António V Lopes
email: antonio.lopes@unbabel.com

Amin Farajian

Rachel Bawden
email: rachel.bawden@ed.ac.uk

André Michael Zhang
email: mjqzhang@cs.washington.edu

F T Martins

M Amin Farajian

André F T Martins
email: andre.martins@unbabel.com

Document-level Neural MT: A Systematic Comparison

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

There has been undeniable progress in Machine Translation (MT) in recent years, so much so that for certain languages and domains, when sentences are evaluated in isolation, it has been suggested that MT is on par with human translation [START_REF] Hassan | Achieving human parity on automatic Chinese to English news translation[END_REF]. However, it has been shown that human translation clearly outperforms MT at the document level, when the whole translation is taken into account [START_REF] Läubli | Has machine translation achieved human parity? a case for document-level evaluation[END_REF][START_REF] Toral | Attaining the Unattainable? Reassessing Claims of Human Parity in Neural Machine Translation[END_REF][START_REF] Laubli | A set of recommendations for assessing human-machine parity in language translation[END_REF]. For example, the Conference on Machine Translation (WMT) now considers inter-sentential translations in their shared task [START_REF] Barrault | heart and soul! N'oubliez pas vos amis: ils sont toujours près de vous! 'Don't forget your friends: they are always near to you' Truncation Neighbor. what have you done? Voisin ? 'Neighbour?'[END_REF]. This sets a demand for context-aware machine translation: systems that take the context into account when translating, as opposed to translating sentences independently.

Translating sentences in context (i.e. at the document level) is essential for correctly handling discourse phenomena whose scope can go beyond the current sentence and which therefore require document context [START_REF] Hardmeier | Discourse in Statistical Machine Translation. a survey and a case study[END_REF][START_REF] Bawden | Going beyond the sentence: Contextual Machine Translation of Dialogue[END_REF][START_REF] Wang | Discourse-Aware Neural Machine Translation[END_REF]. Important examples include anaphora, lexical coherence and cohesion, deixis and ellipsis; crucial aspects in delivering high quality translations which often are poorly evaluated using standard automatic metrics.

Numerous context-aware neural MT (NMT) approaches have been proposed in recent years [START_REF] Tiedemann | Neural machine translation with extended context[END_REF][START_REF] Zhang | Improving the Transformer Translation Model with Document-Level Context[END_REF][START_REF] Maruf | Selective Attention for Contextaware Neural Machine Translation[END_REF][START_REF] Miculicich | Document-Level Neural Machine Translation with Hierarchical Attention Networks[END_REF]Voita et al., 2019b;[START_REF] Tu | Learning to remember translation history with a continuous cache[END_REF], integrating source-side and sometimes target-side context. However, they have often been evaluated on different languages, datasets, and model sizes. Certain models have also previously been trained on few sentence pairs rather than in more realistic, highresource scenarios. A direct comparison and analysis of the methods, particularly concerning their individual strengths and weaknesses on different language pairs is therefore currently lacking.

We fill these gaps by comparing a representative set of context-aware NMT solutions under the same experimental settings, providing:

• A systematic comparison of context-aware NMT methods using large datasets (i.e. pre-trained using large amounts of sentence-level data) for three language directions: English (EN) into French (FR), German (DE) and Brazilian Portgueuse (PT br). We evaluate on (i) document translation using public data for EN→{FR,DE} and (ii) chat translation using proprietary data for all three directions. We use targeted automatic evaluation and human assessments of quality.

• A novel document-level method inspired by the Star transformer approach [START_REF] Guo | Startransformer[END_REF], which can leverage full document context from arbitrarily large documents. NMT systems are based on the encoder-decoder architecture [START_REF] Bahdanau | Neural machine translation by jointly learning to align and translate[END_REF], where the encoder maps the source sentence into word vectors, and the decoder produces the target sentence given these source representations. These systems, by assuming a conditional independence between sentences, are applied to sentence-level translation, i.e. ignoring source-and target-side context. As such, current state-of-the-art NMT systems optimize the negative log-likelihood of the sentences:

p(y (k) |x (k) ) = n t=1 p(y (k) t |y (k) <t , x (k) ), (1)
where x (k) and y (k) are the k th source and target training sentences, and y

(k)
t is the t th token in y (k) . In this paper, the underlying architecture is a Transformer [START_REF] Vaswani | Attention is all you need[END_REF]. Transformers are usually applied to sentence-level translation, using the sentence independence assumption above. This assumption precludes these systems from learning inter-sentential phenomena. For example, [START_REF] Smith | On integrating discourse in machine translation[END_REF] analyzes certain discourse phenomena that sentence-level MT systems cannot capture, such as obtaining consistency and lexical coherence of named entities, among others.

Context-aware NMT

Context-aware NMT relaxes the independence assumption of sentence-level NMT; each sentence is translated by conditioning on the current source sentence as well as other sentence pairs (source and target) in the same document. More formally, given a document D containing K sentence pairs {(x (1) , y (1) ), (x (2) , y (2) ), . . . , (x (K) , y (K) )}, the probability of translating x (k) into y (k) is:

p(y (k) | x (k) ) = n t=1 p(y (k) t | y (k)
<t , X, Y (<k) ), (2) 1 The dataset and scripts are available at https://github.com/ rbawden/Large-contrastive-pronoun-testset-EN-FR where X := {x (1) , . . . , x (K) } are the document's source sentences and Y (<k) := {y (1) , . . . , y (k-1) } the previously generated target sentences.

Chat translation

A particular case of context-aware MT is chat translation, where the document is composed of utterances from two or more speakers, speaking in their respective languages [START_REF] Maruf | Contextual neural model for translating bilingual multi-speaker conversations[END_REF][START_REF] Bawden | DiaBLa: A Corpus of Bilingual Spontaneous Written Dialogues for Machine Translation[END_REF].

There are two main defining aspects of chat: the content type (shorter, less planned, more informal and ungrammatical and noisier), and the context available (past utterances only, from multiple speakers in different languages). Specifically, chat is an online task where only the past utterances are available and context-aware models (see §3) need to be adapted to cope with multiple speakers. In this work we introduce tokens to distinguish each speaker and modifying the internal flow of the method to incorporate both speakers' context. There is also an additional challenge in how to handle both language directions and how using gold or predicted context affects chat models. In this work we consider a simplification of this problem by assuming the language direction of the first speaker is always from a gold set, leaving for future work the assessment of the impact of using predictions of the other speaker's utterances.

Context-aware NMT methods

We compare three previous context-aware approaches (concatenation, multi-source and cachebased) in our experiments. As well as illustrating different methods of integrating context, they vary in terms of which context (source/target, previous/future) and how much context (number of sentences) they can exploit, as shown in Table 1. Although other context-aware methods do exist, we choose these three methods as being representative of the number of context sentences and usage of both source and target side context.

Concatenation: Tiedemann and Scherrer (2017) use the previous sentence as context, i.e. X (k-1) and Y (k-1) , concatenated to the current sentence, i.e. X (k) and Y (k) , separated by a special token. It is called 2to1 when just the source-side context is used, and 2to2 when the target is used too.

Multi-source context encoder:

Zhang et al. (2018) model the previous source sentences, X (<k) with an additional encoder. They modify the transformer encoder and decoder blocks to integrate this encoded context; they introduce an additional context encoder in the source side that receives the previous two source sentences as context (separated by a special token), encodes them and passes the context encodings to both the encoder and decoder, integrating them using additional multi-head attention mechanisms. Similar to the concatenation-based approach, here the context is limited to the previous few sentences.

Cache-based: Tu et al. ( 2018) model all previous source and target sentences, X (<k) and Y (<k) with a cache-based approach [START_REF] Grave | Improving neural language models with a continuous cache[END_REF], whereby, once a sentence has been decoded, its decoder states and attention vectors are saved in an external key-value memory that can be queried when translating subsequent sentences. This is one of the first approaches that uses the global context.

Other methods have been proposed to use both source and target history with different ranges of context. [START_REF] Miculicich | Document-Level Neural Machine Translation with Hierarchical Attention Networks[END_REF] attends to words from previous sentences with a 2-stage hierarchical approach, while [START_REF] Maruf | Selective Attention for Contextaware Neural Machine Translation[END_REF], similarly, attends to words in specific sentences using sparse hierarchical selective attention. (Voita et al., 2019a), which extends the concatenationbased approach to four sentences in a monolingual Automatic Post-Edition (APE) setting; whereas Junczys-Dowmunt (2019) proposes full document concatenation with a BERT model to improve the word embeddings through document context and full document APE. [START_REF] Ng | Facebook fair's wmt19 news translation task submission[END_REF] proposes a noisy channel approach with reranking, where the language model (LM) operates at document-level but the reranking does not. [START_REF] Yu | Putting machine translation in context with the noisy channel model[END_REF] extends the previous work using conditionally dependent sentence reranking with the document-level LM.

#Prev #Fut Src Trg Concat2to1 (1) 1 - Concat2to2 (1) 1 - Multi-source context encoder (2) 2 - Cache-based (3) all - Star (4) -(see §4)
all all (src)

Target APE (5) 3 3 Sparse Hierarchical attn. (6) all -Table 1: A summary of the methods compared (1-4). We also include (5-6) in this summary table for comparative purposes.

Doc-Star-Transformer

We propose a scalable approach to document-level NMT inspired by the Star architecture [START_REF] Guo | Startransformer[END_REF] for sentence-level NMT. We have an equivalent relay node and build sentence-level representations; we propagate this non-local information at document-level and enrich the word-level embeddings with context information.

To do this, we augment the vanilla sentencelevel Transformer model of [START_REF] Vaswani | Attention is all you need[END_REF] with two additional multi-headed attention sublayers. The first sub-layer is used to summarize the global contribution of each sentence into a single embedding. The second layer then uses these sentence embeddings to update word representations throughout the document, thereby incorporating document-wide context.

In §4.1, we describe our model assuming it can attend to context from the entire document without practical memory constraints. Then in §4.2 we show how to extend the model to arbitrarily long contexts by introducing sentence-level recurrence.

Document-level Context Attention

We begin by describing the encoder of the Doc-Star-Transformer (Figure 1). We refer to the sentence and word representations of the k th sentence at layer i as s (k) i and w (k) i respectively. Our Doc-Star-Transformer model makes use of the Scaled Dot-Product Attention of [START_REF] Vaswani | Attention is all you need[END_REF] to perform alternating updates to sentence and word embeddings across the document to efficiently incorporate document-wide context; our method can efficiently capture local and non-local context (at document-level) and, like the Star Transformer, also eliminates the need to compute pairwise attention scores for each word in the document .

Intermediate word representations, H

i , are updated with sentence-level context. These intermediate representation are then used in a second stage of multi-headed attention to generate an embedding for each sentence in the document.

