P Castany

D M Gordin

S I Drob

C Vasilescu

V Mitran

A Cimpean

T Gloriant
email: thierry.gloriant@insa-rennes.fr

Deformation mechanisms and biocompatibility of the superelastic Ti-23Nb-0.7Ta-2Zr-0.5N alloy

Keywords: titanium, superelasticity, plastic deformation, biocorrosion, cytocompatibility

In this study, we have synthesized a new Ti-23Nb-0.7Ta-2Zr-0.5N alloy composition with the aim to obtain useful mechanical properties to be used in medicine such as high strength, good superelastic property, low modulus and large ductility. Thus, mechanical properties including superelasticity and plasticity were investigated in relation with the different deformation mechanisms observed (stress-induced martensitic transformation, twinning and dislocation slip). On the other hand, the corrosion resistance in simulated body fluid (Ringer solution) and the in-vitro cell behavior (MG63 human osteoblasts) of such biomedical alloy were also evaluated in order to assess its biocompatibility.

Introduction

Alloys possessing shape memory or superelastic behavior are of great interest for biomedical functional devices such as stents, osteosynthesis staples, orthodontic arch wires, etc. The alloys commonly used for such devices belong to the NiTi family (e.g. Nitinol) due to their exceptional shape memory and superelastic properties. However, hypersensitivity and toxicity of nickel remain a problem in many clinical cases and the use of nickel must be avoided [START_REF] Wever | Cytotoxic, allergic and genotoxic activity of a nickel-titanium alloy[END_REF].

Consequently, nickel-free titanium-based alloys composed only of non-cytotoxic alloying elements such as Nb, Ta, Zr are now widely studied [START_REF] Niinomi | Fatigue performance and cytotoxicity of low rigidity titanium alloy, Ti-29Nb-13Ta-4.6[END_REF][START_REF] Miyazaki | Development and characterization of Ni-free Tibase shape memory and superelastic alloys[END_REF][START_REF] Laheurte | Mechanical properties of low modulus β titanium alloys designed from the electronic approach[END_REF]. The reason for this interest is due to the fact that, depending to the chemical composition, metastable β titanium-based alloys can be mechanically unstable. Consequently, they can also exhibit shape memory effect and superelastic behavior. Indeed, a reversible martensitic transformation between the parent βphase (austenite) and the α″-phase (martensite) formed is observed in such alloys [START_REF] Kim | Martensitic transformation, shape memory effect and superelasticity of Ti-Nb binary alloys[END_REF][START_REF] Bertrand | Investigation of the martensitic transformation and the damping behavior of a superelastic Ti-Ta-Nb alloy[END_REF]. Superelastic (or pseudoelastic) behavior is obtained when the quenched microstructure is composed of the β-metastable phase at room temperature. In this case, a stress-induced martensitic transformation (β into α″) can directly occur under mechanical stimulation and large elastic recovery can be obtained due to the fact that this transformation is fully reversible once the mechanical stress is released. On the other hand, a much lower elastic modulus is obtained with such superelastic alloys by comparison with the typical Ti-6Al-4V alloy currently used as prosthetic material [START_REF] Miyazaki | Development and characterization of Ni-free Tibase shape memory and superelastic alloys[END_REF][START_REF] Laheurte | Mechanical properties of low modulus β titanium alloys designed from the electronic approach[END_REF][START_REF] Kim | Martensitic transformation, shape memory effect and superelasticity of Ti-Nb binary alloys[END_REF][START_REF] Bertrand | Investigation of the martensitic transformation and the damping behavior of a superelastic Ti-Ta-Nb alloy[END_REF]. Low rigidity is known to be very beneficial to avoid the stress-shielding phenomenon which can cause the premature loss of hip prostheses or dental implants for example [START_REF] Niinomi | Fatigue performance and cytotoxicity of low rigidity titanium alloy, Ti-29Nb-13Ta-4.6[END_REF][START_REF] Laheurte | Mechanical properties of low modulus β titanium alloys designed from the electronic approach[END_REF][START_REF] Huiskes | The relationship between stress shielding and bone resorption around total hip stems and the effects of flexible materials[END_REF]. Numerous works carried out on this kind of alloy have focused on alloys belonging to the binary Ti-Nb system. Unfortunately, the superelastic property observed is far less than that of NiTi and does not exceed 2% of elastic recovery at best [START_REF] Miyazaki | Development and characterization of Ni-free Tibase shape memory and superelastic alloys[END_REF][START_REF] Laheurte | Mechanical properties of low modulus β titanium alloys designed from the electronic approach[END_REF][START_REF] Kim | Martensitic transformation, shape memory effect and superelasticity of Ti-Nb binary alloys[END_REF][START_REF] Bertrand | Investigation of the martensitic transformation and the damping behavior of a superelastic Ti-Ta-Nb alloy[END_REF]. However, it was showed that addition of a third or a fourth element such as Zr, Al or Sn improves the elastic recovery and about 3% of elastic recovery can be reached in some cases [START_REF] Fukui | Mechanical properties of a Ti-Nb-Al shape memory alloy[END_REF][START_REF] Hao | Microstructure and mechanical behavior of a Ti-24Nb-4Zr-8Sn alloy processed by warm swaging and warm rolling[END_REF]. Furthermore, addition of interstitial alloying elements (O, N) was also observed to be beneficial to enhance significantly both the superelasticity and the mechanical strength [START_REF] Tahara | Effect of nitrogen addition and annealing temperature on superelastic properties of Ti-Nb-Zr-Ta alloys[END_REF][START_REF] Besse | Mechanisms of deformation in Gum Metal TNTZ-O and TNTZ titanium alloys: A comparative study on the oxygen influence[END_REF][START_REF] Ramarolahy | Microstructure and mechanical behavior of superelastic Ti-24Nb-0.5O and Ti-24Nb-0.5N biomedical alloys[END_REF].

In this study, we have synthesized a new Ti-23Nb-0.7Ta-2Zr-0.5N alloy composition (at%), which was inspired from the multifunctional β-type Ti-23Nb-0.7Ta-2Zr-1.2O alloy composition, called "gum metal" [START_REF] Saito | Multifunctional alloys obtained via a dislocation-free plastic deformation mechanism[END_REF]. The difference is that we have replaced the oxygen by nitrogen in the original composition. It is worth noting that our first intention was to add 1 at% of N but with such amount of N, the formation of nitride couldn't be avoided probably due the fact that the solubility of N in the beta solid solution is lower than the O one. Thus, the main objective is to show if the claimed "super" mechanical properties of the "gum metal" alloy are still obtained by this alternative alloy composition and to investigate its deformation mechanisms. Indeed, in addition to a superelastic behavior, various mechanisms of plastic deformation can be activated in Ti-Nb based alloys depending on the composition and thus on the stability of the beta phase. It was reported that the plastic deformation can be accommodated by both dislocations slip and twinning in such alloys [START_REF] Hanada | Transmission electron-microscopic observations of mechanical twinning in metastable beta titanium alloys[END_REF][START_REF] Furuhara | Crystallography of alpha precipitated on dislocations and deformation twin boundaries in a beta titanium alloy[END_REF][START_REF] Bertrand | Twinning system selection in a metastable beta-titanium alloy by Schmid factor analysis[END_REF]. To investigate the deformation mechanisms in the present study, uniaxial tensile tests were performed on normalized specimens. Then, EBSD (electron backscattered diffraction) and TEM (transmission electronic microscopy) observations were done after deformation to determine precisely the mechanisms of the plastic deformation. In situ tensile experiments in TEM were also carried out. As the Ti-23Nb-0.7Ta-2Zr-0.5N alloy can be of great interest for biomedical applications, its biocorrosion behavior in simulated body fluid and its cytocompatibility using in vitro tests performed on human MG63 osteoblasts were also evaluated in the present study.

Materials and methods

Alloy synthesis and sample preparation

As titanium, zirconium, tantalum, and niobium have melting points and densities which are very different, the synthesis of the Ti-23Nb-0.7Ta-2Zr-0.5N alloy composition (at%) was realized by cold crucible levitation melting (CCLM) technique under high vacuum, using a high-frequency magnetic induction generator heating system. With this method, the high frequency magnetic field is used to stir the liquid, which is useful in ensuring that alloying elements are fully mixed into the melt without contamination thanks to the restricting contact points between the melt and the cold crucible. The added elements are pure solid metals, except nitrogen, which was introduced through titanium nitride (TiN) powder. After a homogenization treatment at 950°C for 16h, the ingot was cold rolled at room temperature to reach 1 mm in thickness that corresponds to 90% of reduction in thickness.

From the sheet, tensile test samples were machined to obtain normalized shapes: 3 mm width, 1 mm in thickness and a gage length of 15 mm. On the other hand, disc shape samples (diameter: 13 mm, thickness: 1mm) were cut for the biological and the electrochemical tests.

Then, all samples were solution treated under high vacuum at 850°C for 0.5 hour in the betaphase field and water quenched. The aim of this treatment is to restore a fully recrystallized beta microstructure from the cold rolled state. Finally, all samples were mechanically polished on silicon carbide abrasive papers (up to 4000 grit) and then ultrasonically cleaned in acetone, thoroughly washed with ethanol and dried in air.

