Spandan Dey

Goutam Saha
email: gsaha@ece.iitkgp.ac.in

Md Sahidullah
email: md.sahidullah@inria.fr

Cross-Corpora Language Recognition: A Preliminary Investigation with Indian Languages

Keywords: Cross-corpora, language recognition, channel compensation, long-term average spectrum, TDNN

In this paper, we conduct one of the very first studies for cross-corpora performance evaluation in the spoken language identification (LID) problem. Cross-corpora evaluation was not explored much in LID research, especially for the Indian languages. We have selected three Indian spoken language corpora: IIITH-ILSC, LDC South Asian, and IITKGP-MLILSC. For each of the corpus, LID systems are trained on the state-of-theart time-delay neural network (TDNN) based architecture with MFCC features. We observe that the LID performance degrades drastically for cross-corpora evaluation. For example, the system trained on the IIITH-ILSC corpus shows an average EER of 11.80 % and 43.34 % when evaluated with the same corpora and LDC South Asian corpora, respectively. Our preliminary analysis shows the significant differences among these corpora in terms of mismatch in the long-term average spectrum (LTAS) and signalto-noise ratio (SNR). Subsequently, we apply different feature level compensation methods to reduce the cross-corpora acoustic mismatch. Our results indicate that these feature normalization schemes can help to achieve promising LID performance on crosscorpora experiments.

I. INTRODUCTION

Voice assistants and smart devices are becoming a part of our daily life. Various speech processing applications, such as speech recognition, speech translation, speech synthesis, and speaker recognition, are very important component of these devices [START_REF] Ambikairajah | Language identification: A tutorial[END_REF]. These speech-based applications should have a front-end language identification (LID) module to operate on multiple spoken languages efficiently. This module can predict the spoken language from the speech input and accordingly adapt the mode of operation.

In the last few decades, numerous significant attempts have been made to develop efficient LID systems. Different acoustic, prosodic [START_REF] Ng | Spoken language recognition with prosodic features[END_REF], ASR bottleneck features [START_REF] Ferrer | Study of senone-based deep neural network approaches for spoken language recognition[END_REF], [START_REF] Fer | Multilingually trained bottleneck features in spoken language recognition[END_REF] have been utilized along with several kinds of state-of-the-art classifiers, such as, GMM, i-vector backends [START_REF] Dehak | Front-end factor analysis for speaker verification[END_REF], and deep neural network based models [START_REF] Gonzalez-Dominguez | Frame-by-frame language identification in short utterances using deep neural networks[END_REF]- [START_REF] Padi | Attention based hybrid i-vector blstm model for language recognition[END_REF]. These systems are studied mostly using a single corpus. The test data for evaluating these systems comes from the non-overlapping subsets of the same corpora used for system training. This type of evaluation does not consider the cross-corpora variations, indicating a lack of generalization study for deploying in real-world applications. To the best of our knowledge, cross-corpora study has not been conducted explicitly for spoken language recognition. Although the cross-corpora study has not been explored explicitly in LID, researchers conducted cross-corpora study in some other speech processing applications, such as antispoofing [START_REF] Paul | Generalization of spoofing countermeasures: A case study with ASVspoof 2015 and BTAS 2016 corpora[END_REF] and speech emotion recognition [START_REF] Schuller | Cross-corpus acoustic emotion recognition: Variances and strategies[END_REF]. These works have found that the recognition performance degrades significantly when evaluated with audio-data from other corpora. The main reason for this is the corpora-dependent bias due to differences in data collection methods. Achieving good cross-corpora performance has remained a challenging task. In Fig. 1, we have shown several factors which can vary considerably across different corpora, collected in different settings for LID task.