H (k) i = Transformer(w (k) i-1 ), (3)
s (k) i = MultiAtt(s (k) i-1 , H (k) i ), (4)
We then concatenate the newly constructed sentence representations and allow each word in sentence k to attend to all preceding sentences' representations. 2 Finally, we apply a feed-forward net-work, which uses two linear transformations with a ReLU activation to get the layer's final output. The Doc-Star-Transformer decoder follows a similar structure to the encoder, except that the decoder does not have access to the sentence representation of the current sentence k, thus, removing sentence s (k) i from (5). Source-side context is added through concatenation of the previous sentence embeddings from the final layer of the encoder with the decoder's in (5).

H (k) i = MultiAtt(H (k) i , [s (k) i ; s (k-1) i ; . . . ; s (1) i ]), (5)
w (k) i = ReLu(H (k) i ), (6)

Sentence-level Recurrence

To overcome practical memory constraints (due to very long documents), we introduce a sentencelevel recurrence mechanism with state reuse, similar to that used by [START_REF] Dai | Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context[END_REF]. During training, a constant number of sentence embeddings are cached to provide context when translating the next segment. We cut off gradients to these cached sentence embeddings, but allow them to the decoder side. In the document-MT setting, (5) concatenates all sentences' representations to include context from future source-side sentences during translation. be used to model long-term dependencies without context fragmentation. More formally, we allow τ to be the number of previous sentence embeddings maintained in the cache and update as follows:

H (k ) i = MultiAtt(H (k) i , [s (k) i ; s (k) i-1 ; . . . ; s (B) i ; SG(s (B) i ); . . . ; SG(s (B-τ ) i )]),
where B is the index of the first sentence in the batch and SGs are the sentence representations with stopped gradients. In contrast with previous approaches, such as Hierarchical Attention [START_REF] Maruf | Selective Attention for Contextaware Neural Machine Translation[END_REF], this gradient caching strategy has the advantage of letting the model attend to full source context regardless of document lengths and therefore to avoid practical memory issues.

Evaluating Context-Aware NMT

The evaluation of context-aware MT is notoriously tricky [START_REF] Hardmeier | Discourse in Statistical Machine Translation. a survey and a case study[END_REF]; standard automatic metrics such as BLEU [START_REF] Papineni | BLEU: a method for Automatic Evaluation of Machine Translation[END_REF] are poorly suited to evaluating discourse phenomena (e.g. anaphoric references, lexical cohesion, deixis, ellipsis) that require document context. We therefore evaluate all models using a range of phenomenon-specific contrastive test sets.

Contrastive sets are an automatic way of evaluating the handling of particular phenomena (Sennrich, 2017; Rios [START_REF] Gonzales | Improving word sense disambiguation in neural machine translation with sense embeddings[END_REF]. The aim is to assess how well models rank correct translations higher than incorrect (contrastive) ones. For context-aware test sets, the correctness of translations depends on context. Several such sets exist for a range of discourse phenomena and for several language directions: EN→FR [START_REF] Bawden | Evaluating Discourse Phenomena in Neural Machine Translation[END_REF], EN→DE [START_REF] Müller | A large-scale test set for the evaluation of context-aware pronoun translation in neural machine translation[END_REF] and EN→RU (Voita et al., 2019b). In this article, we evaluate using the following test sets for our two language directions of focus, EN→DE and EN→FR: EN-FR: anaphora, lexical choice [START_REF] Bawden | Going beyond the sentence: Contextual Machine Translation of Dialogue[END_REF]): 3 two manually crafted sets (200 contrastive pairs each), for which the previous sentence determines the correct translation. The sets are balanced such that each correct translation also appears as an incorrect one (a non-contextual baseline achieves 50% precision). Anaphora examples include singular and plural personal and possessive pronouns. In addition to standard contrastive examples, this set also contains contextually correct examples, where the antecedent is translated strangely, designed to test the use of past translation decisions. Lexical choice examples include cases of lexical ambiguity (cohesion) and lexical repetition (cohesion).

EN→DE: anaphoric pronouns (ContraPro) (M üller et al., 2018).4 A large-scale automatically created set from OpenSubtitles2018 [START_REF] Lison | OpenSubtitles2018: Statistical rescoring of sentence alignments in large, noisy parallel corpora[END_REF], in which sentences containing the English anaphoric pronoun it (and its corresponding German translations er, sie or es) are automatically identified, and contrastive erroneous translations are automatically created. The test set contains 4,000 examples for each target pronoun type, and the disambiguating context can be found in any number of previous sentences.

EN→FR: large-scale pronoun test set We automatically create a large-scale EN→FR test set from OpenSubtitles2018 [START_REF] Lison | OpenSubtitles2018: Statistical rescoring of sentence alignments in large, noisy parallel corpora[END_REF] in the style of ContraPro, with some modifications to their protocol due to the limited quality of available tools. The test set is created as follows:

1. Instances of it and they and their antecedents are detected using NEURALCOREF.5 Unlike Müller et al. ( 2018), we only run English coreference due to a lack of an adequate French tool.

2. We align pronouns to their translations (il, elle, ils, elles) using FastAlign [START_REF] Dyer | A simple, fast, and effective reparameterization of IBM model 2[END_REF].

3. Examples are filtered to only include subject pronouns (using Spacy6 ) with a nominal antecedent, aligned to a nominal French antecedent matching the pronoun's gender. We also remove examples whose antecedent is more than five sentences away to avoid cases of imprecise coreference resolution.

4. Contrastive translations are created by inverting the pronouns' gender (cf. Figure 2). We modify the gender of words that agree with the pronoun (e.g. adjectives and some past participles) using the Lefff lexicon [START_REF] Sagot | The lefff, a freely available and large-coverage morphological and syntactic lexicon for French[END_REF]).

The test set consists of 3,500 examples for each target pronoun type (cf. Table 2 for the distribution of coreference distances).

Experimental Setup

As mentioned in §1, we aim to provide a systematic comparison of the approaches over the same datasets, training data sizes and language pairs. We study whether pre-training with larger resources (in a more realistic high-resource scenario) has an impact on the methods on language directions that are challenging for sentence-level MT. We consider translation from English into French (FR), German (DE) and Brazilian Portuguese (PT br), which all have gendered pronouns corresponding to neuter anaphoric pronouns in English (it for all three and they for FR and PT br).

We compare the three previous methods ( §3) plus the Doc-Star-Transformer in two scenarios: (i) document MT, testing on TED talks (EN→FR and EN→PT br), and (ii) chat MT testing on proprietary conversation data for all three directions.

Data

For both scenarios, we pre-train baseline models on large amounts of publicly available sentence-level parallel data (∼18M , ∼22M and ∼5M sentence pairs for EN→DE, EN→FR, and EN→PT br respectively). We then separately finetune them to each domain. For the document MT task, we consider EN→DE and EN→FR and finetune on IWSLT17 [START_REF] Cettolo | WIT 3 : Web Inventory of Transcribed and Translated Talks[END_REF]) TED Talks, using the test sets 2011-2014 as dev sets, and 2015 as test sets. For the chat MT task, we finetune on (anonymized) proprietary data of 3 different domains and on an additional language pair (EN→PT br). Dataset sizes are shown in Table 3 (sentence-level pre-training data) and Tables 45(document and chat task data respectively).

Training Configuration

For all experiments we use the Transformer base configuration (hidden size of 512, feedforward size of 2048, 6 layers, 8 attention heads) with the learning rate schedule described in [START_REF] Vaswani | Attention is all you need[END_REF]. We use label smoothing with an epsilon value of 0.1 [START_REF] Pereyra | Regularizing neural networks by penalizing confident output distributions[END_REF] and early stopping of 5 consecutive non-improving validation points of both accuracy and perplexity. Selfattentive models are sensitive to batch size [START_REF] Popel | Training tips for the transformer model[END_REF], and so we use batches of 32k tokens for all methods. 7 For all tasks, we use a subword unit vocabulary [START_REF] Sennrich | Neural machine translation of rare words with subword units[END_REF] with 32k operations. We share source and target embeddings, as well as target embeddings with the final vocab projection layer [START_REF] Press | Using the output embedding to improve language models[END_REF].

For the document translation experiments, we run the same experimental setting with 3 different seeds and average the scores of each model.

For the approaches that fine-tune just the document-level parameters (i.e. cache-based, multi-source encoder, and Doc-Star-Transformer), we reset all optimizer states and train with the same configuration as the baselines (with the base parameters frozen), as described in [START_REF] Tu | Learning to remember translation history with a continuous cache[END_REF][START_REF] Zhang | Improving the Transformer Translation Model with Document-Level Context[END_REF]. For Doc-Star-Transformer we use multi-heads of 2 and 8 heads. All methods are 7 The optimizer update is delayed to simulate the 32k tokens. implemented in Open-NMT [START_REF] Klein | Open-NMT: Open-source toolkit for neural machine translation[END_REF].

Chat-specific modifications

In the case of the concatenation-based approaches, multi-source context encoder, and the Doc-Star-Transformer, we add the speaker symbol as special token to the beginning of each sentence. For the cache-based systems, we introduce two different caches, one per speaker, and investigate different methods for deep fusing them [START_REF] Tu | Learning to remember translation history with a continuous cache[END_REF]: (i) deep fusing the first speaker's cache first and next fusing with the second speaker's cache, (ii) the same method but with the second speaker first, and (iii) jointly integrating the caches. In addition, for the cache-based system we explore the effect of storing full words or subword units in the external memory For the full word approach, we use subword units in the vocab but merge the words when adding to the cache.

Evaluation setup

We perform both automatic and manual evaluation, in order to gain more insights into the differences between the models.

Automatic evaluation:

We first evaluate all methods with case-sensitive detokenized BLEU [START_REF] Papineni | BLEU: a method for Automatic Evaluation of Machine Translation[END_REF]. 8 We then evaluate context-dependent discourse-level phenomena using the previously described contrastive test sets. For EN→DE this corresponds to the large-scale anaphoric pronoun test set of [START_REF] Müller | A large-scale test set for the evaluation of context-aware pronoun translation in neural machine translation[END_REF] and for EN→FR our own analogous large-scale anaphoric pronoun test set (described in §5),9 as well as the manually crafted test sets of [START_REF] Bawden | Going beyond the sentence: Contextual Machine Translation of Dialogue[END_REF] for anaphora and coherence/cohesion.

Manual evaluation: In the case of the chat translation task (using proprietary data), in addition to BLEU, we also manually assess the performance of the systems with professional human annotators, who mark the errors of the systems with different levels of severity (i.e. minor, major, critical). In the case of extra-sentential errors such as agreements we asked them to mark both the pronoun and its antecedent. We score the systems' performance using Multidimensional Quality Metrics (MQM) [START_REF] Lommel | Multidimensional quality metrics: a flexible system for assessing translation quality[END_REF]:

M QM =100 - minor + major * 5 + critical * 10 Word count
By having access to the full conversation, the annotators can annotate both intra-and extrasentential errors (e.g. document-level error examples of agreement or lexical consistency).

We prioritize documents with a large number of edits compared to the sentence-level baseline (normalized by document length) due to documentlevel systems tending to perform few edits with respect to the high performance non-context-aware systems. We request annotations of approximately 200 sentences per language pair and method.

