2 g of VCl 3 used as the vanadium source is introduced in the molten salt and the reaction time is set to 1 minute. To prepare K 3 V 5 O 14 , 5 g of KNO 3 was heated at 380 °C while 0.2 g of V 2 O 5 was used as the vanadium source; the reaction time is only 1 minute. For CaV 2 O 6 and Ca 2 V 2 O 7 , the composition changes with the increase of reaction time; a mixture containing 3 g of KNO 3 and 3 g Ca(NO 3 ) 2 •4H 2 O was heated as a solvent at 480 °C while 0.2 g of V 2 O 5 was used as the vanadium source-the reaction times are 5 minutes and 10 minutes, respectively. The washing and drying procedure is the same as previous.

Physical Characterization. The X-ray diffraction (XRD)

pattern is collected using a D4 ENDEAVOR diffractometer (Bruker, Germany) equipped with Cu Kα radiation (λ = 0 154 nm). Data are collected in the 5 to 50 2θ angle

Supplementary Materials

Table S1: compare the different properties of monovalent ions and multivalent ions. S5a can be indexed to a well-crystallized layered KV 3 O 8 (JCPDS 22-1247); the intensity of the (100) peak is extremely high, suggesting that the (100) planes are probably the major growth direction. Figure S5c confirmed that the KV 3 O 8 had nanofiber features with a length of 10-20 μm and diameters of around 100 nm. As shown in Figure S5d, the monoclinic LiV 3 O 8 (JCPDS 35-0437, space group: P21/m) had typical diameters of around 200 nm and the nanowire morphology.