In this work, we have conducted one of the very first crosscorpora performance analyses for spoken language recognition with three standard speech corpora in Indian languages. India is a culturally and linguistically diverse country with 1.4 billion population and 22 official languages 1 . For verbal interaction with the smart devices, the major portion of the Indian population is more comfortable with their respective native languages rather than English or other global languages. Due to the mutual influence and similarity among the Indian languages [START_REF] Sengupta | Study on similarity among Indian languages using language verification framework[END_REF], developing Indian LID systems has its unique challenges [START_REF] Maity | IITKGP-MLILSC speech database for language identification[END_REF]. Considering these facts, researchers have given special attention to build efficient LID systems [START_REF] Nandi | Implicit excitation source features for robust language identification[END_REF]- [START_REF] Mandava | An investigation of LSTM-CTC based joint acoustic model for Indian language identification[END_REF] for the Indian languages. However, these systems were developed mostly using a single corpus. We have trained three independent LID systems with the three used corpora's training data and evaluated each system with test data from all three corpora. We have shown that the cross-corpora performances are severely inferior as compared to the same-corpora performance. Further, we have analyzed various factors due to which non-lingual biases can be present in the individual corpus. Finally, we use various feature-level compensation methods to reduce the corpora mismatch, which substantially improves cross-corpora generalization.

II. CORPORA DESCRIPTION

We have used three standard datasets for the cross-corpora evaluation, which are widely used in the Indian LID research. These are IIITH-ILSC (IIITH) [START_REF] Vuddagiri | IIITH-ILSC speech database for Indain language identification[END_REF], LDC South Asian (LDC) [START_REF] Karen | Multi-language conversational telephone speech 2011 -South Asian LDC2017S14. web download[END_REF], and IITKGP-MLILSC (KGP) [START_REF] Maity | IITKGP-MLILSC speech database for language identification[END_REF]. The comparative description of the three corpora is given in Table I. For our experiments, we have chosen five languages that are common to all the corpora. These are: Bengali, Hindi, Punjabi, Tamil, and Urdu. All the speech segments are converted into 8 kHz sampling rate, and silence regions are removed before further processing. The IIITH and KGP corpora are already divided into training and testing parts. We have manually split the data into training and testing parts with 80 : 20 ratio for LDC. For all the corpora, the speakers in training and testing data are disjoint. From the available metadata, we can summarize the major differences across the used corpora as follows:

• LDC corpus contains conversational telephone speech (CTS), KGP corpus contains broadcast news (BN) data, and IIITH corpus contains both.

III. ANALYSIS OF THE SPEECH CORPORA

To investigate the differences among the speech corpora, we have analyzed the three corpora by comparing the longterm average spectrum (LTAS) and the signal-to-noise ratio (SNR) histogram. We have chosen these two attributes as they represent fundamental characteristics of audio-data.

A. SNR histogram

The SNR histogram helps to analyze the level of background noise present across the speech segments in a speech corpora. We use the NIST STNR tool to calculate the overall signalto-noise ratio corresponding to each of the speech segments2 . In Fig. 2, histograms of the signal-to-noise ratio values for each of the corpora are shown. Majority of the segments from IIITH corpus have SNR values less than 10 dB, with some segments having SNR values around 20 dB. In contrast, most LDC speech segments have SNR higher than 50 dB, with few low SNR segments. These facts can be justified by the bi-modal nature of the histograms for IIITH and LDC corpora. The histogram for KGP corpus is spread across a wide range of SNR values, indicating more variations in the level of background noise.

B. LTAS analysis

We have compared the corpora in terms of overall spectral information using LTAS analysis. After silence removal, for each segment, the short-time Fourier transform (STFT), S(f, t) ∈ R (F ×T ) is computed. Here, F denotes the number of frequency bins, and T denotes the time frames. Then, power spectrum P (f, t) is calculated from the STFT output. The LTAS spectrum for a segment (L s (f, t)) is calculated by taking the log of the power spectrum:

L s (f, t) = 1 T T t=1 log |S(f, t)| 2 (1)
Then, overall LTAS for a corpus is computed by taking the average across all its segments. In Fig. 3, the LTAS plots are shown for the training and testing parts of the three corpora. We conclude that the spectral information among the corpora differs significantly at specific frequency ranges, mostly below 100 Hz and above 1 kHz. These ranges of frequency components mainly contribute to the non-speech factors [START_REF] Kim | Power-normalized cepstral coefficients (PNCC) for robust speech recognition[END_REF], such as channels, background noise, etc.