7 Results and analysis

Document Translation Task

Table 6 shows the results of the average performance of each system on IWSLT data according to BLEU. Although the approaches have previously shown improved performance compared to a baseline, when a stronger baseline is used, we see marginal to no improvements over the baseline for both language directions. Table 7 shows the average performance of each system for all contrastive sets. The results differ greatly from BLEU results; methods on par or below the baseline according to BLEU perform better than the baseline when evaluated on the contrastive test sets. This is notably the case of the Concat models, which achieve some of the best results on the both large-scale pronoun sets (EN→DE and EN→FR), as shown by the high percentages on the more difficult feminine pronoun Sie for EN→DE and all pronouns for EN→FR.

Most models struggle to achieve high performances for the feminine sie and masculine er, which is likely due to neuter es being the majority class in the training data. For French, although the feminine pronouns are also usually challenging, the high scores seen here are possibly due to the fact that many examples have an antecedent within the same sentence. The Concat2to2 method however performs well across the board, proving to be an effective way of exploiting context. It also achieves the highest scores on both the anaphora and coherence/cohesion test set, which is only possible when the context is actually being used, as the test set is completely balanced. This appears to confirm the findings of [START_REF] Bawden | Evaluating Discourse Phenomena in Neural Machine Translation[END_REF] that target-side context is most effectively used when channelled through the decoder. Surprisingly, the multi-source encoder approach degrades the baseline with respect to this evaluation, suggesting that the context being used is detrimental to the handling of these phenomena.

We note that using OpenSubtitles as a resource for context-dependent translation or scoring, has additional challenges. Figure 3 illustrates four of these, which could make translation more challenging if they affect the context being exploited.

Chat Translation Task

Table 8 shows BLEU score results on the proprietary data, with the modifications described in §3 to address the chat task. As expected, documentlevel information has a larger impact for the lowest resource language pair, EN→PT br, with marginal improvements on EN→FR and EN→DE.

The performance of these methods depends on the language pair and domain. Although it is not conclusive which method performs best, our proposed method improves over the baseline consistently, whereas the cache-based and Concat2to2 methods also perform well in some scenarios. For our Doc-Star-Transformer approach, using predictions rather than the gold history harms the model at inference, showing that bridging this gap could lead to a better handling of target-side context.

There is little correlation between BLEU scores and the human MQM scores (as shown by the comparison for 3 methods in Table 9). Although the difference between BLEU scores are marginal, MQM indicates that quality differences can be seen by human evaluators: the document-level systems (Cache and Star) both achieve higher results for EN→PT br (although the Star approach underperforms for EN→FR). This shows that for certain language directions, the document-level approaches do learn to fix some errors and therefore improve translation quality. This also confirms previous suggestions that BLEU is not a good met- ric to distinguish between strong NMT systems.

Conclusion

We provided a systematic comparison of several context-aware NMT methods. One of the methods in this comparison was a new adaptation of the recently proposed StarTransformer architecture to document-level MT. In addition to BLEU, we reported results of the contrastive evaluation of context-dependent phenomena (anaphora and coherence/cohesion), creating an additional largescale contrastive test set for EN→FR anaphoric pronouns, and we carried out human evaluation in terms of Multidimensional Quality Metrics (MQM). Our findings suggest that existing context-aware approaches are less advantageous in scenarios with larger datasets and strong sentencelevel baselines. In terms of the targeted contextdependent evaluation, one of the promising ap-proaches is one of the simplest: the Concat2to2, where translated context is channelled through the decoder, although our Doc-Star-Transformer method achieves good results according to the manual evaluation of MT quality.

Figure 1 :

 1 Figure 1: Doc-Star-Transformer encoder.

Table 2 :

 2 Context sentenceSome red roses for Your Ladyship. Des rosesfem. pour madame. The distribution of each pronoun type according to distance (in #sentences) from the antecedent.

	Current sentence
		Who could they be from?
		De qui peuvent-ellesfem. bien être ?
	×	De qui peuvent-ilsmasc. bien être ?
	Figure 2: An example from the large-scale EN→FR test set.
		# examples at each distance
	Pronoun	0	1	2	3	4	5
	il	1,628 1,094 363 213 127	75
	elle	1,658 1,144 356 166 106	70
	ils	1,165 1,180 501 302 196 156
	elles	1,535 1,148 409 199 128	81

Table 3 :

 3 Sentence-level corpus sizes (#sentences)

	Train	Dev	Test
	EN-DE 206K 5.4K 1.1K
	EN-FR 233K	5.8k 1.2K

Table 4 :

 4 TED talks document-level corpus sizes (#sentences)

			Domain1 Domain2 Domain3
		Train	674k	62K	13K
	EN-DE	Dev	37K	3.2K	0.6K
		Test	35K	3.6K	0.7K
		Train	395K	108K	110K
	EN-FR	Dev	21K	6.3K	6.1K
		Test	22K	6.2K	6.3K
		Train	235K	61K	13K
	EN-PT br	Dev	13K	3.4K	0.7K
		Test	13K	3.2K	0.7K

Table 5 :

 5 The corpora sizes of the chat translation task. We consider both speakers for this count.

Table 6 :

 6 BLEU score results on the IWSLT15 test set (averaged over 3 different runs for each method).

Table 7 :

 7 Accuracies (in %) for the contrastive sets. Methods outperforming the baseline are in bold.

					EN→DE					EN→FR
			Total Es	Sie	Er	Total		it	they		Anaphora	Coherence/ cohesion(%)
								elle	il	elles	ils	All	All
	Baseline	45.0	91.9 22.9 20.2	79.7	88.1 82.7 76.1 72.2	50.0	50.0
	Concat2to1	48.0	91.6 27.1 25.3	80.9	88.4 83.3 77.2 73.9	50.0	52.5
	Concat2to2	70.8	91.8 61.9 58.7	83.2	89.2 86.2 80.4 77.6	82.5	55.0
	Cache (Subwords)	45.2	92.1 23.5 19.9	79.7	88.0 82.7 76.0 72.0	50.0	50.0
	Multi-src Enc	42.6	62.3 33.9 31.5	59.0	62.0 61.3 57.2 57.3	47.0	46.5
	Star, 8 heads	45.9	91.3 27.0 19.5	79.6	88.0 82.6 76.1 72.0	50.0	50.0
						Domain1				Domain2		Domain3
					EN-DE	EN-FR	EN-PT br	EN-DE	EN-FR	EN-PT br	EN-DE	EN-FR	EN-PT br
	Baseline				78.53	79.71	81.21		72.11	76	73.94	69.67	74.76	74.95
	Concat2to1	S1,S2 + speaker tag S1		78.04 77.97	79.65 79.55	80.36 80.26		71 70.95	75.35 75.21	73.02 73.33	69.92 69.77	74.57 74.47	74.82 74.84
	Concat2to2	S1,S2 + speaker tag S1		79.84 78.88	79.3 79.15	80.33 79.92		70.56 70.13	74.87 74.9	73.52 73.33	69.74 69.59	74.37 74.25	74.56 74.33
	Cache S1 + Cli	JointPolicy Subwords JointPolicy Words		78.62 78.52	79.66 79.63	80.79 80.93		72.12 71.66	75.03 75.93	73.47 73.54	69.47 69.55	74.77 74.77	75.04 74.97
	Cache S1 only	Subwods Words			78.41 78.28	79.46 79.54	81.17 81.04		71.73 71.9	75.92 75.87	74.41 74.33	69.68 69.51	74.8 74.82	74.94 74.94
	Multi-src enc	SEP + speaker tag			78.23	79.64	81.04		71.5	75.87	73.78	-	74.66	74.82
		S1,S2 2 heads Gold target ctx		79.7	80.08	82.64		71.79	75.62	73.67	71.36	74.87	75.03
	Star	S1,S2 2 heads Predicted target ctx S1 2 heads Gold target ctx	78.81 79.35	79.38 79.58	79.63 82.52		71.72 72.16	75.58 75.95	73.7 74.1	69.38 71.33	74.77 75.01	75.11 75.48
		S1 2 heads Predicted target ctx		78.17	79.24	79.83		72.24	75.68	73.9	70.24	74.65	75.21

Table 8 :

 8 BLEU scores on the chat translation task (proprietary data for 3 different domains and language pairs). S1 and S2 refer to the speakers in the case of chat translation task.

		EN→FR	EN→PT br
		BLEU MQM BLEU MQM
	Baseline	74.76	87.46	74.95	92.47
	Cache	74.82	89.02	74,94	93.20
	Star 2 heads 75.01	86.80	75.48	95.20

Table 9 :

 9 The results of automatic and manual evaluation of the context-aware NMT methods in terms of BLEU and MQM on English→French and English→Portuguese.

We describe our method in the online setting and to match

https://github.com/rbawden/discourse-mt-test-sets

https://github.com/ZurichNLP/ContraPro

https://github.com/huggingface/neuralcoref

https://spacy.io

Using Moses'[START_REF] Koehn | Moses: Open source toolkit for statistical machine translation[END_REF] multi-bleu-detok.

For both large-scale test sets, we make sure to exclude the documents they include from the training data.

Acknowledgments

We thank the anonymous reviewers for their valuable feedback. This work is supported by the EU in the context of the PT2020 project (contracts 027767 and 038510) and the H2020 GoURMET project (825299), by the European Research Council (ERC StG DeepSPIN 758969), by the Fundac ¸ão para a Ciência e Tecnologia through contract UID/EEA/50008/2019 and by the UK Engineering and Physical Sciences Research Council (MTStretch fellowship grant EP/S001271/1).


Marie Vernet

Yves Chaix

Ève Meiss

Stéphanie Ducrot

E Meiss

& Ducrot

A computarized Tool for predicting future reading abilities in Pre-Readers Children

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

➢❖

  from different French public schools → Normal or corrected-to-normal vision Participants Vertical naming time HT -Horizontal naming time HE -Horizontal errors HTaj -Horizontal adjusted time CM -Reading accuracy CTL -Reading speed Oculomotor skills and number naming A new software module Inspired by the DEM test Richman & Garzia, the time indexes are correlated with CTL. AIM OF THE STUDY: Using a longitudinal study, the aim was to improve screening for future reading difficulties in preschool children Htaj predicted 19,4 % of the CM index ➢ VT predicted 16,5 % of the CM index ➢ HE predicted 5 % of the CM index ➢ VT predicted 29,5 % of reading speed ➢ HTaj predicted 16 % of reading Necessary to overcome anatomo-functional constraints of the eye Crowding effect and ↘ visual acuity with eccentricity Leibnitz & al., 2016 ❖ Importance of where the eyes first land in a word A left-centered initial landing position = optimal for reading Rayner, 1979 Oculomotor and visuo-attentional skills in reading CONCLUSION AND PERSPECTIVES ➢ DIAGLECT = easy-to-use software to early identify children at risk to develop reading difficulties 1. Check the sensitivity and specificity of the test in the context of learning disabilities (e.g., dyslexia, developmental coordination disorder) 2. Study the neuropsychological profile of children with difficulties in DIAGLECT software modules 3. Develop rehabilitation modules according to the difficulties identified using the tool ➢ Normative data from a large sample of French kindergarten children RESEARCH PROSPECTS CLINICAL IMPLICATIONS 1. Early identification and care for future reading difficulties in preschool children 2. Early implementation in schools, more precisely in kindergarten, of oculomotor skills training

Phonological skills

 Sprenger-Charolles & Colé, 2013As well as Visuo-attentional skills [START_REF] Franceschini | A causal link between visual spatial attention and reading acquisition[END_REF] Visuo-perceptual and visuo-motor skills [START_REF] Bellocchi | Exploring the ling between visual perception, visual-motor integration, and reading in normal developing and impaired children using DTVP-2[END_REF] Oculomotor skills [START_REF] Vernet | Vision, Attention and Reading: Identifying preschool children at risk for reading difficulties[END_REF] These preliteracy skills are crucial for future reading skills from kindergarten onwards.