Microstructural and mechanical characterization methods

In this work, microstructures before and after deformation were observed by optical microscopy (OM). For the OM observations, samples were mechanically "mirror" polished using a colloidal silica suspension (particles size: 50 nm) and etched in a 5% HF, 5% HNO 3 , 90% H 2 O solution. Characterizations by electron backscattered diffraction (EBSD) on deformed samples were also conducted in a scanning electron microscope (Jeol JSM 6400, SEM) equipped with a TSL EBSD system. TEM observations were performed on a Jeol 2010 working with an accelerating voltage of 200 kV. TEM samples were thinned down with a Struers twin-jet electropolishing system using a 4% perchloric acid solution in methanol. A video-rate SIS CCD camera and a Gatan straining holder were used for in-situ straining experiments.

Tensile tests were carried out at room temperature (Instron machine, strain rate: 10 -4 s -1 ). All tensile tests were performed with the tensile direction parallel to the rolling direction. In this study, cyclic tensile tests consisting of applying 0.5% strain increments (each followed by a stress release) were specifically carried out in order to characterize the superelastic property.

An extensometer was used to precisely measure the deformation of the samples.

Electrochemical and corrosion behavior testing

The electrochemical behavior of the Ti-23Nb-0.7Ta-2Zr-0.5N alloy in Simulated Body fluid (SBF) was studied by the potentiodynamic cyclic and linear polarization tests. Commercially pure Ti (CP-Ti grade 2 provided by Goodfellow) was also used as reference in this study. The SBF chosen was the Ringer solution at a neutral pH of about 7.4, which is the normal pH of the human biofluid [START_REF] Cai | In vitro corrosion resistance of titanium made using different fabrication methods[END_REF]. The composition of Ringer solution was (g/L): NaCl -6.8; KCl -0.4; CaCl 2 -0. program and the main corrosion parameters were directly supplied: 𝑖 corr : corrosion current density; 𝑉corr : corrosion rate; 𝑅𝑝 : polarization resistance. Also, using the corrosion rate, we calculated the ion release rate representing the total quantity of ions released into the surrounding biofluid: Ion release rate = 1.016 × 𝑉corr × 102, where the ion release rate is expressed in ng/cm 2 and 𝑉corr in 𝜇m/year [START_REF] Gordin | Surface characterization and biocompatibility of titanium alloys implanted with nitrogen by Hardion+ technology[END_REF][START_REF] Calderon-Moreno | Surface and electrochemical characterization of a new ternary titanium based alloy behaviour in electrolytes of varying pH[END_REF][START_REF] Gordin | Potentiality of the 'Gum Metal' titanium based alloy for biomedical applications[END_REF].

Three samples were used for every experiment and the results reproducibility was very good.

In vitro assessment of osteoblast behavior

The cell culture model used in cytocompatibility studies was represented by a human osteoblast-like cell line, MG63 (American Type Culture Collection, CRL-1427). These cells were seeded onto the tested Ti-23Nb-0.7Ta-2Zr-0.5N and CP-Ti materials at an initial density of 5 × 103 cells⋅cm -2 in Dulbecco's Modified Eagle Medium (DMEM) containing 1‰ glucose, supplemented with 10% heat-inactivated fetal bovine serum and 1% (v/v) penicillin/streptomycin (10,000 units⋅mL -1 penicillin and 10mg⋅mL -1 streptomycin).

Previously to in vitro tests, the titanium-based samples were sterilized by immersion in 70% ethanol, washed with sterile-filtered Milli-Q water, maintained under ultraviolet light in a sterile tissue culture hood for 1 h on each side, and conditioned in culture medium. The cells were maintained in contact with these samples in a humidified atmosphere of 5% CO 2 at 37°C for specific points in time. The medium was exchanged every second day. All experiments have been done in triplicate.

Viability of MG63 osteoblasts cells was evaluated by combining a cytotoxicity test consisting

in the assessment of lactate dehydrogenase (LDH) released into the culture medium and MTT [3-(4, 5-dimethyl thiazol-2-yl) 2,5-diphenyltetrazolium bromide] colorimetric study which also represents a useful indication of cell proliferation rates. LDH assay was carried out by using a cytotoxicity detection kit (Tox-7, Sigma-Aldrich) according to the manufacturer's protocol. Absorbance was evaluated at 490 nm using a microplate reader (Thermo Scientific Appliskan). MTT assay has been performed as previously reported [START_REF] Cimpean | Osteoblast cell behavior on the new beta-type Ti-25Ta-25Nb alloy[END_REF]. Both assays were conducted at 1, 3, and 5 days after seeding.

Statistical analysis was performed with GraphPad Prism software using one-way ANOVA with Bonferroni's multiple comparison tests. Triplicate samples were used in LDH and MTT experiments to ensure the reproducibility of the results. The data are presented as means ± SD (standard deviation). The 𝑝 values < 0.05 were considered to be statistically significant.

Results and discussion

Superelastic deformation

Fig. 1 shows an optical micrograph displaying the typical microstructure of the solutiontreated and quenched Ti-23Nb-0.7Ta-2Zr-0.5N alloy. As it can be observed, the microstructure consists of a fully equiaxed β-grain microstructure with a grain dimension varying between a few tens to a few hundreds of micrometers.

In Fig. 2, it is reported a typical engineering stress-strain curve until rupture obtained from the Ti-23Nb-0.7Ta-2Zr-0.5N alloy by tensile test. On the other hand, the cyclic tensile curve between 0 and 4% of strain is also presented in this figure (center part) in order to characterize properly the superelastic behavior of such alloy. It is worth noting the excellent repeatability of the mechanical experiments because very similar strain-stress tensile curves were obtained for the five tests carried out. It can be clearly observed the nonlinearity of the elastic domain and the presence of hysteresis loops between each loading-unloading cycle, which is a characteristic of a superelastic behavior. From this curve, a relatively high elastic recovery at about 2.2% was evaluated and a low incipient Young's modulus measured at 50 GPa was found, which is very low compared to that obtained from classical titanium alloys currently used in medicine (110 GPa for Ti-6Al-4V) and closer to the one that corresponds to the cortical bone [START_REF] Gordin | Potentiality of the 'Gum Metal' titanium based alloy for biomedical applications[END_REF][START_REF] Cimpean | Osteoblast cell behavior on the new beta-type Ti-25Ta-25Nb alloy[END_REF][START_REF] Morniroli | Study of conditions under which omega-phase forms in Titanium-Niobium and Titanium-Molybdenum alloys[END_REF][START_REF] Tang | Phase transformations in Ti-Nb-Ta and Ti-Nb-Ta-Zr alloys[END_REF][START_REF] Ping | TEM investigations on martensite in a Ti-Nb-based shape memory alloy[END_REF][START_REF] Castany | Dislocation mobility in gum metal β-titanium alloy studied via in situ transmission electron microscopy[END_REF][START_REF] Castany | In situ TEM study of dislocation slip in a metastable β titanium alloy[END_REF][START_REF] Grässel | High strength Fe-Mn-(Al,Si) TRIP/TWIP steels development-properties-application[END_REF][START_REF] Sun | Investigation of early stage deformation mechanisms in a metastable β titanium alloy showing combined twinning-induced plasticity and transformation-induced plasticity effects[END_REF][START_REF] Mitran | Biological behaviour and enhanced anticorrosive performance of the nitrided superelastic Ti-23Nb-0.7Ta-2Zr-0.5N alloy[END_REF][START_REF] Tanaka | Characterization of air-formed surface oxide film on Ti-29Nb-13Ta-4.6Zr alloy surface using XPS and AES[END_REF]. These good properties are due to the fact that a stress-induced martensitic transformation occurred in this alloy. Fig. 3. shows a typical bright field TEM image (a) and the corresponding electron diffraction pattern (b) of the Ti-23Nb-0.7Ta-2Zr-0.5N alloy microstructure after being deformed up to 4% strain. In the bright field image, the typical needle-like morphology of the α" martensitic phase is observed confirming that double yielding observed on the tensile curve for this alloy composition is definitely related to the stress-induced α" martensitic transformation. The electron diffraction pattern exhibits typical diffraction spots related to the presence of both body-centered cubic β matrix and C-centered orthorhombic α" martensite needles. From the electron diffraction pattern, the orientation relationships between β and α" were found to be: <100>β // [100]α " and {110}β // (001)α " and the habit planes were found to be close to {112}β and {113}α " . These orientation relationships are consistent with those found in literature [START_REF] Morniroli | Study of conditions under which omega-phase forms in Titanium-Niobium and Titanium-Molybdenum alloys[END_REF].

In the present alloy composition, the lattice parameters were measured to be: aβ = 0.327 nm, aα " = 0,317 nm, bα " = 0,481 nm and cα " = 0,463 nm. These values are in good accordance with those obtained from similar Ti-Nb based alloy compositions [START_REF] Tang | Phase transformations in Ti-Nb-Ta and Ti-Nb-Ta-Zr alloys[END_REF][START_REF] Ping | TEM investigations on martensite in a Ti-Nb-based shape memory alloy[END_REF].

