Mónica Burriel

Helena Téllez

Richard J Chater

Rémi Castaing

Philippe Veber

Mustapha Zaghrioui

Tatsumi Ishihara

John A Kilner

Jean-Marc Bassat

Influence of orientation and annealing on the oxygen diffusion and surface exchange of La 2 NiO 4+δ

La2NiO4+δ is a mixed ionic-electronic conducting material with the 2D K2NiF4-type structure and with a large interest as a potential intermediate temperature solid oxide fuel cell (IT-SOFC) cathode. The oxygen diffusion along the ab plane exhibiting the highest oxygen ionic conductivity governs the behaviour of the bulk materials in this family of oxides. The oxygen surface exchange processes, however, are not well understood and large differences in surface exchange coefficient (k * ) values can be found in the literature for this and other cathode materials. The Isotopic Exchange Depth Profiling (IEDP) technique was used in combination with Low Energy Ion Scattering (LEIS) measurements on two sets of La2NiO4+δ single crystals with precisely cut crystal faces but different thermal history. For each set of single crystals the oxygen diffusion and surface exchange coefficient were evaluated for 2 different orientations in the temperature range of 450-600 ºC. The differences in k * have been correlated with differences in surface chemistry: surface termination, near-surface rearrangement and presence of extrinsic impurities. Finally, the predominant La-termination at the immediate outer surface is evidenced, confirming recent results in other of Ruddlesden-Popper (RP) phases with mixed ionic-electronic conducting properties.

INTRODUCTION

The first members of the Ruddlesden-Popper (RP) series (An+1NinO3n+1 with n=1) with nickel as transition metal element are promising materials for the next generation of intermediate temperature (500 < T (°C) < 700) solid-oxide fuel cell (SOFC) cathodes [START_REF] Tarancón | Advances in Layered Oxide Cathodes for Intermediate Temperature Solid Oxide Fuel Cells[END_REF][START_REF] Boehm | Oxygen Diffusion and Transport Properties in Non-Stoichiometric LnNiO Oxides[END_REF][START_REF] Aguadero | Materials Development for Intermediate-Temperature Solid Oxide Electrochemical Devices[END_REF][START_REF] Orera | New Chemical Systems for Solid Oxide Fuel Cells †[END_REF][START_REF] Jacobson | Materials for Solid Oxide Fuel Cells †[END_REF][START_REF] Kilner | Materials for Intermediate-Temperature Solid-Oxide Fuel Cells[END_REF][START_REF] Sharma | An Innovative Architectural Design to Enhance the Electrochemical Performance of La2NiO4+δ Cathodes for Solid Oxide Fuel Cell Applications[END_REF] . This type of Ln2NiO4+δ nickelates, with Ln = La, Nd or Pr, possess satisfactory electronic conductivity together with good catalytic, electrochemical and thermo-mechanical properties in the temperature range of interest.

Among them, Pr2NiO4+δ has shown the best performance when included in a single SOFC cell [START_REF] Ferchaud | High Performance Praseodymium Nickelate Oxide Cathode for Low Temperature Solid Oxide Fuel Cell[END_REF] .

However, the lanthanum compound (La2NiO4+δ) has been the most extensively studied one of the series, with a large amount of experimental data combined with theoretical models reported in the literature. Its fundamental properties, including physical properties, their correlation to the structural characteristics, the oxygen over-stoichiometry and their dependence with temperature and oxygen partial pressure, have been reported for La2NiO4+δ polycrystalline samples [START_REF] Boehm | Oxygen Diffusion and Transport Properties in Non-Stoichiometric LnNiO Oxides[END_REF][START_REF] Sayers | Low Temperature Diffusion and Oxygen Stoichiometry in Lanthanum Nickelate[END_REF][START_REF] Skinner | Characterisation of La2NiO4+delta Using in-Situ High Temperature Neutron Powder Diffraction[END_REF][START_REF] Nakamura | Crystal Structure and Mechanical Properties of La2NiO4+delta[END_REF][START_REF] Kharton | Chemically Induced Expansion of La2NiO4+δ -Based Materials[END_REF] , for single crystals [START_REF] Bassat | Anisotropic Ionic Transport Properties in La2NiO4+delta Single Crystals[END_REF] as well as for epitaxial thin films [START_REF] Burriel | Anisotropic Oxygen Diffusion Properties in Epitaxial Thin Films of La2NiO4+δ[END_REF][START_REF] Burriel | Enhancing Total Conductivity of La2NiO4+delta Epitaxial Thin Films by Reducing Thickness[END_REF][START_REF] Garcia | Electrical Conductivity and Oxygen Exchange Kinetics of La2NiO4+delta Thin Films Grown by Chemical Vapor Deposition[END_REF] . La2NiO4+δ can therefore now be considered as a reference material for fundamental studies.

In order to be able to design novel optimized compositions with improved MIEC (Mixed Ionic Electronic Conducting) properties for SOFC cathodes, it is of high importance to precisely identify the oxygen diffusion mechanisms in these RP oxides, which involve three types of oxygen in a two dimensional lattice, leading to highly anisotropic diffusion properties (2D). A number of theoretical calculations have tried to explain and model the oxygen diffusion mechanisms in these nickelates [START_REF] Frayret | Application of Density Functional Theory to the Modeling of the Mixed Ionic and Electronic Conductor La2NiO4+delta: Lattice Relaxation, Oxygen Mobility, and Energetics of Frenkel Defects[END_REF][START_REF] Chroneos | Anisotropic Oxygen Diffusion in Tetragonal La2NiO4+δ: Molecular Dynamics Calculations[END_REF][START_REF] Cleave | Atomistic Computer Simulation of Oxygen Ion Conduction Mechanisms in La2NiO4[END_REF][START_REF] Parfitt | Molecular Dynamics Study of Oxygen Diffusion in Pr(2)NiO(4+delta)[END_REF] , formed from alternating NiO2 and (LnO)2 layers along the c-axis direction. The main difference with simple perovskites (state of the art cathode materials), is that in this Ln2NiO4+δ structure if δ>0 the mobile species are usually oxygen interstitials (and not oxygen vacancies), which can accommodate in the (LnO)2 rock-salt layers. Hence no A-site substitution is required to achieve oxygen mobility in this structure. In addition, acquiring a better understanding of the oxygen reduction reaction (ORR) mechanisms occurring at the surface is key [START_REF] Jacobson | Materials for Solid Oxide Fuel Cells †[END_REF][START_REF] Kuklja | Combined Theoretical and Experimental Analysis of Processes Determining Cathode Performance in Solid Oxide Fuel Cells[END_REF] as, at the intermediate temperatures of interest, the ORR is often the limiting process for the cathode performance and its long-term degradation.