Prerequisites for learning to read

Multiple linear models do not better explain the variability of CM and CTL at grade 1


Dr Guillaume Gouget

Fabrice Mauvy

Dr U-Chan Chung

Dr Sébastien Fourcade

Dr Mathieu Duttine

Marc-David Braida

Dr Thierry Le Mercier

Alain Demourgues
email: alain.demourgues@icmcb.cnrs.fr

Thierry Le Mercier

Prof F Mauvy

Dr. M.-D Braida

Associating and tuning sodium and oxygen mixed-ion conduction in niobium-based perovskites

Keywords: niobate perovskites, oxygen conductivity, sodium conductivity, mixed ion conduction, spark plasma sintering

Introduction

Electrochemical energy storage and conversion devices such as batteries or fuel cells rely on the design of electrode materials with mixed ion/electron conduction and solid electrolytes with high ionic conductivity. [1][2][3][4][5] These properties are strongly dependent on the chemical composition, the solid network architecture and, at the atomic scale, the chemical bonding; which has direct implications on the electronic band diagram, as well as chemical or electrochemical potential for electrons at the Fermi level. [6,7] Such considerations are of great interest to assess the anionic redox processes which occur at the cathode in Li-ion batteries, and their interplay with cationic electrochemistry. [8][9][10] In all solid-state batteries, research focus is primarly dedicated to electrolytes. LISICON materials are lithium super ionic conductors (Li/Al/Ti-based phosphates,  = 10 -3 S.cm -1 at room temperature-RT) which adopt a 3D ribbon network where Li + ions are located in interstitial sites. However, they are electrochemically unstable against Li-metal. [11] Li garnet (Li7La3Zr2O12), which also exhibits a 3D framework, is a promising type of electrolyte for Li-metal batteries due to its high lithium-ion conductivity ( = 10 -4 to 10 -3 S.cm -1 at RT) and better electrochemical stability against lithium-metal. [12,13] Sodium is a second alkali metal that has a larger ionic size than lithium, and is a low-cost and naturally abundant alternative to lithium. [14][15][16][17] However, replacing sodium for lithium will require a lot of improvement from a materials perspective to achieve competing performances.

High Na + ionic conductivity can be achieved with NASICON (Na + super ionic conductor, Na/Zr/Si-based phosphates with  ≈ 10 -4 S.cm -1 ) which also exhibit a 3D ribbon structure where Na + ions occupy interstitial sites. [18,19] In the last few years, efforts on novel electrode and electrolyte materials successfully yielded room-temperature battery devices. [20,21] A new NASICON (Na/Zr/Mg-based silicate-phosphate) has been shown to exhibit high roomtemperature ionic conductivity ( = 3.5 × 10 -3 S.cm -1 ). [22] However, most commercially developed sodium-based accumulators rely on a sodium-sulphur electrochemical cell operated around 320 °C with liquid Na and liquid S as positive and negative electrodes, respectively.

The electrodes are separated by -alumina (Na2O-11Al2O3) as solid electrolyte. [23,24] During the discharge, Na + formed at the anode migrates along the electrolyte to the cathode and forms liquid sodium polysulfides. The network of -alumina is bidimensionnal (intergrowth of spinel blocks and the conduction layer which are alternately stacked) in which Na + ions occupy the loosely packed NaO plane. Na + ionic conductivity in -alumina single crystals with excess Na decreases from 15 S.cm -1 at T = 350 °C to 1.4×10 -2 S.cm -1 at RT. [25] In polycrystalline undoped ceramics, it drops to 5.6×10 -2 S.cm -1 at 350 °C. [26] Despite competing energy and power densities, [27] Na-S battery technology remains limited to niche applications, due to liquid sodium polysulfide reactivity that causes hazardous issues and a drop in electromotive force along the discharge.

Based on the same concept as sodium-sulphur batteries, an original sodium-air electrochemical cell can be proposed by replacing the sulfur species by their oxygen counterpart. In such a case, the reduction of oxygen gas (1/2 O2 + 2 e - O 2-) at the cathode (e.g. Ag electrode) and oxidation of liquid-Na at the anode (2 Na  2 Na + + 2 e -) should take place during the electrochemical process, leading to the formation of Na2O. The theoretical electromotive force or the potential difference is related to the free energy G of Na2O binary oxide corresponding to E = 1.93 V (under Open Circuit Voltage conditions). [28] In this concept, sodium and/or oxygen ion conductors can be used as solid electrolytes. This leads to three questions: (i) Is it possible to design mixed Na + and O 2-ion conductors in order to enhance the global ionic mobility for this application, with a synergy between sodium and oxygen migration in a single framework? (ii) What kind of interactions arise between Na + -and O 2 -sub-networks with various ionic polarizabilities and potential synergic effects involved?(iii) Can we determine both contributions to the total ion conduction through calculation of the ionic transport numbers of each carriers?

In the solid-state chemistry approach, ionic transport associated to ionic diffusion into solids is described by the hopping of ionic species (Li + , Na + or O 2-) from one lattice site to an adjacent one through inter-connected diffusion paths in the framework. [29][30][31] Each hopping mechanism is associated with energy barriers. High concentration of mobile ion carriers (vacancies or interstices), large mobility, and a low activation energy are required to achieve high ionic conductivity. Among solid-state electrolytes in solid oxide fuel cells (SOFC), 8 %mol. yttria stabilized zirconia (YSZ-8), 10 % gadolinium-substituted ceria (CGO), and bismuth oxide display exclusive O 2-conductivity of ca. 10 -4 to 10 -3 S.cm -1 at 400 °C. [32][33][34] Their network is derived from the fluorite-type structure favoring the stabilization of oxygen vacancies. The conductivity of these state-of-the-art oxygen conductors remains lower than the Na + conductivity in NASICON or -alumina in the same temperature range. [19,26] O-deficient perovskites (general formula ABO3) stand amongst the best O 2-ionic conductors at relatively low temperatures (NaNb0.5Al0.5O2.5, NaTa0.5Al0.5O2.5, Na0.5Bi0.49TiO2.985 and Ba3MoNbO8.5), with conductivity varying between 5×10 -5 and 5×10 -4 S.cm -1 at T = 400°C. [35][36][37][38] The activation energies are 0.7-1 eV for O-deficient fluorite-type networks, compared to 0.4-0.5 eV for the perovskite-derived phases mentioned above. This is comparatively higher than values of 0.2 to 0.3 eV reported for Na + -conductive -alumina. [22,25,26] However, in the case of perovskitederived networks, the ambiguity is maintained on the assignement of the mobile carrier through calculation of activation energy. For instance, A-site defective Na3xLa1.33-x□0.67-2xTi2O6 (x ≤ 0.28) are sodium conductors with a higher activation energy of 0.92 eV, and independent on x due to the energetic barrier associated with the hopping mechanism of sodium cations. [39] In perovskite-derived structures with both Na + and O 2-potential conduction, activation energy measurements thus do not enable concluding on the nature of conduction carriers.

Several recent discoveries highlight perovskite-derived structures as efficient oxygen ion conductors below 700 °C, paving the way towards relatively low temperature applications. [36,38] Titanates and niobates with perovskite structures have been widely investigated due to the occurrence of polar phases associated with piezoelectric [40][41][42][43] and ferroelectric [44][45][46][47] properties, as well as a rich polymorphism versus temperature. [48][49][50][51][52][53] This structural complexity extends at room temperature for NaNb1-xTixO3-0.5x (0 ≤ x ≤ 0.20), with the occurrence of two structures, where only one of them is polar and crystallizes in the acentric P21ma space group. [54][55][56][57] Both the inequivalent Na sites are close in energy and stability in P21ma network, whereas they are radically different in the centrosymmetric structure (Pbma space group). Nb 5+ (4d 0 ) and Ti 4+ (3d 0 ) are stabilized in such perovskite networks and exhibit second-order Jahn-Teller distortion (SOJT), which arises from octahedral deformation due to high ionic charge, small ionic size (high polarizing power), and a relatively low bandgap (3.5 eV) involving the mixing p(O) and d(Nb, Ti) orbitals. For NaNbO3, the SOJT distortion of Nb 5+ (4d 0 ) is exhibited in the P21ma network where the two Na atoms sites share the same symmetry operators, which is not the case for Pbma space group. Na sites constrain [NbO6] octahedron to be more distorted but less rigid in the P21ma framework by competitive bonds. Such distortions favor oxygen mobility. [56] NaNb1-xTixO3-0.5x (0 < x ≤ 0.20) complex oxides were very recently shown to preferentially crystallize in the low-temperature form of sodium niobate in the acentric P21ma space group. [57] More specifically, the ionic conductivity in NaNb0.85Ti0.15O2.925 varies between 3×10 -5 and 2×10 -3 S.cm -1 in the studied interval 300 < T < 700 °C. Such performances compete with YSZ-8 ( = 10 -4 S.cm -1 at 400 °C) and CGO ( = 3.10 -4 S.cm -1 at 400 °C). [32] This is also one to two orders of magnitude higher than the conductivity in NaNbO3.

However, in this titanium-substituted sodium niobate series, the nature of the mobile species remains unclear, as Na + and O 2-could potentially contribute to the ionic conductivity mechanism. The activation energy slightly increases from 0.51 to 0.61 eV with Ti content from 5 to 15 %. [57] This can be naturally correlated to the increase of oxygen vacancy rate as well as the crystal-field (SOJT) stabilization energy around Nb 5+ /Ti 4+ centers, yielding facilitated O mobility. The concentration of O 2-carriers is directly linked to O 2-vacancies, whereas their mobility is limited by the hopping between two oxygen sites with an energy barrier for ionic diffusion. The creation of O 2-vacancies is associated with the decrease of Nb(Ti)-O bond lengths and the Nb(Ti)-O orbital overlapping. Thecovalence should then slightly increase, which explains the increase in activation energy. Despite this convincing argument, the unlikely but potential contribution of Na + must be assessed. In this sodium niobate series, the contribution of each Na + and O 2-mobile ions carriers (e.g. their ionic transport number) must first be quantified, then discussed with respect to the general perovskite-type structural family. This is necessary to finally draw structural requirements in order to efficiently associate Na + and O 2-ions mobilities in optimized solid electrolytes with improved and balanced ionic conductivity.