As observed in literature [START_REF] Gordin | Potentiality of the 'Gum Metal' titanium based alloy for biomedical applications[END_REF], the stress-induced martensitic transformation is accompanied by a significant reduction of the Young's modulus and a large strain recovery. On the other hand, the tensile curve of the Ti-23Nb-0.7Ta-2Zr-0.5N alloy shows both high yield strength at around 600 MPa and ultimate tensile strength at about 700 MPa, which are almost twice higher in comparison with the binary Ti-26Nb alloy reported from literature [START_REF] Miyazaki | Development and characterization of Ni-free Tibase shape memory and superelastic alloys[END_REF]. This strengthening is due to the fact that nitrogen, as interstitial element, is well known to involve a solid-solution hardening effect in alloys. In addition, it can be noticed that nitrogen addition leads also to a higher superelasticity (almost by 1.5 higher) in comparison with the Ti-Nb or Ti-Nb-Ta alloys reported from literature [START_REF] Miyazaki | Development and characterization of Ni-free Tibase shape memory and superelastic alloys[END_REF][START_REF] Kim | Martensitic transformation, shape memory effect and superelasticity of Ti-Nb binary alloys[END_REF][START_REF] Bertrand | Investigation of the martensitic transformation and the damping behavior of a superelastic Ti-Ta-Nb alloy[END_REF]. It fact, it was recently established [START_REF] Tahara | Effect of nitrogen addition and annealing temperature on superelastic properties of Ti-Nb-Zr-Ta alloys[END_REF] that the stability of superelasticity was improved by the addition of N due to the increase of the critical stress for slip.

Plastic deformation mechanisms

Fig. 4 shows an optical micrograph displaying the microstructure of the Ti-23Nb-0.7Ta-2Zr-0.5N alloy after being deformed up to 10% strain. It can be observed the formation of numerous large deformation bands of a few micrometers in thickness. In β-type titaniumbased alloys, plastic deformation is known to be accommodated by dislocation glide and, in some cases, by twinning formation. In the present case, most of the β grains presented large deformation bands after deformation such as in Fig. 4. According to the literature of β titanium alloys, such large deformation bands are probably twins instead of dislocation slip bands that are commonly thinner [START_REF] Besse | Mechanisms of deformation in Gum Metal TNTZ-O and TNTZ titanium alloys: A comparative study on the oxygen influence[END_REF][START_REF] Hanada | Transmission electron-microscopic observations of mechanical twinning in metastable beta titanium alloys[END_REF][START_REF] Bertrand | Twinning system selection in a metastable beta-titanium alloy by Schmid factor analysis[END_REF], as confirmed from the EBSD analysis presented in Fig. 5. It was reported that two twinning systems are commonly observed in metastable β titanium alloys: {332} <113> and {112} <111> [START_REF] Hanada | Transmission electron-microscopic observations of mechanical twinning in metastable beta titanium alloys[END_REF][START_REF] Bertrand | Twinning system selection in a metastable beta-titanium alloy by Schmid factor analysis[END_REF].

In the present study, the twinning formation in the Ti-23Nb-0.7Ta-2Zr-0.5N alloy is illustrated from EBSD cartographies presented in Fig. 5. Fig. 5(a) shows several grains containing deformation bands with strong misorientation with the parent grain. Two misorientation profiles along lines denoted AB and BC crossing deformation bands are provided as examples and prove that deformation bands observed by optical microscopy are twins. For each grain, the orientations of the parent crystal and twins were determined by the Euler angles. The twinning system was then characterized from the existence of poles belonging to the parent crystal and the twin. To ensure statistics, about twenty grains on several zones of the tensile specimen were analyzed. By way of illustration, two grains denoted G1 in Fig. 5(b) and G2 in Fig. 5(c) and their twins, respectively denoted T1 and T2 were located on the EBSD cartography presented in Fig. 5(a). In G1, the pole figures of {332} and {113} poles show common poles between the parent grain and the twin (circled on pole figures). The twinning system activated in G1 is then {332} <113>. Conversely, analysis of pole figures in G2 shows common {112} and {111} poles between the twin and the parent grain. In G2, the other twinning system {112} <111> is then activated. It was checked that the CSL (Coefficient Site Lattice) of the {112} <111> twin is a Σ3 boundary, which corresponds to a misorientation of 60° around <111>. When the twinning system is {332} <113>, the CSL boundary is Σ11, which corresponds to a misorientation of 50.57° around <110> (see Fig. 5(a) for examples). Thus, the plastic deformation of the present superelastic alloys is largely accommodated by twinning and the two {332} <113> and {112} <111> twinning systems were observed to be activated.

In order to characterize dislocation slip activity, in situ tensile tests were performed in TEM.

During in situ experiments, dislocations were observed to nucleate first at grain boundaries and then propagate within the grains, as already observed in other β titanium alloys [START_REF] Castany | Dislocation mobility in gum metal β-titanium alloy studied via in situ transmission electron microscopy[END_REF]. All gliding dislocations were found to have a/2<111> Burger vectors, that was determined by regular indexation method using the g.b=0 criterion. Similarly to previous investigations in β titanium alloys, screw segments of dislocations moved much slower than edge segments, leading to a large density of straight screw dislocations that ensure the deformation [START_REF] Besse | Mechanisms of deformation in Gum Metal TNTZ-O and TNTZ titanium alloys: A comparative study on the oxygen influence[END_REF][START_REF] Castany | Dislocation mobility in gum metal β-titanium alloy studied via in situ transmission electron microscopy[END_REF][START_REF] Castany | In situ TEM study of dislocation slip in a metastable β titanium alloy[END_REF]. A typical example of the dislocation motion is shown in Figure 6. Each micrograph from (a) to (d) was taken from a video recorded during an in situ experiment at several times noted on each image. These micrographs were taken using the diffraction vector g = [110] with a tilt angle of 13°. The corresponding stereographic projection of this grain is supplied in Fig. 6(e) with the poles and traces of interest. In order to determine the Burger vectors of dislocations visible on Fig. 6(a-d), a micrograph of the same grain using another diffraction condition is shown in Fig. 6(f) with g' = [0-11]: here, dislocations observed previously are invisible and only dislocations with another Burger vector are visible (it is also worth noting that these dislocations were invisible in previous micrographs). As glissile dislocations in β titanium alloys were only found to have a/2<111> Burger vectors [START_REF] Besse | Mechanisms of deformation in Gum Metal TNTZ-O and TNTZ titanium alloys: A comparative study on the oxygen influence[END_REF][START_REF] Castany | Dislocation mobility in gum metal β-titanium alloy studied via in situ transmission electron microscopy[END_REF][START_REF] Castany | In situ TEM study of dislocation slip in a metastable β titanium alloy[END_REF], present dislocations have thus a/2[111] Burger vector according to the notations used in the Fig. 6(e). An isolated dislocation, labeled with a black arrow in the Fig. 6(a) can be easily followed as an illustration of the typical motion of dislocations. The projection of its Burger vector is indicated in the Fig. 6(b) by the letter "b", showing its screw character. Slip planes were determined from slip traces left by dislocations at the surfaces of the specimen (as the "trace" labeled in Fig. 6d). In order to determine the slip plane, the angle of the slip trace was measured to be about 8° from the horizontal direction of the micrograph and compared to the stereographic projection in Fig. 6(e). As possible slip planes in bcc metals, are known to be {110}, {112} or, less frequently, {123} planes, only poles of these types of planes are indicated on the stereographic projection for a/2[111] Burger vector's dislocations. {110} poles are indicated by blue spots, {112} poles by green spots and {123} poles by black spots (see color online).

Regarding the orientation of the slip trace, only (-312), (-211) or (-321) planes seem potential slip planes. The surface plane of the thin foil was also indexed as (-9 14 20) and its trace was drawn in dark grey as well as the traces of former planes in dark for the (-211) plane and in light grey for both potential {123} planes. Analysis of intersections between possible slip planes and the foil surface shown thus unambiguously that a/2[111] dislocations are gliding in the (-211) plane. Similarly, dislocations visible in Fig. 6(f) were observed to glide in the (110) plane with a a/2[-111] Burger vector. Therefore, {112} and {110} slip planes were observed in accordance with slip systems commonly observed in bcc metals. The motion of the dislocation in Fig. 6 is typical of dislocations in β titanium alloys and bcc metals at low temperature [START_REF] Besse | Mechanisms of deformation in Gum Metal TNTZ-O and TNTZ titanium alloys: A comparative study on the oxygen influence[END_REF][START_REF] Castany | Dislocation mobility in gum metal β-titanium alloy studied via in situ transmission electron microscopy[END_REF][START_REF] Castany | In situ TEM study of dislocation slip in a metastable β titanium alloy[END_REF]: the screw dislocation moves keeping straight and is subject to double cross-slip leading to multiplication. The white arrow in Fig. 6 (b) and(c This multiplication process involving double cross-slip as well as the main presence of straight screw dislocations is characteristic of the three-dimensionally spread core structure of screw dislocations that is assumed to be the key feature controlling the mobility of dislocations in bcc metals and thus in β titanium alloys [START_REF] Besse | Mechanisms of deformation in Gum Metal TNTZ-O and TNTZ titanium alloys: A comparative study on the oxygen influence[END_REF][START_REF] Castany | Dislocation mobility in gum metal β-titanium alloy studied via in situ transmission electron microscopy[END_REF][START_REF] Castany | In situ TEM study of dislocation slip in a metastable β titanium alloy[END_REF].

According to the tensile curve presented in Fig. 3, large plastic deformation is obtained with the Ti-23Nb-0.7Ta-2Zr-0.5N alloy since almost 25% of elongation at rupture can be reached. By comparison, the Ti-6Al-4V titanium alloy currently used for biomedical applications processes a maximum elongation at rupture situated at around 15% of deformation. This large ductility is an interesting result because the presence of interstitial elements such as oxygen or nitrogen is well known to induce brittleness in titanium-based alloys. The reason of such ductility can be explained by the fact that additionally to dislocation glide, a massive twinning was also observed to accommodate the deformation.