For direct experimental measurements of the diffusivity along different directions in this anisotropic structure, single crystals or thin films with very accurate crystallographic orientation must be used. The data available so far are devoted to the measurement of the oxygen diffusion using [START_REF] Chroneos | Anisotropic Oxygen Diffusion in Tetragonal La2NiO4+δ: Molecular Dynamics Calculations[END_REF] O as a tracer (obtaining both the bulk oxygen diffusion D* and the surface exchange coefficient k*) on single crystals oriented along the ab-plane and c-axis directions [START_REF] Bassat | Anisotropic Ionic Transport Properties in La2NiO4+delta Single Crystals[END_REF] , and on high quality epitaxial thin films in the two different directions. [START_REF] Burriel | Anisotropic Oxygen Diffusion Properties in Epitaxial Thin Films of La2NiO4+δ[END_REF] While the Dab* and kab* values for thin films are close to those measured for single crystals for the ab plane, the corresponding values measured along the c-direction are significantly lower (two to three orders of magnitude) [START_REF] Burriel | Anisotropic Oxygen Diffusion Properties in Epitaxial Thin Films of La2NiO4+δ[END_REF] . As the results obtained on both sets of samples did not concern exactly the same temperature range (i.e. roughly above and below 500 °C for the single crystals and thin films, respectively), a possible transition between two different dominating mechanisms at different temperatures could also be anticipated. In addition, recent measurements performed between 450 to 700 °C on high quality Pr2NiO4+δ and Nd2NiO4+δ single crystals [START_REF] Bassat | Anisotropic Oxygen Diffusion Properties in Pr 2 NiO 4+δ and Nd 2 NiO 4+δ Single Crystals[END_REF] confirmed the very large anisotropy between the 2 crystallographic directions (2-3 orders of magnitude). In order to confirm the validity of the previous single crystal data for La2NiO4+δ and compare differences between different sets of samples, additional data for the low temperature range (T < 600 °C) have been performed.

As shown by Ananyev et al [START_REF] Ananyev | Oxygen Isotope Exchange in La 2 NiO 4±δ[END_REF] for La2NiO4+δ a relatively large scatter is observed in the literature both for the oxygen diffusion and surface exchange coefficients, as well as for their activation energies. These values vary for different types of samples (single crystals, thin films or polycrystalline samples), depend on their surface orientation, but also on measuring technique and laboratory of measurement. The source of the discrepancies is not clear, and is generally attributed to different synthesis approaches, surface preparation techniques and differences in microstructure.

However up to now the effect of factors which could be key, such as surface cation rearrangement and surface contaminants, have not been taken into account nor have been systematically evaluated. As for the oxygen reduction reaction (ORR), from the impedance spectra analysis Hildenbrand et al. [START_REF] Hildenbrand | Influence of Configuration and Microstructure on Performance of La2NiO4+δ Intermediate-Temperature Solid Oxide Fuel Cells Cathodes[END_REF] presented a global model based on an oxygen exchange mechanism in which the surface diffusion of charged oxygen species and the charge transfer with oxygen lattice incorporation would be the two major steps. On the other hand, using the oxygen isotope exchange with the gas phase equilibration technique, Ananyev et al. [START_REF] Ananyev | Oxygen Isotope Exchange in La 2 NiO 4±δ[END_REF] concluded that a two-step model is not valid and propose a three step model, in which the dissociative adsorption would be the ratedeterming step. However the k* values they measured are considerably smaller than those reported for other polycrystal samples, with a larger activation energy. Although they reported the presence of silicon as a surface impurity, its possible relationship with the low k* values was not discussed in their work.

On the other hand, recent surface chemistry measurements carried out by Low Energy Ion Scattering (LEIS) on the (110) and (001) faces of cleaved La1.67Sr0.33NiO4+δ single crystals [START_REF] Burriel | Absence of Ni on the Outer Surface of Sr Doped La2NiO4 Single Crystals[END_REF] , on (La,Sr)2CoO4+δ [START_REF] Chen | Segregated Chemistry and Structure on (001) and (100) Surfaces of (La 1-X Sr X ) 2 CoO 4 Override the Crystal Anisotropy in Oxygen Exchange Kinetics[END_REF] and Lan+1NinO3n+1 (n = 1, 2 and 3) [START_REF] Wu | Surface Composition of Layered Ruddlesden-Popper Lan+1NinO3n+1 (n = 1, 2 and 3) Epitaxial Films[END_REF] epitaxial thin films and on La2NiO4+δ 28 and Pr2-xLaxNiO4+δ [START_REF] Druce | Surface Composition of Perovskite-Type Materials Studied by Low Energy Ion Scattering (LEIS)[END_REF] polycrystalline samples have evidenced that after treatments at high temperatures the surfaces of these RP materials are always dominated by the A-site cations (La, Pr or Sr) of these An+1BnO3n+1 structures. This predominant surface structure implies that the transition metals (B-site cations), usually invoked as the active sites for the interaction with the gaseous oxygen species, are hidden below the first atomic surface layer(s) and thus their presence at the outermost surface does not seem to directly control the catalytic activity of these materials [START_REF] Burriel | Absence of Ni on the Outer Surface of Sr Doped La2NiO4 Single Crystals[END_REF][START_REF] Druce | Surface Termination and Subsurface Restructuring of Perovskite-Based Solid Oxide Electrode Materials[END_REF] . Furthermore, for a number of different electrodes materials [START_REF] Téllez | Surface Chemistry Evolution in LnBaCo2O5 + δ Double Perovskites for Oxygen Electrodes[END_REF][START_REF] Téllez | Relating Surface Chemistry and Oxygen Surface Exchange in LnBaCo2O 5-δ Air Electrodes[END_REF][START_REF] Druce | Surface Segregation in Solid Oxide Electrode Materials Occurring at Intermediate Temperatures[END_REF] it has been recently proved surface segregation takes place in a very short time even at low temperatures (e.g. 15 minutes at 400 ºC), giving rise to structural rearrangements. The recent simulation work carried out by Wu et al. [START_REF] Wu | Why Ni Is Absent from the Surface of La2NiO4+δ[END_REF] has provided some plausible answers to the open question of why Ni is absent from the surface of La2NiO4+δ.

The authors found that the decomposition of La2NiO4+δ to produce La2O3 and higher order RP phases is thermodynamically favorable and would leading to a La-terminated and Ni deficient surface.

Hence, the main focus of the present study is to acquire a better understanding of the oxygen exchange processes occurring at the surface of La2NiO4+δ and relating, for the first time, the catalytic activity of these materials with the surface chemistry and surface reconstruction and poisoning during the high temperature treatments. To this end, Low Energy Ion Scattering (LEIS), a technique which consists in measuring the energy distribution of the backscattered ions (from a low-energy noble gas ion beam) after the collision with the surface [START_REF] Brongersma | High-Sensitivity and High-Resolution Low-Energy Ion Scattering[END_REF][START_REF] Brongersma | Surface Composition Analysis by Low-Energy Ion Scattering[END_REF][START_REF] Brongersma | Low-Energy Ion Scattering[END_REF] , will be used to obtain information about the elemental composition of the very first atomic layer and of the near-surface region.

EXPERIMENTAL METHODS

Crystal growth

Single crystals of La2NiO4+δ were synthesized using the floating zone (FZ) method in an image mirror furnace (Cyberstar) equipped with two 1000 W halogen lamps.

Firstly, polycrystalline powder of La2NiO4+δ was prepared using a modified citrate method.

Citric acid, acrylamide and N,N-bis acrylamide were added to a stoichiometric mixture of La(NO3)3 and Ni(NO3)2 solutions (La:Ni=2:1). The mixture was heated up to 80 °C to form a gel.