The starting point to address these issues is the original design of Na + blocking and O 2- conducting solid electrolyte sandwiched electrochemical cells formed during a single Spark Plasma Sintering (SPS) step. This strategy has already been proven successful in the case of monolithic Li-ion batteries. [58] Prior to that, the stabilization of Nb 4+ and oxygen vacancies in sodium niobate was observed after SPS at high temperatures (from 900°C to 1200°C) under reducing atmosphere. Conductivity measurement versus temperature under an argon environment highlights a switch from electronic conductivity (Nb 4+ ) at low temperature to ionic conductivity at temperatures close to 550-600 °C. Niobium oxidation occurs concommintantly to deep structural reorganization characterized by the strong polymorphism of NaNbO3 in this temperature range. Complex impedance diagrams on ceramics with Na + -blocking layers allow the determination of the exclusive O 2-bulk contributions to conductivity in sodium niobates and sodium titanates-niobates. The strong variability of Na + and O 2-relative contributions is demonstrated in a single framework type upon Ti substitution, paving the way toward mixed conductors with finely tuned contributions of both ionic carriers. On the basis of this unprecedented discovery, a strategy is defined towards complex oxides with enhanced mixed Na + /O 2-ionic conductivity.

Results

Composition and total conductivity of dense ceramics of sodium niobate

NaNbO3 ceramics with a relative density of at least 94 % are achieved by SPS. After this treatment, the network remains identical with the Pbma space group (Figure 1a, see also Table S1), as confirmed by a typical signature in the region 35.5 ° < 2Θ < 44.5 ° (Cu Kα source). [45,51,[55][56][57] Despite the similarities of X-Ray diffraction (XRD) patterns of both RT polymorphs, the NbO6 octahedron distortion and complex octahedral tilt schemes vary in connection with Na local environments (Figure 1b). The closest Nb-O bond lengths involving the two apical oxygens (O1 and O2 in the vicinity of Na1 and Na2 respectively, Figure 1b) and the alternation of longer and shorter Nb-O bond distances in the equatorial plane (O3 and O4), underline the octahedral tilts schemes in three different directions, as well as the key role of Na atomic positions which indirectly influence the second order Jahn-Teller distortion. As opposed to the acentric polymorph, the centrosymmetric structure in the Pbma space group displays distinct Na atomic sites by means of environnemnt (symmetry, Na-O lengths) and stability, contributing to a less distorted but more rigid framework. [56] After the SPS treatment, the structure is maintained, but the color of the pellet turns to bluegray, while the powder is initially white. The UV-visible spectrum in Figure 1c displays a strong absorption in the visible range, which is the signature of n-type semiconducting behavior.

The electron spin resonance (ESR) spectrum represented on Figure 1c reveals a broad signal associated with the paramagnetic species in an anisotropic environment with an average g value of ~1.95, attributed to the occurrence of the Nb 4+ (4d 1 ) Jahn-Teller ion stabilized in an elongated octahedral site. In comparing sodium niobates before and after SPS treatment using 93 Nb NMR spectra (Figure 1d), a strong Knight shift is observed. This shift is attributed to electron conduction in a semiconductor, definitively confirming the presence of Nb 4+ stabilized in sodium niobate after SPS at T = 900 °C. Moreover, after annealing of the SPS-treated pellet under air at 900 °C, the sodium niobate turns to white and crystallizes in the Pbma structure (Figure S1). It is noteworthy that a SPS treatment at higher temperatures (T = 1200 °C) affects the unit cell parameters with a global increase of the unit cell volume due to the stabilization of a larger content of Nb 4+ ions (Figure S2). In order to better understand the thermal evolution of the partially reduced sodium niobate conductivity under neutral gas, phase transitions have been evidenced in a first step by X-ray diffraction in the same temperature range (Figure 2a andb). Two different orthorhombic space groups (Pbmn and Cmcm) and one tetragonal (P4/mbm) are identified as the reduced unit cell parameter of the perovskite network acub deviates from the linear thermal expansion. The change of symmetry is directly connected to the NbO6 octahedron tilt scheme and distortion also associated with the Na atomic position and related polarizabilities. Overall, five of the six major polymorphs of NaNbO3 above RT are identified from the reduced sample, at expected temperatures. It is noteworthy that the color of the powder ceramic evolves from blue-grey to white (Figure 2a) after the sample cooled down to room temperature under helium atmosphere.

The thermal variation of the conductivity under argon up to T = 900 °C (Figure 2b) shows two distinct behaviors with two radically different associated activation energies: 0.14 eV with  = 10 -4 S.cm -1 at T = 200°C during the initial raise in temperature, and 0.83 eV above 600 °C and then during the decrease of T, with  = 2×10 -8 S.cm -1 at T = 200 °C in the final stage of the experiment (data from complex impedance spectroscopy). In the first step, from RT to around 550 °C, the n-type conductivity is attributed to promoted d electrons coming from Nb 4+ stabilized in sodium niobates. At temperatures around 550-600°C, several phenomena occur concommitently: (i) Nb 4+ oxidizes into Nb 5+ under low oxygen partial pressure (2×10 -5 atm) of argon or helium atmosphere, as observed by the recovery of a white color, (ii) the conductivity at 600 °C is lower than at 550 °C as a consequence of the loss of electron charge carriers, (iii) ion conduction takes over, as confirmed by the following high activation energy of 0.83 eV, and (iv) major structural rearrangements of the distorted perovskite framework take place (Figure 2d); specifically the transition from the orthorhombic Cmcm to the tetragonal P4/mbm space group, which is accompanied with the decrease of O distinct sites from 3 to 2 and Na distinct sites from 2 to 1. Following the increase of temperature above the critical temperature (550-600 °C) under argon, the conductivity measured under air from T = 900 °C to RT(e.g. without any O-vacancy maintained in the structure) indicates a similar slope in the Arrhenius plot, corresponding to Ea = 0.83 eV. As a consequence, Na + is the sole charge carrier in the oxidized structure. This key feature will be further discussed. SPS sintering is shown to yield partially reduced niobates with a conductive behavior associated with electron carriers. However, heat treatment above a critical temperature and at relatively low oxygen partial pressures allows the recovery of a fully oxidized material with exclusive ion conduction. The color of the powder evolves from gray-blue before the experiment to white, as observed after the sample cooled down to RT in helium atmosphere. b) Deviation of reduced cell parameter to linear dependence with temperature due to phase transition. c) Switch from electronic to ionic conductivity and parallel oxidation of NaNbO3-x with temperature. Starting with the blue pellet, the conductivity was measured under argon for increasing T and under air for decreasing T. After the experiment, the pellet has turned white. Data from complex impedance spectroscopy. d) Reported phase transitions of NaNbO3 with temperature [51] and structural rearrangements during quadratic transition occurring in parallel to NaNbO3-x reoxidation.

Blocking layer method

In the case of sodium (titanate) niobates, ionic conductivity can be attributed to the displacement of either Na + , O 2-or both ions in the perovskite lattice. In this case, one of the key characterstics is to determine the specific transport number of these ions depending on the structure and the chemical compositions. The transport number of a mobile charged species quantifies the contribution of each carrier to the transport of current in the solid. It is defined by Equation 1:

𝒕 𝒊 = 𝝈 𝒊 𝝈 𝒕𝒐𝒕 (1)
where ti is the transport number of the carrier type i, i is the conductivity of the species i and total is the total conductivity of the solid.

In the solid-state electrochemistry approach, different methods exist to estimate the transport number of charge carriers. Excluding the isotopic exchange methods, [59] most of them are applications of Wagner's theory. [60] The following main approaches can be mentioned: the concentration cell method, the mass balance approach, the semi-permeability flow method, [61] the conductivity relaxation method [62,63]

where all the symbols have their original meaning and L is the sample membrane thickness.

In most cases, these methods have been used for materials whose charge carriers are mainly oxygen ions, and more rarely cations. An oxygen activity gradient is necessary and two gas tight compartiments are required to induce an electromotive force (e.m.f. method), or to it is necessary to generate an ionic flow through the dense ceramic sample (semi-permeability flow method). Using these approaches, the determination of the transport numbers is not accurate.

The plateau or inflection points are very difficult to highlight on the chronoamperometry curves when the ionic conduction properties are closed due to the difficulty to maintain both sides perfectly sealed at high temperature. [64] Otherwise, the sample has to be perfectly stable under the activity gradient. This is the reason why the blocking layer method has been selected in the present work.

For this purpose, Yttria Stabilized Zirconia with 8 % of Y2O3 (YSZ-8) has been selected. It is considered as a pure O 2-ionic conductor. This material has a transport number tO2-very close to 1 under air and in the temperature range (RT < T < 900 °C) with a low number of electronic transport te-< 0.001. It is noteworthy that the diffusion of the alkaline cations is close to zero in the zirconia material which can be considered as blocking layer for the diffusion of Na + .

In the present work, the specific ion conduction of O 2-is determined for two representative compositions of the NaNb1-xTixO3-0.5x complex oxides series: x = 0 and 0.10. Symmetrical sandwich-type samples YSZ-8/NaNb1-xTixO3-0.5x/YSZ-8 are sintered in a single step by the SPS method at 1100 °C. As previously mentioned, NaNbO3 sintered by SPS at T = 1200 °C still adopts the structure in the Pbma space group despite a large content of Nb 4+ ions (Figure S2).

An additionnal heat treatment is then performed at 800 °C during 12 h under air, reoxidizing the Nb 4+ centers into Nb 5+ . The reactivity between the niobate materials and YSZ- In sandwiched pellets, O 2-is the only effective charge carrier.

Electrochemical Impedance Spectroscopy (EIS)

The impedance diagrams were measured in the 200-800 °C temperature range under air, using symmetrical cells. Under steady-state conditions, the diagrams show several contributions, as exemplified in Figure 4. Some of the depressed semi-circles are assigned to the intrinsic properties of the materials, and the others to phenomena occurring at the mixed Na + /O 2-ionic conductor (NaNb1-xTixO3-0.5x)/YSZ-8, or at the YSZ-8/noble metal (Au) interfaces. For a specific cell made of given materials, there are different approaches to assign these impedance contributions: either by varying the geometrical factor of the ceramic sample, as it influences the measured resistances and capacitances, or by changing the operating oxygen partial pressure.

