Coralie Pasquier

Stéphane Pezennec

Antoine Bouchoux

Bernard Cabane

Valérie Leche- Valier

Cécile Le Floch-Fouéré

Gilles Paboeuf

Maryvonne Pasco

Benjamin Dollet

Lay- Theng Lee

Sylvie Beaufils
email: sylvie.beaufils@univ-rennes1.fr

Protein transport upon advection at the air/water interface: when charge matters

Keywords: protein, ovalbumin, lysozyme, monolayers, multilayers, neutron reflectivity, nullellipsometry, advection-diffusion, adsorption, air-water interface

The formation of dense protein interfacial layers at a free air-water interface is known to result from both diffusion and advection. Furthermore, proteins interactions in concentrated phases are strongly dependent on their overall positive or negative net charge, which is controlled by the solution pH. As a consequence, an interesting question is whether or not the presence of an advection flow of water towards the interface during protein adsorption produce different kinetics and interfacial structure of the adsorbed layer, depending on the net charge of the involved proteins and, possibly, on the sign of this charge. Here we test a combination of the following parameters using ovalbumin and lysozyme as model proteins: positive or negative net charge, presence or absence of advection flow. The formation and the organization of the interfacial layers are studied by neutron reflectivity and nullellipsometry measurements. We show that the combined effect of a positive charge of lysozyme and ovalbumin and the presence of an advection flow is necessary to induce interfacial multilayers formation. Conversely, negatively charged ovalbumin forms monolayers, whether an advection flow is present or not. We show that an advection/diffusion model cannot describe correctly the adsorption kinetics of multilayers, even in the hypothesis of a concentration-dependent diffusion coefficient like in colloidal filtration for instance. Still, it is clear that advection is a necessary condition for making multilayers through a mechanism that remains to be determined, which paves the way for future research.

Introduction

Proteins in solution form films by accumulation towards hydrophobic interfaces [START_REF] Graham | Proteins at Liquid Interfaces[END_REF][START_REF] Graham | Proteins at Liquid Interfaces: II. Adsorption Isotherms[END_REF][START_REF] Fainerman | Adsorption of Surfactants and Proteins at Fluid Interfaces[END_REF][START_REF] Fainerman | Description of the Adsorption Behaviour of Proteins at Water/Fluid Interfaces in the Framework of a Two-Dimensional Solution Model[END_REF] .These interfaces in turn control the behavior of a wide variety of synthetic or natural systems such as technological foams and emulsions [START_REF] Dickinson | Milk Protein Interfacial Layers and the Relationship to Emulsion Stability and Rheology[END_REF][START_REF] Dickinson | Hydrocolloids at Interfaces and the Influence on the Properties of Dispersed Systems[END_REF][START_REF] Dickinson | Hydrocolloids Acting as Emulsifying Agents-How Do They Do It?[END_REF][START_REF] Berton-Carabin | Structure, and Functionality of Interfacial Layers in Food Emulsions[END_REF][START_REF] Berton-Carabin | Towards New Food Emulsions: Designing the Interface and Beyond[END_REF] . Liquid foams stabilized by proteins are for instance hugely present in the food industry food industry [START_REF] Wierenga | New Views on Foams from Protein Solutions[END_REF] and therefore extensively .extensively studied by researchers [START_REF] Narsimhan | Role of Proteins on Formation, Drainage, and Stability of Liquid Food Foams[END_REF] . The field of biomaterials is also concerned by protein adsorption on various surfaces [START_REF] Andrade | Proteins at Interfaces: Principles, Multivariate Aspects, Protein Resistant Surfaces, and Direct Imaging and Manipulation of Adsorbed Proteins[END_REF] and hydrophobic interfaces are also found in vivo, where proteins for instance adsorb at the liquid-air interface which acts as a barrier for a wide range of organisms [START_REF] Schor | The Diverse Structures and Functions of Surfactant Proteins[END_REF] . In addition, membrane-based techniques are frequently used for the separation and purification of proteins [START_REF] Saxena | Membrane-Based Techniques for the Separation and Purification of Proteins: An Overview[END_REF] , as milk filtration, for instance 15-17 . The formation of a monolayer of protein adsorbed onto the membranes generally impairs the performance of the filtration and is this time a negative phenomenon that needs to be avoided [START_REF] Beier | Adsorption of Amylase Enzyme on Ultrafiltration Membranes[END_REF] . These numerous fields of application explain why adsorption mechanisms related to protein films formation and the structure of such films have been and are still widely studied (see Yano 2012 [START_REF] Yano | Kinetics of Protein Unfolding at Interfaces[END_REF] for a review).

Among the parameters which control the formation of the protein interfacial film, we can of course identify diffusion and convection, the latter being due to inhomogeneities in physical parameters (such as temperature) in the bulk and to internal fluid movement. Diffusion and convection act in conjunction during the first steps of the film formation, and many authors have mentioned the importance of early convection mechanisms in the formation of the interfacial layer [START_REF] Graham | Proteins at Liquid Interfaces[END_REF][START_REF] Sutherland | The Kinetics of Adsorption at Liquid Surfaces[END_REF][START_REF] Benjamins | Dynamic and Static Properties of Proteins Adsorbed at the Air/Water Interface[END_REF][START_REF] Davies | The Behaviour of Glycophorin at the Air-Water Interface[END_REF] . However, it is well-known that evaporation induces advection (i.e. convection toward the interface) in bulk liquids and can be at the origin of spectacular effects such as the tears of wine for instance [START_REF] Fournier | Tears of Wine[END_REF] , or the coffee stain effect [START_REF] Deegan | Capillary Flow as the Cause of Ring Stains from Dried Liquid Drops[END_REF] , where the evaporation-induced advection velocity has been measured. directly [START_REF] Dhavaleswarapu | Experimental Investigation of Evaporation from Low-Contact-Angle Sessile Droplets[END_REF] .

Accordingly, an interesting question is wether or not evaporation -and the associated advection fluxhas an impact on the adsorption of proteins at interfaces. It is all the more interesting that it corresponds to numerous real situations when a permanent evaporation/advection flow is maintained across the interface (e.g. in case of an open air surface). In these cases, we still do not have a clear picture of how the protein interfacial film continues to evolve because of advection. Also in such a situation, one important parameter that needs to be taken into account is the charge of the involved proteins; a characteristic that is known to directly affect film formation [START_REF] Kim | Investigations of Lysozyme Adsorption at the Air/Water and Quartz/Water Interfaces by Vibrational Sum Frequency Spectroscopy[END_REF][START_REF] Roberts | Combined Surface Pressure-Interfacial Shear Rheology Study of the Effect of PH on the Adsorption of Proteins at the Air-Water Interface[END_REF][START_REF] Wierenga | Quantitative Description of the Relation between Protein Net Charge and Protein Adsorption to Air-Water Interfaces[END_REF][29][START_REF] Liao | Protein Assembly at the Air-Water Interface Studied by Fluorescence Microscopy[END_REF] -and therefore quite potentially the evolution of the film upon advection. By charge, we mean not only the net electrical charge of the protein, as it is often only considered in the literature, but also the sign of the charge (+/). An increasing number of reports now indicate that protein interactions -hence interfacial film formation -also depend on forces that are controlled by the sign of this charge rather than its absolute value [START_REF] Boström | Why Forces between Proteins Follow Different Hofmeister Series for PH above and below PI[END_REF][32][START_REF] Hartvig | Formation of Dielectric Layers and Charge Regulation in Protein Adsorption at Biomimetic Interfaces[END_REF][START_REF] Engelhardt | Protein Adsorption at the Electrified Air-Water Interface: Implications on Foam Stability[END_REF] .

To summarize, our objective here is to investigate the combined effects of protein charge (sign and net charge) and advection on the formation and evolution of protein films at an hydrophobic interface (here the air-water interface). Some of our specific questions are: what is the impact of a permanent advection flow on the film formation? Does the sign of the proteins have an importance in this context?

As models, two well-known proteins are considered separately: ovalbumin and lysozyme. Their adsorption at the air-buffer interface is studied by neutron reflectivity and null-ellipsometry, with and without permanent advection flow and for positive and negative net electric charge in case of ovalbumin.

EXPERIMENTAL Sample preparation

Lysozyme hydrochloride powder (lysozyme purity higher than 98%, as determined by reversed-phase high-performance liquid chromatography (HPLC)) was a gift from LIOT (Annezin, France).

Ovalbumin was purified from hen egg white according to the protocol described by Croguennec [START_REF] Croguennec | Simple Rapid Procedure for Preparation of Large Quantities of Ovalbumin[END_REF] .

Egg white was separated from whole eggs and diluted three times with 15 MΩ cm purified water prepared by reverse osmosis, before adjusting the solution pH to 6.0 with HCl and keeping it overnight at 5°C, under agitation. The next day, the pH was adjusted again to 6.0 and the solution was centrifuged at 2000×g, 5°C for 4 minutes. The supernatant pH was adjusted to 8.2 with NaOH, before centrifugation at 25900×g, 4°C, for 20 minutes. The supernatant, a mucin-free egg white solution, was then collected and weighted.

Ovalbumin was then extracted from the solution via anion-exchange chromatography, performed on a LRC column (Pall Life Sciences, Port Washington, USA) packed with Q-Sepharose Fast Flow media (Pharmacia Biotech AB, Uppsala, Sweden). Three solutions were successively run through the column: a 0.035 M NaCl solution (extraction of unwanted proteins), then a 0.14 M NaCl solution (extraction of ovalbumin), then a 1 M NaCl solution (cleaning of the column). Protein concentration was monitored by measuring optical absorption at 280 nm with a UV 325 Dual Wavelength UV-Vis Detector (Agilent Technologies, Santa Clara, USA), using an adsorption coefficient of 𝜀 = 2.93 × 10⁴ M⁻¹ cm⁻¹.