The former was decomposed at 650 °C in air leading to homogeneous and reactive powder, then subsequently annealed at 1000 °C in air to obtain pure La2NiO4+δ phase. The obtained powder was thereafter compacted to prepare feed rods of 6 mm in diameter and 100 mm in length. Dense feed rods were obtained under isostatic pressure of 300 MPa, then subsequent sintered at 1300 °C for 12 hours in air.

The crystal growth was performed in air using an existent La2NiO4+δ single crystal as seed and the growth rate was fixed at 3 mm/h. During the growth process, the seed and the feed were counter-rotated at 30 rpm in order to obtain a homogeneous molten zone.

A single crystalline rod of about 5 mm in diameter and 60 mm in length was obtained from the growth. Its crystallinity was checked by Laue X-ray diffraction (XRD). The cationic composition was checked using Energy Dispersive X-ray analysis (EDX), and the cationic ratio of La over Ni was close to 2 (2.00±0.05). The oxygen content was determined using both Thermo Gravimetric Analysis (TGA) under a reducing atmosphere (flowing 5% H2 in Ar), and iodometric titration on a powder obtained by crushing a piece of single crystal. For TGA analyses, about 100 mg of powder were heated up to 900 °C under Ar/H2 5% flux using a heating rate of 2°C/min. The iodometric titration procedure was as follows: about 50 mg of powder was dissolved in a mixture of HBr acid and KI under nitrogen flow. Note that all solutions used during the titration had previously undergone de-oxygenation. The iodine formed by the reduction of Ni 3+ to Ni 2+ was then titrated by a thiosulfate solution. The titration was performed using an automated potentiometric titration system (Titroline easy). The oxygen content was thus determined from the total weight loss and the equivalence volume of thiosulfate for TGA analyses and iodometric titration, respectively. The oxygen excess was estimated to be δ=0.11±0.01, a result which is in agreement with the tetragonal structure [START_REF] Tranquada | Oxygen Intercalation, Stage Ordering, and Phase Separation in La 2 NiO 4 + δ with 0.05≲δ≲0.11[END_REF] (space group I4/mmm) and cell parameters (a = 3.87 Å and c = 12.63 Å) deduced from the powder XRD pattern obtained from a crushed single crystal ( Figure 1). The cutting of the crystals was performed with a diamond wire saw ESCIL equipped with a 2 circles Micro-check orientation system on which the HUBER goniometer head can be positioned.

An accuracy of less than 1° can be reached between the mechanical cut plane and the desired crystallographic one.

Finally, after a polishing of all the faces (down to 250 nm diamond as standard, although in some cases due to size limitations only a lighter polishing was possible), the orientations of the cut faces were accurately checked by the Laue diffraction method using a silicon single crystal as a reference. For this reference crystal we considered a misalignment between the (511) crystal face and its mechanical plane less than 0.01°. This allowed both the positioning and the determination of crystallographic directions of the nickelate crystal as-cut faces perpendicular to the X-rays beam with an absolute accuracy being less than 1° along the 2-circle-segment axis.

Oxygen isotopic exchange

The oxygen diffusivity (D*) and the surface exchange coefficient (k*) of the La2NiO4+δ single crystals were measured for the low temperature range (450 ºC < T < 600 °C) by the Isotopic Exchange Depth Profile (IEDP) technique, procedure which is described in detail elsewhere [START_REF] Kilner | Oxygen Self-Diffusion Studies Using Negative-Ion Secondary Ion Mass Spectrometry (SIMS)[END_REF][START_REF] De Souza | Determining Oxygen Isotope Profiles in Oxides with Time-of-Flight SIMS[END_REF] .

Prior to each exchange, a pre-annealing step was performed, which consisted in equilibrating the sample at the temperature of interest (same temperature as the subsequent exchange) in dry natural [START_REF] Garcia | Electrical Conductivity and Oxygen Exchange Kinetics of La2NiO4+delta Thin Films Grown by Chemical Vapor Deposition[END_REF] O oxygen (99.9% purity with natural abundances for (all) the oxygen isotopes) at 200 mbar. The time used for the pre-anneal step in natural oxygen was always much longer (at least five times) than the exchange time. Then the sample was exchanged in an [START_REF] Chroneos | Anisotropic Oxygen Diffusion in Tetragonal La2NiO4+δ: Molecular Dynamics Calculations[END_REF] O enriched gas at the same oxygen partial pressure and for a controlled length of time. In order to limit the oxygen stoichiometry change during the heating and cooling ramps, a tubular furnace was rapidly rolled on to set the sample to the annealing temperature and later rolled off to rapidly cool it down. The isotopic oxygen fraction of the [START_REF] Chroneos | Anisotropic Oxygen Diffusion in Tetragonal La2NiO4+δ: Molecular Dynamics Calculations[END_REF] O enriched gas (0.939 isotopic fraction for set A and 0.260 for set B) was measured by SIMS from the composition of an oxide layer formed on a silicon substrate during an oxidation in the [START_REF] Chroneos | Anisotropic Oxygen Diffusion in Tetragonal La2NiO4+δ: Molecular Dynamics Calculations[END_REF] O enriched gas at high temperature (1050 ºC).

Table 1 Heat pre-treatment sequence (including heat treatment and pre-anneal step in natural oxygen) and [START_REF] Chroneos | Anisotropic Oxygen Diffusion in Tetragonal La2NiO4+δ: Molecular Dynamics Calculations[END_REF] O exchange exchanges times for each of the La2NiO4+δ single crystal samples. Two different sets of single crystals have been used for the measurements. With the aim of limiting potential surface segregation processes, the single crystals corresponding to the first set of samples (set A) were exchanged in a gas atmosphere enriched in [START_REF] Chroneos | Anisotropic Oxygen Diffusion in Tetragonal La2NiO4+δ: Molecular Dynamics Calculations[END_REF] O isotope at 456, 520 and 595 ºC after a single short pre-annealing step at the same temperature for 5 h. On the other hand, the second set of samples (set B) were exchanged at similar temperatures (447, 518 and 594 ºC) but had a different thermal history, as each sample from this set was used for several exchange experiments. For set B, between each exchange experiment, in order to re-equilibrate the sample to its natural oxygen content, long re-anneal steps were performed at a temperature of approximately 845 ºC in natural oxygen (99.999% purity) at 200 mbar. The conditions (gas atmosphere, temperature and time) of each exchange together with the heat treatments sequence (temperature and time) performed to each sample prior to the exchange are detailed in Table 1.

The oxygen diffusion profiles were measured by Secondary Ion Mass Spectrometry (SIMS).

The exchange times at each temperature were selected by estimating diffusion length in both directions (from the D* values for La2NiO4+δ thin films [START_REF] Burriel | Anisotropic Oxygen Diffusion Properties in Epitaxial Thin Films of La2NiO4+δ[END_REF] ) to be adequate for the SIMS measurement technique used. For a given exchange time, due to the anisotropy of these nickelates, a much shorter diffusion length is expected for the c-axis (see Figure 2) compared to the ab plane.

Secondary Ion Mass Spectrometry measurements

The SIMS measurements for samples from set A were determined using a FEI FIB200 ion microscope with a quadrupole-based secondary ion mass spectrometry (SIMS) detector and sputter-etching using a 30 keV Ga + ion beam at 3 nA current.