In the case of YSZ-8, its well-known conduction properties do not significantly depend on the oxygen partial pressure (in the T range RT-1000 °C and PO2 range 1-10 -20 bar), while the interface polarizations (electrode reaction) are strongly affected. [65] At constant temperature and oxygen partial pressure, the impedance contributions of all the carriers are simultaneously

𝑪 𝒆𝒒 = 𝑹 𝟏-𝒏 𝒏 . 𝑪𝑷𝑬 𝟏 𝒏 (4)
where frelax , R and Ceq are the frequency relaxation, the resistance and the equivalent capacitive effect, respectively. l and S are the thickness and the surface of the pellet samples. CPE represents the modulus of the Constant Phase Element and n the depression parameter. A comparison of the fitted parameters (Ceq, Frelax and σ calculated from R) and the dimensions of samples are provided in Table S2, at approx. 324 °C for NaNbO3-related samples and 275 °C for NaNb0.9Ti0.1O2.95-related ones. The fitted parameters obtained at various temperatures are also reported on Table S3 and S4. Concerning the YSZ-8 sample sintered using SPS method, only one HF semi-circle is observed. According to the equivalent capacity and the relaxation frequency, it can be concluded that the electrochemical behaviour of this ceramic sample is in good agreement with similar data reported in the literature for YSZ-8. In addition, the relative dielectric permittivity (εR = 23) deduced from the equivalent capacity at room temperature is also close to the value reported in the literature at room temperature (εR = 30). [66,67] The lower value observed with the SPS sintered sample can be assigned to dielectric losses due to the reducing condition of the SPS process. Furthermore, as the temperature increases, the YSZ-8 ceramic cannot be considered as a pure capacitor anymore as the temperature increases, because of the oxygen ion mobility. The classical RC equivalent circuit used for dielectric material is not efficient in this case. Finally, the HF arc can be assigned to the bulk conductivity of the YSZ-8.

Concerning single phase samples, the direct assignement of the Na + and O 2-conductivitiy from fitted parameters is not possible. At 325 °C, the conductivity on NaNbO3, is 50 times lower than in YSZ-8. Similarly, only one depressed semi-circle is observed for the NaNb0.9Ti0.1O2.95.

The Ceq and relaxation frequencies frelax are closer to YSZ-8. However, slightly higher Ceq and frelax values account for lower conductivity (σ = 2.65 × 10 -6 S.cm -1 at 275 °C).

Intrepretation of impedance spectra for YSZ-8/NaNbO3/YSZ-8 is straightforward, as the contributions of each material occur in significantly different frequency regimes. Especially, the contribution of YSZ-8 bulk conductivity is not observed anymore at 415 °C and above (Figure S5). For the YSZ-8/NaNb0.9Ti0.1O2.95/YSZ-8 sample, the two main impedance contributions are observed. In the HF range, the impedance data can be assigned to oxygen ion conductivity through the YSZ-8 layer. Indeed, both the capacitive effect and the relaxation frequency are very similar to the pure YSZ-8 contributions. Because Na + is blockedby the YSZ-8 layer, the MF contribution is attributed to the O 2-ion displacement through the NaNb0.9Ti0.1O2.95 mixed conductor.

To assist the interpretation of the electrochemical data of the cells, the plots of the relaxation frequencies (frelax) and equivalent capacitances (Ceq) of each relevant impedance contribution as a function of the reverse of the temperature are represented in Figure 5a and b, respectively (Arrhenius plots). The graphs display only selected contributions of each experimental impedance diagram for the sake of clarity, and can be considered a reference for interpreting a given experimental impedance diagram. [68][69][70] The relaxation frequency (frelax) is particularly interesting as it does not depend on geometric factors, and therefore it can be directly compared from one sample to another. Resistances are also plotted as a function of the reverse of the temperature (Figure 5c). The results obtained for the Au/YSZ-8/Au cell obtained here are in agreement with previous works. [32] In the temperature range T > 320 °C, only one high frequency (HF) semi-circle can be observed. This impedance contribution has been assigned to the bulk conductivity of the YSZ-8 solid electrolyte. The associated equivalent capacitive effect (Ceq) is stable in the working temperature range and lower than 10 -10 F. This value is very close to values reported in the literature for YSZ-8 materials. In the lower temperature range T < 320 °C, two depressed semi-circles could be observed. In that case, the arcs can be assigned to the bulk (HF) and grain boundary (MF) conductivities of the YSZ-8 electrolyte. Using the SPS sintering process, one should notice that the grain boundary contribution is not observed for a temperature higher than 320 °C, likely due to the overlapping of intra-granular and inter-granular impedances. Over the By comparing the MF conductivity (O2-(MF), green and red triangles in Figure 5c) assigned to O 2-mobile species in the two niobates, it can be concluded that the titanium-doped sodium niobate is ca. 100 times more O 2-conductive than the undoped NaNbO3. These measurements are therefore in good agreement with the presence of oxygen vacancies in the framework induced by the Ti 4+ substitution on Nb 5+ sites. For both samples considered seperately, the contribution of sodium and oxygen to total ionic conductivity is evaluated in the next section through the calculation of ionic transport numbers.

Ionic transport numbers

On the basis of the EIS measurements performed on single-phase pellets NaNbO3 and NaNb0.9Ti0.1O2.95 compared to the Na + symmetrical blocking layer (sandwich-type cells), the oxygen and sodium ionic transport numbers are deduced according to Equation 6 and 7, respectively:

𝒕 𝑶 𝟐-= 𝝈 𝑶 𝟐- 𝝈 𝑵𝒂 ++𝝈 𝑶 𝟐-+𝝈 𝒆 -= 𝝈 𝑶 𝟐- 𝝈 𝒕𝒐𝒕𝒂𝒍 (6)
𝒕 𝑵𝒂 + = 𝝈 𝑵𝒂 + 𝝈 𝑵𝒂 ++𝝈 𝑶 𝟐-+𝝈 𝒆 -= 𝝈 𝑵𝒂 + 𝝈 𝒕𝒐𝒕𝒂𝒍 (7).
The sodium ionic conductivity (Na+) is thus obtained from the subtraction of the contribution of oxygen O2-(MF) (measured with blocking layers) to the total conductivity total (measured without blocking layers).

Based on the EIS measurements involving the sandwiched pellet Au/YSZ-8/NaNb1-xTixO3-0.5x/YSZ-8/Au and only titanium-doped sodium niobates Au/NaNb1-xTixO3-0.5x/Au, the sodium and oxygen ionic transport numbers can be estimated separately. In pure sodium niobate (x = 0), Na + ions are the majority mobile species with tNa+  88%, independent of temperature (Figure 6). However, the substitution of Ti 4+ for Nb 5+ up to 10 % leads to the creation of oxygen vacancies, inducing oxygen mobility. Starting with the pristine material (NaNbO3) where Na + conductivity is dominant, the O 2-mobility should also take place in the Ti-substituted complex oxide. From around 220 °C to 350 °C, the contribution of O 2-progressively increases over Na + .

For higher temperatures, several contributions overlap on the impedance spectrum for the sandwiched pellet. The overlap leads to higher uncertainty on the conductivity. When the conductivity for the sandwiched pellet is higher than that of the single NaNb0.9Ti0.1O2.95, which has no physical meaning, the transport number of O 2-is considered close to unity tO2-= 1 (dashed red line).. In this high temperature range, the Na + ionic conductivity is then neglected.

Comparing NaNbO3 and NaNb0.9Ti0.1O2.95 above T = 350 °C, the increase of total conductivity when substituting Ti 4+ for Nb 5+ is thus experimentally demonstrated to originate from the introduction of oxygen vacancies for the first time, confirming assumptions made by comparing activation energies that are hardly valuable when it comes to potential mixed ionic conduction.

Discussion

In summary, the blocking electrolyte method characterized by electrochemical impedance spectroscopy measurements allows one to separately estimate the contributions of two mobile ionic species in a perovskite framework. The evaluation of the transport ionic numbers of Na + and O 2-carriers in the same network has never been undertaken before, and this knowledge will enable designing new frameworks with tuned mixed ionic conductivities.

SPS proved to be a valuable technique to design dense pellets with complex sandwich-type architecture. [58] In the case of Nb-and Ti-based materials, the sintering is associated primarily with vacuum (ca. 10 Pa), high temperatures (900 to 1200 °C), a strong electric current (several Amperes) and an elemental carbon-based environment. These combined conditions are responsible for the formation of paramagnetic Nb 4+ and Ti 3+ together with oxygen vacancies, leading to a semiconducting behavior with electronic conductivity ( = 10 -4 S.cm -1 at T = 200 °C and low activation energy of 0.14 eV for NaNbO3-x). During a conventional heat treatment, full reoxidation occurs at 550-600 °C, even under inert gas (PO2 = 2×10 -5 atm), thus revealing a pure ionic conductivity for the sodium niobate. Interestingly, major reorganization of Na and O atomic positions occurs around 550 °C, with a structural transition from the orthorhombic Cmcm to tetragonal P4/mbm space group. It is proposed that both phenomena are strongly related, although a dedicated study on this temperature range with more resolved data should be performed to definitively draw their interplay.

Symmetrical sodium-blocking/oxygen-specific electrolytes on each side of the sandwich sample enabled measurementof the ionic transport number of O 2-, where Na + contribution was then obtained by deduction. Reciprocally, using NASICON or β-Alumina as O 2-blocking layers would allow the estimation of the tNa+ sodium ionic transport numbers and to deduce the tO2oxygen ionic transport number. In the pure sodium niobate, both Na + (tNa+ = 88 %) and O 2- (tO2-= 12 %, independent of temperature) contributeto the conductivity in a poor ion conductor.

Accordingly, vacancy formation does not occur in either the Na site or in the O site after the annealing treatment under air. The activation energy of 0.83 eV related to NaNbO3 is close to values found in perovskite-derived frameworks such as Na3xLa1.33-x□0.67-2xTi2O6 (0.92 eV) [39] rather than in Na/Zr/Mg-based silicate-phosphates (0.25 eV). [22] The slightly smaller value compared to the titanate can be attributed to facilitated Na diffusion pathways, limited by smaller bottlenecks formed by four adjacent [TiO6] octahedra in Na3xLa1.33-x□0.67-2xTi2O6

(average Ti-O distance of 1.95 Å) [39] than four adjacent [NbO6] in NaNbO3 (Nb-O distances from 1.90 to 2.09 Å, average 1.97 Å). [56] For both oxygen and sodium, the absence of site vacancy accounts for poor overall conductivity. However, the O 2-mobility is sufficient to compete with Na + carrier displacements which are mainly governed by steric effects (e.g. bond distances) coordination number and diffusion paths with energy barriers. More interestingly, the thermal activation of the conductivity is quantitatively the same when either both carriers or only oxygen are enabled, suggesting a correlation to be elucidated between the two carriers. polyhedra in Pbma-NaNbO3), and consequently to distortion in the equatorial plane. [57] Therefore, Ti 4+ substitution for Nb 5+ ions and the creation of oxygen vacancies in the perovskite network lead to an increased transition of metal crystal-field splitting, as well as the SOJT effect and Nb(Ti)-O bond covalency.

In the case of NaNb0.9Ti0.1O2.95, the ionic conductivity varies between 1.8×10 -5 and 6×10 -4 S.cm -1 in the interval 350-530 °C. This material cannot be referred as a Na + /O 2-mixed conductor in this temperature range. While both ionic species take part in the overall ion conductivity in NaNbO3 with a 88/12 transport number ratio, an ideal electrochemical cell using a Na + /O 2- mixed ionic conductor as solid electrolyte has an optimized transport number ratio of 50/50.