IV. METHODS FOR MISMATCH REDUCTION

The analysis conducted in Sec. III shows that the mismatch among the corpora is mainly due to varying channel effects and background noise. This section discusses several feature compensation schemes to reduce the impact of those variations and apply the same in this work. Among several compensation techniques, we have applied some of the most commonly used ones in the literature, such as CMVN, feature warping, RASTA filtering, along with the relatively newer PCEN approach. Our objective is to prove the effectiveness of these popular techniques for achieving better cross-corpora generalization.

A. Cepstral mean and variance normalization (CMVN)

CMVN assumes that the channel to be static throughout the entire utterance. Thereby, it provides channel-compensated features by making mean zero with mean subtraction followed by variance unity with scaling by the inverted standard deviation. If only mean is subtracted, then this method is called cepstral mean subtraction (CMS). CMVN is expressed as,

X = X -µ σ (2)
where, X ∈ R N d ×T is the feature matrix for an utterance with N d dimensions and T frames. µ, σ ∈ R N d ×1 are the mean and standard deviation respectively across the dimensions. We have also applied windowed CMVN (W-CMVN), where CMVN is applied over windows of three seconds in the utterance. In W-CMVN, the channel is assumed to remain static for a smaller duration, which is a realistic assumption.

B. Feature warping (FW)

Feature warping (FW) warps the short-term distribution of the cepstral features to a standardized distribution [START_REF] Pelecanos | Feature warping for robust speaker verification[END_REF]. FW increases feature robustness against slowly varying additive noise and various channel and transducer mismatches.

C. Relative spectral (RASTA) processing

RASTA [START_REF] Hermansky | RASTA processing of speech[END_REF] acts as a bandpass filter and removes the static and slowly varying channel effects present in the speech signal. In the high-frequency regions, this bandpass filter also reduces the effect of convolutional noise. Hence, RASTA improves the robustness against environmental variations present in the data. The filter transfer function [START_REF] Hermansky | RASTA processing of speech[END_REF] is expressed as,

H(z) = 0.1 * z 4 * 2 + z -1 -z -3 -2z -4 1 -0.98z -1 (3)

D. Per-channel energy normalization (PCEN)

We have applied PCEN [START_REF] Lostanlen | Per-channel energy normalization: Why and how[END_REF] on the mel-spectrograms (E(f, t)). During mel-spectral processing, PCEN replaces the logarithmic compression with the following stages [START_REF] Wang | Trainable frontend for robust and far-field keyword spotting[END_REF]: temporal integration (4), adaptive gain control (AGC) [START_REF] Dehak | Front-end factor analysis for speaker verification[END_REF], and finally dynamic range compression (DRC) [START_REF] Gonzalez-Dominguez | Frame-by-frame language identification in short utterances using deep neural networks[END_REF],

M (f, t) = (E * φ T )(t, f ) = sE(t, f )+(1-s)M (t-τ, f ) (4) G(t, f ) = E(t, f ) (M (t, f ) + ) α (5) P CEN (t, f ) = (G(t, f ) + ∆) r -∆ r (6)
Where, φ T (t) is a first-order IIR filter with 0 < s < 1 and τ as hop size, 0 < α < 1, ∆ > 1, and r > 0. PCEN increases the robustness against stationary background noise as well against foreground loudness variations [START_REF] Wang | Trainable frontend for robust and far-field keyword spotting[END_REF].

V. EXPERIMENTAL SETUP

A. Language recognition system

We have computed 20-dimensional mel-frequency cepstral coefficients (MFCCs) features from the silence removed speech using 20 ms frame-size and 10 ms overlap. For classification, we have implemented time-delay neural network (TDNN) based architecture as described in [START_REF] Snyder | Spoken language recognition using x-vectors[END_REF] using the PyTorch library [START_REF] Paszke | PyTorch: An imperative style, high-performance deep learning library[END_REF]. This architecture has five convolutional layers, followed by statistical pooling, and three fully connected layers. We have used categorical cross-entropy as the loss function and AdamW [START_REF] Loshchilov | Decoupled weight decay regularization[END_REF] as the optimizer with a learning rate of 0.001. The systems are trained for 30 epochs with validation loss based early stopping criteria and patience of 3 epochs. We follow an end-to-end approach for classification. It gives better validation performance as compared to the backend-based approaches [START_REF] Snyder | X-vectors: Robust DNN embeddings for speaker recognition[END_REF]. Using the training data of each of the three corpora, we have trained three independent LID models. Then, each model is evaluated with the test data from all three corpora. If the corpora for training and test are the same, we call this as within-corpora evaluation condition. In contrast, cross-corpora evaluation considers the test data from different corpora than training.