Such massive twinning provides effective obstacles to dislocations motion as it is the case for the well-known TWIP steels [START_REF] Grässel | High strength Fe-Mn-(Al,Si) TRIP/TWIP steels development-properties-application[END_REF]. It is worth noting that we have observed a similar behavior in a recent work carried out in a highly deformable Ti-Mo metastable β-alloy in which a new TRIP (TRansformation Induced Plasticity)-TWIP (TWinning Induced Plasticity) mechanism was highlighted [START_REF] Sun | Investigation of early stage deformation mechanisms in a metastable β titanium alloy showing combined twinning-induced plasticity and transformation-induced plasticity effects[END_REF].

Electrochemical and corrosion behavior

From the cyclic potentiodynamic polarization experiments, the main electrochemical parameters obtained for the superelastic Ti-23Nb-0.7Ta-2Zr-0.5N alloy in comparison with CP-Ti are listed in Table 1.

It can be observed that 𝐸corr and 𝐸𝑝 values for the Ti-23Nb-0.7Ta-2Zr-0.5N alloy are about 70 mV and 50 mV more electropositive than those of CP-Ti denoting the enhancement of the corrosion resistance. On the other hand, |𝐸corr -𝐸𝑝| value for the Ti-23Nb-0.7Ta-2Zr-0.5N alloy is lower compared with CP-Ti, which means a stronger, more rapid and easier passivation.

The corrosion resistance was evaluated from Tafel representations and the main corrosion parameters obtained for both Ti-23Nb-0.7Ta-2Zr-0.5N alloy and CP-Ti are listed in Table 2.

It resulted that the values of the corrosion current density, 𝑖corr, the corrosion rate, 𝑉corr, and the ion release rate for the Ti-23Nb-0.7Ta-2Zr-0.5N alloy significantly decreased in comparison with those of CP-Ti. Thus, the Ti-23Nb-0.7Ta-2Zr-0.5N alloy demonstrates a very high corrosion resistance. On the other hand, the polarization resistance, 𝑅𝑝, of the Ti-23Nb-0.7Ta-2Zr-0.5N alloy increased by around 20 and the ion release is 30 times lower compared to CP-Ti. Consequently, the Ti-23Nb-0.7Ta-2Zr-0.5N alloy possesses a perfect chemical stability, which is due to the presence of the alloying elements. Indeed, the composition and the thickness of native passive film formed on the Ti-23Nb-0.7Ta-2Zr-0.5N alloy was analyzed by X-ray photoelectron microscope in a previous study [START_REF] Mitran | Biological behaviour and enhanced anticorrosive performance of the nitrided superelastic Ti-23Nb-0.7Ta-2Zr-0.5N alloy[END_REF]. It was detected a dense passive layer of about 6.5 nm composed of oxides and oxynitrides of the transition Ti, Nb, Zr, Ta metals that assured the alloy structural integrity and anticorrosion resistance. This result is in accordance with others biocorrosion studies carried out on similar Ti-based alloys [START_REF] Tanaka | Characterization of air-formed surface oxide film on Ti-29Nb-13Ta-4.6Zr alloy surface using XPS and AES[END_REF][START_REF] Okazaki | Corrosion resistance, mechanical properties, corrosion fatigue strength and cytocompatibility of new Ti alloys without Al and V[END_REF][START_REF] Mareci | Comparative corrosion study of Ti-Ta alloys for dental applications[END_REF].

In vitro behavior of human osteoblasts

It has to be highlighted that very few studies addressed the in vitro biocompatibility of the superelastic Ni-free Ti-based alloys [START_REF] Cimpean | Osteoblast cell behavior on the new beta-type Ti-25Ta-25Nb alloy[END_REF][START_REF] Park | Improved pre-osteoblast response and mechanical compatibility of ultrafine-grained Ti-13Nb-13Zr alloy[END_REF][START_REF] Xue | Superelasticity, corrosion resistance and biocompatibility of the Ti-19Zr-10Nb-1Fe alloy[END_REF][START_REF] Ion | In vitro bio-functional performances of the novel superelastic beta-type Ti-23Nb-0.7Ta-2Zr-0.5N alloy[END_REF] and there is no available literature on their in vivo osseointegration capacity. In a recent study [START_REF] Xue | Superelasticity, corrosion resistance and biocompatibility of the Ti-19Zr-10Nb-1Fe alloy[END_REF], in vitro experiments with MC3T3-E1 preosteoblasts carried out on a novel superelastic Ti-19Zr-10Nb-1Fe alloy demonstrated almost similar extent of cell adhesion and proliferation on both the Ti-19Zr-10Nb-1Fe and NiTi alloys. In a previous study [START_REF] Ion | In vitro bio-functional performances of the novel superelastic beta-type Ti-23Nb-0.7Ta-2Zr-0.5N alloy[END_REF], the Ti-23Nb-0.7Ta-2Zr-0.5N alloy was shown to support MC3T3-E1 pre-osteoblasts attachment, spreading and proliferation to a similar level with that displayed by the Ti-6Al-4V control sample. However, a substantial increase in the differentiation and mineralization ability of osteoblasts was observed for Ti-23Nb-0.7Ta-2Zr-0.5N substrate and no significant inflammatory response was elicited in macrophage cells cultured on this material. An important feature of any biomaterial for clinical applications is the lack of cytotoxicity. In order to determine the possible detrimental effects exerted by all biomaterials on the cell viability, the release of lactate dehydrogenase (LDH) into the culture media was quantified as an index of cell death. As it can be seen in Figure 7(a), MG63 cells exhibit a comparable viability on CP-Ti and Ti-23Nb-0.7Ta-2Zr-0.5N. Thus, the timedependent profiles of LDH activity revealed no significant differences between the two analyzed substrates at any point in time. Moreover, LDH activity recorded approximately similar optical density (OD) values at 1 and 3 days after seeding. A higher activity but not a significant one for the loss of membrane integrity was remarked between the third and fifth days of culture. This could be associated with the confluence initiated cell death.

Consequently, both samples elicit no significant cytotoxic responses from MG63 osteoblasts and do not alter cell viability. Furthermore, the proliferation status of the total population of cells was assessed by MTT colorimetric method. As shown in Figure 7(b), the number of viable metabolically active osteoblasts on the analyzed substrates equally increased from the first to the fifth day of culture. By day 5, the proliferation rates on the two surfaces were significantly higher than those found after 1 and 3 days of culture. In a very recent study [START_REF] Mitran | Biological behaviour and enhanced anticorrosive performance of the nitrided superelastic Ti-23Nb-0.7Ta-2Zr-0.5N alloy[END_REF],

we have observed on the Ti-23Nb-0.7Ta-2Zr-0.5N alloy the cell-to-substrate interaction by double fluorescent staining of vinculin and actin filaments. These observations have revealed the typical appearance of osteoblast cells with well-expressed stress fibers oriented parallel to one another and to the long axis of the cell and punctiform vinculin signals at the termini of actin microfilament bundles. On the other hand, no significant differences in terms of cell spreading, cytoskeleton organization, and focal contact formation could be observed between Ti-23Nb-0.7Ta-2Zr-0.5N and CP-Ti [START_REF] Mitran | Biological behaviour and enhanced anticorrosive performance of the nitrided superelastic Ti-23Nb-0.7Ta-2Zr-0.5N alloy[END_REF]. Taken together, these findings prove that the studied Ti-23Nb-0.7Ta-2Zr-0.5N alloy favors cell proliferation without showing any deleterious effect suggesting increased biocompatibility.

Conclusion

In this study, the deformations mechanisms and the biocompatibility of a new superelastic Ti-23Nb-0.7Ta-2Zr-0.5N alloy composition were investigated.

By tensile tests, high tensile strength (700 MPa), low Young's modulus (50 GPa) and excellent ductility (25% of elongation at rupture) were observed for this alloy. On the other hand, its superelastic behavior was evidenced by cyclic tensile tests, which is due to the reversible stress-induced α" martensitic transformation occurring. Consequently, a high elastic recovery of about 2.2% was obtained demonstrating the good superelastic property of this alloy. The high tensile strength observed is due to the nitrogen addition, which is well known to involve a solid-solution hardening effect in alloys.

The plastic deformation of the present superelastic alloys was shown to be largely accommodated by twinning and the two {332} <113> and {112} <111> twinning systems were observed to be activated by EBSD. Dislocation activity also takes place during plastic deformation. The dislocation behavior was found to be similar to other metastable β titaniumbased alloys with mainly a/2<111> screw dislocations gliding in {110} or {112} planes. Thus, the plastic deformation was shown to be accommodated by both dislocation glide and massive twinning which contribute to the high ductility observed. Moreover, all electrochemical and corrosion parameters obtained in neutral Ringer solution showed that the Ti-23Nb-0.7Ta-2Zr-0.5N presents nobler electrochemical behavior and superior anticorrosive resistance in comparison with CP-Ti. On the other hand, cell culture experiments with MG63 osteoblast-like cell line proved that the studied alloy favor cell proliferation and the absence of any deleterious effect on cultured cells suggests increased biocompatibility. Thus, all the characteristics observed for the superelastic Ti-23Nb-0.7Ta-2Zr-0.5N alloy make this material potentially very interesting for biomedical applications.