Such a ratio could be found in NaNb1-xTixO3-0.5x for a single x value comprised between 0 and 0.10. However, Ti-substituted sodium niobates can stabilize higher O-deficiency concentrations, at the origin of even higher oxygen ionic conductivity. [28,57] Strategies to improve Na + contributions in a high Na + /O From solid-state chemistry, to achieve high oxide ion conduction, oxygen vacancies are created through the partial substitution of a low valent cation for the 6-coordinated octahedral site (B) of the perovskite network; a strategy that can be generalized to other structures. In the perovskite-related structure, ion conduction can also be driven by polarizable cations with 12fold coordinated to oxygen in the (A) site. This is especially true when the A site is partially vacant, again due to the stabilization of the low valent cation in the B site or the high valent cation in A site (such as Ca 2+ ). The Ca2Nb2O7 pyrochlore phase can be easily stabilized. [71,72] From a theoreticalperspective, the stability of the perovskite type is governed by the ionic radii and the well-known Goldschmidt tolerance factor. [73] Taking into account the ionic radius ratio between cations in A and B sites, for r(A n+ )/r(B m+ ) > 1.80, the 3D-or 2D-perovskite network is generally stabilized, whereas the pyrochlore structure (A2B2O7) is obtained for 1.46 < r(A n+ )/r(B m+ ) < 1.80, and finally the fluorite framework is favored for r(A n+ )/r(B m+ ) < 1.46. The introduction of vacancies on the A site contributes to the creation of cations ordering and forming superstructures, identified, for instance, in hexagonal tungsten bronze (NaxWO3). [74,75] Supercells are required to give a pertinent crystallographic description of the structure and cationic conduction properties strongly depend on the pathways available for the cations into the framework. The perovskite, the pyrochlore, and the fluorite-type structures (AO2) are also among the networks which exhibit the best oxygen mobility associated with the easy formation of oxygen vacancies. In summary, the precise control of structural features in the large perovskite family coupled with controlled introduction of mixed valence in both the A and B sites should lead to high and balanced mixed ionic conductivities. Finally, in order to achieve both sodium and oxygen vacancies in NaNbO3, without aliovalent doping in A and B sites, a possibility is the reaction by SPS between NaNbO3 and either Nb2O5 or Nb2O5-WO3 solid-solution. [76][77][78][79] In these complex systems, homoepitaxy or epitaxial growth should occur, generating intergrowth at the interface and diffusion to stabilize the defects containing Na + /O 2-vacancies. Such intergrown structures must also be explored among the socalled (i) Ruddlesden-Popper phases with alternating perovskite blocks and rocksalt-type layers, and (ii) Aurivillius phases which have alternating perovskite blocks with fluorite-like (Bi2O2) 2+

units. [80][81][82][83][84] In these frameworks, Na + ionic mobility should take place in a specific unit whereas O 2-ionic carriers should migrate into the perovskite blocks, creating independent channels for mobile species. In these families, interfacial reorganization should be of utmost importance to enhance mixed Na + /O 2-ionic conductivity.

Conclusion

Our study provides a simple strategy to independently measure Na + and O 2-ionic conductivity in a complex oxide, and consequently, to design higher performing mixed ionic conductors.

Experimental Section

Synthesis: 0.810 g Nb2O5 (99.9 %, Sigma-Aldrich) was suspended in 20 mL of NaOH (6 M) and heated in an autoclave equipped with 40 mL Teflon vials, using a P330 oven (Nabertherm).

The sample was heated to 200 °C for 24 h, with heating and cooling ramp rates of 2°C min -1 .

The white sediment and supernatant were both transferred in a 200 mL centrifuge tube (Nalgene) and centrifuged (Sigma 3-30K apparatus) 15 min at 7 krpm. The supernatant was removed, the pellet was dispersed in approx. 100 mL of deionized water, and the dispersion was centrifuged 15 min at 7 krpm. The separation, dispersion, and centrifugation process was repeated once. Finally, the supernatant was removed and the pellet was dried at 80 °C overnight.

Annealing treatments were performed under air in tubular ovens connected to a Eurotherm temperature controller. NaNbO3 structures of Pbma and P21ma space groups were obtained after 24 h at 950 °C and 6 h at 600 °C, respectively, with systematic 2 °C min -1 heating and cooling ramp rates.

Spark Plasma Sintering: For the NaNbO3 and ZrO2-TZY sample, 0.8 g of powder from hydrothermal synthesis and 0.9 g of ZrO2 doped with Y2O3 (8 %mol.) (Tosoh 8Y, > 99.5 %), respectively, was introduced in a 10 mm graphite dye covered with Papyex. For the sandwiched sample, (i) ZrO2-TZY (0.45 g), (ii) NaNbO3 from hydrothermal synthesis (0.55 g) and (iii)

ZrO2-TZY (0.45 g) again were consecutively introduced in a 10 mm graphite dye, with intermediate manual compaction, taking special care of the planarity of the surface before adding another SPS experiments were performed on a 515S Syntex (Dr. Sinter) apparatus. A dynamic vacuum at approx. 10 Pa was maintained during the experiments. For NaNbO3, the temperature was monitored using a thermocouple. The uniaxial pressure was increased to 7.9 kN (100 MPa) in 1 min prior to heating the sample at 50 °C min -1 to 900 °C and maintaining it at 900 °C during 5 min. The sample was left to cool 1 min and then the pressure was released from 7.9 to 0.5 kN (minimal charge) in 3 min. For ZrO2-TZY and ZrO2-TZY/NaNbO3/ZrO2-TZY, the temperature of the sample was followed using a pyrometer (sensitivity starting at approx. 600 °C). The sample was heated to 600 °C in 4 min and then at 600 °C for 3 min. In the meantime, uniaxial pressure of 7.9 kN (100 MPa) was applied in 1 min at the beginning of the heating and maintained constant. The sample was heated from 600 to 1000 °C at 100 °C min -1 and then 1000 to 1100 °C at 50 °C min -1 . After heating 10 min at 1100 °C, the temperature was decreased linearly to 600 °C in 20 min. The pressure was released 1 min after the sample cooled down to 600 °C, from 7.9 to 0.5 kN in 3 min. All samples were polished using abrasive SiC sandpaper with increasing grit sizes from 120 to 2400.

Powder X-ray diffraction: XRD was performed on a PANalytical X'pert PRO MPD apparatus equipped with an X'Celerator multichannel detector. CuKα1/Kα2 radiations were generated at Table S2. Geometrical dimensions of pellets and fit results of impedance diagrams recorded at approx. 325 °C for YSZ-8, NaNbO3 and YSZ-8/NaNbO3/YSZ-8 samples and 275 °C for YSZ-8, NaNb0.9Ti0.1O2.95 and YSZ-8/NaNb0.9Ti0.1O2.95/YSZ-8 samples. For sandwich pellets thicknesses, the first value refers to inner niobate layer, the second one to the overall sample.

Figure 1 .

 1 Figure 1. NaNbO3-x obtained from Spark Plasma Sintering. a) XRD Rietveld refinement of in the Pbma space group after SPS at 900 °C during 5 min. The zoom in the region 35.5 ≤ 2θ ≤ 44.5 ° highlights the stability of the structure versus the acentric polymorph (P21ma space group). b) Structure of NaNbO3 in the Pbma space group, c) diffuse reflectance of initial NaNbO3 (white powder) and powdered pellet from SPS (gray-blue powder). Insets: (lower) room temperature X-band ESR spectra of sodium niobate before and after SPS showing strong Nb IV coupling and (upper) band diagram of NaNbO3-x typical of n-type semi-conductors. Free electrons in the forbidden band are promoted in the conduction band (CB) through absorption in the visible range. VB: valence band. d) 93 Nb MAS NMR spectra of sodium niobate before and after sintering (* spinning sidebands, MAS rate: 30 kHz).

Figure 2 .

 2 Figure 2. Switch in conduction mode of sodium niobate driven by phase transition. a) Structural transitions and parallel oxidation of NaNbO3-x with temperature under helium. Note the Co Kα1/Kα2 X-ray source used here (λ = 1.7890/1.7919 Å). Reflection positions were calculated from Rietveld refinements (black curves) of XRD patterns (orange to black crosses).The color of the powder evolves from gray-blue before the experiment to white, as observed after the sample cooled down to RT in helium atmosphere. b) Deviation of reduced cell parameter to linear dependence with temperature due to phase transition. c) Switch from electronic to ionic conductivity and parallel oxidation of NaNbO3-x with temperature. Starting with the blue pellet, the conductivity was measured under argon for increasing T and under air for decreasing T. After the experiment, the pellet has turned white. Data from complex impedance spectroscopy. d) Reported phase transitions of NaNbO3 with temperature[51] and structural rearrangements during quadratic transition occurring in parallel to NaNbO3-x reoxidation.

  Figure 3a and Figure S4, respectively. The three different layers can be clearly distinguished.

Figure 3 .

 3 Figure 3. Na + blocking-O 2-conducting-YSZ-8 solid electrolyte sandwiching NaNb1-xTixO3-0.5x (x = 0, 0.10). a) YSZ-8/NaNbO3/YSZ-8 sandwiched pellet (D x e = 10,00 x 3,07 mm 2 ) after SPS followed by annealing under air, b) SEM images and EDX mapping at the YSZ-8/NaNbO3 interface. Cross-section view of the sandwiched pellet. c) Symmetrical system used for complex impedance spectroscopy. Electrodes consist of Au thin layer deposited on YSZ-8 by ion sputtering. YSZ-8 electrolytes prevent from Na + conduction in NaNb1-xTixO3-0.5x (x = 0, 0.10). In sandwiched pellets, O 2-is the only effective charge carrier.

4 .

 4 measured in the frequency space and very difficult to deconvolute without reference samples. Consequently, EIS measurements on Au/YSZ-8/Au and Au/NaNb1-xTixO3-0.5x/Au samples referred to as single-phase cells are compared to results from sandwich-type cells, allowing identification and assignment of most contributions. All EIS diagrams recorded at various temperatures between 200 and 800 °C under air are reported on Figure S5 and S6. A typical example of Nyquist plots measured at 275 °C for NaNb0.9Ti0.1O2.95 pellet with symmetrical YSZ-8 blocking layers is reported on Figure Experimental data has been fitted on the basis of an equivalent circuit constituted of Resistance-Constant Phase Element (R-CPE)elements in parallel associated in series. Each R and CPE can be assigned to the resistance and capacitance associated to a specific electrochemical process. Usually one or two arcs more or less overlapp in the high frequency (HF) range (10 6 -10 4 Hz) and in the medium frequency (MF) range (10 4 -1 Hz). In the lower frequency (LF) range (1-0.01 Hz), the electrode reaction occurs (Au/air interface) and is modeled using the Warburg-type impedance. In the present study, our attention is focused on the HF and MF contributions where the studied material behavior is observed. On the basis of the fitted data, the conductivity , the relaxation frequency frelax and the associated capacitive effect Ceq of each HF and MF contributions are deduced using

Figure 4 .

 4 Figure 4. Typical impedance diagram obtained at 275 °C for NaNb0.9Ti0.1O2.95 with symmetrical YSZ-8 blocking layers (the numbers reported in the figure are the frequency logarithms).