B. Performance evaluation metrics

We have evaluated the LID performance in terms of two standard metrics: equal error rate (EER) [START_REF] Brümmer | Application-independent evaluation of speaker detection[END_REF] and cost average (C avg ). Using detection error trade-off (DET) plot, the false acceptance and false rejection rates are varied by changing the threshold, and EER is found at the value for which they are equal. In NIST language recognition evaluation (LRE) [START_REF] Sadjadi | The 2017 NIST language recognition evaluation[END_REF] and OLR challenge [START_REF] Li | AP20-OLR challenge: Three tasks and their baselines[END_REF], C avg was used as the primary evaluation metric. It is defined as follows [START_REF] Sadjadi | The 2017 NIST language recognition evaluation[END_REF]:

C avg = 1 N Lt P T arget • P M iss (L t ) + Ln P N on-T arget • P F A (L t , L n ) (7)
where, L t and L n are the target and non-target languages. P M iss , P F A are the probability of missing and false alarm. P T arget = 0.5 is the prior-probability of the target languages. P N on-T arget = (1 -P T arget )/(N -1), where, N is the total number of languages. The lower value of EER and C avg indicates better classification performance.

VI. RESULTS

A. Cross-corpora evaluation: baseline experiment

The evaluation results of our baseline experiment are shown in Table II. The results show that the average EER across within-corpora utterances is 11.80%, 27.20%, and 11.18% for the systems trained with IIITH, LDC, and KGP corpus respectively. The relatively higher within-corpora EER for LDC corpus indicates that this corpus contains significant non-lingual variations and is difficult to learn. Cross-corpora evaluations are severely inferior as compared to within-corpora evaluations. The reason for this is the mismatches among the corpora, aroused due to variations in channel and background noise levels, as discussed in Section III. This performance gap shows that LID systems trained on a single corpus can have poor generalization if deployed in real-world scenarios where the environmental variations are even more diverse.

B. Effect of feature post-processing

In Table III, we have shown the cross-corpora evaluation for the modified features. The results show that the cross-corpora performances are substantially improved as compared to the baseline performances due to the reduction in mismatch. The within-corpora performances are also improved considerably. For IIITH and KGP trained systems, RASTA processing, and for LDC trained system, PCEN achieve the best cross-corpora improvement. Generally, language recognition performance improves if the test utterance duration is increased [START_REF] Li | Spoken language recognition: from fundamentals to practice[END_REF], [START_REF] Fernando | Bidirectional modelling for short duration language identification[END_REF]. However, for our experiments, this improvement is not very prominent. The TDNN systems are trained with chunks of 3s, and the models are prone to be biased for this 3s duration [START_REF] Raj | Probing the information encoded in x-vectors[END_REF]. In Fig. 4, the performance comparison of the different compensation techniques for the IIITH-trained system and 6s test utterances are shown, using DET plot. The crosscorpora performance gap reduces more effectively between the IIITH and KGP corpus as compared to the LDC corpus. This is because the mismatch is higher between LDC and the other two corpora, which is also justified from Fig. 3. Crosscorpora performance is considerably poor when the KGPtrained systems are evaluated with LDC test set. In these cases, even after the compensation, cross-corpora evaluations show EER more than 50%, which is an interesting fact for further investigation. This indicates that the classifier captures the nonlingual similarities, which affect the similarity score between the target language and test audio [START_REF] Sturm | A simple method to determine if a music information retrieval system is a "horse[END_REF].