Ovalbumin solutions were then dialyzed for 3 days against several successive baths of 15 MΩ cm purified water, then centrifuged and freeze-dried for storage.

Protein charges were computed with the PDB2PQR [START_REF] Dolinsky | PDB2PQR: An Automated Pipeline for the Setup of Poisson-Boltzmann Electrostatics Calculations[END_REF] and PROPKA [START_REF] Olsson | PROPKA3: Consistent Treatment of Internal and Surface Residues in Empirical PKa Predictions[END_REF] software from the lysozyme and ovalbumin structures (PDB ID 1HEL and 1OVA, respectively).

Bulk solutions and buffer

Solutions of ovalbumin and lysozyme were prepared at a 1 g.L -1 concentration in buffered deuterium oxide D2O. The deuterium analog of pH in D2O solutions, pD, was measured by adding 0.4 to the pH-meter reading, after standardization of the electrode in H2O buffers [START_REF] Covington | Use of the Glass Electrode in Deuterium Oxide and the Relation between the Standardized PD (PaD) Scale and the Operational PH in Heavy Water[END_REF] . Ionic strength I=20 mM, pD 7.0 buffer was prepared using 11.3 mM bis-tris propane (1,3bis(tris(hydroxymethyl)methylamino)propane, Sigma-Aldrich, St-Louis, USA) adjusted to pD 7.0 with HCl. I=20 mM, pD 3.6 buffer was prepared using 56.4 mM lactic acid-sodium lactate.

I=170 mM buffers were prepared by adding 150 mM NaCl to the I=20 mM buffers.

Neutron reflectivity

Specular neutron reflectivity experiments were carried out on the time-of-flight neutron reflectometer G3bis at the ORPHEE reactor (Laboratoire Léon Brillouin, CEA-Saclay) using a polychromatic beam with wavelength λ ≈ 2.5 to 25 Å. The incident beam was bent with a supermirror onto the liquid surface at a grazing incident angle θ = 1.54° with angular resolution δθ/θ ≈ 0.05 as calibrated with pure D2O, giving a corresponding wave vector range 𝑄 = 4 𝜋𝑠𝑖𝑛𝜃 𝜆 ⁄ of about 0.014 to 0.14 Å -1 .

Under this configuration, there is adequate total reflection plateau from the deuterated solvent subphase for 𝑄 < 𝑄 : ≈ 0.018 Å -1 where 𝑄 : is the critical total reflection edge. The sample container was a Teflon trough (35 mm×95 mm) that was enclosed in an air-tight aluminum cell with quartz windows to allow the neutron beam to pass through with minimal absorption. The cell was equipped with a temperature control system to monitor the experimental temperature to T = 20.0 °C ± 0.2 °C and the entire setup was positioned on an anti-vibration support. Most measurements were carried out under this hermetically-enclosed condition hence no advective flow due to evaporation took place during the measurements. Some experiments were also performed without the cover of the trough (called "free surface configuration") to allow evaporation and advective flow during the measurements. Reflectivity spectra were acquired at one or two-hour intervals.

The basic principles of neutron reflectivity have been discussed in detail in several past literature 39- 41 Experimentally, reflectivity is measured as a function of of 𝑄 and 𝑅(𝑄) = 𝐼 (𝑄) 𝐼 ? ⁄ (𝑄), where 𝐼(𝑄)

and 𝐼 ? (𝑄) are intensities of the reflected and the incident beam, respectively. The reflectivity profile depends on the neutron refractive index profile normal to the surface 𝑛(𝑧) which is defined (neglecting absorption) as: 𝑛(𝑧) = 1 -(𝑁𝑏 (𝑧) 2 ⁄ 𝜋)𝜆 D where 𝑧 is the distance from the interface, 𝑁𝑏(𝑧) is the scattering length density given by 𝑁𝑏 = ∑ 𝑏 F F 𝑛 F where 𝑏 F is the neutron scattering length and 𝑛 F the number density of the atomic species j. The difference in scattering length density of the proteins and the deuterated buffer is negative. For lysozyme, Δ𝑁𝑏 = 𝑁𝑏 H -𝑁𝑏 I = -2.67 x 10 -6 Å - 2 where 𝑁𝑏 H = 3.65 × 10 -6 Å -2 is the theoretically calculated scattering length density of the protein using densityρ = 1.43 g•cm -3 7 and taking into account H-D exchange of labile hydrogen; 𝑁𝑏 I = 6.32 × 10 -6 Å -2 is the experimentally determined scattering length density of the deuterated buffer solution.

The corresponding values for ovalbumin are: Δ𝑁𝑏= -3.26 × 10 -6 Å -2 where 𝑁𝑏 H = 3.07×10 -6 Å -2 and ρ = 1.36 g•cm -3 . In the presence of an adsorbed protein layer, the reflectivity is thus decreased with respect to that of the pure solvent and therefore the normalized reflectivity gives R/RF < 1. RF is the reflectivity of the deuterated buffer solution taking into account angular resolution. In this work, all reflectivity spectra are expressed in the normalized form, R/RF. In this representation, all deviations of R/RF from unity are attributed only to the adsorbed layer, and the higher the adsorption, the larger is the deviation from unity.

Data analysis: The reflectivity curves are modeled using an n-slice step function of uniform scattering length density given by:

𝑁𝑏(𝑧) = J K 𝑁𝑏 L -𝑁𝑏 LMN 2 O P ? Q1 -𝑒𝑟𝑓 (𝑧 -𝑧 L ) 𝜎 L V
𝑁𝑏 L is the scattering length density and 𝑧 L -𝑧 LMN the thickness (di) of slice i, and 𝜎 L is the interfacial roughness between slice i and i+1 described by an error function. n = 0 and n = N represent the two semi-infinite media air and bulk buffer, respectively. The adjustable parameters are 𝑁𝑏 L , di and 𝜎 L . In a first fitting, 𝜎 L is found to fall between 0.3 to 2.3 Å with the majority falling around 0.7 -1.5 Å, except for the innermost roughness (between the last layer and the subphase) that gives larger variations depending on the protein volume fraction and thickness of the layer. In order to reduce the number of fitting parameters, 𝜎 L is fixed at 1 Å except for the innermost roughness which is allowed to float; the fitted values of this last roughness range from about 2 to 8 Å (increasing with the thickness of the slice). The best-fit parameters are determined by iteration and minimization of the χ 2 parameter between the experimental and theoretical curves. From the fitted scattering length density profile 𝑁𝑏(𝑧), the protein density profile 𝜙(𝑧) can be estimated using the relations: 𝑁𝑏 = 𝜙 H 𝑁𝑏 H + 𝜙 I 𝑁𝑏 I

and 𝜙 H + 𝜙 I = 1. 𝑁𝑏 is the fitted scattering length density, 𝑁𝑏 H and 𝑁𝑏 I are as defined above, and 𝜙 H and 𝜙 I are the volume fractions of protein and solvent respectively. Note that the expression of the n-slice profile refers to an adsorbed interfacial layer that can be described by n regions of uniform scattering length density each (in the z-direction); it does not necessarily correspond to n molecular layers.

Ellipsometric measurements at the air-water interface

Adsorption layers were prepared on a circular trough, the surface of which (S=25 cm 2 ) is directly in contact with air. Hence, an advective flow develops during adsorption kinetics. The speed of the evaporation front (ie flux density) was estimated through the recording of the evaporated mass of water with time; its value was found to be constant, equal to 21 nm.s -1 . The ellipsometric measurements were carried out with a home-made ellipsometer, in the so-called "null-ellipsometer configuration" operated with He-Ne laser (λ=632.8 nm, Melles Griot, Carlsbad, CA) that was polarized with a Glan-Thompson polarizer. The incidence angle of the light on the surface was fixed, equal to 1° away from the Brewster angle. The laser beam probed a surface of 1 mm 2 and a depth of the order of 1 μm.

After reflection on the water surface, the laser light passed through a λ/4 retardation plate, a Glan-Thompson analyzer, and a photomultiplier. Through a computer-controlled feedback loop, the analyzer and the polarizer automatically rotated towards the extinction position, giving the two ellipsometric angles Δ and ψ.

In case of ellipsometric measurements on the air-water interface, adsorbed layers are transparent (<10 nm) with low refractive index contrast and the angle of incidence of the laser beam is fixed. In that case, the ellipsometric angle Δ changes when the layer is formed while relative changes of the other angle ψ remain of low magnitude. We used the ellipsometric angle Δ to semi-quantitatively measure the protein amount adsorbed at the air-water interface. Depending on the protein and the physical-conditions of the buffer, a 10° ellipsometric angle Δ corresponds to protein concentrations between 0.5-2 mg.m -2 (ref [START_REF] Van Alstine | Ethylene Glycol) Amphiphile Adsorption and Liposome Partition[END_REF] and Figs. 2 and4,5).

For each kinetic measurement, initial values of the ellipsometric angle (Δ0) and surface tension of pure buffer solutions were recorded on the subphase for at least half an hour. These values have been subtracted from all data presented below. Then, the buffer solution was removed and the protein solution was poured in the trough. Values of Δ and surface pressure (Π) were recorded every 4 s with a precision of ±0.5° and ±0.5 mN/m, respectively.

Ellipsometry was performed at least in duplicate for each analysed condition in independent experiments. The overall uncertainty of ellipsometric measurements, as estimated from replicate experiments (at least three replicates), can essentially be attributed to the variability of protein adsorption and was thus estimated from replicates to be +/-1° for Δ in case of monolayers and much more (20°-30°) when multilayers are formed, this point being discussed below.