The diffusion profiles along the c-axis were measured on a Focused Ion Beam (FIB) milled and FIB polished ramp surface. The ramp was positioned in approximately the centre of the sample on the top ab plane surface and the polished surface of the ramp was approximately at 10 of slope to this ab plane surface (9-15º, depending on the sample). The area of the ramps was approximately of 120 μm x 105 μm. Oxygen negative secondary ion mass images were obtained from the ramp surface in order to map the [START_REF] Chroneos | Anisotropic Oxygen Diffusion in Tetragonal La2NiO4+δ: Molecular Dynamics Calculations[END_REF] O isotopic fraction down the ramp. A background SIMS map at mass 18.6 amu was also recorded to subtract the non-zero background with the instrument conditions for recording SIMS images. The ramp was also measured in the optical microscope-based whitelight interferometer (Zygo Corp, USA NewView200) in order to determine an estimated depth scale. This result also enabled the position of the start of the ramp to be determined and thus the origin of the depth scale. A polished sample of (La,Sr)MnO3 oxide which had not been exchanged was also analysed in the same SIMS session with the same measurement conditions in order to determine the lower limit of detection of [START_REF] Chroneos | Anisotropic Oxygen Diffusion in Tetragonal La2NiO4+δ: Molecular Dynamics Calculations[END_REF] O isotopic fraction.

For the oxygen diffusion along the ab plane, in which the diffusion lengths were expected to be much longer, measurements were taken from a FIB ion milled and polished face perpendicular to the c-axis, parallel to the original top surface, making sure that it is deep enough to reach a background value of c-axis diffusion (see Figure 3). The measured surfaces were at approximately 28, 23 and 70 m below the top surface for samples A_450, A_520 and A_600, respectively. The oxygen negative SIMS spectra were measured from a series of sputter-etched craters (rectangular 50 m x 2 m and approx. 1 m deep) oriented in the b direction along the polished surface and using a 3 nA 30 keV Ga + ion beam. The depth scale for the measurement craters was established using optical microscopy (Zygo). Although for simplicity we will refer to the b-direction, it should be pointed out that as we refer to a tetragonal structure, the a and b directions are equivalent.

Finally, as can be observed in Figure 3, one more crater was measured at the top surface to obtain the exact [START_REF] Chroneos | Anisotropic Oxygen Diffusion in Tetragonal La2NiO4+δ: Molecular Dynamics Calculations[END_REF] O isotopic fraction for length=0. The exchanged single crystals from set B were measured by time-of-flight SIMS on a TOF.SIMS 5 instrument (IONTOF GmbH, Münster, Germany) equipped with a pulsed bismuth liquid metal ion gun incident at 45° operated in the burst alignment mode (7 or 8 peaks) and the Cs + beam (~ 200 nA, 2 kV at 45 incidence) for sputtering. The depth profiling mode for oxygen isotopes described in detail by De Souza et al. [START_REF] De Souza | Determining Oxygen Isotope Profiles in Oxides with Time-of-Flight SIMS[END_REF] , was used for the c-axis diffusion measurement, as it allows determining species distribution in depth from the outer surface of the material using a high depth resolution. The depth profile was measured in a face perpendicular to the c-axis, in the center of the sample to ensure no contribution from the ab-plane diffusion (see Figure 2). For the measurement of the oxygen diffusion along the ab plane, a crater was sputtered with the Cs + beam (2 kV) at the edge of the crystal on a face perpendicular to the c axis. In this configuration the SIMS measurements were recorded from the center of the receding base of the sputtered crater as a series of images [START_REF] De Souza | Determining Oxygen Isotope Profiles in Oxides with Time-of-Flight SIMS[END_REF] .

After the SIMS measurement, the depth of the sputter-etched craters (c-axis profiles) was measured using the optical microscope-based interferometer (Zygo Corp. NewView 200).

Low Energy Ion Scattering (LEIS) measurements

The outermost surface composition of the samples was measured with monolayer atomic resolution by Low Energy Ion Scattering (LEIS) (Qtac 100 , IonTOF GmbH, Germany). Prior to the analyses, the samples were cleaned ex-situ in an ultrasonic bath (10 min in acetone/ 10 min in ethanol / 10 min in de-ionised water) and dried in air. Since LEIS is very surface-sensitive, the sample surface was also cleaned in-situ prior to the analysis in order to remove the organic contaminants remaining from the brief exposure to the atmosphere. This cleaning process was performed by oxidation using reactive atomic oxygen flux (O) that removes the hydrocarbons on the surface (i.e. the O atoms react with the adventitious hydrocarbons forming volatile species that are pumped out of the preparation chamber). The pressure in the preparation chamber during the cleaning process is about ~5 x 10 -5 mbar due to the flux of the reactive atomic oxygen. The sample was then transferred from this preparation chamber into the main analysis chamber (base pressure 1 x 10 -10 mbar) without further air exposure. The effectiveness of the cleaning was checked by analysing the surface with a 3 keV He + beam to check the presence of a C peak (theoretical position of about 846 eV). The He + ion dose used during these analyses was very low in order to avoid surface sputtering that would remove the organic contamination and could be misinterpreted as an effective cleaning by oxidation with atomic oxygen. Therefore, each analysis was acquired using less than 4x10 [START_REF] Bassat | Anisotropic Ionic Transport Properties in La2NiO4+delta Single Crystals[END_REF] ions/cm 2 per analysis, and the total ion dose for the sequential analyses on the same area was less than 2x10 14 ions/cm 2 for the total cleaning check. Note that, for those cases where there are carbonates on the surface, the cleaning procedure would be ineffective to remove these species and a C peak will be still detectable in the He + spectrum. A second indicator of the surface cleaning is given by the surface peaks corresponding to other heavier cations (e.g. La), which shows much higher yields than the C atoms. Therefore, the oxidation was repeated until identical surface spectra were obtained for two consecutive He + analyses, showing the same La surface coverage (peak areas).

The LEIS surface analysis was performed using a 3 keV He + ion beam at normal incidence to the surface over an area of 1 mm 2 . The ion fluence during the analysis was kept below 5 x 10 ions/cm 2 in order to avoid a significant surface damage. For depth profiling, the dual beam mode was used combining analysis steps with a 3 keV He + beam followed by sputter steps using a eV Ar + beam at 59° incidence angle to erode the material. The mean projected range for the sputter ions under these conditions is estimated to be 1.0 nm [START_REF] Ziegler | The Stopping and Range of Ions in Solids[END_REF] . The ion fluence per sputtering step was about 1 x 10 15 ions/cm 2 , in order to remove the more extended atomic mixing caused by the primary ion beam (due to the energy and angle of sputtering beam, the mixing due to sputtering is much lower than that produced during the analysis).

RESULTS AND DISCUSSION

Oxygen diffusion and surface exchange coefficients along the two main crystallographic directions

The first aim of present study is to measure both D* and k* coefficients in the two main crystallographic directions on La2NiO4+δ single crystals for the low temperature range (400 < T < 600 °C). For this purpose a new device was used for the preparation of single crystal samples with highly precise crystallographic orientations (< 1° for both directions), as described in the Experimental section.