VII. CONCLUSIONS

We have studied the cross-corpora performance for spoken language recognition with three corpora. We train three independent LID systems with audio-data from each corpus using a TDNN-based language recognition system. During the evaluation, test data is used from all three corpora. In the baseline experiment, we have shown that the cross-corpora performance is almost around the chance level. We have analyzed that the environmental mismatch is one of the major causes for this. Based on the analysis, we have shown that with the feature level compensation techniques, the corpora mismatch reduces, which leads to a significant improvement in the cross-corpora performance. Among the techniques, CMS and RASTA is found to be more effective for improving generalization. The used compensation techniques can be further improved by tuning several important parameters in a learnable approach. Apart from processing at the feature level, we will also explore the effectiveness of signal level processing. We would also like to solve this cross-corpora problem from domain adaptation perspective in future study.

Fig. 1 .

 1 Fig. 1. Sources of potential corpora-dependent information in LID process.

Fig. 2 .

 2 Fig. 2. Comparison of SNR histograms for the segments in each corpora.

Fig. 3 .

 3 Fig. 3. Comparison of overall LTAS of the corpora.

Fig. 4 .

 4 Fig. 4. DETs of cross-corpora performances of the compensation techniques when the IIITH corpus is used in training.

TABLE I DESCRIPTION

 I OF THE THREE CORPORA USED IN THIS STUDY.

	Corpora	IIITH	LDC	KGP
	Languages	23	5	27
	Mode of speech BN and CTS	CTS	BN
	Environment	Studio, real-world Real-world	Studio
	Total speakers	1150	584	300
	Duration	103.5 hours	118.3 hours	27 hours
	Audio format	16 kHz (.wav)	8 kHz (.flac) 8 kHz (.wav)

TABLE II BASELINE

 II RESULTS FOR CROSS-CORPORA LANGUAGE RECOGNITION. Cavg × 100 FOR DIFFERENT FEATURE COMPENSATION METHODS. M0 INDICATES CMS, M1 INDICATES CMVN, M2 INDICATES W-CMVN, M3 INDICATES FW, M4 INDICATES RASTA AND M5, INDICATES PCEN.

			Training: IIITH			Training: LDC			Training: KGP
		IIITH-test	LDC-test	KGP-test	IIITH-test	LDC-test	KGP-test	IIITH-test	LDC-test	KGP-test
	Duration	EER / Cavg	EER / Cavg	EER / Cavg	EER / Cavg	EER / Cavg	EER / Cavg	EER / Cavg	EER / Cavg	EER / Cavg
	3 sec	12.69 / 14.51	43.39 / 46.23	46.26 / 43.18	44.65 / 46.66	28.59 / 29.31	46.58 / 48.00	59.80 / 50.00	52.13 / 46.05	12.33 / 12.39
	6 sec	11.65 / 13.30	43.39 / 46.00	45.17 / 42.88	44.75 / 46.36	26.73 / 28.30	45.92 / 44.40	58.56 / 50.00	53.01 / 45.69	11.22 / 10.28
	9 sec	11.07 / 13.19	43.24 / 45.89	45.00 / 42.57	45.09 / 45.84	26.27 / 27.98	45.88 / 46.50	59.53 / 50.00	58.19 / 45.68	10.00 / 9.63
					TABLE III
	RESULTS IN TERMS OF EER IN % /

https://censusindia.gov.in/2011-common

https://www.nist.gov/itl/iad/mig/tools


Emilie Calvié

Julien Réthoré

Lucile Joly-Pottuz

Sylvain Meille

Jérome Chevalier
email: jerome.chevalier@insa-lyon.fr

Vincent Garnier

Yves Jorand

Claude Esnouf

Thierry Epicier

J B Quirk

K Masenelli-Varlot

Mechanical behavior law of ceramic nanoparticles from transmission electron microscopy in situ nano-compression tests