2 ;

 2 MgSO 4 .7H 2 O -0.2048; NaH 2 PO 4 .H 2 O -0.1438; NaHCO 3 -1.1; glucose -1. The electrochemical experiments took place in a glass electrochemical cell. Discs of Ti-23Nb-0.7Ta-2Zr-0.5N alloy and CP-Ti were used as the working electrodes connected with saturated calomel electrode (SCE) by a Luggin-Haber capillary; auxiliary electrode was a platinum plate. The working electrodes were ultrasonically degreased in acetone and bidistilled water for every 30 min and dried in air. The measurements were performed with Voltalab 80 equipment. Cyclic potentiodynamic polarization curves were recorded starting from a value of about 300 mV more negative than the open circuit potential and continue to positive direction till +1000 mV (versus SCE) with a scan rate of 1mV/s. The main electrochemical parameters were determined: 𝐸corr : corrosion potential as zero current potential; 𝐸𝑝 : passivation potential where the current density becomes constant; |𝐸corr -𝐸𝑝|: tendency to passivation with low values characterizes a strong, easy passivation; 𝑖p : passive current density representing the corrosion resistance of the passive layer. Linear potentiodynamic polarization was carried out for ±50mV around the open circuit potential at a scan rate of 0.1mV. Tafel representations were adjusted by VoltaMaster 4

  Fig. 6(d), the white arrow indicates the point where the initial dislocation is separated from the created loop. The loop can next expand and contribute to the deformation of the material.

Fig. 2 .

 2 Fig. 2. Engineering stress-strain tensile curves until rupture and loading/unloading cycles between 0 and 4% of strain (center part) for the Ti-23Nb-0.7Ta-2Zr-0.5N alloy

Fig. 5 .Fig. 6 .Fig. 7 :

 567 Fig. 5. Inverse Pole Figure (IPF) EBSD cartographies from the Ti-23Nb-0.7Ta-2Zr-0.5N alloy after being deformed: (a) general cartography with two misorientation profiles along AB and BC lines; (b) and (c) zoomed cartographies with corresponding pole figures showing the twinning relationship between G1 and T1, and G2 and T2, respectively (colors of grains and twins do not correspond to crystallographic orientation here)

Table 1 .

 1 Main electrochemical parameters for CP-Ti and Ti-23Nb-0.7Ta-2Zr-0.5N alloy in Ringer solution at neutral pH and at 37°C

	Material	𝐸corr (mV) 𝐸𝑝 (mV)	Δ𝐸𝑝 (mV) |𝐸 corr -𝐸𝑝| (mV)	𝑖p (µA/cm 2 )
	CP-Ti	-320	-200	>1000	120	15.2
	Ti-23Nb-0.7Ta-2Zr-0.5N	-250	-150	>1000	100	2.3

Table 2 .

 2 Main corrosion parameters for CP-Ti and Ti-23Nb-0.7Ta-2Zr-0.5N alloy in Ringer solution at neutral pH and at 37°C

	Material	𝑖corr (µA/cm 2 ) 𝑉corr (µm/Y)	Ion release (ng/cm 2 ) 𝑅𝑝 (kΩcm 2 )
	CP-Ti	0.724	8.326	845.9	18.2
	Ti-23Nb-0.7Ta-2Zr-0.5N	0.031	0.277	28.2	351.3

Acknowledgments

This study was financially supported by the Romanian Ministry of National Education (project PN-II-ID-20-RO-FR-2014) and by the French National Research Agency (project ANR-13-IS09-0008-01). The authors also acknowledge financial support from the French CNRS and CEA METSA network for in situ TEM experiments.


Guillaume Coiffier
email: guillaume.coiffier@chu-rennes.fr

Jean-David Albert

François Robin

Pascal Guggenbuhl

Reply to the comment of Rothschild B. "Maltese cross interpretation"

A

  c c e p t e d M a n u s c r i p t Reply to the comment of Rothschild B. "Maltese cross interpretation". Guillaume Coiffier a,b,c , Jean-David Albert a,b,c , François Robin a,b,c , Pascal Guggenbuhl a,b,c a Service de Rhumatologie, CHU de Rennes, Hôpital Sud, 16, boulevard de Bulgarie, BP 90347, 35203 Rennes cedex 2, France b INSERM UMR 991, 35043 Rennes, France c Université Rennes 1, Faculté de médecine, 35043 Rennes, France

Table 1 .

 1 Characteristics of the different microcrystals which can be organized into microspherules in the synovial fluid.

We thank Rothschild B. [1] for the attention paid to our review on arthritis induced by phopholipid microspheres [1]. It is highly probable that all microcrystals may form extra cellular microspherules under certain physicochemical conditions (as with a decrease in temperature in the case of delayed examination of the synovial fluid and in the presence of a high protein or lipid concentration in the synovial fluid). This is the case with sodium urate and various calcium crystals (carbonate, phosphate, pyrophosphate or calcium oxalate) [2][3][4]. The latter differ by their birefringence polarity and their Alizarin red staining potential (Table 1). Recently, Li B et al. [5] have reported a series of 174 frozen synovial fluids, about 5% of which contained negatively birefringent alizarine red stained microspherules, which were on Raman spectroscopy predominantly composed of calcium carbonate rather than calcium phosphate less favorable in the formation of microspherules.

We therefore insist on the importance of demonstrating the intra-leukocyte position of the spherules (which eliminates a hypothetical post-puncture formation), on the positive polarity of birefringence and as recalled by Rothschild B., on their well-defined contour (unlike those formed by starch) to assert pathological character of phospholipid microspheres.


domain: chim phys

text:
Liujiang Zhou
email: ljzhou86@lanl.gov

Amanda J Neukirch

Dayton J Vogel

Dmitri S Kilin

Laurent Pedesseau

Marcelo A Carignano

Aditya D Mohite

Jacky Even

Claudine Katan

Sergei Tretiak

Density of States Broadening in CH 3 NH 3 PbI 3 Hybrid Perovskites Understood from ab initio Molecular Dynamics Simulations