From the [START_REF] Garcia | Electrical Conductivity and Oxygen Exchange Kinetics of La2NiO4+delta Thin Films Grown by Chemical Vapor Deposition[END_REF] O -and 18 O -SIMS intensity data acquired, the normalized [START_REF] Chroneos | Anisotropic Oxygen Diffusion in Tetragonal La2NiO4+δ: Molecular Dynamics Calculations[END_REF] O isotopic fraction c'(x)

was calculated as showed in Equation 1:

𝑐′(𝑥) = 𝑐 * (𝑥)-𝑐 𝑏𝑔 * 𝑐 𝑔 * -𝑐 𝑏𝑔 *
(Equation 1)

Where c * (x) is the [START_REF] Chroneos | Anisotropic Oxygen Diffusion in Tetragonal La2NiO4+δ: Molecular Dynamics Calculations[END_REF] O isotope fraction obtained by SIMS, i.e. [START_REF] Chroneos | Anisotropic Oxygen Diffusion in Tetragonal La2NiO4+δ: Molecular Dynamics Calculations[END_REF] O/( 18 O+ 16 O), c bg * is the background isotope fraction and c g * is the isotope fraction of the annealing gas. The data were fitted using the solution of the diffusion equation given by Crank [START_REF] Crank | The Mathematics of Diffusion[END_REF] 2): 2)

𝑐 ′ (𝑥) = 𝑒𝑟𝑓𝑐(𝑥′) -𝑒𝑥𝑝(2ℎ ′ 𝑥′ + ℎ ′ 2 ) × 𝑒𝑟𝑓𝑐(𝑥′ + ℎ′) (Equation
where D* is the tracer oxygen diffusion coefficient and k* the tracer surface exchange coefficient. very low h' values are obtained, which results in very small differences between the surface and the background [START_REF] Chroneos | Anisotropic Oxygen Diffusion in Tetragonal La2NiO4+δ: Molecular Dynamics Calculations[END_REF] O levels. Along the ab plane direction (fast diffusion direction) low [START_REF] Chroneos | Anisotropic Oxygen Diffusion in Tetragonal La2NiO4+δ: Molecular Dynamics Calculations[END_REF] O surface concentrations, only slightly above background, were obtained for the lowest measured temperature (~450 ºC) for set A (c'(0) ≈ 0.001-0.002) and for all temperatures for set B (c'(0) ≈ 0.004-0.015). In those cases it was not possible to extract reliable surface exchange and diffusion coefficients from the fits. A large anisotropy was measured for the oxygen diffusion, being 3 orders of magnitude larger along the a-b plane than along the c-axis for the measured temperature range (see Figure 5 and Table 2). The Dab * values (>10 -8 for T≥520 ºC) are similar (slightly larger) to those previously reported for single crystals [START_REF] Bassat | Anisotropic Ionic Transport Properties in La2NiO4+delta Single Crystals[END_REF] and slightly higher to reported for polycrystalline bulk samples [START_REF] Boehm | Oxygen Diffusion and Transport Properties in Non-Stoichiometric LnNiO Oxides[END_REF][START_REF] Sayers | Low Temperature Diffusion and Oxygen Stoichiometry in Lanthanum Nickelate[END_REF][START_REF] Skinner | Oxygen Diffusion and Surface Exchange in La2-xSrxNiO4+delta[END_REF] but with a similar activation energy. This clearly indicates that the diffusion along the ab plane (Dab * ) governs the behaviour of the bulk material. The Dc * values obtained for the single crystals with and without heat treatments (sets B and A) are quite similar, although the small activation energy obtained points to a possible limitation in experimental method (lower limit of about (2±1)

x 10 -11 cm 2 s -1 ) and thus the values obtained correspond to the lower bound of the diffusion coefficient along the c-axis. Furthermore, the good agreement with the Dc * values previously reported for thin films [START_REF] Burriel | Anisotropic Oxygen Diffusion Properties in Epitaxial Thin Films of La2NiO4+δ[END_REF] confirm the very large anisotropy between both directions (≥10 [START_REF] Aguadero | Materials Development for Intermediate-Temperature Solid Oxide Electrochemical Devices[END_REF] ) and indicates that the Dc * values had been overestimated in previous single crystal measurements due to previous orientation and cutting limitations [START_REF] Bassat | Anisotropic Ionic Transport Properties in La2NiO4+delta Single Crystals[END_REF] .

Figure 5 Diffusion coefficients obtained for the La2NiO4+δ single crystals and comparison to literature data on ceramic pellets 2,9,43 , single crystals [START_REF] Bassat | Anisotropic Ionic Transport Properties in La2NiO4+delta Single Crystals[END_REF] (s.c.) and thin films 14 (t.f.). The fitted k* coefficients in both directions for all the measured samples (sets A and B) and temperatures and their comparison with literature values for other La2NiO4+δ samples are included in Figure 7. It can be observed that for set A (samples with a short pre-anneal step) for the measured temperature range the kab * and kc * values are quite comparable (although slightly larger for the caxis). As the similarity in surface exchange coefficient for both orientations was unexpected, this motivated an in-depth study of the outer and near-surface chemistry. As will be explained in the next section, the surface chemistry of this type of compounds is dynamic and will depend on the composition and thermal history of each sample and face, being the surface exchange coefficient differences directly related to these time-dependent chemical differences.

Figure 7 Surface exchange coefficients obtained for the La2NiO4+δ single crystals and comparison to literature data on ceramic pellets 2,9,43 , single crystals [START_REF] Bassat | Anisotropic Ionic Transport Properties in La2NiO4+delta Single Crystals[END_REF] (s.c.) and thin films 14 (t.f.).

Figure 8 shows the comparison between the k* coefficients in both directions for the La2NiO4+δ single crystals measured after a short pre-anneal step (set A) and the literature values for Pr2NiO4+δ and Nd2NiO4+δ single crystals. It can be observed that both the a-b plane surface exchange coefficients and their activation energy are very similar for the 3 compositions (La, Pr and Nd).

However the kc * value obtained for the La2NiO4+ δ single crystals is larger than for the other compounds, and not very different from its kab * value. pre-annealed at 456ºC in natural oxygen for 5 h prior to the [START_REF] Chroneos | Anisotropic Oxygen Diffusion in Tetragonal La2NiO4+δ: Molecular Dynamics Calculations[END_REF] O exchange, while sample B_450 had followed a sequence of anneals including 113.8 h at 845 ºC (see Erreur ! Source du renvoi introuvable.). for both orientations was found to be similar. A very clean surface was measured in both cases, with no contamination peaks detected. Three main elements are present in the outermost surface of the crystals, which correspond to the 3 detected peaks: [START_REF] Garcia | Electrical Conductivity and Oxygen Exchange Kinetics of La2NiO4+delta Thin Films Grown by Chemical Vapor Deposition[END_REF] O, [START_REF] Chroneos | Anisotropic Oxygen Diffusion in Tetragonal La2NiO4+δ: Molecular Dynamics Calculations[END_REF] O and La (theoretical peak positions at 1181.7, 1316.2 and 2701.3 eV, respectively). The expected position of the Ni peak (theoretical peak position of 2332.2 eV, for the most abundant isotope) is also marked in the spectra. The lack of a peak in this position reveals that no Ni can be detected at the outermost surface of these crystals, at least to the detection limit of the technique that is estimated to be 15%

Impact of surface orientation on the surface exchange coefficient

for Ni using 3 keV He + , and thus it can be concluded that both surfaces are LaO-terminated.