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

In materials science, a constitutive law describes the response of a material to an external solicitation. With the growing importance of nanotechnology in materials design and fabrication, access to constitutive laws at the nanoscale is a topical issue [START_REF]European second regulatory review on nanotechnology[END_REF]. Several studies have dealt with the determination of the Young 0 s modulus of nano-objects with high aspect ratios [START_REF] Poncharal | Electrostatic deflections and electromechanical resonances of carbon nanotubes[END_REF][START_REF] Löffler | Robust determination of Young 0 s modulus of individual carbon nanotubes by quasi-static interaction with Lorentz forces[END_REF][START_REF] Bao | Catalyst-free synthesis and structural and mechanical characterization of single crystalline Ca 2 B 2 O 5 Á H 2 O nanobelts and stacking faulted Ca 2 B 2 O 5 nanogrooves[END_REF][START_REF] Li | Synthesis, structural, optical and mechanical characterization of SrB 2 O 4 nanorods[END_REF], eventually incorporating the yield or failure stress [START_REF] Arenal | Young modulus, mechanical and electrical properties of isolated individual and bundled single-walled boron nitride nanotubes[END_REF]. For example, plasticity could be observed in silicon, which is known to exhibit brittle behavior at the macroscopic scale [START_REF] Stauffer | Strain-hardening in submicron silicon pillars and spheres[END_REF]. In parallel, the development of in situ nano-indentation in TEM has been a major breakthrough, since it allows both local determination and the observation in real time of the nanoparticles 0 mechanical behavior [START_REF] Arenal | Young modulus, mechanical and electrical properties of isolated individual and bundled single-walled boron nitride nanotubes[END_REF][START_REF] Stauffer | Strain-hardening in submicron silicon pillars and spheres[END_REF][START_REF] Minor | A new view of the onset of plasticity during the nanoindentation of aluminium[END_REF][START_REF] Zheng | Electron-beamassisted superplastic shaping of nanoscale amorphous silica[END_REF][START_REF] Shan | Ultrahigh stress and strain in hierarchically structured hollow nanoparticles[END_REF]. However, no attempt was made to obtain their mechanical behavior constitutive law.

The plastic deformation of small commercial alumina nanoparticles has recently been reported [START_REF] Calvié | Real time TEM observation of alumina ceramic nano-particles during compression[END_REF]. Based on these observations, the objective of the present work was therefore to obtain constitutive laws from in situ nano-compression experiments in the transmission electron microscope (TEM) from image processing and load-displacement curves. The transition alumina nanoparticles are currently used for the fabrication of ceramic bulk materials. However, their mechanical properties remain unknown since the transition phases are not present in the sintered state and cannot be experimentally tested with conventional mechanical techniques.

Materials and methods

The commercial transition alumina powder (NanoTek s , Nanophase Technologies Corporation, Romeoville, IL, USA) is produced by Physical Vapor Synthesis (PVS). It was dispersed in acidified water at pH 4 using a 100 W ultrasound probe for 2 min, in order to test particles individually [START_REF] Tang | Electrophoretic deposition of aqueous nano-γ-Al2O3 suspensions[END_REF][START_REF] Azar | Effect of initial particle packing on the sintering of nanostructured transition alumina[END_REF].

In situ nano-indentation tests were carried out using a dedicated straining sample holder from Nanofactory Instruments, fitted in a JEOL 2010F microscope operating at 200 kV accelerating voltage. The sample holder was equipped with a truncated diamond tip with a flattened area of about 500 nm 2 and a load cell (maximum load of 3 mN). Particles were positioned on a sapphire substrate of 0.75 mm thick, moving towards the tip during compression at a controlled displacement rate (0.5 nm/s). Images of the experiment were directly recorded using a Gatan Orius 200 camera and video sequences acquired by the freeware CamStudio (v2.0, http://www.rendersoftware.com/products/camstudio).

The real displacement applied to the nanoparticle was determined by using Digital Image Correlation (DIC) from the experimental micrographs. By comparing two successive images, the displacement of the grey level transition at the boundary of the support and at the boundary of the tip was estimated. DIC usually allows arbitrary displacement fields to be estimated with a subpixel resolution (about 1/100 pixel), but in the present work only a rigid translation was searched for the measurement of this displacement; the actual displacement applied to the particle was obtained. Initially measured in pixels, this was further converted into nanometers by using the TEM scale bar.