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

Solution-processed lead-halide perovskites have emerged as a promising optoelectronic technology due to many unique advantages including direct band gap, strong light absorption, high carrier mobility, and low fabrication cost. [START_REF] Saparov | OrganicInorganic Perovskites: Structural Versatility for Functional Materials Design[END_REF] For example, the photovoltaic efficiency has jumped spectacularly up to 15-22.1% for methyl ammonium lead iodine (MAPbI 3 , MA = CH 3 NH 3 ) materials. [START_REF] Nie | High-efficiency Solutionprocessed Perovskite Solar Cells with Millimeter-scale Grains[END_REF][START_REF] Kim | Beneficial Effects of PbI 2 Incorporated in Organo-Lead Halide Perovskite Solar Cells[END_REF][START_REF] Yang | Iodide management in formamidinium-leadhalide-based perovskite layers for efficient solar cells[END_REF] The underlying mechanisms behind these attractive photoelectronic properties have been widely explored in terms of defects, [START_REF] Srimath Kandada | Nonlinear Carrier Interactions in Lead Halide Perovskites and the Role of Defects[END_REF] ion migration, [START_REF] Eames | Ionic Transport in Hybrid Lead Iodide Perovskite Solar Cells[END_REF][START_REF] Yang | The Significance of Ion Conduction in a Hybrid OrganicInorganic Lead-Iodide-Based Perovskite Photosensitizer[END_REF][START_REF] Zhang | Charge Selective Con-17 tacts, Mobile Ions and Anomalous Hysteresis in Organic-inorganicPerovskite Solar Cells[END_REF][START_REF] Li | Extrinsic Ion Migration in Perovskite Solar Cells[END_REF][START_REF] Yuan | Ion Migration in Organometal Trihalide Perovskite and Its Impact on Photovoltaic Efficiency and Stability[END_REF][START_REF] Lee | Direct Experimental Evidence of Halide Ionic Migration under Bias in CH 3 NH 3 PbI 3-x Cl x -Based Perovskite Solar Cells Using GD-OES Analysis[END_REF] polaronic effects (including both small [START_REF] Neukirch | Polaron Stabilization by Cooperative Lattice Distortion and Cation Rotations in Hybrid Perovskite Materials[END_REF][START_REF] Nie | Light-activated Photocurrent Degradation and Self-healing in Perovskite Solar Cells[END_REF] and large polarons), [START_REF] Miyata | Large Polarons in Lead Halide Perovskites[END_REF][START_REF] Zhu | Charge Carriers in Hybrid OrganicInorganic Lead Halide Perovskites Might Be Protected as Large Polarons[END_REF] ferroelectric order, [16][START_REF] Liu | Ferroelectric Domain Wall Induced Band Gap Reduction and Charge Separation in Organometal Halide Perovskites[END_REF][START_REF] Kutes | Direct Observation of Ferroelectric Domains in Solution-Processed CH 3 NH 3 PbI 3 Perovskite Thin Films[END_REF] structural and electronic dimensionality, [START_REF] Xiao | Searching for Promising New Perovskite-based Photovoltaic Absorbers: the Importance of Electroni Dimensionality[END_REF] etc. Studies of the relationship between the organic cations and device efficiency are rare and are mainly focused on the orientation of the MA and the induced distortion of the PbI 6 octahedral cage as well as direct-indirect band gap transition. [START_REF] Motta | Revealing the Role of Organic Cations in Hybrid Halide Perovskite CH 3 NH 3 PbI 3[END_REF] Moreover, the spontaneous generation of free carriers from exciton screening originating from the collective orientational motion of the organic cations has been experimentally confirmed. [START_REF] Miyata | Direct Measurement of the Exciton Binding Energy and Effective Masses for Charge Carriers in Organic-inorganic Tri-halide Perovskites[END_REF] Upon change of the organic cation, the carrier self-trapping phenomena, [START_REF] Neukirch | Polaron Stabilization by Cooperative Lattice Distortion and Cation Rotations in Hybrid Perovskite Materials[END_REF] interband transition properties, and optical absorption strength [START_REF] Kato | Universal Rules for Visible-light Absorption in Hybrid Perovskite Materials[END_REF] are significantly altered. Additionally, due to thermal effects, MA is associated with various molecular vibrational modes and motionally disordered orientations, [START_REF] Kawamura | Structural Study on CubicTetragonal Transition of CH 3 NH 3 PbI 3[END_REF] which play an important role in the carrier mobility. 24 The molecular vibrational modes have already been measured by means of Infrared (IR) [START_REF] Bakulin | Real-Time Observation of Organic Cation Reorientation in Methylammonium Lead Iodide Perovskites[END_REF] and Raman 26 spectroscopies. Although MA electronic states are not the main contributors around the Fermi level, we expect their vibrations to partly affect material's functionality via enhancing the electronic dimensionality and band transport in devices. [START_REF] Xiao | Searching for Promising New Perovskite-based Photovoltaic Absorbers: the Importance of Electroni Dimensionality[END_REF] Current theoretical calculations do not match the experimentally measured density of states (DOS) deep within the valence band (VB) of MAPbI 3 materials. Calculated DOS has sharp features within the valence band that are in stark contrast to the "flattened" nature of the experimentally measured DOS. [START_REF] Lindblad | Electronic Structure of TiO 2 /CH 3 NH 3 PbI 3 Perovskite Solar Cell Interfaces[END_REF][START_REF] Miller | Substrate-controlled Band Positions in CH 3 NH 3 PbI 3 Perovskite Films[END_REF] Literature has previously stated that due to a higher photo-ionization cross-section, only the Pb and I ions interact with high energy sources, [START_REF] Lindblad | Electronic Structure of TiO 2 /CH 3 NH 3 PbI 3 Perovskite Solar Cell Interfaces[END_REF] making the MA cation a spectator deep within the VB. If this is the case, electronic state 3 separation due to spin orbit coupling (SOC), mainly associated with Pb and I, [START_REF] Even | Importance of Spin-Orbit Coupling in Hybrid Organic/Inorganic Perovskites for Photovoltaic Applications[END_REF][START_REF] Katan | Interplay of Spinorbit Coupling and Lattice Distortion in Metal Substituted 3D Tri-chloride Hybrid perovskites[END_REF] could be the main factor in DOS broadening. Lack of direct experimental signatures from MA may be attributed to the low photoionization cross sections of light elements, consequently signals of C, N and H atoms are difficult to detect at high photon energies in hard X-ray photoelectron spectroscopy (HAXPES). [START_REF] Motoki | Degradation of CH 3 NH 3 PbI 3 Perovskite Due to Soft x-ray Irradiation as An-20 alyzed by an X-ray Photoelectron spectroscopy time-dependent measurement method[END_REF] Computed valence spectra provide a qualitative agreement with experiment if the DOS peaks are broadened with a 0.3-0.5 eV wide Gaussian function. [START_REF] Lindblad | Electronic Structure of CH3NH3PbX3 Perovskites: Dependence on the Halide Moiety[END_REF][START_REF] Endres | Valence and Conduction Band Densities of States of Metal Halide Perovskites: A Combined ExperimentalTheoretical Study[END_REF] Such an ad hoc way to account for the effect of molecular motion does not provide insights into the contributing atomic species. However, another hypothesis explaining the difference between the calculated and measured DOS is that the experimental spectra reflect only the average DOS resulting from a convolution of molecular motion and time resolution of spectral equipment. This is expected to recreate experimental observations deep within the VB and thus clarify the good X-ray detection ability of the material. [START_REF] Wei | Sensitive X-ray Detectors Made of Methylammonium Lead Tribromide Perovskite Single Crystals[END_REF][START_REF] Yakunin | Low-threshold Amplified Spontaneous Emission and Lasing from Colloidal Nanocrystals of Caesium Lead Halide Perovskites[END_REF][START_REF] Yakunin | Detection of X-ray Photons by Solution-processed Lead Halide Perovskites[END_REF] Moreover, the much more flattened and broadened characters of VB dispersion determined by angle resolved photoemission experiments further provides evidence for the feasibility of broadening the DOS by vibrations of MA. [START_REF] Lee | First Determination of the Valence Band Dispersion of CH 3 NH 3 PbI 3 Hybrid Organicinorganic Perovskite[END_REF] The only way to get a detailed atomistic information on the processes taking place and to quantify the effects of molecular vibrational motions, inorganic lattice anharmonicity, and SOC is to perform molecular dynamics simulations of MA and Cs perovskite systems in different thermodynamic ensembles.

To address the discrepancies between theory and experiment, we consider factors possibly influencing the theoretical DOS. Contributing physical properties, such as SOC and temperature induced distortions (octahedral tilting), [START_REF] Knutson | Tuning the Band Gap in Hybrid Tin Iodide Perovskite Semiconductors Using Structural Templating[END_REF][START_REF] Bernasconi | Direct Evidence of Permanent Octahedra Distortion in MAPbBr 3 Hybrid Perovskite[END_REF][START_REF] Prasanna | Gap Tuning via Lattice Contraction and Octahedral Tilting in Perovskite Materials for Photovoltaics[END_REF][START_REF] Lee | Resolving the Physical Origin of Octahedral Tilting in Halide Perovskites[END_REF] may play an important role in the shape and broadening of the DOS. SOC predominantly affects the orbitals of heavy atoms in systems. Previous theoretical calculations stated that the VB just below the Fermi level is derived from Pb-6s and I-5p states and the conduction band minimum (CBM) is dominated mostly by Pb-6p states, suggesting that SOC mainly influences the CBM in all temperature phases. [START_REF] Even | Importance of Spin-Orbit Coupling in Hybrid Organic/Inorganic Perovskites for Photovoltaic Applications[END_REF][START_REF] Katan | Interplay of Spinorbit Coupling and Lattice Distortion in Metal Substituted 3D Tri-chloride Hybrid perovskites[END_REF][START_REF] Even | Modelling of the Phase Transitions of Lead and Tin Halide Perovskites for Photovoltaic Cells[END_REF] The distortion of the PbI 6 octahedral cage induces a direct-indirect band gap transition [START_REF] Berdiyorov | Role of Cations on the Electronic Transport and Optical Properties of Lead-Iodide Perovskites[END_REF] and modifies the electronic states around the Fermi level. [START_REF] Kato | Universal Rules for Visible-light Absorption in Hybrid Perovskite Materials[END_REF] Given that the en- ergy difference between DOS peaks deep within the VB are on the order of up to 0.5 eV, a substantial change in either atomic orientation or electronic distribution must occur in order to justify the wide range of absorption energies experimentally measured. [START_REF] Wei | Sensitive X-ray Detectors Made of Methylammonium Lead Tribromide Perovskite Single Crystals[END_REF][START_REF] Yakunin | Low-threshold Amplified Spontaneous Emission and Lasing from Colloidal Nanocrystals of Caesium Lead Halide Perovskites[END_REF][START_REF] Yakunin | Detection of X-ray Photons by Solution-processed Lead Halide Perovskites[END_REF] Identification of the atomic species participating in the state energy fluctuations can possibly answer if the broadened DOS primarily originates from molecular motion or re-distribution of electronic states. Addressing this issue successfully will enrich our understanding of photo-physics in hybrid perovskites and facilitate the experimental search for realistic optoelectronic applications. In this letter, we systematically investigate that the effects of SOC and vibrational motion of the organic cations in MAPbI 3 via first-principles calculations as outlined in Methods in the Supporting Information (SI). Our simulations determine the DOS broadening within the VB in cubic, tetragonal and orthorhombic phases at 400, 300K and 100K temperatures, respectively. This phenomenon stems from both the molecular vibrations in the cations and the anharmonicity in the motion of the iodine atoms. The MA cations' vibrations are associated with the moderate C-N stretch and CH 3 bend, as well as the strong CH 3 and NH + 3 stretches. Knowledge of the specific atomistic motions and interactions that dominate structural and electronic properties is helpful when substituting the organic cation in order to tune materials properties.

Electronic structure calculations for the optimized structures of MAPbI 3 (Figure 1) provide a starting point for pinpointing the cause of broadened DOS captured by experimental work. Figure 2 presents the DOS plots with and without SOC for the cubic phase of MAPbI 3 .

These are compared to those of pure inorganic CsPbI 3 models taking the same lattice parameters as the corresponding MAPbI 3 does. We notice that addition of SOC leads to a shift in energy near the CB edge producing a reduced band gap, which agrees with previously published electronic structure calculations. [START_REF] Even | Importance of Spin-Orbit Coupling in Hybrid Organic/Inorganic Perovskites for Photovoltaic Applications[END_REF] The effect of SOC is not localized to specific momentum values but is known to shift band energies across all sampled k-points in the system. The SOC energy gaps are 0.67 and 0.63 eV for cubic MAPbI 3 and the corresponding CsPbI 3 model, respectively. These values are significantly corrected by about 0.99 and 0.94 5 eV compared to results obtained without SOC. Similar corrections of 0.9 and 1.0 eV are also observed for tetragonal and orthorhombic phases, respectively (Figure S1 and S2), in agreement with previous results. [START_REF] Katan | Interplay of Spinorbit Coupling and Lattice Distortion in Metal Substituted 3D Tri-chloride Hybrid perovskites[END_REF] When focusing on electronic states deeper in the VB, one can see a distinction in how SOC affects the Cs and MA systems. For the CsPbI 3 system, there exists a Cs peak located near -8.5 eV with a SOC splitting amounting to 1.53 eV from the Cs p orbitals (Figure 2a andc). From atomic energy level tables, [START_REF] Kramida | NIST ASD Team (20l8)[END_REF] the +1 oxidation state of a Cs cation has a SOC splitting of about 1.22 eV between the p orbitals of total angular momentum J = 1/2 and J = 3/2, which is about 0.31 eV lower than the calculated splitting.

In contrast, the energy structure deep within the VB for the MAPbI 3 system, is relatively unchanged with the addition of SOC (Figure 2b), rationalized by a negligible SOC effect from light-elements-constituted MA molecules. Additionally, SOC leads to the subsequent splitting of Pb-5d orbitals at about -17 eV into two individual peaks (Figure S3), displaying a SOC splitting of 2.58 eV between the 5d orbitals of total angular momentum J = 3/2 and J = 5/2, in nice agreement with 2.65 eV as reported in atomic energy level tables. [START_REF] Kramida | NIST ASD Team (20l8)[END_REF] This splitting has a minor impact on the electronic structure due to its extremely deep position.

In the energy range from -12.5 to -4 eV, there are only a few electronic states associated with Pb or I atoms (Figure 2d). Moreover, SOC does not produce any sizable enlargement of the total DOS in this energy range down to -12.5 eV (Figure 2b).

Next, we consider the effect of molecular motion as a possible cause of a broadened DOS within the VB. To this end, we run a series of MD trajectories for Cs and MA-based perovskites adopting NVT thermostat condition. These simulations were performed at temperatures of 400, 300 and 100 K for the cubic, tetragonal and orthorhombic phases, respectively, on different sizes of periodic cells (see Methods in SI). Since SOC does very little to modify the electronic DOS in the energy range of interest, we neglect SOC in the calculations of MD. The radial pair distribution functions (RDF's) between the different atoms provides a clear picture of the magnitude of the vibrations of the different atoms around their equilibrium positions. As shown in Figures S4-7, the RDF's for the inorganic PbI 3 lattice are 6 typical for a solid with clearly defined peaks broadened around their optimized positions.

However, owing to higher mobility, the situation is different for RDF's involving atoms of the organic cation. There is much more variability for N-N pairs in MAPbI 3 than Cs-Cs pairs in CsPbI 3 , especially for the high temperature cubic phase. This effect also appreciable in the other two phases, overall being in a good agreement with previous studies. [START_REF] Roiland | Multinuclear NMR as a Tool for Studying Local Order and Dynamics in CH 3 NH 3 PbX 3 (X = Cl, Br, I) Hybrid Perovskites[END_REF][46][START_REF] Carignano | Critical Fluctuations and Anharmonicity in Lead Iodide Perovskites from Molecular Dynamics Supercell Simulations[END_REF] It is expected that the high frequency motions and vibrations of the organic cations could broaden the DOS, especially deep in the VB. We next identify the atomic species participating in the state energy fluctuations so that we can investigate whether the broadened DOS is based on molecular motion or not. While it has been established that SOC has very little effect on the molecular motion and lattice parameters, [START_REF] Egger | Role of Dispersive Interactions in Determining Structural Properties of OrganicInorganic Halide Perovskites: Insights from First-Principles Calculations[END_REF] in order to test the effect of SOC on the electronic structure we calculated the time-averaged DOS over 100 configurations with SOC along the 15 ps NVT MD trajectories on the 2 × 2 × 2 cubic MAPbI 3 cell. As shown in Figure S8, we can find that SOC does not lead to any sizable DOS broadening in this energy range related to the electronic states of PbI 6 octahedrons. Consequently, we exclude the SOC effect in forthcoming calculations of massive DOS dynamics, for which the final 400 geometries along each MD trajectory were extracted. Figure 3a demonstrates three broadened DOS peaks (denoted as peak I, II, III) existing deep inside the VB for cubic MAPbI 3 , located around -5.0, -9.2 and -12.5 eV, respectively. Similar peak broadening is also found in the other two lower temperature phases of MAPbI 3 , differing only by a narrower half-width of three main broadening peaks (Figure 3b andc). This is due to a reduction in disordered states [START_REF] Kawamura | Structural Study on CubicTetragonal Transition of CH 3 NH 3 PbI 3[END_REF][START_REF] Roiland | Multinuclear NMR as a Tool for Studying Local Order and Dynamics in CH 3 NH 3 PbX 3 (X = Cl, Br, I) Hybrid Perovskites[END_REF][46][START_REF] Carignano | Critical Fluctuations and Anharmonicity in Lead Iodide Perovskites from Molecular Dynamics Supercell Simulations[END_REF] and weakened vibrational motion of the MA cations from temperature effects. Indeed, for CsPbI 3 (Figure S9) the time averaged DOS over the entire energy range is almost the same as the ground state of CsPbI 3 , i.e. without significantly broadened DOS peaks as found in the hybrid MAPbI 3 . The lack of DOS broadening in the Cs system is thus attributed to the absence of MA vibrational modes. As the electronic dimensionality is increased, the electron mobility is enhanced. Although these electrons do not contribute directly to important electronic transitions in devices, they increase the electronic 7 dimensionality deep within the VB. [START_REF] Xiao | Searching for Promising New Perovskite-based Photovoltaic Absorbers: the Importance of Electroni Dimensionality[END_REF] Note that since our MD calculations are based on a volume-fixed ensemble to match the experimental lattice of MAPbI 3 in each phase, the fluctuations in the system may not be strictly gauged. As reported in ref.

, 46 We have calculated the intra-molecular vibrational modes of the free MA cation. There are 18 molecular vibrational modes, associated with the C 3v symmetry of the structure, dividing the internal modes into one A2, five symmetric A1 and twelve two-fold degenerate asymmetric E species. [START_REF] Onoda-Yamamuro | Calorimetric and IR Spectroscopic Studies of Phase Transitions in Methylammonium Trihalogenoplumbates (II)+[END_REF][START_REF] Oxton | The Infrared Spectrum and Force Field of the Methyl-ammonium Ion in (CH 3 NH 3 ) 2 PtCl 6[END_REF] The calculated vibrational frequencies of the isolated MA cation at its optimized configuration are listed in Table 1 and are visualized in Figures S10-S11.

The six types of vibrational modes in ascending order are C-N stretch (281, 871 cm -1 ), CH 3 -NH + 3 rock (909, 1256 cm -1 ), CH 3 bend (1437, 1473 cm -1 ), NH + 3 bend (1545, 1679 cm -1 ), CH 3 stretch (2963, 3064 cm -1 ), and NH + 3 stretch (3260, 3341 cm -1 ), being in a good 8 agreement with previous results. [START_REF] Brivio | Lattice Dynamics and Vibrational Spectra of the Orthorhombic, Tetragonal, and Cubic Phases of Methylammonium Lead Iodide[END_REF][START_REF] Onoda-Yamamuro | Calorimetric and IR Spectroscopic Studies of Phase Transitions in Methylammonium Trihalogenoplumbates (II)+[END_REF][START_REF] Oxton | The Infrared Spectrum and Force Field of the Methyl-ammonium Ion in (CH 3 NH 3 ) 2 PtCl 6[END_REF][START_REF] Quarti | The Raman Spectrum of the CH 3 NH 3 PbI 3 Hybrid Perovskite: Interplay of Theory and Experiment[END_REF][START_REF] Defrees | Molecular Orbital Predictions of the Vibrational Frequencies of Some Molecular Ions[END_REF][START_REF] Glaser | Infrared Spectroscopic Study of Vibrational Modes in Methylammonium Lead Halide Perovskites[END_REF] Switching to MAPbI 3 periodic systems, each MAPbI 3 phase manifests similar vibrational properties. The corresponding vibrational spectrum is mainly divided into three energetic regions: (1) the low frequency band from 0-150 cm -1 ; (2) a mid frequency range from 280-1700 cm -1 , and (3) a high-frequency window from 2900-3300 cm -1 . [START_REF] Bakulin | Real-Time Observation of Organic Cation Reorientation in Methylammonium Lead Iodide Perovskites[END_REF][START_REF] Brivio | Lattice Dynamics and Vibrational Spectra of the Orthorhombic, Tetragonal, and Cubic Phases of Methylammonium Lead Iodide[END_REF] The lowfrequency modes are related entirely to the vibrations of the PbI 6 octahedra, while the midand high-frequency modes are linked to the vibrations of MA cations. We computed the Fourier transforms of the state energies in the region of interest, deep within the VB, in order to determine which molecular vibrational modes strongly couple to the electronic degrees of freedom (see Methods in SI). The resulting molecular vibrational spectra for the three crystal phases are shown in Figures 4 and S11-12 for peak I, II and III, respectively, which are in a good agreement with previous experimental values (Table 1). [START_REF] Oxton | The Infrared Spectrum and Force Field of the Methyl-ammonium Ion in (CH 3 NH 3 ) 2 PtCl 6[END_REF][START_REF] Glaser | Infrared Spectroscopic Study of Vibrational Modes in Methylammonium Lead Halide Perovskites[END_REF] In cubic MAPbI 3 , the main vibrations contributing to peaks I and III originate from the CH 3 /NH + 3 bend (about 1400 cm -1 ) and CH 3 stretch a about 3000 cm -1 (Figure S12-13). The predominant vibrations contributing to peak II are mainly from CH 3 bend (about 1400 cm -1 ), NH + 3 stretch (about 3100 cm -1 ), as well as small amounts of C-N stretch (about 950 cm -1 ) and NH + 3 bend (about 1600 cm -1 ) (Figure 4). Similar results are obtained for the tetragonal and orthorhombic phases, except that the intensities are more attenuated due to the weakened vibrational amplitudes as temperature decreases (Figures S11-12). Exceptions are the broadened peaks In summary, we computationally study the origin of the density of states broadening 9 experimentally reported in the hybrid organic-inorganic perovskite MAPbI 3 , using CsPbI 3 as a reference material. We show that spin-orbit coupling mainly modifies the density of states close to the Fermi level and does not contribute to its broadening deep within the valence band. From ab initio molecular dynamics simulations and electronic structure calculations,