The preferential A-site termination at the immediate outer surface of Ruddlesden-Popper (RP) phases containing Ni as the transition metal ion has also been recently observed for La1.67Sr0.33NiO4+δ single crystals [START_REF] Burriel | Absence of Ni on the Outer Surface of Sr Doped La2NiO4 Single Crystals[END_REF] and for La2NiO4+δ [START_REF] Druce | Surface Termination and Subsurface Restructuring of Perovskite-Based Solid Oxide Electrode Materials[END_REF] and Pr2-xLaxNiO4+δ [START_REF] Druce | Surface Composition of Perovskite-Type Materials Studied by Low Energy Ion Scattering (LEIS)[END_REF] polycrystalline samples after anneal treatments in air at 450 ºC and in pure oxygen at 800 and 1000 ºC, respectively. Even after the deposition of La2NiO4+δ epitaxial thin films by pulsed-laser deposition (PLD) at about 700 ºC (c-axis oriented), the preferred surface termination determined by LEIS is the LaO-plane, as reported by Wu [START_REF] Wu | Surface Composition of Layered Ruddlesden-Popper Lan+1NinO3n+1 (n = 1, 2 and 3) Epitaxial Films[END_REF] . Further evidence of layer re-arrangements leading to AO surface termination in Ruddlesden-Popper (LaO)(LaNiO3)n phases has been theoretically

predicted and experimentally demonstrated in reference 44. Hence these measurements support the postulation that the general assumption of the B-site cations exposed to the environment controlling the catalytic activity of the materials may be incorrect. Depth profiling analysis of the single crystals was performed by alternating the analysis cycle (using the 3 keV He + analytical beam) and low-energy sputtering steps (using 500 eV Ar + sputtering, with an ion fluence of 10 15 ions/cm 2 for each sputtering cycle). The LEIS yield depth profiles and surface cation fractions obtained for the single crystal treated at 450°C (sample A_450) are shown in Figure 9.c and 9.e for the (001) face (c-axis direction) and in Figure 9.d and 9.f for (010) face (ab-plane). The fractions were estimated by using the bulk cation intensities as a reference value for the bulk stoichiometry of the La2NiO4+ single crystal. For both orientations there is a fast increase of the Ni intensity after removing the first layer of atoms, with a maximum at an ionic fluence of 5x10 [START_REF] Burriel | Enhancing Total Conductivity of La2NiO4+delta Epitaxial Thin Films by Reducing Thickness[END_REF] ions/cm 2 . After this maximum, the Ni intensity decreases again reaching an intensity plateau after a sputtering fluence of approximately 20x10 [START_REF] Burriel | Enhancing Total Conductivity of La2NiO4+delta Epitaxial Thin Films by Reducing Thickness[END_REF] ions/cm 2 . The Ni cation fractions (normalized to the bulk stoichiometry) revealed a Ni-enriched subsurface for both faces, reaching values of 0.44 for the (001) face (Figure 9.e) and of 0.51 for the (010) face for sample A_450. This clearly demonstrates that a cation rearrangement has taken place within the La2NiO4+ and that the outer surface might have lost its structural anisotropy due to the formation of other phases at the surface and sub-surface. The existence of this Ni-rich near-surface region is in agreement with previous studies performed both on La2NiO4+ ceramic samples after high temperature treatments [START_REF] Druce | Surface Termination and Subsurface Restructuring of Perovskite-Based Solid Oxide Electrode Materials[END_REF] and on as-deposited Ruddlesden-Popper Lan+1NinO3n+1 (n = 1, 2 and 3) epitaxial films. [START_REF] Wu | Surface Composition of Layered Ruddlesden-Popper Lan+1NinO3n+1 (n = 1, 2 and 3) Epitaxial Films[END_REF] Gauquelin et al [START_REF] Gauquelin | Long-Term Structural Surface Modifications of Mixed Conducting La2NiO4+δ at High Temperatures[END_REF] had shown that long-term annealing of La2NiO4+δ single crystals in air at very high temperatures (1273 K) leads to the formation of nickel-rich Ruddlesden-Popper phases (n = 2 and 3) at the single-crystal surfaces. Recent studies on epitaxial (La,Sr)2CoO4+δ RP thin films showing similar B-site enriched regions, revealed that this B-enrichment seems to be related to the formation of additional phases due to the decomposition of the RP phase at the nearsurface region [START_REF] Chen | Segregated Chemistry and Structure on (001) and (100) Surfaces of (La 1-X Sr X ) 2 CoO 4 Override the Crystal Anisotropy in Oxygen Exchange Kinetics[END_REF] . Furthermore, as previously explained, a recent evaluation of the thermodynamic stability of La2NiO4+δ 33 suggests that a partial decomposition of La2NiO4+δ is thermodynamically favorable and could take place at the surface when exposed to air. The decomposition would lead to a stacking of (La2O3)-(La3Ni2O7 and/or La4Ni3O10)-(La2NiO4), that would be responsible for the observed Ni-absence and for the Ni:La non-stoichiometry at La2NiO4+δ surfaces. This explanation is in perfect agreement with our results and would explain the higher Ni cation fraction observed for the sample which had been subject to longer anneal times, as will be shown in the next section.

The similar compositional rearrangement found for both orientations (Figure 9e and9f) could be at least in part responsible for the lack of anisotropy in the surface exchange coefficients (Figure 7) obtained for these La2NiO4+δ single crystals (set A). Any sub-surface atomic rearrangement that might affect the near-surface composition could override the expected anisotropy of the oxygen exchange at the surface. Similar findings have also been recently found for (La,Sr)2CoO4+δ epitaxial thin films with RP structure [START_REF] Chen | Segregated Chemistry and Structure on (001) and (100) Surfaces of (La 1-X Sr X ) 2 CoO 4 Override the Crystal Anisotropy in Oxygen Exchange Kinetics[END_REF] , which was explained by surface segregation effects that override the effect of the structural anisotropy.

In view of these results, it is evident that the time used for the pre-anneal step (usually recommended at least 10 times longer compared to the exchange itself for the IEDP technique [START_REF] De Souza | Oxygen Exchange and Diffusion Measurements: The Importance of Extracting the Correct Initial and Boundary Conditions[END_REF] ), as well as any other anneal steps carried out, must be taken into consideration when comparing k * values for different sets of samples. Alteration of the composition due to matrix atom segregation at high and even intermediate temperatures is certainly possible, and these chemical variations should be carefully considered when evaluating the surface exchange of electrochemically active materials.

Impact of long anneal treatments and impurities on the surface exchange coefficients

A large variation in the k* coefficients can be observed for different sets of samples when comparing among the different literature values for La2NiO4+δ (Figure 7). For example a 2-orders of magnitude difference can be observed between the polycrystal samples measured by Boehm et al. [START_REF] Boehm | Oxygen Diffusion and Transport Properties in Non-Stoichiometric LnNiO Oxides[END_REF] and those measured by Sayers et al. [START_REF] Sayers | Low Temperature Diffusion and Oxygen Stoichiometry in Lanthanum Nickelate[END_REF] These results indicate that differences between batches and the thermal history of the samples can have a larger effect in the surface exchange properties of the material than the crystal orientation.