Finite element (FE) simulations were performed using ABA-QUS s software. The initial particle was modelled as a sphere, its radius being estimated from the first image of the sequence. An axisymmetric model was built and the analysis accounted for geometrical non-linearities and contact with the tip and the support. Among the data available from the analysis, the reaction force for applying the displacement was extracted. Then, based on an inverse method, the parameters of the material constitutive model were adapted so that the reaction force matches the force measured during the experiment. 29-1486), with proportions of about 30 and 70 wt%, respectively, in agreement with X-ray diffraction [START_REF] Deneen | In situ deformation of silicon nanospheres[END_REF]. In order to preserve the integrity of the particles during exposure to the electron beam, no extensive electron diffraction work was performed before testing to identify their precise crystallographic nature, and characterize the twins possibly present. However, as twins are mostly observed in the biggest nanoparticles, and because we tested only perfect spheres, it is thought that the in situ nanoindentation experiments were carried out on nanoparticles without twins.

Results and discussion

An experimental force-real displacement curve, recorded for a nanoparticle of 96 nm in diameter with compression of 50 nm, is displayed in Fig. 2 (see Video 1, as Supporting information). We confirm the existence of plasticity at the nanoscale, even on a material exhibiting fragile behavior at the macro-scale. The parameters of a constitutive law have been extracted from the forcedisplacement curve using two different methods, namely an analytical oneusing either the theory of a Hertz contact in a sphere-plane geometry for the load curve or the elastic response of a cylinder for the unload curveand the inverse method described above.

Supplementary material related to this article can be found online at http://dx.doi.org/10.1016/j.matlet.2014.01.002.

In the case of DIC-FE analysis, the force-displacement curve was fitted up to the onset of strain localization. To obtain a satisfying fit between the computed and the measured forces, a Von Mises elastic-plastic model with linear isotropic hardening is used. The yield limit is thus a linear function (initial value s y , slope H) of the accumulated plastic strain. The constitutive model used herein thus involves four parameters: the Poisson ratio ν which has been fixed to 0.3, the Young 0 s modulus E, the initial yield stress s y and strain hardening coefficient H. The Poisson 0 s ratio was fixed to 0.3, since this is a conventional value generally observed on crystalline solids. This is also roughly the value for bulk alumina. Moreover, its value had a negligible influence on the other, the most important parameters. E, H and s y are adjusted until a satisfying agreement between the experimental and the computed response is obtained, as illustrated in Fig. 2 and summarized in Table 1. The Young 0 s modulus and the yield stress of the nanoparticle are equal to 115 GPa and 10 GPa, respectively. Strain hardening can be considered as negligible. The excellent agreement with the values obtained from the analytical elastic model validates the DIC-FE procedure. It is noteworthy that the same constitutive law, namely a perfect elastic-plastic model with very similar values of E and s y , has also been obtained from several experiments similar to the one described in the present figures.

It should also be noticed that the value of E and s y found here for the nanoparticles cannot be compared with that corresponding to bulk alumina, since bulk alumina crystallises in a different form (the α phase) during sintering, which exhibits brittle behavior.

One of the major advantages of in situ nano-indentation in the TEM is the ability to observe the structural modifications inside the nanoparticle during the tests, which are revealed by diffraction contrasts. Clearly, for small loadings, Bragg fringes appear in the nanoparticle (see Figs. 2 and3a), which are similar to those observed on other types of nanoparticles and possibly attributed to dislocations and elastic deformation [START_REF] Deneen | In situ deformation of silicon nanospheres[END_REF][START_REF] Carlton | In situ TEM nanoindentation of nanoparticles[END_REF].I nFig. 3a, we present a superposition of the experimental image (deformation 39%) with a map of the total equivalent plastic strain, calculated by FE simulations using the previously determined constitutive law. The contours of the maximum equivalent plastic strain have been highlighted. A good agreement between the experimental image and the calculated map indicates that the observed Bragg fringes are indeed the most probably caused by plastic deformation. The physical origin of plasticity in α alumina (obtained through nano-indentation tests on bulk samples for example) is generally associated to dislocations motion. Its origin in the present transition alumina is unknown and the current set of results does not allow to give a definitive physical interpretation. However, the elastic-plastic behavior law obtained through the inverse method is compatible with the most common plastic mechanisms by slipping. The theoretical shear strength of a single crystal without dislocation is given by τ Eth $ (E/16). It would therefore lead to yield stress of s yth $ (E/8) for a Schmid factor of 0.5. Given a Young 0 s modulus of 115 GPa as measured experimentally, this simple calculation would lead to a theoretical yield stress of s yth $ 14 GPa, whichisofthesameorderastheexperimentalyieldstressmeasured experimentally (10 GPa). At higher loadings, corresponding to approximately 45% deformation, damage occurs with the formation of tilted parallel lines, which can be regarded as cracks (see Fig. 3b). For a compressed sphere, fracture is expected to occur in brittle solids through a crack initiating at the center of the spheredue to a tensile stress stateand propagating perpendicular to the compressed surfaces. This was observed in silicon nanospheres [START_REF] Shan | Ultrahigh stress and strain in hierarchically structured hollow nanoparticles[END_REF] of larger diameters (range of 170-250 nm). In our case, plasticity occurs almost in the whole nanoparticle and the stress reaches the yield stress within the plastic domain. Fig. 3b displays both the experimental image and a calculation of the Tresca shear strain, just before the first crack appears. Parallel dashed lines indicate the observed direction of the first crack. The excellent agreement clearly demonstrates that the formation of cracks is governed by shearing, and that plastic deformation occurs well before fracture.