Additionnaly, a set of ellipsometric measurements without advective flow was performed by pouring the protein solution in a closed glass container. however continues to grow and to reorganize with time; after 10 h a two-slice model becomes inadequate and a three-slice model is necessary to fit the reflectivity data. Thus, the adsorption process can be modelled by the formation of a first slice that is saturated within 4 h and subsequent additional slices that continue to grow over a longer period of time. All the fitted values are contained in table I. Similar measurements were performed without the cover of the trough, in the "free surface configuration" to allow for evaporative advection. (see SI-1 for R/RF and concentration profiles). In this case, the adsorption process continues to evolve over several hours. The R/RF curves at high-𝑄 show an upward turn that indicates an impending weak oscillation that arises from the formation of a thick layer, the interference fringes of which are detected within the 𝑄-range of the measurement.

RESULTS AND DISCUSSION

Positively charged lysozyme, adsorption at low ionic strength

The weak and unusual shape of the oscillation are due to the dilute nature of the layer and a nonhomogeneous internal structure, as evidenced by the three-step concentration profile (see SI). The while two other slices are necessary to describe the whole profile, the volume fraction of which increases without evidence of saturation at 7 h. Note that for this open configuration, there is significant absorption of water vapor by the D2O subphase, resulting in a decrease in the solvent scattering length density from 6.32 to 4.32 x 10 -6 Å -2 after 7h. This effect reduces progressively the contrast between the protein and the solvent, and consequently increases the uncertainty in the measured values (as can be seen by the large error bars). For each reflectivity curve with time, it is necessary to re-evaluate 𝑁𝑏 I from the critical total reflection edge, 𝑄 : = 4Z𝜋𝑁𝑏 I . In the data fitting, the modified values of 𝑁𝑏 I and 𝑁𝑏 H with time are taken into account and the corresponding RF calculated accordingly. Due to this constantly changing protein-solvent contrast between spectra, the relative changes in adsorption cannot be perceived qualitatively from the R/RF curves, and these constant changes might also contribute to the unusual appearances of the curves.

In each model slice, the surface concentration excess 𝛤 (in mass per unit area) can be calculated from: 𝛤 = 𝜙 H × 𝑑 × 𝜌 where 𝜙 H is the protein volume fraction in the slice, d the thickness of the slice and 𝜌 the protein volumetric mass. The contributions of all slices are summed up to give the overall surface concentration excess in the adsorbed layer.

The adsorption densities of lysozyme at I=20 mM are shown on Figure 2a for the airtight trough and the free surface configuration. In the latter case, it can be noticed that the excess surface density increases with time, without evidence of saturation. it proves that it comes from the sample and not from the apparatus. We hypothesis that the interface is highly heterogeneous in these conditions and, as the laser probes a surface of 1mm 2 , the Delta value depends strongly on the thickness of the point of impact of the laser. The adsorption densities show clearly that in the presence of NaCl, the adsorption is (i) faster, since it saturates after 6 h against 10h at low ionic strength, and (ii) higher, with a surface concentration excess of 2.3 mg•m -2 for I=170 mM compared to 2.0 mg•m -2 for I=20 mM. Figure 4 shows adsorption of ovalbumin at pD 3.6, (net charge +28), I=20 mM, measured by neutron reflectivity as a function of time in the airtight trough. On Figure 4a and 4b, the Y-scales have been maintained to the same value as the previous graphs to facilitate comparisons. The adsorption density under these conditions is very low and a one-slice model adequately fits the reflectivity curve (R/RF shown in SI-3).

Positively charged Lysozyme, adsorption at high ionic strength

Positively charged ovalbumin, adsorption at low ionic strength

Figure 5 shows the plot of the ellipsometric angle Δ as a function of adsorption time, for ovalbumin at pH 3.6, I=20 mM, in the free surface trough (with advective flow) and in the airtight trough (without advective flow). Without advective flux, saturation is reached within 2-3 hours, which is a bit slower but still in the same range than lysozyme in comparable conditions (Fig. 2b) with the same reproducibility shown by the colored filled area. In the presence of an advective flow (we only have ellipsometry results here as neutron experiments were not performed in open-air conditions for ovalbumin at pH 3.6), we also find a behavior that is comparable with lysozyme (Fig. 2b), with a strong variability, suggesting an heterogeneous layer (the colored filled area contains the three replicates), a very fast adsorption at initial times, and then a monotonic increase in adsorption with time over hours.

Positively charged Ovalbumin, adsorption at high ionic strength

At pD 3.6 when the ionic strength is increased to 170 mM using NaCl, adsorption increases, as expected due to Debye screening, and a two-slice model is required to fit the data (Fig. 4). Note that at pD 3.6 and I=170 mM, although 𝑑 N is about the same value as for lysozyme at pD 7 and I=20 mM, 𝜙 N does not reach the same extent of saturation.

Negatively charged ovalbumin, adsorption at low ionic strength

The adsorption kinetics and evolution of the structure within the adsorbed layer for ovalbumin at pD 7 (net charge -10) and I=20 mM in airtight trough (without advective flow) are shown in Figure 6. The adsorption characteristics are similar to those observed for lysozyme at an equivalent absolute charge (+8 vs -10). At the initial stage of adsorption, a two-slice structure is already evident. The first slice 𝑑 N reaches saturation after around 4 to 6 h, while slices 𝑑 D and 𝑑 ] continue to build and reorganize over longer times. After 10h, the total thickness of the adsorbed layer has grown to about 90 Å. The R/RF curve shows an oscillation that appears more distinct (see SI-4). Nevertheless, even though the total adsorption density appears to approach a near-equilibrium plateau, the internal structure may still be evolving. The evolution of Γ with time (shown on Fig. 6) barely reaches a constant value after 10 h of adsorption, similarly to lysozyme. The maximum value of Γ ≈ 2.1 mg•m -2 is compatible with a monolayer [START_REF] De Feijter | Ellipsometry as a Tool to Study the Adsorption Behavior of Synthetic and Biopolymers at the Air-Water Interface[END_REF][START_REF] De Feijter | Adsorption Kinetics of Proteins at the Air-Water Interface[END_REF] . The total adsorption is higher compared to the one at pD 3.6 at 20 mM (<1 mg•m -2 ) which could result from a lower absolute charge at pD 7.0 (-10 e at pH 7 versus + 28 e at pH 3.6) and thus less repulsions between the proteins as they form the interfacial layer. Fig. 7 shows the plot of the ellipsometric angle Δ as a function of adsorption time, for ovalbumin at pH 7.0, I=20 mM, in the free surface trough (with advective flow). In these conditions, no multilayers are formed: on the contrary, the ellipsometry angle is constant after a few hours, suggesting the saturation of a monolayer. However, as for ovalbumin and lysozyme in the other conditions but in the similar free surface trough, we find again a very rapid initial adsorption with an ellipsometric angle Δ > 5° at short times.

Negatively charged ovalbumin, adsorption at high ionic strength

Surprisingly, when the ionic strength is increased, without advective flow, the adsorption is decreased significantly; in this case, due to the low signal, a one-slice model is sufficient to fit the neutron reflectivity profile. The adsorbed layer is decreased both in thickness and in density, the saturation value of the excess surface concentration being close to 0.7 mg•m -2 (Fig. 6, R/RF curves given in SI-4 and SI-5). This result is contrary to the expected effect of charge screening, which decreases electrostatic repulsion between neighbouring molecules. Several elements can be taken into account to explain this effect (image charge, absolute value of the protein charge, charge of the interface, nature of buffer ions) and would require a more in depth study to go further.

Advection combined with positively charged protein are both necessary to produce multilayers

The objective of this paper was to examine the effect of a permanent interfacial advection flow on the thickness and structure of a protein air-water interfacial film that forms versus time, with a specific focus on the relation between the film properties and the charge properties of the protein involved.

The most important result of our study is the evidence that the combined effect of the two factors, namely the permanent advection flow and a positive net electrical charge of the protein, induces the formation of a multilayer interfacial film. If one of these two factors is missing, multilayers do not form and only the 'trivial' formation of a protein monolayer is observed.

We obtain this result through experiments performed using neutron reflectivity and ellipsometry. In the conditions given above, i.e., with positively charged lysozyme (+ 8 e at pH 7.0) or ovalbumin (+ 28 e at pH 3.6), and in the presence of a permanent advective flow towards the surface, both experimental techniques indicate that film grows in a non-saturating way over several hours, well above the classical thickness of a monolayer.

The thickness of the film, estimated by neutron measurements is as high as 14 nm in the case of lysozyme (see SI-1). If we suppress the advection flow, positively charged lysozyme and ovalbumin cease to form multilayers but form monolayers, as shown on Fig. 2 and Fig. 5, respectively. If this time we conserve the advection flow but switch the sign of ovalbumin from positive to negative (-10 e at pH 7), the protein also ceases to form multilayers and simply adsorb as a 'classical' interfacial monolayer.

The classical advection-diffusion model does not predict multilayers formation

In a first attempt to explain our results, it seems important -if not mandatory -to examine if a classical advection-diffusion model is capable of describing the adsorption kinetics of the multilayer films, once the first interfacial layer is formed. The advection-diffusion equation is the combination of diffusion and convection (advection) equations that describes in this case the particle transport inside the physical system formed by the bulk solution and the air-water interface.

To adjust experimental kinetics of surface concentration vs time, the following points must be considered : i) as the model only describes the evaporation-driven protein advection towards the interface and does not account for the adsorption-driven irreversible formation of the first interfacial monolayer, the monolayer is then considered as the interface ii) since the experimental measurements are only sensitive to the surface concentration excess, we fit the difference [𝐶(𝑥 = 0, 𝑡) -𝐶 cdef ] to the experimental data; iii) the concentration obtained from this model (in mg.m -3 ) must be integrated over a thickness h to obtain a surface concentration (in mg.m -2 ).