Figure 5 .

 5 Figure 5. a) Arrhenius plots of the HF and MF relaxation frequencies for the different impedance contributions, b) associated HF and MF capacitive effects and c) Arrhenius plots of the conductivities of single phase pellets YSZ-8 and NaNb1-xTixO3-0.5x (x = 0, 0.10) and sandwich-type pellets. Contributions from YSZ-8 (squares) and NaNb1-xTixO3-0.5x (triangles) are distinguished from the thermal evolution of equivalent capacities and frequencies plots.

10 F

 10 entire working temperature range, the calculated activation energy (EA  1.0 eV) and ionic conductivity of the solid electrolyte are also in good agreement with the previously reported values. Concerning the single phase cells Au/NaNb1-xTixO3-0.5x/Au (x = 0, 0.10), the results are reported on Figure5a-c as well. For both compounds, only one depressed semi-circle is observed in the HF and MF range. Additionally, the associated capacitive effect (Ceq  5×10 -) remains within the same order of magnitude versus the temperature, meaning that no significant change occurs in the ceramic sample. This impedance contribution is used to calculate the total conductivity of the sample total. Finally, for both sandwich-type cells YSZ-8/NaNb1-xTixO3-0.5x/YSZ-8 (x = 0, 0.10), the HF relaxation frequencies and equivalent capacitive effects (frelax and Ceq) are similar to the YSZ-8 bulk impedance in the studied working temperature range. Consequently, no Na + diffusion occurs into the YSZ-8 materials, in agreement with SEM on the native fully oxidized sandwich-type samples. According to this electrochemical behavior, the HF impedance contribution can be assigned to the pure O 2-ionic conductivity in the YSZ-8 layer. Concerning the MF impedance observed in the sandwich-type samples, this additional contribution is assigned to the the pure O 2-ionic conductivity through the niobate compounds. For the sandwiched pellets including NaNb1-xTixO3-0.5x (x = 0, 0.10) oxides, the higher the ionic conduction of the material, the higher the relaxation frequency (Figure5c), meaning that the ionic transfer at the interface NaNb1-xTixO3-0.5x/YSZ-8 is enhanced. For the sample YSZ-8/NaNb0.9Ti0.1O2.95/YSZ-8 in the temperature range RT < T < 400 °C, the different impedance HF and MF contributions can be separated whereas above T = 400 °C, MF impedance contribution from the niobate and HF contribution from YSZ-8 significantly overlap (FigureS6). This experimental observation does not allow extracting the O 2-ionic conductivity of NaNb0.9Ti0.1O2.95 above T = 400°C (Figure5c, dashed red line).

Figure 6 .

 6 Figure 6. a) Inversion in Na + and O 2-transport numbers between b) NaNbO3 (Na + major, O 2- minor) and c) NaNb0.9Ti0.1O2.95 (O 2-exclusive) above 350 °C.

  Ionic transport numbers depend more strongly on temperature in NaNb0.9Ti0.1O2.95 complex oxide. O 2-progressively takes over Na + up to around T = 350 °C. Above T = 350 °C, the O 2- contribution switches from minor in NaNbO3 to exclusive in NaNb0.9Ti0.1O2.95 complex oxide, given some uncertainty on the conductivity measurement of the sandwich-type pellet. Both the introduction of O vacancies and a positive effect from competitive bonds affect Na1(2)-O1(2)-Nb-O3(4), stabilizing the P21ma structure which leads to dramatic enhancement of the overall conductivity, and a significant decrease of the activation energy. The strong variation of Na1-O1 and Na2-O2 bond lengths after Ti substitution leads to the reduction of the Nb/Ti-O1 and Nb/Ti-O2 apical distortions (elongation of the Nb(Ti)O6 octahedra compared to NbO6

45 kV and 40

 40 mA. Data were acquired on the reflexion Bragg-Brentano θ-θ mode, 8 ° ≤ 2θ ≤ 80 ° with 0.017 ° steps, acquisition time of 6 h 37 min. Samples were prepared from softened powder (particle size < 45 µm) flattened with the edge of a razor blade to avoid any Frequency Response Analyser, applied a signal with a 200 mV amplitude in the 100 mHz-1 MHz frequency range, with 10 steps per decade. Nyquist diagrams were recorded from 200°C to 900°C under argon atmosphere. Equilibrium time (at least 1 hour) has been respected before each measurement during the heating and cooling thermal cycle in order to achieve ready state conditions. The data were analyzed using ZView 2 software of Scribner Associate Inc.

Figure S5 .

 S5 Figure S5. Nyquist diagrams of (black) YSZ-8, (light blue) NaNbO3 and (green) YSZ-8/NaNbO3/YSZ-8 for temperatures comprised between 200 and 600 °C. The numbers reported in the figure are the frequency logarithms.

Figure S6 .

 S6 Figure S6. Nyquist diagrams of (black) YSZ-8, (deep blue) NaNb0.9Ti0.1O2.95 and (red) YSZ-8/NaNb0.9Ti0.1O2.95/YSZ-8 for temperatures comprised between 200 and 500 °C. The numbers reported in the figure are the frequency logarithms.

  and the Coulometric techniques. According to Wagner, the steady oxygen permeation flux density controlled by bulk diffusion in a mixed conductor is

	given by Equation 2:
	𝐽 𝑂 2 =	𝑅𝑇 16.𝐹 2 .𝐿 ∫ 𝑃 𝑂 2 𝑟𝑖𝑐ℎ 𝑃 𝑂 2 𝑙𝑒𝑎𝑛	𝜎 𝑖 .𝜎 𝑒 𝜎 𝑖 +𝜎 𝑒	. 𝑐 ln 𝑃 𝑂 2

  2-mixed ion conductor are discussed hereafter.First, it is noteworthy that in NASICON or -alumina as well as in LISICON or Li-garnet, the strong covalence of phosphate(silicate) groups in NASICON and LISICON, Al 3+ -based spinel blocks in -alumina, and Zr-O bonds in Li-garnet prevent any creation of oxygen vacancies in these oxide frameworks. Therefore, ion conduction involving both Na + and O 2-species with comparable mobilities in the same temperature range necessarly occurs best in oxygen-

	conductor frameworks. Sodium niobate has been chosen because it crystallizes with a derived-
	perovskite lattice. This is a structure well investigated for oxygen mobility, as oxygen vacancies
	can be induced by substitution of low valent cations. Furthermore, Nb 5+ ions adopt a second
	order Jahn-Teller (SOJT) distortion and the octahedra remain highly distorted in the equatorial
	planes (Pbma space group), alternating shorter (1.90 Å) to longer (2.09 Å) bond lengths with
	various octahedral tilting in three different directions. Such a SOJT distortion emphasizes the
	enhanced oxygen mobility.

  This is exemplified with NaNbO3 and NaNb0.9Ti0.1O2.95 in the 350-700 °C temperature range, with major Na + /minor O 2-and exclusive O 2-conduction, respectively. The library of derivedperovskite oxides should be revisited, taking this new and promising angle into account. Finally, the concept of Na + /O 2-mixed conductivity should be regarded more generally to any anion/cation couple; for instance, considering Li + instead of Na + .

Acknowledgements

This work was supported by Solvay and CNRS. The authors thank Austin W. Keller for editing the manuscript.

Received: ((will be filled in by the editorial staff))

preferential orientation. Refinements were performed on JANA2006 software. [START_REF] Petrícek | A. Demourgues* Associating and Tuning Sodium and Oxygen Mixed-ion Conduction in Niobium-based Perovskites[END_REF] Isotropic displacement parameters βiso were always maintained at 0.5 for Nb and 1 for Na and O.

93

Nb nuclear magnetic resonance: NMR spectra were acquired at a 11.7 T static magnetic field (Larmor frequency: 122.3 MHz) with a single pulse excitation of 1.5 μs (RF field strength: ca.

166 kHz) and a recycling delay of 0.2 s. Magic angle spinning experiments were performed at a spinning frequency of 30 kHz with a 2.5 mm Bruker probe. Chemical shifts were calibrated according to a saturated solution of NbCl5/CH3CN (δ = 0.0 ppm).

Electron spin resonance: experiments were conducted with a Bruker EMX spectrometer operating at X-Band (9.45 GHz). The presented powder spectra were recorded at room temperature (293 K) with a microwave power of 10 mW and a magnetic field modulation amplitude of 1 mT (frequency: 100 kHz). The magnetic field scale was calibrated using a DPPH standard sample (g=2.0036) and the Bruker software suite (WinEPR and WinSimfonia) was used to analyze the observed ESR signals.

Diffuse reflectance: spectra were recorded on powders in the 200-800 nm range from measurements obtained on a Carry-Varian 5000, in integrating sphere configuration. MgO powder was used as a white reference.

Scanning electron microscopyenergy-dispersive X-ray spectrometry: Data were obtained on a JSM 6700F (JEOL) field emission gun SEM equipped with an EDX detector.

Acceleration tension of the source was 5 kV for low-magnification imaging and 20 kV for medium-and high-magnification imaging as well as EDX mapping. The sample was fixed to a conductive carbon scotch and an approx. 10 nm-thick Au-Pd layer was deposited to ensure conductivity.

Complex impedance spectroscopy: densified pellets from SPS were analyzed. A thin film of metallic gold electrodes was deposited on both sides of the pellets by sputtering in partial argon atmosphere for 15 min to achieve a homogenous compact gold film. A two-electrode configuration was used for complex impedance spectroscopy measurements. An Autolab

Supporting Information

Supporting Information is available from the Wiley Online Library or from the author.

Supporting Information

Associating and Tuning Sodium and Oxygen Mixed-ion Conduction in Niobium-based Perovskites

Guillaume Gouget, Fabrice Mauvy, U-Chan Chung, Sébastien Fourcade, Mathieu Duttine, Marc-David Braida, Thierry Le Mercier, and Alain Demourgues* Table S1. Unit cell parameters, atomic coordinates and thermal displacements refined in the Pbma space group by XRD Rietveld analysis of sodium niobate powder annealed under air at T = 950°C and powdered dense ceramic from SPS at T = 900 °C under primary vacuum). Table S3. Conductivities (σi, i = 1, 2 or 3), equivalent capactities (Ceq i) and relaxation frequencies (frelax i) for YSZ-8, NaNbO3 and YSZ-8/NaNbO3/YSZ-8. Values are calculated from fitting the Nyquist curves (Figure S5) with R-CPEs in parallel. Conductivities are reported after taking the thickness and surface of the pellets (Table 1) into account. When Ceq1 and frelax1 are not reposrted, σ1 is considered as Z' for minimal ӏZ"ӏ. Table S4. Conductivities (σi, i = 1, 2 or 3), equivalent capactities (Ceq i) and relaxation frequencies (frelax i) for NaNb0.9Ti0.1O2.95 and YSZ-8/NaNb0.9Ti0.1O2.95/YSZ-8. Values are calculated from fitting the Nyquist curves (Figure S6) with R-CPEs in parallel. Conductivities are reported after taking the thickness and surface of the pellets (Table 1 in main text) into account.