As for the comparison between both sets of single crystals, despite having shown very similar diffusion coefficients (see Figure 7), a very large difference in the surface exchange is observed between the samples submitted to long heat treatments (set B) and those only submitted to a short pre-anneal (set A). kc * decreases more than 2 orders of magnitude after the high temperature treatments. Although it was not possible to extract accurate kab * coefficients for set B, this limitation (low C' at the surface) clearly comes from the fact that the kab * coefficients are also very low. The spatial distribution of the contaminants on the surface can be obtained from the integration images of the LEIS depth profiles, as shown in Figure 11. Although the images were obtained with low resolution in order to avoid damage by focussing the beam onto a small surface spot, some regions covered by the impurities were clearly observed. In the case of the (001) face of sample B_450, mainly a small region at the edge of the analysed area showed the presence of Na and Ca impurities, while Pt was found over all the analysed surface. Interestingly, the [START_REF] Chroneos | Anisotropic Oxygen Diffusion in Tetragonal La2NiO4+δ: Molecular Dynamics Calculations[END_REF] O and [START_REF] Garcia | Electrical Conductivity and Oxygen Exchange Kinetics of La2NiO4+delta Thin Films Grown by Chemical Vapor Deposition[END_REF] O images showed a positive correlation with the impurities chemical maps. The Pt intensity is low and easily removed after a few sputtering cycles. Long-term surface poisoning due to external impurities as well as surface cation segregation processes have implications for the electrochemical performance of SOFCs, leading to the degradation of the cell components [START_REF] Druce | Surface Segregation and Poisoning in Materials for Low-Temperature SOFCs[END_REF] . Na, Ca, Cr and Pt are common elements forming part of the SOFC ceramic layers, chromium-containing interconnects and experimental setup elements (thermocouples, wires, electrodes, etc), and can be therefore common impurities in typical electrochemical experiments and devices. Thus the influence of these impurities in the properties of these cathode materials is of great interest of the application of these compounds in real electrochemical devices.

Erreur

After long heat treatments the surface exchange coefficient measured for the (001) faces was observed to decrease more than 2 orders of magnitude (from 1.60 10 -8 and 8.0 10 -11 at 450ºC from sample A_450 to sample B_450) (see Figure 7) for an estimated surface coverage of impurities of around 27%, while the effect on the (010) faces was such that resulted in an un-measurable diffusion profile along the ab plane (i.e. estimated impurity coverage of about 81%). In order to compare the near-surface composition between samples and faces, Figure 10.e and f show the surface cation fractions as a function of the sputtering fluence for the (001) and (010) faces of sample B_450. It should be mentioned that the sputtering fluence for each set of samples might vary due to the surface roughness differences as the erosion rate might be faster for the rougher surface. For instance, the B_450 samples were subjected to long heat treatments, and hence, the roughness is affected by the annealing step. In addition, the impurities at the outer region of the B_450 samples might also show a different sputtering rate compared to the pristine La2NiO4+δ surface. Therefore, any comparison between the depth profiles must consider the sputtering rate difference depending on the outer composition and the surface roughness.

As for the in-depth variation of the surface cation fractions obtained by LEIS, for face (001)

there is a fast increase of the Ni intensity after removing the first layer of atoms, with a maximum at an ionic fluence of 5x10 [START_REF] Burriel | Enhancing Total Conductivity of La2NiO4+delta Epitaxial Thin Films by Reducing Thickness[END_REF] ions/cm 2 , followed by a decrease reaching an intensity plateau after a sputtering fluence of approximately 20x10 15 ions/cm 2 (Figure 10.e). This in-depth rearrangement of the La and Ni cations is very similar to that observed the uncontaminated sample submitted to short heat treatments (Figure 9.e), although higher Ni cation fractions (up to 0.57) where measured for sample B_450 (after long-time anneals) compared to 0.44 for sample A_450. As for the surface cation fractions for face (010), these are strongly affected by a large amount of surface impurities and reach the stoichiometric values after a sputtering fluence of approximately 85x10 15 ions/cm 2 .

These results clearly highlight the strong detrimental effect that common impurities have upon the oxygen exchange rate for La2NiO4+. A relationship between the surface exchange and cathode performance decrease with the appearance of surface contaminants has been previously been observed by other authors for contaminants such as C, S, Si, Na, Ca and Cr for both electrode and electrolyte materials [START_REF] Druce | Surface Segregation and Poisoning in Materials for Low-Temperature SOFCs[END_REF][START_REF] Ridder | Oxygen Exchange and Diffusion in the near Surface of Pure and Modified Yttria-Stabilised Zirconia[END_REF] . In particular by performing LEIS surface measurements, De Ridder et al.

showed that bulk impurities, such as SiO2, CaO and Na2O, segregate to the outermost surface layer of YSZ until they completely cover it creating an impenetrable barrier for oxygen. This surface exchange reduces to zero for a completely covered surface by reducing the area available for oxygen exchange.

CONCLUSIONS

The oxygen diffusion of high quality La2NiO4+ single crystals was measured along 2 perpendicular directions using the IEDP technique. An anisotropy of 3 orders of magnitude was obtained for the measured temperature range (450-600 ºC), the diffusivity being larger along the The oxygen diffusion coefficient is not affected by the thermal history of the sample. However the surface exchange is strongly related to the thermal history of the sample and very largely affected by the presence of common impurities and surface rearrangement processes, which explains the large scatter in k * values commonly found in the literature for a given materials composition. It has been proved that even in the absence of external impurities, the surface of La2NiO4+ tends to decompose and reconstruct into other RP phases. Similar kc * and kab * values were obtained for the 2 orientations, which is thought to be related to similar cationic surface rearrangement for different surface orientation. The lack of anisotropy in the surface exchange values for both surfaces measured in this work is most likely related to the surface segregation process overriding the intrinsic anisotropy of the material.

In addition, the surface exchange coefficient kc * has been shown to decrease more than 2 orders of magnitude after long temperature treatments which seems to be related to the existence of surface impurities. These elements can come directly from the gas surrounding the surface or from traces of impurities (from the materials synthesis for instance) which could segregate from the bulk of the oxide to the outer surface during the high temperature anneal. This demonstrates the difficulty of measuring the "intrinsic" surface exchange coefficient of these complex oxide materials. The observed interplay between segregation, decomposition and reorganization of the surface and subsurface layers and their complex evolution with time and temperature, coupled with the probable sensitivity to the ambient gas phase composition makes inter-comparison of experimental values of the surface exchange coefficient difficult.

Financial supports is acknowledged from the 7th European Community Framework Programme of the European Union (Marie Curie Intra European fellowship PIEF-GA-2009-252711 for M.B.), from wpi-IC2NER and from the Japanese Society for Promotion of Science (JSPS postdoctoral fellowship and Kakenhi Grant-in-Aid P13770 for H.T.). The authors also thank Dr. John Druce (Kyushu University) for assistance with LEIS measurements.