We choose to test the advection-diffusion model for lysozyme, for which we have the most complete data set. Given the intrinsic variability of the kinetics, due to the sample itself in multilayer conditions, our objective is not to describe precisely the adsorption kinetics, but to test if the model can account for the shape of the kinetics with reasonable values for the layer thickness h and the diffusion coefficient D.

The ellipsometry angle D is converted in excess surface concentration using the values obtained for a monolayer: D = 10° 45 corresponding to G = 2 mg/m 2 46 . The order of magnitude of the thickness can be estimated from neutron reflectivity measurements in presence of an advective flow (Fig. 2): hexp-neutron = 14 nm after several hours while the diffusion coefficient of lysozyme in water is around Dfree = 10 -10 m 2 .s -1 [START_REF] Xu | The Role of Chemical Potential in the Adsorption of Lysozyme at the Air-Water Interface[END_REF] . Fig. 8 shows the experimental ellipsometric angle D together with the value predicted by the model with the parameters (hexp-neutron, Dfree) as stated above. Clearly, in this case, the model does not predict multilayer formation. Additional couples of the parameters (D,h) are therefore tested: either we put h =14 nm and let Dadjust as adjustable parameter or alternatively we choose Dfree = 10 -10 m 2 .s -1 and we let hadjust as adjustable parameters. The results show that none of these conditions are satisfactory: if h is equal to the thickness estimated by neutron reflectivity, the adjusted diffusion coefficient is very low and, more problematically, the model does not describe the curvature of the experimental kinetics. On the contrary, if D is fixed to the free diffusion coefficient Dfree = 10 -10 m 2 .s -1 , the curvature of the experimental kinetics is correctly described, but the thickness used to estimate the surface concentration excess (7.1 10 -6 m) has to be more than two orders of magnitude higher that the experi- We conclude that the advection/diffusion model, that is based on the basic competition between advection towards the interface (due to the evaporation flow) and diffusion towards the bulk cannot describe correctly the experimental kinetics. In other words, the model tells us that, in the absence of any other effect, diffusion should be able to counterbalance by orders of magnitude the transport toward the interface due to evaporation, thus and preventing the formation of multilayers.

A possible limitation of our model is the hypothesis of a concentration-independent diffusion coefficient, whereas it is known that collective dynamics may arise between colloids at high concentration due to direct interactions between the objects [START_REF] Bowen | Gradient Diffusion Coefficients-Theory and Experiment[END_REF][START_REF] Bacchin | A Unifying Model for Concentration Polarization, Gel-Layer Formation and Particle Deposition in Cross-Flow Membrane Filtration of Colloidal Suspensions[END_REF] , thus resulting in a change in the diffusion coefficient. We therefore, we test a model with a diffusion coefficient D(F) that depends on concentration in the volume fraction range [0.1 -0.5]. D(F) is calculated from osmotic stress measurements performed in a previous study [START_REF] Pasquier | Osmotic Pressures of Lysozyme Solutions from Gaslike to Crystal States[END_REF] on lysozyme solutions, following the formalism detailed in Bacchin (2002) [START_REF] Bacchin | A Unifying Model for Concentration Polarization, Gel-Layer Formation and Particle Deposition in Cross-Flow Membrane Filtration of Colloidal Suspensions[END_REF] for colloidal particles. The equation is numerically solved using Mathematica toolbox. Using the thickness hexp-neutron = 14 nm, the graph C(t) versus time is flat, similar to the red curve on figure 8 (data not shown). In other words, the advection-diffusion model, even with a concentration-dependent coefficient D(F) estimated from osmotic stress data, cannot describes either the formation of a protein multilayer.

In our case, the mean volume fraction estimated by neutron reflectivity in the sublayer region is around F = 0.15 and corresponds, in the experimental pressure-volume fraction diagram, to the concentration regime where the very first signs of attractive interactions are observed in bulk.

However, in this latter work, it does not produce aggregation nor bulk instability, while aggregation seems to occur near the interfacial layer upon evaporation in the present case, leading to multilayers. Such a distinction between bulk instability and surface-induced instability could be reminiscent of the observations of Linse and Wennerström [START_REF] Linse | Adsorption versus Aggregation. Particles and Surface of the Same Material[END_REF] , who have shown that attractive interactions could result in multilayer adsorption even if they are not strong enough to induce bulk aggregation.

We propose that the net charge of ovalbumin and of lysozyme, which should a priori induce electrostatic repulsion and is thus unfavourable to a local increase of protein concentration, yet allows attractive protein-protein interactions when it is positively charged (+ 28 e for ovalbumin and +8 e for lysozyme), as revealed at the interface upon advection and in accordance with the osmotic pressure measurements we already reported [START_REF] Pasquier | Osmotic Pressures of Lysozyme Solutions from Gaslike to Crystal States[END_REF] .

If however ovalbumin is negatively charged, the presence of an advection flow does not induce multilayers but, on the contrary monolayers (Fig. 7) as shown by the typical value of the ellipsometric angle, typical of monolayer values (close to 10°). Such an asymmetry cannot be tested for lysozyme which is positively charged at all experimental pH (its pI being about 10.7). However, this trend has been evidenced on ovotransferrin which forms multilayers when positively charged [START_REF] Floch-Fouéré | Moderate Conformational Impact of Citrate on Ovotransferrin Considerably Increases Its Capacity to Self-Assemble at the Interface[END_REF] and monolayer when negatively charged [START_REF] Floch-Fouéré | Unexpected Differences in the Behavior of Ovotransferrin at the Air-Water Interface at PH 6.5 and 8[END_REF] .

All these results and observation together suggest that protein-protein interaction is repulsive (or at least not attractive) for negatively charged ovalbumin and prevents the formation of multilayers after the formation of the first interfacial layer, despite the advection flow which brings proteins towards the interface.

Note that multilayer adsorption involving proteins has been thoroughly described, e.g. in the case of cooperative adsorption of multiple components, under conditions of mutual attractive interactions [START_REF] Holmberg | Competitive Protein Adsorption Multilayer Adsorption and Surface Induced Protein Aggregation[END_REF] .

It forms the basis of layer-by-layer biopolymer deposition onto solid surfaces [START_REF] Vander Straeten | Protein-Based Polyelectrolyte Multilayers[END_REF] . Mixed biopolymers are commonly used to stabilize food dispersed systems [START_REF] Dickinson | Mixed Biopolymers at Interfaces: Competitive Adsorption and Multilayer Structures[END_REF] . We also have described cooperative adsorption in a binary system of globular proteins [START_REF] Floch-Fouéré | Synergy between Ovalbumin and Lysozyme Leads to Non-Additive Interfacial and Foaming Properties of Mixtures[END_REF][START_REF] Floch-Fouéré | Sequential Adsorption of Egg-White Proteins at the Air-Water Interface Suggests a Stratified Organization of the Interfacial Film[END_REF] .

Far from these conditions, for single-protein systems, multilayer adsorption at the air-water interface has essentially been observed under conditions of minimal repulsions at the isoelectric point pH [START_REF] Engelhardt | Protein Adsorption at the Electrified Air-Water Interface: Implications on Foam Stability[END_REF] or at high ionic strength [START_REF] Georganopoulou | Adsorption of Glucose Oxidase at Organic-Aqueous and Air-Aqueous Interfaces[END_REF] in the presence of protein aggregates in the bulk solution [START_REF] Rullier | β-Lactoglobulin Aggregates in Foam Films: Correlation between Foam Films and Foaming Properties[END_REF] or in the presence of denaturant [START_REF] Perriman | Effect of the Air-Water Interface on the Structure of Lysozyme in the Presence of Guanidinium Chloride[END_REF] .

Far from the isoelectric point pH, multilayers formed by single-protein solutions were only mentioned for positively charged lysozyme at pH 7.0 [START_REF] Graham | Proteins at Liquid Interfaces: II. Adsorption Isotherms[END_REF][START_REF] Yano | Kinetics of Protein Unfolding at Interfaces[END_REF] , for positively charged ovotransferin [START_REF] Floch-Fouéré | Moderate Conformational Impact of Citrate on Ovotransferrin Considerably Increases Its Capacity to Self-Assemble at the Interface[END_REF] and for negatively charged beta and kappa casein [START_REF] Benjamins | Dynamic and Static Properties of Proteins Adsorbed at the Air/Water Interface[END_REF] while the propensity of ovalbumin to form multilayers when carrying a net positive charge, shown in this report, has never been mentioned before to our knowledge.

Hence, for globular proteins, when the specific conditions mentionned above are not met, monolayer adsorption at the air-water interface is commonly encountered [START_REF] Theodoratou | Equilibrium Protein Adsorption on Nanometric Vegetable Oil Hybrid Film/Water Interface Using Neutron Reflectometry[END_REF][START_REF] Hähl | Dynamic Assembly of Class II Hydrophobins from T. Reesei at the Air-Water Interface[END_REF][START_REF] Delahaije | Quantitative Description of the Parameters Affecting the Adsorption Behaviour of Globular Proteins[END_REF] .

The fact that the main result of the present work -advection flow leads to the formation of multilayers protein films at the air-water interface for positive proteins only -is essentially new in the field can possibly be explained by a few reasons. First, the adsorbed amount of proteins must be monitored on a surface exposed to the ambient atmosphere for at least several hours for being able to detect multilayers formation, which is not usual. Second, a positive net charge is not frequently found in the domain of protein adsorption kinetic measurements at the air-buffer interface. Apart from the basic lysozyme, most of the studied proteins studied in food science are acidic proteins (ovalbumin, ovotransferrin, beta-casein, beta-lactoglobulin, to cite a few) and are consequently negatively charged at a pH close to neutrality. These proteins would be positively charged at acidic pH (around 4.0). However, first, adsorption measurements are scarce in these conditions and the conditions mentioned above (free surface and several hours of kinetics) are never simultaneously fulfilled.