we further analyze the contribution of thermal vibrations to three phases of MAPbI 3 . As expected, upon reducing the temperature, the broadening gradually reduces when going from the cubic to tetragonal and to orthorhombic phases, consistent with experimental findings.

The density of states broadening is ascribed to two different contributions. For states about 12.5 eV below the top of the valence band, this broadening can be traced back to the anharmonicity in the motion of the iodine atoms. In additional, vibrational modes of the MA cation provide important additional contributions to the density of states broadening in a wide energy range. Contrastingly, SOC does not produce any sizable broadening of the total DOS. Specifically, MA cations' vibrations mainly stem from the C-N stretch (about 950 cm -1 ), CH 3 bend (about 1400-1600 cm -1 ) and CH 3 and NH + 3 stretches (from 2950-3300 cm -1 ). These results present a detailed theoretical perspective on the structural dynamics in hybrid perovskites, rationalize experimental observations, and may guide future studies toward desired functionalities in optoelectronic applications.

Supporting Information Available

The following files are available free of charge. Methods, Ground state DOS for tetragonal and orthorhombic CsPbI

4 Page

 4

  the MA cations may rotate in NPT conditions that allow volume fluctuations. As soon as the volume restriction is relaxed in the MD simulations, the large distribution of PbI 6 octahedral tilting accompanied by an increase in the anharmonicity in the motion of the iodine atoms will occur, which has been observed in CsPbI 3 , MAPbI 3 and FAPbI 3 crystals.46,[START_REF] Carignano | Critical Fluctuations and Anharmonicity in Lead Iodide Perovskites from Molecular Dynamics Supercell Simulations[END_REF] It is expected that such anharmonicity in the iodine atom motion could influence the behaviors of DOS broadening. To confirm this point, MD calculations based on the NPT ensemble were carried out on cubic phase MAPbI 3 at 450 K, which are based on a 4 × 4 × 4 supercell by replicating the cubic unit cell four times in each Cartesian direction (see ref.[START_REF] Carignano | Critical Fluctuations and Anharmonicity in Lead Iodide Perovskites from Molecular Dynamics Supercell Simulations[END_REF] for details). As demonstrated in Figure3dthere exists an obvious broadening of the electronic states up to 0.5 eV at around -11.5 eV. This confirms that the anharmonicity in the motion of the iodine atoms does contribute to DOS broadening in specific energy regions. Reversely and noteworthy, NVT calculations are not able to reveal any broadening related to the inorganic framework (vide supra). Although the anharmonicity of the I atoms does broaden the DOS, it is a smaller contribution compared to the effect of MA vibrations. Thus, we analyze next the contribution from MA vibrations to the broadening of the DOS.

I

  and II which couple to a slightly enhanced vibration along the C-N axis as compared to that in the cubic phase. Moreover, the CH 3 bends for peak I and III in the orthorhombic phase are almost non-existent due to the temperature effect. The two CH 3 stretches (2963, 3064 cm -1 ) for peaks I and III become distinct from each other. Altogether, we mainly attribute widening of DOS deep inside VB in the three MAPbI 3 phases to mostly asymmetric CH 3 /NH + 3 stretches, moderate CH 3 bend, and C-N stretch. Thus the observed coupling is exclusive to mid-frequency and high-frequency vibrational modes.

3

 3 and MAPbI 3 phases, partial DOS of cubic MAPbI 3 with Pb-d states included, radial distribution functions in tetragonal and orthorhombic phases, time averaged DOS for CsPbI 3 and for MAPbI 3 with SOC, calculated vibrational eigenvectors of isolated MA cation and Fourier transforms of the electronic state I and III in three MAPbI 3

Figure 1 : 12 Page

 112 Figure 1: (a): Schematic diagram of the MA molecule. Three main vibrational modes of MA molecule's vibration are marked. (b) MAPbI 3 crystal structures for (b) cubic, (c) tetragonal and (d) orthorhombic phases.

Figure 2 :

 2 Figure 2: Ground state electronic structure corresponding to the cubic CsPbI 3 (a, c) and optimized MAPbI 3 (b, d) models. The top panels compare the calculated density of states (DOS) with and without spin-orbit coupling (SOC) as dashed red and solid blue lines, respectively. The bottom panels provide the SOC partial density of states (PDOS) with Pb (red), I (green), and the Cs or MA cations (blue), respectively. The Fermi energy is set to zero.

Figure 3 :

 3 Figure 3: Time averaged DOS of (a) cubic, (b) tetragonal and (c) orthorhombic MAPbI 3 along MD trajectories under NVT conditions, overlaid with the ground state DOS. The Fermi levels are set to 0. The broadened DOS peaks from MA cations are indicated by Roman numbers of I, II and III in panel (a). (d) Time averaged DOS for cubic MAPbI 3 along MD trajectories performed under NPT conditions and 4 × 4 × 4 supercell, overlaid with the static DOS. The red circle indicates the contribution from the anharmonicity of I atoms' motion.

Figure 4 :

 4 Figure 4: Fourier transforms of the state energies of the electronic states relevant to peak II (Figure 3a) in three phases of MAPbI 3 : (a) cubic, (b) tetragonal, (c) orthorhombic. The energy fluctuations are due to molecular vibrational modes of the MA cations. Peak assignments for modes in panel (a) are suggestions only.

Table 1 :

 1 Fundamental Vibrations of the Isotopic MA cation Calculated by B3LYP and MP2 Methods and, Experimental Measured Vibrational Modes for MAPbI 3 from references[START_REF] Oxton | The Infrared Spectrum and Force Field of the Methyl-ammonium Ion in (CH 3 NH 3 ) 2 PtCl 6[END_REF][START_REF] Glaser | Infrared Spectroscopic Study of Vibrational Modes in Methylammonium Lead Halide Perovskites[END_REF] (cm -1 ).

	Mode	Species	MA this work MP2 53	MAPbI 3 Ref 50 Ref 53
	υ 12 , CH 3 -NH + 3 rock	E	909	1032	903.4	911
	υ 5 , C-N stretch	A 1	871	982	990	960
	υ 11 , CH 3 -NH + 3 rock	E	1256	1409	1248.9 1250
	υ 4 , sym. CH 3 bend	A 1	1437	1597	1415	1385
	υ 10 , asym. CH 3 bend	E	1473	1620	1452.3 1423
	υ 3 , sym. NH + 3 bend υ 9 , asym. NH + 3 bend	A 1 E	1545 1679	1691 1809	1469.9 1469 1581 1577
	υ 6 , torsion	A 2	281
	υ 2 , sym. CH 3 stretch	A 1	2963	3164	2896	2916
	υ 8 , asym. CH 3 stretch	E	3064	3263	2974.8 2958
	υ 1 , sym. NH + 3 stretch υ 7 , asym. NH + 3 stretch	A 1 E	3260 3341	3446 3519	3188 3225.6 3179 3132

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Acknowledgement

The work at Los Alamos National Laboratory (LANL) was supported by the LANL LDRD program (L.Z., A.J.N. and S.T.). This work was done in part at the Center for Nonlinear Studies (CNLS) and the Center for Integrated Nanotechnologies (CINT), a U.S. Department of Energy and Office of Basic Energy Sciences user facility, at LANL. This research used resources provided by the LANL Institutional Computing Program. LANL is operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of the U.S. Department of Energy under contract DE-AC52-06NA25396. The work in France was supported by Cellule Energie du CNRS (SOLHYBTRANS Project) and University of Rennes 1 (Action Incitative, Défis Scientifique Emergents 2015).

AUTHOR INFORMATION

Corresponding Author * L.Z.: Email: ljzhou86@lanl.gov * S.T: Email: serg@lanl.gov

Notes

The authors declare no competing financial interest.