Figure 1

 1 Figure 1 XRD diffraction pattern recorded from a crushed La2NiO4+δ single crystal

Figure 2

 2 Figure 2 Sketch of the oriented crystals used for the oxygen diffusion measurements along and perpendicular to the c-axis including schematics for the relative 18 O diffusion profiles.

Figure 3 FIB

 3 Figure 3 FIB secondary electron images of the c-axis orthogonal polished surface (112 m x 68

  * 𝑡 for diffusion in a semi-infinite medium with surface limitation and constant c g * 42 (Equation

Figure 4

 4 Figure 4 Normalised 18 O diffusion profile along the c axis for the single crystal exchanged at T =

Figure 4

 4 Figure 4 shows an example of a diffusion profile obtained along the c axis for the La2NiO4+δ

Figure 6

 6 Figure 6 shows the comparison between the D* coefficients in both directions for all the

Figure 6

 6 Figure 6 Diffusion coefficients obtained for the La2NiO4+δ single crystals along and perpendicular to the c-axis crystals and comparison to literature data on Pr2NiO4+δ and Nd2NiO4+δ 22

Figure 8

 8 Figure 8 Surface exchange coefficients obtained for the La2NiO4+δ single crystals along and perpendicular to the c-axis crystals and comparison to literature data on Pr2NiO4+δ and Nd2NiO4+δ 22

Figure 9 .

 9 Figure 9.a and 9.b show the outer surface LEIS spectra obtained with a 3 keV He + beam of the

Figure 9 .

 9 Figure 9. Sample A_450 (La2NiO4+ single crystal treated at 450°C): He + LEIS spectra for the

  ! Source du renvoi introuvable. a and b show the LEIS surface spectra of the (001) and (010) faces of the single crystal sample B_450 after long exchange and heat treatment, which included a total of 113.8 h at 845 ºC. In this casem in addition to the[START_REF] Garcia | Electrical Conductivity and Oxygen Exchange Kinetics of La2NiO4+delta Thin Films Grown by Chemical Vapor Deposition[END_REF] O,[START_REF] Chroneos | Anisotropic Oxygen Diffusion in Tetragonal La2NiO4+δ: Molecular Dynamics Calculations[END_REF] O and La peaks, the surface shows the presence of several contaminants, mainly Na for an onset energy (theoretical position) of 1581.2 eV ( 23 Na), Ca or K (2081.1 eV for[START_REF] De Souza | Determining Oxygen Isotope Profiles in Oxides with Time-of-Flight SIMS[END_REF] Ca and 2061.5 eV for 39 K), Cr (around 2265.2 eV) and Pt or Au (2784.1 eV for 195 Pt and 2786.2 eV for 197 Au). Although the same contaminants were found for both faces of the single crystal, the intensity of each peak (element) largely depends on the region and face analysed as the contamination over the surface is nonuniform. As the position for[START_REF] De Souza | Determining Oxygen Isotope Profiles in Oxides with Time-of-Flight SIMS[END_REF] Ca and 39 K peaks and for195 Pt and 197 Au peaks are very close, ToF-SIMS measurements were used to check the correct assignment of the peaks, confirming the presence of Ca and Pt as minor outer surface contaminants.

Figure 10

 10 Figure 10 Sample B_450 (La2NiO4+ single crystal treated at 450°C): He + LEIS spectra for the

Figure 11

 11 Figure 11 Elemental chemical maps obtained for the constituent elements and impurities after the

a-b

  plane than along the c-axis. From the intrinsic oxygen diffusion and surface exchange values obtained it can be concluded that for the intermediate temperature range of operation (450-600 ºC) La2NiO4+ δ and Pr2NiO4+δ are the most promising cathode materials within the family, as they possess the highest D* and similar k * values.

Table 2 .

 2 The oxygen diffusivity (D ab * and Dc * ), the surface exchange coefficient (kab * and kc

			ab plane				c-axis
	Temp.
	(ºC)	Dab* (cm 2 /s)	kab* (cm/s)	h'	Dc* (cm 2 /s)	kc* (cm/s)	h'
		Set A	Set A	Set A	Set A	Set B	Set A	Set B	Set A Set B
	456/447			<<	2.8 10 -11	4.0 10 -12	1.6 10 -8	8.0 10 -11	0.137 0.002
	520/518 2.0 10 -8	7.0 10 -8	0.027 3.0 10 -11	1.3 10 -11	2.0 10 -7	1.5 10 -9	1.58	0.018
	595/594 5.6 10 -8	5.1 10 -7	0.101 3.4 10 -11	2.9 10 -11	3.1 10 -6	1.3 x 10 -8 15.9	0.074

* ) values and the dimensionless parameter h' along and perpendicular to the c-axis calculated from the experimental oxygen diffusion profiles.

AUTHOR INFORMATION

Corresponding Author

* Mónica Burriel, monica.burriel@grenoble-inp.fr, Univ. Grenoble Alpes, CNRS, LMGP, F-38000 Grenoble, France

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ACKNOWLEDGMENT


Miguel Delgado
email: medelgado@fcnym.unlp.edu.ar.

Luis Miguel Ramírez

Kaustubh Adhikari

Macarena Fuentes-Guajardo

Clément Zanolli

Rolando González-José

Samuel Canizales

Maria-Catira Bortolini

Giovanni Poletti

Carla Gallo

Macarena Fuentes- Guajardo

Rolando Gonzalez-José

Francisco Rothhammer

Gabriel Bedoya

Andres Ruiz-Linares
email: andresruiz@fudan.edu.cn

División Antropología

Andrés Ruiz-Linares

Variation in dental morphology and inference of continental ancestry in admixed Latin Americans

Keywords: dental morphology, admixture, ancestry inference, Latin America

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche

INTRODUCTION

Due to the great preservation of teeth and their considerable morphological variation dental traits have been used extensively in human evolutionary studies, including the analysis of archaeological remains and the diversity of contemporary populations [START_REF] Scott | The Anthropology of Modern Human Teeth: Dental Morphology and its Variation in Recent Human Populations, 2 nd Edition[END_REF][START_REF] Irish | A companion to dental anthropology[END_REF][START_REF] Guatelli-Steinberg | What teeth reveal about human evolution[END_REF]. The differentiation of dental traits among continental populations has also been exploited, usually in a forensic setting, for the purpose of assignment of ancestry to human remains of unknown origin [START_REF] Scott | The Anthropology of Modern Human Teeth: Dental Morphology and its Variation in Recent Human Populations, 2 nd Edition[END_REF][START_REF] Alsoleihat | A new quantitative method to predict forensic racial identity based on dental morphological trait analysis[END_REF][START_REF] Edgar | Prediction of race using characteristics of dental morphology[END_REF][START_REF] Edgar | Testing the utility of dental morphological traits commonly used in the forensic identification of ancestry[END_REF][START_REF] Edgar | Estimation of ancestry using dental morphological characteristics[END_REF][START_REF] Edgar | Dental morphological estimation of ancestry in forensic contexts[END_REF][START_REF] Irish | Dental nonmetric variation around the world: using key traits in populations to estimate ancestry in individuals[END_REF][START_REF] Scott | rASUDAS. A new web-based application for estimate ancestry from tooth morphology[END_REF]. