Anne Baillot

Ellen Carter
email: ellencarter@unistra.fr

Thierry Grass

Pablo Ruiz Fabo

Towards robotic translation? -Introduction

INTRODUCTION

The appearance on the web in 2017 of new translation services based on "deep learning" artificial intelligence algorithms [LeCun et al., 2016;[START_REF] Koehn | Neural Machine Translation[END_REF] such as DeepL and Google Translate [START_REF] Kutylowski | DeepL -Press Information[END_REF][START_REF] Wu | Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation[END_REF] corresponded to a new leap forward in machine translation (MT). These recent systems, like the previous generation of statistical machine translation and factored machine translation [START_REF] Koehn | Factored translation models[END_REF][START_REF] Koehn | Statistical Machine Translation[END_REF], rely on large aligned corpora and produce results whose quality is in some cases comparable to some human translations. It follows that to produce added value, the translator must provide something extra compared to the machine. This added value may be inherent in fields where the use of machines is not in itself of much interest because of the essentially aesthetic dimension of translation: this is the case for the translation of certain literary genres. Although much academic translation research refers to this field, it represents only a small fraction of the existing professional translation activity. 2As the machine allows productivity gains of 150 to 200% (some translators reach outputs of 6,000 to 8,000 words per day), the post-editing technique is becoming increasingly important in the language industries, as confirmed in 2017 by the introduction of the ISO 18587 standard "Translation services -Post-editing of machine translation output -Requirements" [ISO, 2017]. Post-editing poses a moral dilemma for translators: accepting that the machine, and not them, is the source of their own translation.

Will the profession of translator one day be supplanted by algorithms? Comparing technology with translations provided by amateur translators, some people are already predicting that humans will be overtaken by machines: this is the case of industry experts and academics who, according to a survey initiated by Katja Grace (Future of Humanity Institute, University of Oxford), predict that artificial intelligence will overtake translation by humans who are proficient in both source and target languages but are not professional translators by 2026 [START_REF] Grace | When Will AI Exceed Human Performance? Evidence from AI Experts[END_REF]. For others, the machine's main obstacle remains its lack of knowledge of the world and therefore of understanding and interpreting it: some texts, such as legal or aesthetic texts, remain resistant to machine translation. Trials have been carried out to systematically put into perspective the advances of neural translation and the gap between its results and professional "biotranslation" or human translation on various types of text; [START_REF] Poibeau | Human Parity" and "Super Human Performance[END_REF] provides a synthesis. Complex linguistic phenomena, whose translation may require access to context beyond the sentence, remain particularly challenging for MT [START_REF] Bawden | Evaluating Discourse Phenomena in Neural Machine Translation[END_REF]. However, the tasks of the translator are changing and diversifying: post-editing is supplanting overwriting in many fields, localisation requires intercultural skills, and layout involves mastering desktop publishing tools. This issue brings together articles that do not aim to take stock, but rather to present reflections and practical experience not only from professional translators but also from academics specialising in teaching and/or researching translation. The rapid development of artificial intelligence is forcing not only professional translators but also translation courses to adapt. The approaches put into dialogue in the framework of the interdisciplinary conference held at the University of Strasbourg in 2021 concern translation, but also software, linguistics, translation studies and language teaching.

I HISTORICAL AND LINGUISTIC APPROACHES

Machine translation is in line with different disciplinary traditions, some of them ancient. This section does not explore these traditions in their entirety, but at least it sheds light on some of their salient dimensions in the recent context of translation studies (Nicolas Froeliger) and in their historical context with an in-depth perspective on the precursors of formal logic (Marc Lebon).

Nicolas Froeliger begins by outlining the history of the positions taken by translation studies, mainly in France, regarding machine translation, since the end of the 1950s. He distinguishes three stages: that of a prejudicial objection in which machine translation served above all as a deterrent and as an exercise in thinking about what translation cannot be; that of popularisation, as the world and the market become aware of technological advances; and finally, today, that of convergence, with strong interdisciplinary content. As Nicolas Froeliger points out, the challenge in this hybridization is to maintain the scientific, professional, and societal relevance of translation studies.

In his contribution, Marc Lebon goes back much further in time: he looks at the attempts to encode and automate languages as they have been developed since the 17 th century, in particular by Athanasius Kircher, John Wilkins and Gottfried Leibniz. He analyses on the one hand the principles underlying the development of their machines for making equivalences between languages, and on the other hand the mechanisms that may have led to their failure. His contribution sheds light on the conceptual proximity between these computational devices and the machines developed since the end of the twentieth century for the purpose of automating translation, pointing out that the debates we may have around these processes are perhaps older than we imagine.

II PEDAGOGICAL PRACTICES

The three articles in this section investigate the pedagogical use of machine translation and post-editing for undergraduate and graduate translation students in Spain (Julio de Los Reyes Lozano), the Netherlands (Joop Bindels and Mark Pluymaekers) and Switzerland (Lise Volkart et al.). The issues examined include translation quality for dubbing with and without machine translation, or under the influence of different post-editing strategies, as well as the spontaneous use of machine translation by students.

In the first contribution, Julio de Los Reyes Lozano presents a teaching experiment combining machine translation and audiovisual translation with translation students in Spain. After translating an excerpt from a television series for dubbing, the participants post-edited the same text and then evaluated the time spent and the typology of errors generated by the machine translation. While the results show difficulties in inserting machine translation into a dubbing project, a reduction in overall time was observed, which encourages further research in this area. results argue for a comprehensive approach to the development of machine translation knowledge and post-editing skills.

In their contribution, Lise Volkart et al. conducted an experiment with translation students to evaluate the influence of two different post-editing strategies on three aspects: post-editing time, the ratio of corrected errors and the number of optional edits per word. Their results show that the chosen strategy has no influence on the post-editing time, nor on the ratio of corrected errors. However, it does have an influence on the number of optional changes per word. Two other observations also stand out: firstly, the ratio of errors corrected shows that students only correct half of the machine translation errors, which highlights the need for post-editing practice. Second, when students are not required to read the source segment first, they tend to do monolingual post-editing.

III BIOTRANSLATION VS. MACHINE TRANSLATION

Through post-editing, which has become essential in many fields, human translation or "biotranslation" is increasingly adapting to the requirements of machine translation. For the time being, human translators are still irreplaceable in the translation process, even if they intervene at the end of the chain as post-editor. Adapting to machine translation requires that biotranslators are not only aware of the biases of machine translation, but also that their linguistic skills in the source and target languages are optimal compared to the increasingly powerful systems.

Maryam Alrasheed's article examines the positive aspect of human subjectivity as a tool for comprehension and contextualisation compared to the subjectivity of the machine, which could reside in the set of subjectivities present in the corpora used to train it.

For Françoise Bacquelaine, despite the progress of neural machine translation, artificial intelligence still does not allow the machine to avoid all the pitfalls of translation, especially those related to lexical ambiguity, phraseology, syntax, and semantics [START_REF] Koehn | Neural Machine Translation[END_REF]. She studied the translation into French of two Portuguese polylexical phraseological units with a medium degree of structural and/or lexical stability thus having the characteristics of "pre-fabricated construction units" described by [START_REF] Schmale | Qu'est-ce qui est préfabriqué dans la langue ? Réflexions au sujet d'une définition élargie de la préformation langagière[END_REF]. Therefore, they fall within the scope of phraseology in the broad sense and need to be translated as a block. The block translation of these pre-fabricated construction units is a challenge for the machine, especially because of the syntactic properties of splitting and inversion of elements on the syntagmatic axis. A sample of 168 occurrences of these units in phrasal context was taken from a Portuguese journalistic corpus. This sample was translated into French by DeepL and Google Translate in 2019 and 2021. The raw machine translations were compared with a biotranslation model (a set of linguistic strategies for biotranslation) developed based on analysis of parallel or aligned Portuguese-French corpora and analysed according to two general criteria (non-literality and acceptability) and some challenges specific to each unit. The analysis evaluates the evolution of these two machine translation systems in the face of phraseological ambiguity and draws conclusions about the threat of extinction for biotranslation and the implications of these powerful tools on the training of future language service providers.

The contribution of Katell Hernández Morin and Franck Barbin presents the OPTIMICE project (optimising machine translation of metadata and its integration into the editorial chain). This project aims to design a method combining neural machine translation and human post-editing to improve the quality of article metadata translated from French to English in the editorial process of scientific journals and formulates recommendations for writing and translating metadata.

Hanna Martikainen presents an experiment in adaptive machine translation. As part of a course on machine translation and post-editing, second-year Master's students carried out group projects on the Lilt platform. Hanna Martikainen analyses the students' views on the machine translation engine, focusing on their interaction with the technology. While the students recognise the potential of adaptive machine translation to enhance the role of the human in the loop, the quality of the machine translation and the usability of computer-assisted translation in general seem to have a greater influence on usability than the interaction with the machine.

IV CHALLENGES FOR PROFESSIONAL TRANSLATION

For professional translators, the emergence of machine translation is leading to considerable shifts in practice. This section looks at two important dimensions of these practices: the skills required and the ways in which the result is evaluated. A third article completes these analyses by presenting a survey that sheds light on the field of medical translation.

Ralph Krüger's article focuses on the skills needed by translation professionals in the context of increasing process automation. In particular, he makes the link with the European Union's Digital Competence Framework, and with existing data literacy training initiatives. The competency-based approach allows him to conclude by making the link with professionalizing pedagogical practices developed at the TH Köln -University of Applied Sciences.

Eric Poirier, for his part, looks not at upstream skills, but at the evaluation of the result downstream. His analysis focuses on the methodology for evaluating translations and revisions and shows that digital methods can also make a substantial contribution to this dimension of translation work. The notion of information volume is at the heart of the suggested measures, defined here as a function of the number of characters and lexical words in the aligned segments to be compared. Heteromorphic segments (with different information volumes) are more likely to contain translation errors or to warrant revision. Alongside other methods, those suggested by Eric Poirier are applicable in the context of professional translation to assess how close a translation is to a predefined quality objective, and to what extent correction or revision is required.

The last contribution in this section, presented by Magali Vidrequin, offers practical insights into professional translation practices. She presents a survey of freelance translators working in the medical field. Magali Vidrequin analyses the different profiles and practices of professionals in terms of postediting. The results she highlights underline the integration of machine translation in the translation environment of these professionals.

V THE CONTRIBUTION OF CORPORA

The so-called "empirical" approach to natural language processing (NLP), which includes statistical machine translation and neural machine translation, consists of inferring useful representations for carrying out a language task from corpora; in the case of machine translation, it is a matter of inferring models capable of translating based on aligned corpora [see Poibeau, 2017, ch. 7 and 9]. When large corpora are available for a language pair, it is mainly neural translation that has led to impressive gains in translation quality for a variety of text types. However, an inherent danger of corpus-based methods is the reproduction by machine learning models of the societal biases from the context in which these corpora are produced, as biases are reflected in the selection of documents included in the corpora and in the content of these documents [START_REF] Bolukbasi | Man is to Computer Programmer as Woman is to Homemaker? Debiasing Word Embeddings[END_REF][START_REF] Kumar | Nurse is Closer to Woman than Surgeon? Mitigating Gender-Biased Proximities in Word Embeddings[END_REF][START_REF] Lu | Gender Bias in Neural Natural Language Processing[END_REF][START_REF] Sun | Mitigating Gender Bias in Natural Language Processing: Literature Review[END_REF], be they gender, racial or other biases.

The first paper in this section by Damien Hansen et al. illustrates the use of corpora in machine translation in a rather original way, focusing on training models from literary corpora. Next, Isabelle Rivas-Ginel and Sarah Theroine examine gender bias in machine translations of video games, bringing new results to existing analyses of this type of bias in machine translation [START_REF] Prates | Assessing gender bias in machine translation: A case study with Google Translate[END_REF][START_REF] Saunders | Neural Machine Translation Doesn't Translate Gender Coreference Right Unless You Make It[END_REF][START_REF] Savoldi | Gender bias in machine translation[END_REF].

The work of Hansen and his co-authors presents a system trained particularly for the translation of literary works, specifically heroic fantasy, with the English-French language pair. Literary machine translation in the narrative domain with this language pair had not yet been tackled with neural methods, although experiments with statistical machine translation exist. Two neural models were tested, specifically transformers 3 , which are at the heart of recent advances in natural language processing and machine translation. The quantitative evaluation metrics of the machine translations obtained for the http://jdmdh.episciences.org eISSN 2416-5999, an open-access journal https://doi.org/10.46298/jdmdh.10446 literary corpus are, not surprisingly, lower than the scores achieved in other domains. However, the experiments carried out show the extent to which it is possible to adapt a model to the literature and style of a specific author, or even to the style of a specific translator, in contrast to the results obtained with generic neural systems, not fine-tuned on literary corpora, which erase these stylistic features. The potential usefulness of these literature-specific models for computer-assisted literary translation is also discussed.

Studying the localisation of video games, María Isabel Rivas Ginel and Sarah Theroine analyse the percentage of gender bias resulting from the use of Google Translate, DeepL and SmartCat when translating content from English into French in the case of video games. Their study focuses on the three games DeltaRune, The Devil's Womb and The Faces of the Forest due to the presence of nonbinary characters, non-sexualised characters, and female protagonists. By creating a parallel corpus, they compare the results of the three tools to identify and analyse differences in gender-related errors, to visualise the semantic and grammatical directions of words, and to extract collocations and concordance lines that represent gender identity by analysing the patterns in the source language.

VI FEEDBACK FROM PROFESSIONAL TRANSLATORS

One of the aims of the conference was to bring together research on machine translation with the everyday experience of translation professionals. This section sheds light on the experience of professional translators in industry and academia. It also shows how neural translation influences translation activities and the pedagogical practices of translation teachers.

Alain Volclair's article focuses on the specific case of legal translation. His paper raises translation questions and provides some answers through the prism of the legal translation of lawyers' letters from Italian into French. He also ponders good post-editing practices and the transfer of performativity through machine translation. Finally, he wonders whether it is desirable to let artificial intelligence resolve civil law litigation.

In a different vein, Dominique Defert humorously shares his experience of the recent contribution of neural translation to his work as a literary translator since 1984, specialising in authors such as Dan Brown, Patricia Cornwell, and John Grisham. He shows how (even neural) machine translation cannot, of course, translate humour, that which is left unsaid, or textual or rhetorical devices aimed at "intriguing, surprising, charming" readers. He thus compares his translations of bestsellers already on the market with what a neural translation would return for the same source text. However, he stresses that, in his literary translation practice, the usefulness of recent neural translation tools lies elsewhere: they are valuable to him as a reference tool and help him find information quickly, "without taking his hands off the keyboard".

Finally, Jean-Yves Bassole explores the implications of free machine translation tools for teaching translation. Translation errors made by seven free online machine translation tools are examined, based on nine extracts from literary texts (by Louis-Ferdinand Céline), containing spoken and colloquial language. The article addresses the concern of translation teachers who note a lack of critical reflection in the use of these tools, but also their pedagogical usefulness. It also shows how translation teachers try to make students understand various translation challenges based on translation errors made by machine translators.

  Secondly, Joop Bindels and Mark Pluymaekers' study investigates the use of machine translation by undergraduate students for different learning tasks. The results suggest that most students use machine translation regularly, although the frequency of use decreases as they progress in their studies. The http://jdmdh.episciences.org eISSN 2416-5999, an open-access journal https://doi.org/10.46298/jdmdh.10446

Authors appear in alphabetical order.

Even in the case of poetry, a genre that presents considerable challenges for machine translation, early attempts at neural translation[START_REF] Chakrabarty | t Go Far Off: An Empirical Study on Neural Poetry Translation[END_REF][START_REF] Ghazvininejad | Neural Poetry Translation[END_REF] hint at the systems' potential.

LSTM: Long short-term memory. One of the models suggested to help manage long-distance linguistic dependencies (e.g., subject away from its verb).


Sébastien Merkel

Deformation and plasticity of materials under extreme conditions

Understanding mechanical properties and their microscopic origins is fundamental for multiple fields in condensed matter research. They are controlled by defects, dislocations, diffusion, as well as microstructures, which are not trivial to study under extreme conditions. This chapter summarizes the last 25 years of advances in high pressure devices, x-ray measurements, and data interpretation capabilities for addressing the deformation and plasticity of materials under extreme conditions, from experiments in large volume presses or diamond anvil cells, texture and stress analysis in powder x-ray diffraction, multigrain crystallography, to self consistent models of materials behavior. Examples of applications are then provided in the fields of geophysics and materials science along with perspectives for studies of plastic deformation under extreme conditions in the coming years.

Introduction

Mechanical properties are important for a range of applications, from the design of materials with advanced properties to the dynamics of planetary interiors. The plastic behavior of solid is controlled by defects, dislocations, diffusion, as well as microstructures, a generic term describing the arrangement of a material from the nm to the cm scale. Microstructures in minerals, for instance, are important for the dynamics of the deeper layers of the Earth (Karato et al. 2000). For such application, materials of interest include the high pressure phase of Fe, ε-Fe [START_REF] Wenk | The plastic deformation of iron at pressures of the Earth's inner core[END_REF][START_REF] Lincot | Multiscale model of global inner-core anisotropy induced by hcp alloy plasticity[END_REF], bridgmanite and ferropericlase [START_REF] Miyagi | Texture development and slip systems in bridgmanite and bridgmanite + ferropericlase aggregates[END_REF][START_REF] Marquardt | Slab stagnation in the shallow lower mantle linked to an increase in mantle viscosity[END_REF][START_REF] Girard | Shear deformation of bridgmanite and magnesiowüstite aggregates at lower mantle conditions[END_REF][START_REF] Nzogang | Characterization by scanning precession electron diffraction of an aggregate of bridgmanite and ferropericlase deformed at HP-HT[END_REF], or post-perovskite [START_REF] Merkel | Deformation of (Mg,Fe)SiO3 post-perovskite and D" anisotropy[END_REF][START_REF] Miyagi | Slip systems in MgSiO 3 post-perovskite: Implications for D" anisotropy[END_REF][START_REF] Dobson | Strong inheritance of texture between perovskite and post-perovskite in the D" layer[END_REF], most of which are not stable under ambient pressure and temperature and should be studied in-situ. Hydrostatic pressure also induces phase transformations in metals. Titanium and zirconium, for instance, are hexagonal-closepacked metals under ambient conditions. Under high pressure, they transform to another hexagonal structure, the ω phase, which is not compact and for which mechanical properties are poorly constrained [START_REF] Yu | High pressure phase-transformation induced texture evolution and strengthening in zirconium metal: Experiment and modeling[END_REF], Wenk et al. 2013[START_REF] Kumar | Role of twinning on the omega-phase transformation and stability in zirconium[END_REF]. In other cases, high pressure has been used as a fine-tuning parameter for optimizing strength and grain sizes (e.g. [START_REF] Zhou | High-pressure strengthening in ultrafine-grained metals[END_REF]. As such, the study of mechanical properties in-situ under extreme conditions is of general interest.

The last 25 years have seen tremendous advances in high pressure instruments coupled with synchrotron radiation that allow studies of microstructures and mechanical properties under high pressure and high temperature [START_REF] Raterron | In situ rheological measurements at extreme pressure and temperature using synchrotron x-ray diffraction and radiography[END_REF]. The group at the Geophysical Laboratory and H.-K. Mao provided key contributions to this field, through the design of new methods and ground-breaking publications (e.g. [START_REF] Hemley | X-ray imaging of stress and strain of diamond, iron & tungsten at megabar pressures[END_REF], Mao et al. 1998[START_REF] Wenk | The plastic deformation of iron at pressures of the Earth's inner core[END_REF][START_REF] Merkel | Deformation of polycrystalline MgO at pressures of the lower mantle[END_REF]. Nowadays, millimeter size samples are deformed in large volume presses (LVP) up to Earth's uppermost lower mantle pressures. High pressures and lower dimension samples are deformed and studied in diamond anvil cells (DAC). In all cases, samples are submitted to a macroscopic deformation to induce plasticity and deformation microstructures. Their properties are then studied in-situ using X-ray diffraction and imaging. X-ray radiography allows the measurement of macroscopic properties, such sample size and the applied macroscopic deformation. X-ray diffraction on polycrystals allows for extracting average sample properties by the study of lattice preferred orientations (LPO) and the average stress state. Multigrain Xray diffraction (sometimes labeled as 3D-XRD) addresses single-grains inside a polycrystalline matrix and, in some cases, allows for measuring densities of defects such as dislocations. As such, the properties of deforming materials can be studied in-situ, in their stability field or conditions of application.

In this chapter, I will present the experimental techniques for the high pressure study of materials plasticity. I will start with a description of the experimental devices, then present the characterization techniques using in-situ X-rays, modeling using self-consistent calculations, sample results for Earth's and other materials, and perspectives for the years to come.

Experimental techniques

Plasticity in the large volume press

The Deformation-DIA (D-DIA), Rotational Drickamer (RDA), and deformation T-Cup (D-Tcup) are the main LVP for deformation experiments coupled with in-situ characterization under high pressure. All allow the controlled deformation of millimeter size samples. In addition, new apparatuses such as the RoToPEc (rotational tomographic Paris Edinburgh cell) and high-pressure X-ray tomography microscope (HPXTM) are devices under development.

The D-DIA (Wang et al. 2003, Fig. 1) is a hydraulic press in which a cubic assembly is deformed under the action of 6 anvils. Heating sleeves allow temperatures up to ≈2000 K. Hydrostatic compression is obtained by advancing all 6 anvils (4 horizontal and 2 vertical) at the same velocity. Axial compression deformation at constant pressure is obtained by advancing the upper anvils while retracting the horizontal anvils. Lateral compression is obtained by retracting the vertical anvils and advancing the horizontal anvils. The D-DIA allows experiments at strain rates ranging from 10 -7 to 10 -2 s -1 and pressures and temperatures up to 18 GPa and 1900 K [START_REF] Kawazoe | Seismic anisotropy in the mantle transition zone induced by shear deformation of wadsleyite[END_REF]). It has also been adapted for deformation using a shear geometry up to 25 GPa and 1873K (e.g. Fig 2a, Tsujino et al. 2016[START_REF] Nishihara | Deformation-induced crystallographic-preferred orientation of hcp-iron: An experimental study using a deformation-DIA apparatus[END_REF].

Work is underway to develop new generations of D-DIA-like presses such as the D-DIA-30 allowing reaching higher pressures and working on larger samples (e.g. [START_REF] Wang | High-pressure experimental studies on geo-liquids using synchrotron radiation a the Advanced Photon Source[END_REF]. The D-TCup [START_REF] Hunt | Deformation T-Cup: A new multi-anvil apparatus for controlled strain-rate deformation experiments at pressures above 18 GPa[END_REF][START_REF] Hunt | Note: Modified anvil design for improved reliability in DT-cup experiments[END_REF]) is a similar setup with second stage anvils being developed to allow deformation experiments at pressures and temperatures exceeding those of the D-DIA. In all cases, the imposed macroscopic strain of the cell assembly is axial and measured in-situ using X-ray radiography (see below). Lateral macroscopic strain is reconstructed based on the axial macroscopic strain and the sample's change of volume, deduced from x-ray diffraction. The rotational Drickamer (RDA, Fig. 2b) is an opposed anvil high pressure device that has been modified to perform large strain deformation experiments in simple shear geometry [START_REF] Yamazaki | High-pressure rotational deformation apparatus to 15 GPa[END_REF].Samples can be sheared between two anvils under pressure by a rotation actuator, with strains exceeding γ≈6 at high pressure at strain rates similar to those of the D-DIA. Early sample designs used disks of less that 0.8 mm thick and up to 4 mm outer diameter (e.g. [START_REF] Yamazaki | High-pressure rotational deformation apparatus to 15 GPa[END_REF] while recent experiments rely on rings of 0.2 mm thickness, 0.45 mm inner diameter and 1 mm outer diameter for a better control of sample strain (Fig 2c, Girard et al, 2016). The RDA was successfully used to obtain quantitative creep results on wadsleyite [START_REF] Nishihara | Plastic deformation of wadsleyite and olivine at high-pressure and high-temperature using a rotational Drickamer apparatus (RDA)[END_REF][START_REF] Kawazoe | Shear deformation of polycrystalline wadsleyite up to 2100 K at 14-17 GPa using a rotational drickamer apparatus (RDA)[END_REF][START_REF] Farla | High-pressure and hightemperature deformation experiments on polycrystalline wadsleyite using the rotational drickamer apparatus[END_REF], ringwoodite [START_REF] Miyagi | Plastic anisotropy and slip systems in ringwoodite deformed to high shear strain in the rotational Drickamer apparatus[END_REF], and bridgmanite and magnesiowüstite aggregates [START_REF] Girard | Shear deformation of bridgmanite and magnesiowüstite aggregates at lower mantle conditions[END_REF] up to 27 GPa and 2150 K. In the RDA, the stress applied to the sample is evaluated using x-ray diffraction and is a combination of pure shear and axial compression [START_REF] Xu | Development of a rotational drickamer apparatus for largestrain deformation experiments at deep earth conditions[END_REF].

New advances in the field also include the coupling deformation in simple shear using torsion devices such as the RoToPEc and HPXTM with tomographic measurements. Proofs of principles have been published [START_REF] Philippe | Rotating tomography Paris-Edinburgh cell: a novel portable press for micro-tomographic 4-D imaging at extreme pressure/temperature/stress conditions[END_REF][START_REF] Wang | In situ high-pressure and hightemperature X-ray microtomographic imaging during large deformation: A new technique for studying mechanical behavior of multiphase composites[END_REF] and the devices are currently in use at synchrotron sources.

Plasticity in diamond anvil cells

Large volume presses allow controlled deformation at constant pressure and temperature but do not cover the entire range of conditions found in the Earth's interior. DAC, on the other hand, allow static experiments at pressures exceeding that at the center of the Earth [START_REF] Dewaele | Toroidal diamond anvil cell for detailed measurements under extreme static pressures[END_REF]) and combined pressures and temperatures of the Earth's core [START_REF] Tateno | The structure of iron in Earth's inner core[END_REF]). In addition to confining pressure, diamonds in the DAC impose an axial compressive stress. In most experiments, the compressive stress is reduced by using pressure media around the sample. In plasticity studies, this comes at a benefit that allows macroscopic deformation of the sample. Unlike deformation in LVP, however, pressure and deformation can not be decoupled. Deformation experiments in the DAC are not performed at constant pressure nor at controlled stress or strain rates. The total plastic strain in DAC experiments, estimated from the magnitude of texture evolution, is on the order of 10 to 30%. It is applied over a duration of 5 minutes to a few hours, translating to a strain rate estimate ranging from 10 -5 to 10 -3 s -1 .

In most DAC experiments, the sample properties are studied through the diamond anvils which are transparent over a broad range of wavelength, including X-rays (Fig. 3a). For plasticity studies, it can be useful to have the incoming x-ray beam perpendicular to the loading axis (Fig. 3b). In the early radial diffraction experiments, the sample itself served as a gasket material [START_REF] Kinsland | Strength of MgO and NaCl polycrystals to confining pressures of 250 kbar at 25 C[END_REF]. The sample stress state however, was complex with large pressure gradients across the sample. The technique was then improved by the group at the Geophysical Laboratory with the use of beryllium gaskets [START_REF] Hemley | X-ray imaging of stress and strain of diamond, iron & tungsten at megabar pressures[END_REF]) for a better controlled sample pressure and stress state, and further improved with the use of amorphous boron / epoxy composite gaskets [START_REF] Merkel | X-ray transparent gasket for diamond anvil cell high pressure experiments[END_REF]. Early radial x-ray diffraction experiments were performed at ambient temperature [START_REF] Hemley | X-ray imaging of stress and strain of diamond, iron & tungsten at megabar pressures[END_REF], Mao et al. 1998[START_REF] Wenk | The plastic deformation of iron at pressures of the Earth's inner core[END_REF][START_REF] Merkel | Deformation of polycrystalline MgO at pressures of the lower mantle[END_REF]. High temperature deformation studies have been attempted by combining laser heating and diffraction in the radial geometry, with limited success due to large temperature gradients in the sample [START_REF] Miyagi | In situ phase transformation and deformation of iron at high pressure and temperature[END_REF]. In order to obtain homogeneous conditions of stress, pressure, and temperature, efforts were hence invested in developing dedicated DAC systems combined with resistive heating allowing for radial x-ray diffraction [START_REF] Liermann | New experimental method for in situ determination of material textures at simultaneous high-pressure and temperature by means of radial diffraction in the diamond anvil cell[END_REF][START_REF] Immoor | An improved setup for radial diffraction experiments at high pressures and high temperatures in a resistive graphite-heated diamond anvil cell[END_REF], sometimes also complemented with additional laser-heating [START_REF] Miyagi | Combined resistive and laser heating technique for in situ radial X-ray diffraction in the diamond anvil cell at high pressure and temperature[END_REF]. Under ambient temperature, radial diffraction experiments reached pressures of nearly 300 GPa [START_REF] Hemley | X-ray imaging of stress and strain of diamond, iron & tungsten at megabar pressures[END_REF]. Combined conditions of 62 GPa at 1400 K were obtained in the resistive heating setup [START_REF] Immoor | Evidence for {100}<011> slip in ferropericlase in earth's lower mantle from high-pressure/high-temperature experiments[END_REF] and 69 GPa at 2273 K for setups combining laser and resistive heating [START_REF] Miyagi | Combined resistive and laser heating technique for in situ radial X-ray diffraction in the diamond anvil cell at high pressure and temperature[END_REF].

In addition, deformation experiments can be performed using a rotational diamond anvil cell (rDAC). In the rDAC, one of the diamond anvils is allowed to rotate which produces a torsional deformation like in the RDA [START_REF] Blank | Diamond chamber for examining the effects of shear deformation on the structure and properties of solids at pressures up to 43 GPa[END_REF]. The rDAC has the potential to achieve large-strain under ultra-high pressure conditions while attaining a steady-state deformation [START_REF] Levitas | High-pressure mechanochemistry: Conceptual multiscale theory and interpretation of experiments[END_REF], Nomura et al. 2017). To this day, however, the use of the rDAC for true deformation experiments has been limited due to the complex stress and strain field in rDAC experiments [START_REF] Ma | Effect of shear strain on the α-ε phase transition of iron: a new approach in the rotational diamond anvil cell[END_REF][START_REF] Zarechnyy | Coupled plastic flow and phase transformation under compression of materials in a diamond anvil cell: Effects of transformation kinetics and yield strength[END_REF]. The reliability of rDAC experiments is being improved, with new anvil designs for slip-free experiments which could considerably improve the usability of the technique [START_REF] Azuma | Anvil design for slip-free high pressure deformation experiments in a rotational diamond anvil cell[END_REF].

Computational plasticity

Experimental techniques can be limited. In particular, when addressing the plastic properties of minerals in planetary interiors, experiments are performed at strain rates that are orders of magnitude above those of nature. As such, numerical approaches can become useful to understand, model, and extrapolate materials behavior.

Plastic deformation is the results of the complex, collective behavior of a large collection of defects within a material microstructure. Until recently, this task was not within the reach of numerical techniques but recent developments open the door to such studies (e.g. [START_REF] Cordier | Modelling the rheology of MgO under Earth's mantle pressure, temperature and strain rates[END_REF][START_REF] Boioli | Pure climb creep mechanism drives flow in Earth's lower mantle[END_REF][START_REF] Reali | Modeling viscosity of (Mg,Fe)O at lowermost mantle conditions[END_REF]. Such methods go beyond the scope of the current chapter but a detailed description can be found in Cordier and Goryaeva (2018).

In situ caracterization techniques

Deformation

In LVPs, the sample's macroscopic deformation is measured using X-ray radiography. Strongly x-ray absorbing samples are visible directly while, for less-absorbing samples, one places foils of gold, platinum, or molybdenum in the sample assembly (e.g. Fig. 1c). Based on the displacement, shortening, or tilting of the metal makers, one can then reconstruct the macroscopic deformation applied to the sample (e.g. Raterron andMerkel 2009, Farla et al. 2015). Strain vs. time plots are then used to evaluate the sample strain rate.

In DACs, deformation is rarely controlled and occurs during pressure increases. Moreover, the sample thickness is on the order of 20 μm. Decent sample images can be obtained using changes in X-ray transmission contrasts [START_REF] Merkel | X-ray transparent gasket for diamond anvil cell high pressure experiments[END_REF] but deformation are not very well resolved and, hence, these are rarely used. This could be improved using phase contrast imaging (e.g. [START_REF] Schropp | Imaging Shock Waves in Diamond with Both High Temporal and Spatial Resolution at an XFEL[END_REF] which allows for a much better resolved imaging of interfaces, and particularly so at upgraded synchrotron sources such as ESRF-EBS with an improved performance by a factor of 100 in beam coherence. To my knowledge, this has not been attempted yet.

Polycrystal properties

Powder x-ray diffraction is a standard technique for assessing average macroscopic sample properties, and can be applied to both DAC and LVP experiments. The diameter of the incident x-ray beam and sample microstructures, however, should be adjusted so that a statistically relevant number of grains contribute to the diffraction signal. Otherwise, statistical assumptions with the powder x-ray diffraction processing methods will fail and may lead to inconsistent results.

Lattice preferred orientations

Often, crystallites in a polycrystal are not randomly distributed in orientation and materials develop lattice preferred orientations (LPO). LPO can arise from processes such as nucleation, phase transformation, or plastic deformation. LPO have a strong influence on mechanical properties as physical properties become anisotropic [START_REF] Kocks | Texture and Anisotropy: Preferred Orientations and their Effects on Material Properties[END_REF]. They also affect the propagation of seismic waves and are hence of great interest in geosciences [START_REF] Mainprice | The seismic anisotropy of the earth's mantle: from single crystal to polycrystal[END_REF]. In high pressure deformation experiment, LPO measurements are often used to constrain plastic deformation mechanisms [START_REF] Wenk | Deformation textures produced in diamond anvil experiments, analysed in radial diffraction geometry[END_REF]). In fact, plastic deformation mechanisms and, in particular, dislocation glide will give rise to specific LPO in a polycrystals. LPO measurements, combined with texture modeling (see below) allow the identification of the active plastic deformation mode in a material.

Sample LPO appear as variation of diffraction intensities with orientation (Fig. 4) and can be extracted from the diffraction images using either Multifit [START_REF] Merkel | Multifit/polydefix: a framework for the analysis of polycrystal deformation using x-rays[END_REF] and BEARTEX [START_REF] Wenk | Beartex: a windows-based program system for quantitative texture analysis[END_REF] or MAUD [START_REF] Lutterotti | MAUD: a friendly Java program for materials analysis using diffraction[END_REF][START_REF] Wenk | Rietveld texture analysis from synchrotron diffraction images. ii. complex multiphase materials and diamond anvil cell experiments[END_REF].

Stress and strains

Stress-strain and stress-pressure curves are a critical element to characterize the mechanical properties of materials. In-situ determination of stress, however, is not trivial in high pressure experiments. Unlike classical, low pressure, deformation experiments, the applied stress is not measured directly. Early publications estimated stress based on pressure gradients across a relatively large sample (e.g. [START_REF] Meade | Yield strength of MgO to 40 GPa[END_REF], with the limitation that pressure and stress is heterogeneous in such sample, leading to discrepancies with other measurements [START_REF] Reynard | High-pressure yield strength of rocksalt structures using quartz raman piezometry[END_REF]. Internal quartz calibrants can be used for in-situ piezometry in the DAC. Raman vibrational mode frequencies shift with pressure and deviatoric stresses induce TO-LO splitting of the lowest frequency E mode of quartz. All have been calibrated recently [START_REF] Reynard | High-pressure yield strength of rocksalt structures using quartz raman piezometry[END_REF]. Most high pressure deformation experiments, however, rely on in-situ xray diffraction for stress evaluation.

Residual stress analysis using x-ray diffraction is a common technique in materials science [START_REF] Noyan | Residual stress: measurements by diffraction and interpretation[END_REF] and was adapted to high pressure research in the mid-1990's (e.g. [START_REF] Hemley | X-ray imaging of stress and strain of diamond, iron & tungsten at megabar pressures[END_REF], Singh et al. 1998). Hydrostatic pressure changes the unit cell parameters of a material, and hence the average dspacings of all powder x-ray diffraction lines. Deviatoric stresses add an additional component with changes of the measured d-spacings with orientation (Fig. 4a). Theories relating deviatoric stress and the measured strains using x-ray diffraction are available in the literature, both for axial [START_REF] Singh | Analysis of lattice strains measured under non-hydrostatic pressure[END_REF] and shear [START_REF] Nishihara | Plastic deformation of wadsleyite and olivine at high-pressure and high-temperature using a rotational Drickamer apparatus (RDA)[END_REF] deformation experiments. All rely on elasticity theory and assume continuity of stress or strain within the deforming aggregate.

The elastic assumption for stress inversion, however, fails when plastic deformation is at play [START_REF] Li | X-ray strain analysis at high pressure: Effect of plastic deformation in MgO[END_REF], Merkel et al. 2006). In fact, as materials deform, stresses will relax in grains in soft orientations (i.e.

for which plastic deformation can be easily activated) while other grains, whose orientations do not favor plastic deformation, will remain highly stressed. For each orientation, the measured d-spacing in powder

x-ray diffraction is the average d-spacing of all grains contributing to the diffraction, either soft or hard. This heterogeneity of stress within grains contributing to the same diffraction peak is not well captured by elasticity-based models. The average stress state and intergranular stress heterogeneities in a deforming material, however, can be modeled using self-consistent techniques (see below, Fig. 7).

Another approach to circumvent the issue of stress evaluation using X-ray diffraction is to use an internal standard. Al2O3, for instance, is well-known and was calibrated using self-consistent techniques (Raterron et al 2013). Pyrope is another option as experiments have shown that it is plastically isotropic with less that 10 % variation for stresses deduced between different diffraction lines (e.g. Girard et al 2020). Deformation experiment are best interpreted using self-consistent (SC) methods. SC calculations treat each grain of the polycrystal as an inclusion in a homogeneous but anisotropic medium (Fig. 5). The properties of the medium are determined by the average of all inclusions. At each deformation step, the inclusion and medium interact and the macroscopic properties are updated iteratively until the average strain and stress of all inclusions equals the macroscopic strain and stress.

Interpretation using self-consistent models

The Elasto-Plastic Self-Consistent (EPSC) approximation of [START_REF] Turner | A study of residual stresses in zircaloy-2 with rod texture[END_REF], later extended by [START_REF] Clausen | Reorientation and stress relaxation due to twinning: Modeling and experimental characterization for Mg[END_REF] and [START_REF] Neil | Modeling lattice strain evolution at finite strains and experimental verification for copper and stainless steel using in situ neutron diffraction[END_REF], accounts for elasticity of the material as well as stress relaxation and grain rotation due to twinning and dislocation slip. Plasticity in EPSC calculations, however, is not dependent on strain rates. Visco-Plastic Self-Consistent (VPSC) calculations account for stress relaxation and grain rotation due to twinning and dislocation slip, accounting for a strain-rate dependent plasticity, but do not account for elasticity [START_REF] Lebensohn | A self-consistent visco-plastic model: calculation of rolling textures of anisotropic materials[END_REF]. Finally, the Elasto-Visco-Plastic Self-Consistent (EVPSC) formulation, such as in [START_REF] Wang | A finite strain elastic-viscoplastic self-consistent model for polycrystalline materials[END_REF], accounts for elastic stresses, grain rotation, and relaxation due to plasticity, as well as strain rate dependence of the plastic behavior. EPSC or EVPSC will allow interpreting both the experimental texture and lattice strains [START_REF] Merkel | A modeling analysis of the influence of plasticity on high pressure deformation of hcp-Co[END_REF][START_REF] Lin | Elasto-viscoplastic self consistent modeling of the ambient temperature plastic behavior of periclase deformed up to 5.4 GPa[END_REF][START_REF] Li | X-ray strain analysis at high pressure: Effect of plastic deformation in MgO[END_REF]).

For ε-Fe at 17 GPa and 400 K, for instance, a comparison between experimental data and the results of EPSC models indicates that plastic deformation is dominated by the activity of basal slip and {10 1 2} tensile twinning (Fig. 6). The critical resolved shear stress (CRSS) of basal slip is low (0.05 GPa) but, due to intergranular interactions and effects of grain orientations, the overall macroscopic stress reaches t=2.0 GPa after 12% axial compression. Fig. 7 highlights one of the advantages on self-consistent models for analyzing the results of high pressure deformation experiments. Stresses deduced from elastic models are inconsistent due to stress heterogeneities between grains in soft orientations, for which stresses are relaxed through plastic deformation, and grains in hard orientations, which experience a higher stress. The results in an apparent stresses that can vary by up to 50% or more depending on the choice of measurement which will, later, translate into inconsistent flow laws. One should keep in mind, however, that x-ray diffraction is sensitive to strains at the local scale, for grains contributing to diffraction, and not stress. Self-consistent calculations (EVPSC in Fig. 7) allows determining the true stress value, consistent with all strain measurements using x-ray diffraction.

Plasticity at the grain scale

Recently, experimental studies of microstructures and plastic deformation reached a new milestone with techniques allowing the characterization of individual grains or subgrains within a polycrystalline material [START_REF] Ludwig | New opportunities for 3D materials science of polycrystalline materials at the micrometre lengthscale by combined use of x-ray diffraction and x-ray imaging[END_REF]. Multigrain x-ray diffraction allows for a rapid, in-situ, and non-destructive study of microstructural elements. These elements can also be followed in situ as a function of time or external parameters such as stress, pressure, or temperature. Moreover, samples in high pressure experiments and, in particular, those of DAC are often small and do not contain enough grains for a statistically relevant powder diffraction analysis. They are, on the other hand, perfectly suited for multigrain x-ray diffraction.

Multigrain crystallography

Multigrain x-ray diffraction allows for the extraction of the orientation and crystal structure of hundreds of elements inside a polycrystalline material [START_REF] Poulsen | Three-Dimensional X-Ray Diffraction Microscopy: Mapping Polycrystals and their Dynamics[END_REF]). Extensions of the technique further allow the determination of the position and stress state for each of those elements [START_REF] Oddershede | Determining grain resolved stresses in polycrystalline materials using three-dimensional x-ray diffraction[END_REF].

The method has been applied to DAC experiments [START_REF] Nisr | High resolution three-dimensional x-ray diffraction study of dislocations in grains of MgGeO3 post-perovskite at 90 GPa[END_REF][START_REF] Rosa | Evolution of grain sizes and orientations during phase transitions in hydrous Mg2SiO4[END_REF][START_REF] Zhang | Disproportionation of (Mg,Fe)SiO3 perovskite in Earth's deep lower mantle[END_REF][START_REF] Langrand | Reliability of multigrain indexing for orthorhombic polycrystals above 1mbar: application to MgSiO3 post-perovskite[END_REF]) including pioneering works involving H.-K. Mao [START_REF] Ice | Adapting polychromatic x-ray microdiffraction techniques to high-pressure research: energy scan approach[END_REF]). The method is not restricted to DAC experiments and could also be applied to LVP experiment but this remains to be reported. Multigrain x-ray diffraction consists in a search for diffraction spots while exploring reciprocal space (Fig. 8). A first analysis generates a database of experimental diffraction spots, along with their 2θ, ω, and η angles and intensities. Algorithms such as GrainSpotter [START_REF] Schmidt | Grainspotter: a fast and robust polycrystalline indexing algorithm[END_REF]) then use the experimental diffraction spots database and scan the grain orientation space to reconstruct the number and orientations of the individual diffracting sample grains.

In the work of [START_REF] Rosa | Evolution of grain sizes and orientations during phase transitions in hydrous Mg2SiO4[END_REF], for instance, we used multigrain x-ray diffraction in order to study the effect of olivine-wadsleyite-ringwoodite chain of phase transformations on microstructures up to 22 GPa and 940 K. We follow the number of grains for each phase, their orientations, a distribution of grain sizes, at each step of the phase transformation (Fig. 9). Such measurement allow the study of phase transformation mechanisms and associated microstructures, with important applications for constraining deep-Earth processes. They can, as well, be extended to follow microstructures induced by plastic deformation.

Defects

X-ray line profile analysis (XLPA) is an effective technique for the study of grain level microstructures using x-ray diffraction [START_REF] Kerber | Xray line profile analysis -An ideal tool to quantify structural parameters of nanomaterials[END_REF]. The shape of Bragg diffraction peaks can be quantitatively evaluated not only in terms of the crystallite size and its distribution, but also in terms of the density, type and arrangement of dislocations, twins and stacking faults (e.g. Fig. 10). The advantages of the XPLA method are that i) the resolution increases with a decreasing grain size and increasing defect density, and ii) it relies on x-ray diffraction and can hence be applied to high pressure experiments. The effect of dislocations on peak broadening, for instance, can be measured when their density increases above 10 12 m -2 . On the other hand, it requires a high angular resolution (below 0.01°) and relative accuracy of 10 -4 on diffraction intensities at the edges of diffraction peaks. Also note that, unlike techniques such as high resolution back-scattered electron diffraction (HR-EBSD), XLPA is sensitive to the total dislocation density, including both geometrically necessary and statistically stored dislocations [START_REF] Ribárik | Global optimum of microstructure parameters in the CMWP lineprofile-analysis method by combining Marquardt-Levenberg and Monte-Carlo procedures[END_REF] and can not distinguish between both.

Under high pressure, the XPLA technique, combined with multigrain crystallography was used for the study of dislocations in deep Earth materials. Experiments on MgGeO3 in the post-perovskite structure, for instance, allowed the identification of dominant dislocation types in this material at 90 GPa [START_REF] Nisr | High resolution three-dimensional x-ray diffraction study of dislocations in grains of MgGeO3 post-perovskite at 90 GPa[END_REF].

Sample results

Deep Earth materials

Iron is one of the most abundant metals, a widely used technological material, and the main constituent of the Earth's core. As such, the plastic properties of iron under pressure and temperature have received much attention during the past decades. Nothing was known on the plasticity of ε-Fe in the mid-1990's and geophysical models of inner-core behavior often relied on simple assumptions such as the comparison of c/a ratios between ε-Fe and other hcp metals (e.g. [START_REF] Jeanloz | Convection and anisotropy of the inner core[END_REF]. Pioneering works were performed at the Geophysical Laboratory with radial x-ray diffraction on Fe up to 220 GPa [START_REF] Mao | Elasticity and rheology of iron above 220 GPa and the nature of the earth's inner core[END_REF]) and paved the way to the determination of the plastic properties of ε-Fe under high pressure [START_REF] Wenk | The plastic deformation of iron at pressures of the Earth's inner core[END_REF][START_REF] Merkel | Deformation of polycrystalline iron up to 30 GPa and 1000[END_REF], 2012[START_REF] Gleason | Strength of iron at core pressures and evidence for a weak Earth's inner core[END_REF][START_REF] Nishihara | Deformation-induced crystallographic-preferred orientation of hcp-iron: An experimental study using a deformation-DIA apparatus[END_REF].

Our current understanding is that basal slip and tensile twinning are the dominant plastic deformation mechanism of ε-Fe at high pressure and room temperature [START_REF] Wenk | The plastic deformation of iron at pressures of the Earth's inner core[END_REF], Merkel et al. 2012). The strength of each deformation was characterized with D-DIA measurements at 13-17 GPa and 400-700 K [START_REF] Merkel | Texture and elastic strains in hcp-iron plastically deformed up to 17.5 GPa and 600 K: experiment and model[END_REF][START_REF] Nishihara | Deformation-induced crystallographic-preferred orientation of hcp-iron: An experimental study using a deformation-DIA apparatus[END_REF]. These new interpretations also highlight the important contribution of tensile twinning to understand the evolution of stress and texture at those conditions.

Measurements up to 200 GPa at ambient temperature combined with a numerical model also indicate that the bulk shear strength of Fe is ≈1 GPa at inner-core pressures and temperatures [START_REF] Gleason | Strength of iron at core pressures and evidence for a weak Earth's inner core[END_REF]. This suggests that the inner core is rheologically weak and supports dislocation creep as the dominant creep mechanism influencing deformation. Deformation experiments on Fe, however, have only reached pressures of ≈200 GPa at ambient temperature and combined pressure and temperatures of ≈17 GPa and ≈700 K. These remain far from those in the inner core (above 300 GPa and 5000 K). Future efforts will be hence invested in extending the pressure and temperature range of experiments analyzing the plastic behavior of Fe.

Ferropericlase, (Mg,Fe)O, is another interesting material regarding high pressure plasticity studies. MgO is a very well-known crystalline ceramic whose mechanical properties are thoroughly studied in materials science [START_REF] Amodeo | Dislocations and plastic deformation in MgO crystals: A review[END_REF], both experimentally (e.g. Korte andClegg 2011, Tromas et al. 2000) and using numerical plasticity techniques (e.g. [START_REF] Amodeo | Modelling the effect of pressure on the critical shear stress of MgO single crystals[END_REF], Cordier et al. 2012). (Mg,Fe)O is also the second dominant phase in the Earth's lower mantle. For the above reasons, numerous studies of the plastic properties of (Mg,Fe)O under high pressure and temperature can be found in the literature (e.g. [START_REF] Merkel | Deformation of polycrystalline MgO at pressures of the lower mantle[END_REF], Cordier et al. 2012, Amodeo et al. 2012, 2016[START_REF] Yamazaki | Fabric development in (Mg,Fe)O during large strain, shear deformation: implications for seismic anisotropy in Earth's lower mantle[END_REF], Tommaseo et al. 2006[START_REF] Lin | Deformation of lowermantle ferropericlase (Mg,Fe)O across the electronic spin transition[END_REF][START_REF] Long | Lattice preferred orientation in deformed polycrystalline (Mg,Fe)O and implications for seismic anisotropy in D[END_REF][START_REF] Mei | Experimental investigation of the creep behavior of MgO at high pressures[END_REF][START_REF] Uchida | Yield strength and strain hardening of MgO up to 8 GPa measured in the deformation-DIA with monochromatic x-ray diffraction[END_REF][START_REF] Lin | Elasto-viscoplastic self consistent modeling of the ambient temperature plastic behavior of periclase deformed up to 5.4 GPa[END_REF][START_REF] Marquardt | Slab stagnation in the shallow lower mantle linked to an increase in mantle viscosity[END_REF][START_REF] Immoor | Evidence for {100}<011> slip in ferropericlase in earth's lower mantle from high-pressure/high-temperature experiments[END_REF][START_REF] Kinsland | Strength of MgO and NaCl polycrystals to confining pressures of 250 kbar at 25 C[END_REF][START_REF] Lin | Competing deformation mechanisms in periclase: Implications for lower mantle anisotropy[END_REF][START_REF] Girard | Deformation of periclase single crystals at high pressure and temperature: Quantification of the effect of pressure on slip-system activities[END_REF][START_REF] Heidelbach | Fabric evolution during high shear strain deformation of magnesiowüstite (Mg0.8Fe0.2 O)[END_REF][START_REF] Stretton | Dislocation creep of magnesiowüstite (Mg0.8Fe0.2O)[END_REF].

Under ambient temperature, pure MgO deforms through dislocation slip on {110} ⟨1 1 0 ⟩ (Merkel et al. 2002, Lin et al. 2017) with an increased activity of {110 } ⟨100⟩ with increasing temperature (Paterson and Weaver 1970). Recent calculations also predict a transition between {110} ⟨1 1 0 ⟩ and {110} ⟨100⟩ slip with increasing pressure [START_REF] Amodeo | Modelling the effect of pressure on the critical shear stress of MgO single crystals[END_REF]) and that, moreover, in the Earth's mantle, extremely low strain rates counteract the influence of pressure with MgO deforming in the athermal regime where dislocation motion is purely controlled by dislocation interactions rather than lattice friction [START_REF] Cordier | Modelling the rheology of MgO under Earth's mantle pressure, temperature and strain rates[END_REF]. Deformation experiments on single crystal do show a trend consistent with such change of slip system with pressure [START_REF] Girard | Deformation of periclase single crystals at high pressure and temperature: Quantification of the effect of pressure on slip-system activities[END_REF] and deformation experiments on ferropericlase show evidence of both {110} ⟨1 1 0 ⟩ and {110 } ⟨100⟩ slip at ≈1400 K in a range of 30-60 GPa (Immoor et al. 2018). Recent ambient temperature measurements and modeling on pure MgO up to 50 GPa, however, predict an increasing activity of {110} ⟨1 1 0 ⟩ slip with pressure (Lin et al. 2019). As such, the effect of pressure (and strain rate) on the plasticity of pure MgO remains an active field of research.

The addition of Fe in (Mg,Fe)O does not seem to drastically affect the type of dominant slip systems in (Mg,Fe)O [START_REF] Tommaseo | Texture development and elastic stresses in magnesiowüstite at high pressure[END_REF][START_REF] Long | Lattice preferred orientation in deformed polycrystalline (Mg,Fe)O and implications for seismic anisotropy in D[END_REF][START_REF] Yamazaki | Fabric development in (Mg,Fe)O during large strain, shear deformation: implications for seismic anisotropy in Earth's lower mantle[END_REF][START_REF] Stretton | Dislocation creep of magnesiowüstite (Mg0.8Fe0.2O)[END_REF][START_REF] Immoor | Evidence for {100}<011> slip in ferropericlase in earth's lower mantle from high-pressure/high-temperature experiments[END_REF]. Between 40 and 80 GPa however, Fe in (Mg,Fe)O undergoes electronic spin-pairing transition from a high-spin to a low-spin state [START_REF] Badro | Iron partitioning in earth's mantle: Toward a deep lower mantle discontinuity[END_REF] with potential effects of on sample stress [START_REF] Lin | Deformation of lowermantle ferropericlase (Mg,Fe)O across the electronic spin transition[END_REF]. Measurements up to 100 GPa at ambient temperature also seem to indicate that the strength of (Mg,Fe)O increases by a factor of three at pressures from 20 to 65 GPa [START_REF] Marquardt | Slab stagnation in the shallow lower mantle linked to an increase in mantle viscosity[END_REF] with important consequences regarding the stagnation of slabs sinking through the shallow lower mantle. These conclusions remain to be confirmed at mantle temperatures and strain rates.

Materials science

Simple metals were quickly recognized as a field of study regarding high pressure mechanical properties (e.g. Re, Mo and Au, Duffy et al. 1999bDuffy et al. , 1999a)). These first publications were followed by studies on Pt [START_REF] Kavner | Elasticity and rheology of platinum under high pressure and nonhydrostatic stress[END_REF], Os (Chen et al. 2010a[START_REF] Weinberger | Osmium metal studied under high pressure and nonhydrostatic stress[END_REF], Gd [START_REF] Xiong | Strength and structural phase transitions of gadolinium at high pressure from radial x-ray diffraction[END_REF], W (He andDuffy 2006, Xiong et al. 2018), Co [START_REF] Merkel | A modeling analysis of the influence of plasticity on high pressure deformation of hcp-Co[END_REF], or Al [START_REF] Singh | Aluminum as a pressuretransmitting medium cum pressure standard for x-ray diffraction experiments to 200 GPa with diamond anvil cells[END_REF]), slowly constituting a database of strength and deformation mechanisms in simple metals as a function of pressure. It turns out that the yield strength of Os is significant larger than that of other stiff pure metals (≈12 GPa at 60 GPa), followed by Re and W. Other metals, such as Ti or Zr, undergo phase transitions at relatively low pressure. This motivated studies of texture and strength, both during the phase transformation and for the higher pressure phase. [START_REF] Wenk | Orientation relations during the α-ω phase transition of zirconium: In situ texture observations at high pressure and temperature[END_REF], for instance, studied the α ↔ ω transition in Zr and found i) a martensitic mechanisms with (0001) α ∥(11 20 ) β and ii) remarkable orientation memory during the reverse transformation. This was then followed by further studies on the α ↔ ω transition in Zr and the mechanical properties of both phases [START_REF] Yu | High pressure phase-transformation induced texture evolution and strengthening in zirconium metal: Experiment and modeling[END_REF][START_REF] Kumar | Role of twinning on the omega-phase transformation and stability in zirconium[END_REF], with the aim to design Zr microstructure and strengthen its mechanical properties for high-pressure applications.

The Hall-Petch relationship predicts that the strength of materials should increase with smaller grain sizes. It is verified down to grain sizes of about 30 nm for which an inverse Hall-Petch effect is often observed, with a decrease of strength with decreasing grain size. This inverse Hall-Petch effect is attributed to a transition from dislocation-based plasticity to grain boundary sliding, rotation, or diffusion but this remains controvertial [START_REF] Naik | The hall-petch and inverse hall-petch relations and the hardness of nanocrystalline metals[END_REF]. This motivated studies on the effect of grain sizes on the plastic behavior of nanocrystalline materials under pressure (e.g. [START_REF] Singh | Strength of polycrystalline coarse-grained platinum to 330 GPa and of nanocrystalline platinum to 70 GPa from high-pressure x-ray diffraction data[END_REF]. The application of hydrostatic pressure is found to have a strong effect on the transition from the Hall-Petch to inverse Hall-Petch effect. In fact, evidences for dislocation activity were observed in 3 nm Ni compressed to 18.5 GPa [START_REF] Chen | Texture of nanocrystalline nickel: Probing the lower size limit of dislocation activity[END_REF]. Moreover, recent work on pure Ni report a continuous strengthening in samples with grain sizes from 200 nm down to 3 nm, with the strengthening enhanced (rather than reduced) at grain sizes smaller than 20 nanometres [START_REF] Zhou | High-pressure strengthening in ultrafine-grained metals[END_REF]. These recent works await confirmation in other materials and a better understanding of the combined effect of pressure and grain sizes on dislocation-based plasticity. They do, however, illustrate how studies under high pressure can help solve fundamental issues in materials science.

Other applications in materials science include the design of new, strong materials either as pure phases [START_REF] Xiong | Radial x-ray diffraction of tungsten tetraboride to 86 GPa under nonhydrostatic compression[END_REF][START_REF] Kiefer | Strength, elasticity, and equation of state of the nanocrystalline cubic silicon nitride γ-Si3N4 to 68 GPa[END_REF][START_REF] Dong | Elastic moduli and strength of nanocrystalline cubic BC2N from x-ray diffraction under nonhydrostatic compression[END_REF][START_REF] He | Strength and equation of state of boron suboxide from radial x-ray diffraction in a diamond cell under nonhydrostatic compression[END_REF], Liermann et al. 2007[START_REF] Chen | Strength and elastic moduli of TiN from radial x-ray diffraction under nonhydrostatic compression up to 45 GPa[END_REF] or with a controlled microstructure [START_REF] Conil | Elastic behavior and strength of Al2O3 fiber/Al matrix composite and implications for equation of state measurements in the diamond anvil cell[END_REF], as well as the peculiar effect of phase transitions on microstructures in oxides [START_REF] Yue | Deformation behavior across the zircon-scheelite phase transition[END_REF]. All remain an active field of study.

Perspectives

Multiphase aggregates

The vast majority of rocks that constitute the Earth are not made of a single material but rather an assemblage of multiple minerals. The microstructure, i.e. the arrangement of each phase, the orientation and size of each grain, has an influence on the overall mechanical properties of the rock. As such, the mechanical properties of multiphase aggregate are of great interest for the geosciences. They are also fundamental to materials science application, for which the design of composite materials with a predefined microstructure and physical properties are of great interest. Despite their relevance however, the mechanical properties of polyphase aggregates under pressure remain poorly understood.

In the Earth's lower mantle, for instance, bridgmanite is substantially stronger than ferropericlase and experiments indicate that ferropericlase accommodates most of the strain [START_REF] Wang | Highpressure, high-temperature deformation of CaGeO3 (perovskite)±MgO aggregates: Implications for multiphase rheology of the lower mantle[END_REF], Miyagi and Wenk 2016[START_REF] Girard | Shear deformation of bridgmanite and magnesiowüstite aggregates at lower mantle conditions[END_REF]. A simple approach indicates that, if the weaker ferropericlase is not interconnected, then rheology of the lower mantle will mostly depend on bridgmanite, but if ferropericlase is interconnected, then it will control deformation. The microstructural arrangement of bridgmanite and ferropericlase, however, is controlled by plastic deformation, which in turn, is controlled by the properties of both phases. It is therefore required to understand this complex interplay between microstructure, the properties of each phase, and the material's macroscopic response. Moreover, stress percolates through polycrystalline materials that have heterogeneous elastic and plastic properties. The pattern of stress percolation is related to the degree of heterogeneity in and statistical distribution of the elastic and plastic properties of the constituent grains in the aggregate [START_REF] Burnley | The importance of stress percolation patterns in rocks and other polycrystalline materials[END_REF]. To this day, the understanding and modeling of the feedback between single phase plasticity, microstructures, and macroscopic behavior of multiphase materials remains a challenge that has seldomly been attempted in high pressure research [START_REF] Kaercher | Two-phase deformation of lower mantle mineral analogs[END_REF][START_REF] Kasemer | Deformation heterogeneity and intragrain lattice misorientation in high strength contrast, dual-phase bridgmanite/periclase[END_REF]).

In addition, pressure, temperature, and deformation can induce mineralogical reactions which will affect the mechanical properties of the aggregate. In olivine + serpentines aggregates, for instance, it has been shown that dehydration reactions of deforming samples containing only 5 vol% of antigorite suffices to trigger significant stress transfer and embrittlement [START_REF] Ferrand | Dehydration-driven stress transfer triggers intermediate-depth earthquakes[END_REF]. A strong weakening of cold subducting slab was also reported due to the olivine to ringwoodite phase transformation (Mohiuddin et al. 2020). The mechanical properties of aggregates undergoing phase transformations are relevant for mantle dynamics and the generation of deep earthquakes deep inside the Earth. Such approach could, also, find multiple application for the understanding of mechanical properties of materials undergoing phase transformations at other conditions of extreme pressure and temperature.

Technical developments

This chapter mostly focused on coupling in-situ deformation, x-ray diffraction, and radiography. In the coming years, high pressure deformation studies could greatly benefit from further technological developments. For the study of deep earthquakes for instance, the D-DIA deformation press has been coupled with devices recording the sample's acoustic emissions during deformation [START_REF] Schubnel | Deep-focus earthquake analogs recorded at high pressure and temperature in the laboratory[END_REF]. The acoustic emission signals can even be further processed to understand the nature of the focal mechanisms, their distribution in both space and time during deformation, and further waveform analysis could be possible [START_REF] Wang | A laboratory nanoseismological study on deep-focus earthquake micromechanics[END_REF]. The combination of high pressure plastic deformation experiments with the tracking of the sample's acoustic emissions could be of great interest for high pressure plasticity studies. In fact, plastic mechanisms such as twinning or dislocation slip are known to trigger acoustic emissions in ambient pressure deformation experiments [START_REF] Weiss | Statistical analysis of dislocation dynamics during viscoplastic deformation from acoustic emission[END_REF][START_REF] Vinogradov | On the limits of acoustic emission detectability for twinning[END_REF][START_REF] Muránsky | Investigation of deformation twinning in a fine-grained and coarse-grained ZM20 mg alloy: Combined in situ neutron diffraction and acoustic emission[END_REF]) and this field of study could open new doors to high pressure research.

Presently, strain measurements in DAC deformation experiments is limited to average measurements in polycrystals. Multigrain crystallography allows strain mapping at the grain level [START_REF] Oddershede | Determining grain resolved stresses in polycrystalline materials using three-dimensional x-ray diffraction[END_REF] and can be used, for instance, to evaluate strain localization in deformation experiments [START_REF] Sedmák | Grainresolved analysis of localized deformation in nickel-titanium wire under tensile load[END_REF]). Strain mapping using multigrain crystallography has been tested in DAC experiments [START_REF] Nisr | Three-dimensional x-ray diffraction in the diamond anvil cell: application to stishovite[END_REF]) but the method remains to be strengthened, tested, and applied to topics such as stress percolation in heterogeneous aggregates.

Advanced imaging techniques, often relying on the high coherence of synchrotron x-ray beams, such as Bragg coherent diffractive imaging, ptychography, or dark-field x-ray microscopy, allow for revealing strains and heterogeneities within a single grain [START_REF] Yau | Bragg coherent diffractive imaging of single-grain defect dynamics in polycrystalline films[END_REF][START_REF] Hruszkewycz | High-resolution three-dimensional structural microscopy by single-angle bragg ptychography[END_REF][START_REF] Simons | Dark-field x-ray microscopy for multiscale structural characterization[END_REF], may be used under operando conditions, and some have been tested in DAC experiments [START_REF] Yang | Coherent diffraction imaging of nanoscale strain evolution in a single crystal under high pressure[END_REF]. These proof-of-concept experiments show that three-dimensional strain distribution with a spatial resolution of 30 nm can be measured inside a 400 nm crystal within a DAC. At present, these techniques represent a steep technical challenge but, with the advent of new, powerful, and highly coherent sources at ERSF, PETRA, SPRING-8, and APS, may become more routine measurements in the future. Local strain mapping techniques allowing, for instance, the determination and mapping of dislocation types and densities [START_REF] Wallis | Dislocation interactions in olivine revealed by HR-EBSD[END_REF] could then be performed in situ under high pressure.