The asymmetric interfacial behaviour of positively and negatively charged proteins raises interesting questions, which would need a specific experimental approach, that is clearly beyond the scope of the present work. However, we may hypothesize that a part of the answer lies in the asymmetric strength of interaction of hydrated cations and anions with the side-chains of amino-acids and backbone of polypeptides [START_REF] Lund | Specific Ion Binding to Macromolecules: Effects of Hydrophobicity and Ion Pairing[END_REF] . This ion-specific effect is described by Okur for instance [START_REF] Okur | Beyond the Hofmeister Series: Ion-Specific Effects on Proteins and Their Biological Functions[END_REF] : ions are ordered by their ability to salt out proteins (the Hofmeister series [START_REF] Jungwirth | Specific Ion Effects at the Air/Water Interface[END_REF][START_REF] Jungwirth | Ions at Aqueous Interfaces: From Water Surface to Hydrated Proteins[END_REF][68] ) due to local interaction of ions with their surface, cations and anions being inversely ordered. Hence, the attractive interaction between proteins, leading to multilayers, would be non-symmetrically modulated by the ions present in the buffer. Following this idea and taking into account the phenomenon of charge regulation [START_REF] Lund | On the Charge Regulation of Proteins[END_REF][START_REF] Lund | Charge Regulation in Biomolecular Solution[END_REF] would certainly allow to go further.

CONCLUSION

The presence of an advection flow, together with a positive electric charge of the protein, are necessary conditions to observe multilayers formation with lysozyme or ovalbumin solutions. The presence of multilayers may be explained by the presence of attractive protein-protein interactions in these conditions, as it is also found in the bulk through the equation of state of lysozyme established by Pasquier in comparable ionic conditions [START_REF] Pasquier | Osmotic Pressures of Lysozyme Solutions from Gaslike to Crystal States[END_REF] . So the positive charge of ovalbumin and of lysozyme, which is a priori unfavourable to an increase in local concentration, yet seems to induce attractive protein-protein interactions in particular situations. An important difference between the bulk and the interface is that those attractive interactions lead to bulk lysozyme crystallization in the first case, while we have no evidence of crystallization of lysozyme during multilayers formation at the interface, although we cannot definitively rule it out.

For negatively charged ovalbumin, the formation of multilayers after the formation of the first interfacial layer is not observed, even in the presence of an advection flow and we have the classical monolayer formation reported in the literature. So in this case, and even with advection, proteinprotein interactions stay repulsive in these conditions -which is the a-priori situation.

These results suggest that interfacial multilayers induced by advection flow strongly depends on the sign of the protein charge. This hypothesis should now be checked with a wider range of proteins in various conditions of charge, both in terms of sign and absolute value.

Supporting Information

Neutron reflectivity measurements, Normalized reflectivity.

Figure

  Figure1ashows R/RF, measured by neutron reflectivity, for adsorption of lysozyme at pD 7, (ie net

Figure 1 .

 1 Figure 1. Kinetics of adsorption of lysozyme from D2O at pD 7 (net charge +8) and I=20 mM measured by neutron reflectivity in airtight trough (without advective flow). (a) Normalized reflectivity after 2h (black squares), 4h (blue triangles), 10h (red circles); the solid lines are best-fit curves with the corresponding concentration profiles shown in (b) (same color code).

  0.01 0.02 0.03 0.04 0.05 0.06 0

  adsorbed layer, at the initial stage of formation (after 1 h), is best described by a two-slice model, a first slice of intermediate volume fraction 𝜙 N ~0.35 and thickness 𝑑 N ~20 Å, and a second dilute slice of volume fraction 𝜙 D ~0.05 and thickness 𝑑 D ~50 Å. With increase in adsorption time, 𝜙 N increases up to a value 𝜙 N ~0.4 after 7 h (the corresponding thickness remains almost constant around 𝑑 N ~20 Å)

Figure 2 .

 2 Figure 2. (a) Adsorption density versus time of lysozyme at pD 7 (net charge +8) and I = 20 mM without advective flow (blue squares) and with advective flow (red squares) measured by neutron reflectivity. (b) Ellipsometry measurements: ellipsometric angle Δ without advective flow (red lines) and with advective flow (blue line); the colored filled area shows the spread from three replicates.

Fig. 2 .

 2 Fig. 2.b shows plot of the ellipsometric angle Δ as a function of the adsorption time, for lysozyme at

Figure. 3

 3 Figure. 3 shows the effect of NaCl on the adsorption of lysozyme at pD 7, (net charge +8), I=170 mM,

Figure 3 .

 3 Figure 3. Effect of NaCl on adsorption of lysozyme measured by neutron reflectivity in airtight trough (without advective flow) at pD 7 (net charge +8). (a) Concentration profiles after 10h at I = 20 mM (red line) and I = 170 mM (green line); the inset shows the corresponding effect of NaCl on adsorption at shorter time (after 2 h), same color code. (b) Adsorption density versus time at I = 20 mM (open rectangles) and I = 170 mM (closed rectangles).

Figure 4 . 6 (

 46 Figure 4. Effect of NaCl on adsorption of ovalbumin measured by neutron reflectivity (without advective flow) at pD 3.6 (net charge +28). (a) Concentration profiles after 10h at I = 20 mM (black line) and 170 mM (green line). (b) Adsorption density versus time at I = 20 mM (open circles) and I = 170 mM (closed circles).

  Corresponding author sylvie.beaufils@univ-rennes1.fr

Figure 5

 5 Figure 5 Ellipsometric angle Δ of ovalbumin at pH 3.6, I = 20 mM without advective flow (light blue line), the repetability shown by the colored filled area and with advective flow (dark blue line) where the colore filled area shows the spread of three replicates.

Figure 6 .

 6 Figure 6. Adsorption of ovalbumin measured by neutron reflectivity (without advective flow) at pD 7 (net charge -10). (a) Concentration profiles at I = 20 mM after 2h (black line), 4h (blue line), 10h (red line); the inset compares concentration profiles after 10h for I = 20 mM (red line) and 170 mM (green line). (b) Adsorption density versus time at I = 20 mM (open circles) and I = 170 mM (closed circles).

Figure 7

 7 Figure 7 Ellipsometric measurements in free surface trough (i.e. with advection flow): ellipsometric angle Δ of ovalbumin at pH 7.0, I = 20 mM. Two replicates are drawn together.

  mental one. This trend indicates that the model, with constant diffusion coefficient, cannot describe at the same time spatial and temporal gradients. Additional examples are shown in Supp. Mat. Fig. SI-6.

Figure 8

 8 Figure 8 Fit of the advection/diffusion model to the experimental adsorption kinetics of lysozyme measured by ellipsometry, pH 7.0 (20 mM), blue curve, (a) D fixed to the free diffusion coefficient Dfree = 10 -10 m 2 .s -1 , thickness fixed to the value measured by neutron reflectivity hneutron = 14 nm (red curve) (b) D adjusted by the model , thickness fixed to the value measured by neutron reflectivity hneutron = 14 nm (orange curve), (c) D fixed to the free diffusion coefficient Dfree = 10 -10 m 2 .s -1 , thickness h adjusted by the model (green curve)

Figure SI- 1

 1 Figure SI-1 showing the Kinetics of adsorption of lysozyme from D2O at pD 7 (net charge +8) and I=20 mM measured by neutron reflectivity in open trough (with advective flow).

Figure SI- 2

 2 Figure SI-2 showing the Effect of NaCl on adsorption of lysozyme measured by neutron reflectivity in airtight trough (without advective flow) at pD 7 (net charge +8) after 10h.

Figure SI- 3

 3 Figure SI-3 showing the Effect of NaCl on adsorption of ovalbumin measured by neutron reflectivity (without advective flow) at pD 3.6 (net charge +28) after 10h.

Figure SI- 4

 4 Figure SI-4 showing the Kinetics of adsorption of ovalbumin measured by neutron reflectivity (without advective flow) at pD 7 (net charge +28) and I = 20 mM.

Figure SI- 5

 5 Figure SI-5 showing Effect of NaCl on adsorption of ovalbumin measured by neutron reflectivity (without advective flow) at pD 7 (net charge -10) after 10h.

  ± 0.13 0.85 ± 0.13

Table T

 T

-1 summarizes protein charge values, in supplementary materials.

Resolution of the advection-diffusion model

Details on resolution the advection-diffusion model.


C Toulouse

J Fischer

S Farokhipoor

L Yedra

F Carlà

A Jarnac

E Elkaim

P Fertey

J.-N Audinot

T Wirtz

B Noheda

V Garcia

S Fusil

I Peral

M Guennou

J Kreisel

Patterning enhanced tetragonality in BiFeO 3 thin films with effective negative pressure by helium implantation

Helium implantation in epitaxial thin films is a way to control the out-of-plane deformation independently from the in-plane strain controlled by epitaxy. In particular, implantation by means of a helium microscope allows for local implantation and patterning possibilities down to the nanometer resolution, which are of interest for device applications. We present here a study of bismuth ferrite (BiFeO3) films where strain was patterned locally by helium implantation. Our combined Raman, XRD and TEM study shows that the implantation causes an elongation of the BiFeO3 unit cell and ultimately a transition towards the so-called super-tetragonal polymorph via states with mixed phases. In addition, TEM reveals the onset of amorphization at a threshold dose that however does not seem to impede the overall increase in tetragonality. The phase transition from the R-like to T-like BiFeO3 appears as first-order in character, with regions of phase coexistence and abrupt changes in lattice parameters.

I. INTRODUCTION

Strain engineering has arisen in the last decade as an essential means to tune physical properties in functional thin films. The most common way to tune strain in films is by using epitaxial strain, imposing an in-plane biaxial strain to the material due to the lattice misfit with the substrate on which the film is grown. The strain state can be varied by using different substrates, or even in some instances, can be tuned continuously, for example by an electric field applied on a piezoelectric substrate [START_REF] Bilani-Zeneli | [END_REF][2][3] . Using this approach, it has been demonstrated that the properties of the films can be controlled and modified, sometimes spectacularly. Remarkable results have included induced ferroelectricity [4][5][6][7] , a modified magnetic ground state of multiferroic compounds [8][9][10] or strain-induced structural transitions [11][12][13][14] . In this classical approach of strain engineering, only the in-plane biaxial strain is controlled; the out-of-plane strain is fixed by the elastic equilibrium of the system, but cannot be controlled independently.

Controlling this additional strain parameter, and in particular achieving an elongation of the unit cell ("negative pressure"), is of high interest. Negative pressure has, indeed, been theoretically predicted to trigger various properties modifications [15][16][17][18] . Experimentally, it can be achieved by helium implantation. Due to its nobility, helium implants interstitially, without chemical substitution, thus inducing a 'swelling' of the host material's unit cell volume 19 . Helium implantation is customarily achieved by lab ion sources 7,[20][21][22][23] similar to the ones used for wafer processing in semiconductor engineering. Another route -the one chosen in the present work -is to use a helium ion microscope as a way to implant ions locally. This technique has recently started to be used as a means of defect engineering 24,25 , but our study is aiming at using a helium microscope for strain-engineering purposes. The interest of this new method lies in particular in the nano-patterning possibilities allowed by the sub-nanometer resolution of the microscope [START_REF] Zeiss | Microscopy resolution record claimed by Carl Zeiss[END_REF] . Moreover, it has been demonstrated recently that helium implantation is a reversible process and that the helium trapped can be released with annealing at high temperatures above 650 °C and under oxygen atmosphere 20 , allowing for reversible properties tuning. For instance, a very recent study on FeRh thin films shows that local helium implantation allows for direct writing of nanoscale domains with a metamagnetic order tunable with the implanted dose, demonstrating the application potential of this technique [START_REF] Cress | ACS Applied Materials & Interfaces[END_REF] .

Here, we demonstrate the use of a helium ion microscope to perform strain engineering by helium implantation on bismuth ferrite (BiFeO 3 ) thin films. BiFeO 3 is one of the most studied multiferroic compounds as it exhibits multiferroicity well above room temperature. In its bulk form it develops below T C = 1143 K a very large ferroelectric polarization [START_REF] Lebeugle | [END_REF] (P = 100 µC cm -2 ) along the [111] direction of its pseudo-cubic structure and exhibits below T N = 643 K a G-type antiferromagnetic ordering of the iron spins with a superimposed long range cycloidal modulation in a plane containing the ferroelectric local mode vector 29 . In its thin film form, BiFeO 3 undergoes a structural transition under epitaxial strain. At low strain, it crystallizes in a so-called R-phase in the monoclinic M A phase, slightly distorted from the bulk rhombohedral structure in the R3c space group. At high strain or under certain growth conditions, BiFeO 3 can exhibit a structural phase with enhanced tetragonality (with a c/a ratio between 1.22 and 1.25) in the monoclinic M C space group, called the super-tetragonal or T-phase in which an enhanced ferroelectric polarization has been observed and theoretically reproduced 30 . Many studies report the existence of intermediate mixed R-T phases in BiFeO 3 films, with a 3 • tilt of the monoclinic angle between the phases 31 . Epitaxial strain has been shown to modify the ferroic properties of BiFeO 3 films: the ferroelectric Curie transition temperature is decreased under epitaxial strain 32 while the bulk-like magnetic cycloid present at low strain is destroyed at high epitaxial strain, both tensile and compressive, leaving place to a canted antiferromagnetic state 9,10 .

Relying on the interplay between epitaxial strain and helium implantation, a full tridimensional control of strain in thin films can be achieved. The lattice misfit between the substrate and the film's native bulk compound causes a biaxial strain in the plane of epitaxy (Fig 1 .a and 1.b). Due to the in-plane clamping of the film to its substrate, helium implantation gives rise to an out-ofplane negative strain, without modification in-plane (Fig 1 .c). In the case of BiFeO 3 thin films, helium implantation allows to trigger the transition towards the supertetragonal phase, by enhancing tetragonality due to this out-of-plane strain tuning. It has been shown recently that large scale helium implantation on epitaxial BiFeO 3 films can induce the super-tetragonal phase on LSAT substrate, while enhancing tetragonality in R-like and Tlike films grown on SrTiO 3 and LaAlO 3 respectively 23 . This raises important questions regarding the the transition from the R-like to T-like structure, here caused by continuously varying the helium dose: character of the transition, possibility of coexistence between the two phases, presence of interfaces, etc. Here, by combining local and non-local probes, we bring insight on the mechanism of this R to T structural transition under helium implantation, that appears first order in character. In addition, we show that local helium implantation allows to pattern the tetragonality of the structure while preserving crystal quality, demonstrating for the first time the possibility to structurally pattern BiFeO 3 films.

II. EXPERIMENTAL DETAILS

BiFeO 3 epitaxial films were grown by pulsed laser deposition on (001) oriented SrTiO 3 (-1.5 % lattice misfit with BiFeO 3 ) and DyScO 3 (-0.4 % lattice misfit) substrates with a 5 nm thick SrRuO 3 bottom electrode as described in refs [33-35]. The thickness of the film grown on DyScO 3 was set to 60 nm in order to ensure that they remain fully strained. For the 60 nm thick film grown on SrTiO 3 , the formation of in-plane ferroelastic 71 • domains induce partial strain relaxation already at 60 nm thickness, but their alternation allows for overall epitaxial matching with the substrate 36 .

Helium implantation of our films was performed using an Orion NanoFab helium ion microscope (HIM) 37 . Various doses of 6 keV helium ions were implanted into square regions with sizes ranging from 10 × 10 µm 2 to 500 × 500 µm 2 (Fig. 1.f). We kept the doses below 1×10 16 ions cm -2 , which, at the energy used, is below the threshold for structural defect formation [38][39][40] . The implantation parameters, in particular the beam energy and the impact angle, were determined by SRIM 41 (Stopping Range of Ions in Matter) and TRIM (TRansport of Ions in Matter) simulations in order to have the maximum of the implantation profile inside the film (Fig. 1.d,e). The samples were therefore tilted 49 • from the normal to reduce helium implantation of the bottom electrode and the substrate while also avoiding channeling through the crystal structure's easy planes. The TRIM simulations of the implanted ion distribution and depth profile -taking density values of 8.408 g cm -3 for BiFeO 3 , 6.49 g cm -3 for SrRuO 3 and of 5.11 g cm -3 for SrTiO 3 as taken from the literature [START_REF] Schneeloch | [END_REF]43 -are shown on Fig. 1.d and 1.e.

To probe our implanted samples, we used Raman spectroscopy, electron microscopy and X-ray diffraction (XRD) techniques. Micro-Raman measurements were performed with a 442 nm He-Cd laser in an inVia Renishaw micro-Raman spectrometer. Depth profiles were acquired by varying the focus, meaning the distance between the objective and the sample, with 0.2 µm steps. Principle Components Analysis (PCA) and Non-negative Matrix Factorization (NMF), using the R-DATA software as described in Ref. [44], allow to extract the layer's signal from the overall substrate's contribution.

Transmission Electron Microscopy (TEM) studies of cross-sectional samples were performed in a probe corrected FEI Titan 3 G2 60-300, working at 300 kV in scanning mode (STEM) using a High Angle Annular Dark-Field detector (HAADF). The microscope is equipped with a Brucker Super-X Energy-Dispersive X-ray spectroscope (EDX), used for obtaining elemental maps. Geometrical Phase Analysis (GPA) 45 using Strain++ software, was applied on atomically resolved HAADF images in order to measure local deformations of the lattice.

The XRD synchrotron data were collected at two different synchrotron sources. Diffracted intensity maps were recorded at the ID03 Surface Diffraction beamline of the ESRF using the 6-circle vertical diffractometer. The experiment was conducted using an incident wavelenght of 0.516 Å (24 keV) and a beamsize of 43 × 28 µm 2 (horizontal x vertical). For the grazing incidence experiments, an incidence angle of 3 degrees was used and allowed to produce a beam footprint on the sample surface with a size comparable to the area of the implanted region. The implanted region was aligned in the beam using a camera with a macro lense and the visible fluorescence of the sample under the x-ray beam irradiation. The data were collected using a Maxipix pixel detector and processed using the BINoculars code. At the CRISTAL Beamline of SOLEIL Synchrotron, we performed localized XRD measurements on a 6-circle diffractometer, using a beam size of 30 × 100 µm 2 ), with an imXpad pixel detector and a wavelength of 1.2471 A. All the diffraction data are reported using the substrate lattices as reference systems.

III. RESULTS AND DISCUSSION

A. Raman spectroscopy Raman spectroscopy measurements have been performed on our implanted samples to study the effect of implantation on the lattice via the phonon modes. Thin films make it naturally increasingly difficult to single out the signal of the film from the substrate contribution. However, due to the broad peaks of Raman signal of SrTiO 3 , some sharper Raman modes from the BiFeO 3 layer were possible to observe in our BiFeO 3 //SrTiO 3 sample. Raman spectra measured on regions with different doses are shown in Fig. 2.a. Two low energy phonon modes can be seen emerging from the substrate's signal at 146 and 184 cm -1 . These phonon modes correspond to Raman excitations with A 1 (LO) symmetry, usually measured around 145-147 and 176-180 cm -1 respectively 46,47 .

Furthermore, we performed Raman depth profiles by continuously varying the distance between the sample and the Raman objective, following the approach described in Ref. [44]. Fig. 2.b and Fig. 2.c, present the Principal Component Analysis (PCA) of the Raman signal obtained on the non-implanted part of the film. Fig. 2.b shows the signal associated to the first two components while Fig. 2.c shows their intensity profile as a function of the depth. The first component of the PCA visibly corresponds to the SrTiO 3 signal: it has the same shape than the well-known SrTiO 3 2 nd -order Raman signal (Fig. 2.b, top) while its intensity continuously increases when the distance between the sample and the objective decreases (Fig 2.c, top). This is in agreement with the signal coming from the substrate, further away from the objective. The second component of the PCA presents a signal where 3 narrow peaks can be observed at 146, 184 and 226 cm -1 (Fig. 2.b, bottom). These peaks corresponds to the two BiFeO 3 Raman modes observed in the spectra of Fig. 2.a, with an additional peak at 226 cm -1 also associated to an A 1 (LO) Raman mode of BiFeO 3 in the literature 46,47 . The intensity depth profile of this second component presents a maximum in the depth range corresponding to the film (Fig. 2.c, bottom) which confirms that we can indeed attribute it to the Raman signal of the BiFeO 3 film.

By comparing the evolution of the Raman signal with the implanted helium dose, we observe that the Raman signal of the BiFeO 3 film disappears with increasing dose while not shifting in frequency. Indeed, the two phonon modes are visible only for the virgin film and the lowest dose (5×10 14 He cm -2 , Fig. 2.a). The Raman spectrum of BiFeO 3 could not be seen for the films deposited on DyScO 3 substrate, due to a stronger substrate contribution.

Several causes can be envisioned to explain the disappearance of the Raman signal. In the context of BiFeO 3 in particular, the Raman signal of the super-tetragonal phase is weaker by one order of magnitude than the signal for the rhombohedral-like structure 48 . The disappearance of the Raman signal under implantation can therefore be a signature of a transition towards an increased tetragonality, as we would expect (cf. Fig. 1.c and Ref. [23]). Furthermore, a vanishing Raman spectrum can be associated to a transition towards a metallic character, which in BiFeO 3 is known to happen at very high temperatures and pressure. In this particular context, it is also conceivable that an increase in band gap -i.e. a decrease in absorption -would lead to a decrease in intensity of the Raman spectrum as compared to the substrate. Finally, we cannot exclude an effect directly due to the presence of He in the BiFeO 3 lattice, decreasing the Raman intensity.

B. Transmission Electron Microscopy

To gain more insight on the effect of implantation at the local scale, Transmission Electron Microscopy was performed on prepared samples from a BiFeO 3 layer grown on a SrTiO 3 (001) substrate, with doses 5×10 15 and 1×10 16 He cm -2 .

The High-Angle Annular Dark Field (HAADF) STEM images of the BiFeO 3 /SrTiO 3 interfaces, in the two implanted regions are shown on Fig. 3.a and 3.b. No amorphization of the BiFeO 3 layer is visible under implantation for the region with 5×10 15 He cm -2 dose : the epitaxial columns are clearly visible throughout the film although some structural defects are present (as expected under implantation). When the implanted dose is increased to a higher level, however, some regions of amorphization are observed (Fig. 3.b). Their characteristic size is of the order of the nanometer, and is reminiscent of the observation of defect "nano-bubbles" previously reported upon He implantation on silicon 38 .

To gain insight on the strain induced locally by helium implantation, Geometric Phase Analysis (GPA) has been performed on samples prepared with 5×10 15 and 1×10 16 He cm -2 doses, taking as a reference the SrTiO 3 lattice to extract local deformations. We see in Fig. 3.c and 3.e the in-plane strain for both doses, while the out-of-plane strain is shown on Fig. 3.d and 3.f. While it is apparent from the GPA strain maps that local deformations in-plane are scarce, we observe stronger out-of-plane deformations, consistent with an out-of-plane swelling induced by implantation. The strain seems to increase with the dose between Fig. 3.d and 3.f, as expected for an enhanced tetragonality.

Furthermore, we extracted the average lattice parameters by performing the Fourier transform of TEM images in the two regions with 5×10 15 and 1×10 16 He cm -2 doses as well as in a pristine -non-implanted-region as a reference. They are given in Table I. Each lattice parameter was estimated from 10 images and the error bars arise from the standard deviation of the measurements. We can clearly see that the in-plane lattice parameter stays unchanged while a c-lattice expansion, increasing with the Helium dose, is observed with implantation. Moreover, we can observe that in the region implanted with the highest dose, the c-axis lattice parameter extracted by Fourier transform has a much broader error bar, consistent with a loss of crystallinity of the film as visible from Fig. 3.b.

Finally, Energy Dispersive X-Ray Spectroscopy (EDX) chemical analysis of the atoms at the interface between the substrate and the film (with a 5 nm thick SrRuO 3 bottom electrode) has been performed and is presented l (r.l.u.) 3.79 ± 0.02 A 3.92 ± 0.03 A BFO pristine 3.82 ± 0.02 A 4.02 ± 0.02 A 1.03 BFO (5×10 15 He cm -2 ) 3.79 ± 0.01 A 4.38 ± 0.05 A 1.12 BFO (1×10 16 He cm -2 ) 3.78 ± 0.04 A 4.57 ± 0.10 A 1.17 TABLE I: Lattice parameters extracted from the STEM measurements. The discrepancy between the usual SrTiO3 cubic lattice parameter of 3.905 A and the extracted ones in the a direction comes from the calibration of the microscope combined with sample drift. We chose to keep the values as extracted from the images, the values in the c-axis being in agreement with literature. The last column shows the c/a ratio, calculated with the a lattice parameter of SrTiO3 from literature: aST O =3.905 A in Fig. 3.g. The chemical compositions of the substrate, the bottom electrode and the layer are well resolved and the compositional interfaces correspond to those of the HAADF image with no indication of chemical intermixing. Furthermore, no migration of the atoms of the layer to the bottom electrode or substrate is observed under implantation.

C. Synchrotron XRD

To determine the effect of helium implantation on the structure of our BiFeO 3 layers, we performed micro-XRD, using specular reflectivity and grazing incidence geometry. Fig. 4.a shows the specular reflectivity curve measured inside an implanted region (with 5×10 15 He cm -2 dose) on a BiFeO 3 film grown on SrTiO 3 substrate. It shows, in addition to the (001) Bragg peaks of the SrTiO 3 substrate and the BiFeO 3 layer, a new phase with a c-lattice expansion, visible with the new peak appearing at l =0.89 r.l.u (Fig. 4.a).

From the in-plane diffracted intensity maps measured at different l values it was possible to verify that all the phases have the same in-plane lattice parameters of the substrate, as observed locally from the TEM results.

A comparison between the hk maps collected at l =0.96 for the implanted and non-implanted regions (Fig. 4.b) shows no difference in the positions of the BiFeO 3 Bragg peaks, indicating no modification of the in-plane lattice parameter as a consequence of the implantation process: as expected, the clamping to the substrate locks the film parameters in the epitaxial plane. Fig. 4.c shows the hl maps around the (001) Bragg peak of the SrTiO 3 substrate outside and inside an implanted region (with 5×10 15 He cm -2 dose). The (001) peak of the substrate and, at lower l, of the BiFeO 3 layer, are clearly visible while a new phase, with a c-lattice expansion of 7.9% (from 4.072 to 4.395 A) is observed in the implanted region, consistent with the values extracted from the TEM images. Fig. 4.d shows a close-up of the (10l ) rod around the (001) region, in which the coexistence of the new structural phase and the pristine BiFeO 3 layer are visible. This can be explained by a mixing of the two structural phases, the pristine R-like phase and the new phase with enhanced tetragonality in the implanted region. Alternatively, the R-type signal could also arise from neighboring non-implanted regions, partly probed due to the X-ray spot size that was slightly larger than the implanted region.

In order to study the conditions of appearance of this new phase under helium implantation, we performed implantations with increasing doses. The θ(2θ) XRD scans, around the (001) Bragg peak of the SrTiO 3 substrate for doses ranging between 5×10 14 and 5×10 15 He cm -2 are shown on Fig. 4.e. We observe the (001) peak of the BiFeO 3 layer progressively shifting towards higher c-axis lattice parameters with dose. Under 2.5×10 15 He cm -2 (region 1 ○, in green Fig. 4.e), the layer's (001) peak shifts continuously. At 2.5×10 15 He cm -2 , however, we observe an abrupt change in the (001) Bragg signal of the layer (region 2 ○, in green Fig. 4.e), with a strong shift of the layer peak, that we interpret as the appearance of the new phase previously observed in Fig. 4.c,d and the onset of the R-like to T-like BiFeO 3 structural transition. In this new phase (at 2.5×10 15 He cm -2 dose and above), we also observe the presence of a peak at the position of the (001) peak of the virgin (non-implanted) BiFeO 3 layer, as observed in Fig. 4.c,d. In this measurement, the spot size was well below the size of the implanted regions and its centering by means of (x,y) scans ruled out the possibility of signal coming from non-implanted BiFeO 3 . The presence of the (001) virgin BiFeO 3 peak therefore indicates a mixing of phases between the highly implanted one and the R-like phase of the unimplanted film.

The lattice parameters were extracted directly from the (001), ( 101) and (011) XRD peaks of the film in the different regions. They are shown, as a function of the implanted helium dose, in Fig. 4.f, the dotted line marking the lattice parameter of the SrTiO 3 cubic substrate.

As observed previously, the in-plane lattice parameters are not modified under implantation.