Knowing the mechanical behavior laws of nanoparticles may be of importance for phenomena such as third body wear particle in contact mechanics, milling of nanoparticles which may exhibit a plastic behavior below a certain size, or particle compaction during green body preparation of ceramics. It is for example usually considered that ceramic nano-powders just re-arrange without plastification during compaction. Fig. 4 shows a TEM image of a focused ion beam (FIB) thin section of a powder compact composed of the same transition alumina and pressed at ambient temperature under a pressure of 5 GPa. It definitively proves that plastification of ceramic nanoparticles can occur during compaction at ambient temperature.

Conclusion

A constitutive law has been determined and values for the Young 0 s modulus and the yield stress could be obtained for the nanoparticles. An example was given here on transition alumina nanoparticles. This methodology can be applied to any type of nanoparticlesregarding their composition and crystallographyand can thus open new routes for the understanding and optimization of materials via a bottom-up approach.

Fig. 1

 1 Fig. 1 displays high resolution transmission electron micrographs of several nanoparticles. They are well crystallized, with eventually twin boundaries in very few of them. The indexation of the electron diffraction patterns revealed the presence of transition phases of Al 2 O 3 , namely δ (ICCD no. 16-0394) and γ (ICCD no.

Fig. 1 .

 1 Fig. 1. High resolution TEM micrographs of several alumina nanoparticles, showing the crystallinity quality and the presence of twin boundaries (in very few particles).

a

  method. H is equal to zero. Average contact pressure at the end of the elastic domain.

Fig. 2 .

 2 Fig. 2. TEM in situ nano-indentation force-displacement curve. Images are displayed at key points of the force-displacement curve. The simulations using DIC-FE (red curve) or the analytical method (blue curves) are also displayed. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 3 .

 3 Fig. 3. (a) Superposition of an experimental image with the corresponding map of the total equivalent plastic strain calculated by DIC-FE, for the case of a 96 nm diameter nanoparticle. The contours of the maximum equivalent plastic strain are highlighted with dotted lines. (b) Superposition of an experimental image with the corresponding map of the Tresca shear strain calculated by DIC-FE, in the case of a 96 nm diameter nanoparticle. The direction of the first crack is indicated by a dotted line.

Fig. 4 .

 4 Fig. 4. TEM image showing plastic deformation of alumina nanoparticles in a powder compact during a pressing experiment at ambient temperature, under a pressure of 5 GPa. Arrows indicate nanoparticles highly deformed.

Table 1

 1 Young 0 s modulus E and yield stress s y derived from DIC-FE and from the analytical

Acknowledgments

Acknowledgments to the Centre Lyonnais de Microscopie (CLYM; http://www.clym.fr) for the access to the JEOL 2010F, to Region Rhone-Alpes (Cluster MACODEV) and the Institut Universitaire de France for financial support, and Stephane Pailhes, ILM University Lyon, for the high pressure experiments.