3D X-ray tomography also offers avenues for new experiments in LVP (e.g. [START_REF] Urakawa | Development of high pressure apparatus for X-ray microtomography at Spring-8[END_REF][START_REF] Wang | In situ high-pressure and hightemperature X-ray microtomographic imaging during large deformation: A new technique for studying mechanical behavior of multiphase composites[END_REF][START_REF] Philippe | Rotating tomography Paris-Edinburgh cell: a novel portable press for micro-tomographic 4-D imaging at extreme pressure/temperature/stress conditions[END_REF], Yu et al. 2016) with the ability to resolve small heterogeneities under high pressure and temperature and various strain conditions. This allows in situ tracking of various components in complex materials, with implications on their mechanical properties, connectivity, or permeability. [START_REF] Wang | In situ high-pressure and hightemperature X-ray microtomographic imaging during large deformation: A new technique for studying mechanical behavior of multiphase composites[END_REF] and [START_REF] Todd | The effects of shear deformation on planetesimal core segregation: Results from in-situ X-ray micro-tomography[END_REF], for instance, studied the effect of deformation on microstructures of metal-silicate aggregates with implications for the mechanical properties of composite materials relevant to the Earth's mantle and the formation of planetary cores. One could also refer to ongoing on work on serpentines-olivine aggregates, with implications for subduction zones [START_REF] Mandolini | Microstructural evolution in deforming olivine-serpentine aggregates at subduction zones conditions using in-situ X-ray tomography[END_REF] or the in-situ monitoring of the orientations and mobility of interfaces during phase transitions (e.g. [START_REF] Boulard | Following the phase transitions of iron in 3D with X-ray tomography and diffraction under extreme conditions[END_REF].

Finally, the present chapter focused on measurements performed in "static" experiments. With the advent of gas-gun or laser-driven dynamic compression techniques coupled with either synchrotron or x-ray free electron lasers and faster detectors, time-resolved measurements at rapid strain rates are now achievable (e.g. [START_REF] Wehrenberg | In situ X-ray diffraction measurement of shock-wave-driven twinning and lattice dynamics[END_REF][START_REF] Chen | Capture Deformation Twinning in Mg during Shock Compression with Ultrafast Synchrotron X-Ray Diffraction[END_REF]. Combined with deformation experiments at low strain rates, as described in this chapter, intermediate strain rate experiments in a dynamic diamond anvil cell [START_REF] Méndez | A resistively-heated dynamic diamond anvil cell (RHdDAC) for fast compression x-ray diffraction experiments at high temperatures[END_REF], and dynamic compression experiments will allow investigating the effect of orders of magnitude in strain rate on deformation and plasticity. Nowadays, the studies of mechanical properties under extreme conditions is a thriving field of research, with applications in geosciences, for which it was first intended, but also materials sciences, as highlighted in the latest section of this chapter. Recent works, relying on multi-grain crystallography now allow the study of microstructures and plasticity at the grain scale and will open new doors to this field of research, offering a quantitative and comprehensive description of materials microstructure at the micrometre lengthscale. Strain mapping within a grain, along with the identification of deformation defects and densities is also within reach.

Conclusion

Plasticity depends on pressure, temperature, microstructures, but also strain rates. Further works should hence not only focus on extending the pressure and temperature conditions of the experiments, in order to reach those of the innermost sections of our planet, but also on exploring strain rates, from extremely fast processes at 10 10 s -1 in a shock wave, to deep Earth conditions of 10 -15 s -1 . To this day, this remains an experimental and numerical challenge.

Figure 1 :

 1 Figure 1: (a) Main module of the D-DIA deformation press at the ID06 beamline of the ESRF synchrotron. The main anvils, labeled as here E, W, N, and S, apply a load on secondary anvils to generate deformation. The lower (hidden) and top (opened) anvils are not visible on the image. (b) Principle of the D-DIA. Vertical and horizontal anvils can be moved independently. (c) Typical sample assembly placed between the 6 anvils for deformation experiments. For simplicity, the thermocouples measuring temperature are not shown.

Figure 2 :

 2 Figure 2: Typical sample assemblies for shear deformation in the LVP. (a) Shear deformation in the D-DIA (e.g. Tsujino et al. 2016). Axial strain (red arrows) is applied to the cell assembly, which translates to shear strain on the sample. (b) Torsion in the RDA. Pressure is applied by advancing the top and bottom anvils. The cell assembly is submitted to torsion by rotating one of the anvils. (c) Simplified top view of the cell assembly in the RDA in Girard et al. 2016. The sample is a ring of 0.2 mm thickness, 0.45 mm inner diameter and 1 mm outer diameter.

Figure 3 :

 3 Figure 3: Geometries for x-ray diffraction DAC experiments. The axial geometry (a) is most common, with the incident x-ray beam aligned with the compression direction. The radial geometry (b) is commonly used in deformation experiments. The incoming and diffracted x-ray beams are perpendicular to compression, and pass through an x-ray transparent gaskets made of beryllium or composite materials.

Figure 4 :

 4 Figure 4: Diffraction images for ε-Fe at 17 GPa and 400 K (Merkel et al. 2012) measured at the start of the deformation (a) and after 11.5% axial strain in a D-DIA (b). Variations of peak intensities and positions with azimuth are indicative of the sample LPO and stress, respectively. Measured inverse pole figure of the compression direction at the start of deformation (c) and after 11.5% axial strain (d). (e) Results of a self-consistent model after 12% axial strain reproducing the measured sample strain and textures and constraining the strength of basal, prismastic and pyramidal slip as well as tensile twinning in ε-Fe at those conditions.

Figure 5 :

 5 Figure 5: Polycrystalline simulation (after Amodeo et al. 2018). (a) In a polycrystal, stress and strain distributions are heterogeneous. The behavior of each grain depends on its local environment, elastic, and plastic properties. (b) In self-consistent models, each grain is treated as an elliptical inclusion inside a homogeneous medium.

Figure 6 :

 6 Figure 6: Plasticity of ε-Fe at 17 GPa and 400 K (after Merkel et al. 2012). (a) Dominant deformation mechanisms deduced from the data in Fig. 4. τ0 is the initial CRSS, before hardening later in the deformation. (b) Differential stress vs. axial strain. All SC calculations can be used to model the evolution of polycrystalline textures. Comparing the experimentally measured LPO and the results of SC calculations allows for the identification of dominant plastic deformation mechanisms and, in particular, dislocation slip or twinning. VPSC calculations, however, will not model macroscopic or intergranular stress, nor lattice strains measured in experiments.

Figure 7 :

 7 Figure 7: Stress in polycrystalline MgO plastically deformed at 5 GPa and 300 K in the D-DIA (Lin et al. 2017). The plot displays apparent stresses deduced from an elastic model and x-ray diffraction measurements on the 111, 200, and 220 diffraction lines. Solid back line is the result of EVPSC calculations. Plastic deformation results in different stress values in the elastic model, which is inconsistent: average stress in the polycrystal should be unique. This can be solved by modeling the experiment using self-consistent calculations.

Figure 8 :

 8 Figure 8: Setup for multigrain crystallography at high pressure. The sample is confined in a DAC in axial geometry with an ω rotation parallel to the Z direction. Diffraction patterns are collected on a flat panel detector orthogonal to the incoming X-ray beam over Δω ranges of ≈50° in steps of δω≈0.5°. Individual grains inside the polycrystalline sample give rise to diffraction spots at specific 2θ, ω, and η angles.

Figure 9 :

 9 Figure 9: Sample results from multigrain crystallography in the DAC (Rosa et al. 2016). Pole figures presenting the orientations of individual olivine and ringwoodite grains during a phase transformation at ≈18 GPa and 880 K. White circles are individual grain orientations. Background color scale is recalculated based on an orientation distribution function fitted to sample. Scale in m.r.d. (multiples of a random distribution).

Figure 10 :

 10 Figure 10: Principles of defect analysis using x-ray diffraction. Unlike a perfect crystal (a), defects such as dislocations induce a local distortion of the crystal structure (b). The presence of defects induces a broadening of the x-ray diffraction peak which, unlike that of grain sizes for instance, is anisotropic and depends on the hkl indices of the reflection and the type of dislocation.

  This chapter summarized the last 25 years of development of high pressure measurements of mechanical properties. The team around H.-K. Mao at the Carnegie Institution pioneered the development of radial xray diffraction in the DAC. The following years saw the development of LVP experiments, externalheating radial x-ray diffraction in the DAC, or multigrain crystallography. Conceptual advances, from the first theories of lattice strains in the 1990's to more advanced self-consistent calculations have also been a key component of such research. Early results and interpretation of high pressure deformation experiments lacked understanding of the fundamentals of plasticity and its effect on materials properties and x-ray diffraction measurements. The introduction of self-consistent calculations was hence an important contribution to the field.

Acknowledgments

The author would like to thank the two anonymous reviewers and N. Hilairet for constructive comments, as well as F. Lin for providing the raw data for Fig. 7. S. M. received support from the I-SITE UNLE grant MetalCore (R-ERCGEN-19-006-MERKEL).