To investigate the combined effect of epitaxial strain and implantation, we performed implantations with the same helium doses on a film synthesized on a DyScO 3 susbtrate, which has a lattice parameter closer to BiFeO 3 (-0.4 % lattice misfit 35 ). Fig. 4.g shows the θ(2θ) XRD scans, around the (001) Bragg peak of the DyScO 3 substrate for doses ranging between 5×10 14 and 5×10 15 He cm -2 . We see the (001) peak of the BiFeO 3 layer progressively shifting with dose, showing an increase of the out-of-plane lattice parameter. Contrary to the results on the SrTiO 3 substrate, no abrupt modification is observed and the c lattice parameter (reported in Fig. 4.h) is in the same range than in the 1 ○ region of the Fig. 4.f on the SrTiO 3 sample. This indicates a strained Rlike structure with no phase transition. As in the case on SrTiO 3 , we observe no modification of the in-plane a and b lattice parameters, locked by the DyScO 3 lattice parameter (dotted line, Fig. 4.h).

D. Discussion

By combining Raman spectroscopy, electron microscopy and X-ray diffraction, we could access the structural changes due to implantation at different length scales, allowing for a more complete insight into the transition between the rhombohedral and super-tetragonal phases of BiFeO 3 films than previously reported. Specifically, helium implantation is a way to observe the transition with a continuously varying parameter, as opposed to epitaxial strain that typically takes only a few discrete values fixed by the substrates.

Our TEM measurements, in particular, clearly show both the elongation of the unit cell and the partial amorphization. We indeed observe amorphized regions at dose 1×10 16 He cm -2 , while at the same time, the c-axis lattice parameter extracted by Fourier transform from the non-amorphized regions present a ratio with the a-axis lattice parameter which is close to the c/a ratio of the super-tetragonal phase 30 . It therefore seems that despite the structural damage due to the loss of crystallinity of some regions, we continue to enhance the tetragonality of the still crystalline regions of the film, towards the Tphase. It is not possible to know if amorphization was also present in the previous study on He-implantation of BiFeO 3 films using a large scale ion implantor 23 as XRD is only sensitive to the crystalline regions. In our XRD data, where the dose was kept low enough to avoid amorphization, the elongation of the unit cell does not reach the c/a typical of the super-tetragonal phase. Whether or not it is possible to fully transform into the supertetragonal phase on SrTiO 3 while remaining fully crystalline, is still to be investigated.

The picture provided by our TEM and XRD data shows significant differences when compared to the same phase transition reported in Ref. 23 on (LaAlO 3 ) 0.3 (Sr 2 TaAlO 6 ) 0.7 (LSAT) and SrTiO 3 . We observe the transition towards a mixed phase with an enhanced tetragonality both at lower epitaxial strain and at lower doses: Herklotz et al. 23 observe a structural transition towards the T phase on LSAT, with a -2.6% lattice misfit and a 6×10 15 He cm -2 dose, whereas we already see a similar behaviour with enhanced tetragonality on SrTiO 3 where the lattice misfit is only -1.5% at a 2.5×10 15 He cm -2 dose. These discrepancies are not negligible, and their origin is for the moment unclear. They could be due to an inaccurate estimation of the implanted dose or to a different local behaviour, resulting in a strain gradient, that may be due to the difference in implantation technique. In particular, the presence of interfaces between implanted and non-implanted regions, yielded by the patterning possibilities of our implantation technique, can impact the strain relaxation mechanisms and account for a higher applied strain with respect to the dose than it is the case with large scale implantation techniques. Moreover, the thickness and possible domain structure differences can give rise to different stress field landscapes, that may account for the differences in our study. Furthermore, the energy of the accelerated He ions with the He-FIB we use is higher than with a large scale ion implanter as used in Ref. [23]. Special attention should therefore be paid to these aspects in future studies.

A noticeable difference also lies in the way the transition proceeds with increasing dose. In Ref. [23], the transition is described as appearing continuously under implantation with a progressive shift of the Bragg peak (cf. Fig. 1.b of the Ref. [23] for the film grown on LSAT). They further support the scenario of a continuously rotating polarization based on PFM and SHG observations. In our measurements, in contrast, the emergence of the T-like phase appear the be step-like with a visible phase coexistence, reminiscent of a first-order transition. We believe this is not incompatible with their raw XRD data, where a splitting of the Bragg peak may be seen at intermediate doses. We hypothesize that the continuous character observed in PFM and SHG could result from an averaging effect that does not reflect the details of the local picture.

Finally, the comparison between Raman and XRD data sheds light on the disappearance of the Raman spectrum. We can see that the Raman signal disappears at a dose (1×10 15 He cm -1 ) where the BFO is still clearly in a slightly elongated R phase. Indeed, the θ(2θ) XRD scan (Fig. 4.e) shows a still narrow 001 Bragg peak, shifted from the pristine BiFeO 3 , but still showing no sign of transition from the rhombohedral-like structure. Therefore, the vanishing of the Raman signal cannot be attributed to the lower Raman intensity known for the T phase, and cannot be understood as a signature of the transition towards the tetragonal-like structure. Instead, we suggest that it reflects a decrease of Raman susceptibility and polarizability due to the insertion of helium ions. This might be significant also for the dielec-tric properties of the implanted films.

IV. CONCLUSION

Helium implantation has arisen recently as a powerful technique with the potential to modify and tune the strain state in a perovskite film. We have shown here, in particular, that local helium implantation by means of a helium ion microscope can enhance tetragonality in (001)-oriented BiFeO 3 thin films, increasing the outof-plane lattice parameter up to 4% in films grown on DyScO 3 and up to 9% in films grown on SrTiO 3 , inducing locally a structural phase transition towards a mixed R-T phase.

Combined Raman spectroscopy, electron microscopy and X-Ray diffraction measurements allowed us to probe the structural changes both at the large scale and locally. Our local (TEM) study allowed us to determine the threshold dose for which amorphization starts to appear in implanted regions, while observing elongations of the unit cell along the c-axis up to the values nearing the super-tetragonal lattice distortion. Synchrotron XRD performed in the locally implanted regions allowed us to probe the onset of the transition between the rhombohedral-like structure and the super-tetragonal phase. Our data suggest that this transition appears as a first-order transition, with an abrupt jump of the caxis expansion at a threshold dose (2.5×10 15 He cm -1 on SrTiO 3 ), which opens the discussion for understanding the underlying mechanisms at stake in this structural transition under implantation.

More generally, this work demonstrates the use of a helium microscope as a powerful mean for strainengineering by local helium implantation and opens technical possibilities for property tuning and patterning.

FIG. 1 :

 1 FIG. 1: Schematic representations of (a) compressive and (b) tensile epitaxial strain and of (c) the out-of-plane negative pressure induced by helium implantation. TRIM simulations (see "Experimental details" section for details) of (d) the helium ion distribution and (e) the implantation depth profile of 6 keV helium ions inside BiFeO3(70 nm)/SrRuO3(5 nm)//SrTiO3 with an incident angle of 49 • . (f) Secondary electron images (SEM-HIM) of patterned BiFeO3 films with various sizes of implanted regions.

  FIG.2:(a) Raman spectra performed on different regions of the BiFeO3//SrTiO3 film. The underlying intense signal of SrTiO3 is very visible but some BiFeO3 phonon modes can be singled out. The inset shows these phonon modes, with a baseline substraction. The colored regions and dotted lines are guides for the viewer.(b,c) Principal component analysis of the depth profiles on a non-implanted region of the film: we can see the component signal (b) and the associated depth profiles (c) for the first two components.

16 FIG. 3 :

 163 FIG. 3: (a,b) STEM images (HAADF) of BiFeO3/SRO//SrTiO3 samples implanted with doses 5×10 15 (a) and 1×10 16 (b) He cm -2 . (c-f) GPA (Geometrical Phase Analysis) of the strain in the epitaxial plane (c,e) and out of plane (d,f), using the SrTiO3 substrate as a reference, of the samples with dose 5×10 15 (c,d) and 1×10 16 (e,f) He cm -2 .(g) EDX chemical analysis of the interface in the sample implanted with 5×10 15 He cm -2 .

FIG. 4 :

 4 FIG. 4: X-ray diffraction results of non-implanted and implanted (with a 5×10 15 He cm -2 dose) regions of a BiFeO3//SrTiO3 thin film. (a) Specular reflectivity. (b) (h,k ) reciprocal space maps integrated in the -0.05<l <0.05 range. (c) (h,l ) reciprocal space maps measured at k = 0.96 and (d) the corresponding 1-D plot by integrating the intensity of the map contained in the 0.98<h<1.02 range. (e) θ(2θ) scans of regions implanted with various helium doses. (f) Extracted out-of-plane (blue triangles) and in-plane (green circles) lattice parameters (from 001, 101 and 011 Bragg peaks) as a function of the helium dose. The out-of-plane lattice parameters estimated from STEM observations are added as red diamonds. Similar experiments for a BiFeO3//DyScO3 sample with (g) θ(2θ) scans of regions implanted with various helium doses and (h) the extracted out-of-plane (blue triangles) and in-plane (green circles) lattice parameters (from 001, 101 and 011 Bragg peaks) as a function of the helium dose.

Acknowledgments

This work was supported by the Fond National de la Recherche (FNR) of Luxembourg (PEARL CO-FERMAT, Project code FNR/P12/4853155/Kreisel). We acknowledge SOLEIL for provision of synchrotron radiation at CRISTAL beamline (proposal number 20190831). TEM sample preparation and observation was carried out within the MATMECA consortium and supported by the ANR under contract number ANR-10-EQPX-37. It has benefited from the facilities of the Laboratory MSSMat, CNRS, CentraleSupélec, Université Paris-Saclay, France. The author Inma Peral is supported by the National Research Fund of Luxembourg (Grant No FNR-Inter2015/LRSF). Saeedeh Farokhipoor acknowledges financial support from a VENI grant (016.veni.179.053) of the Netherlands Organisation for Scientific Research (NWO).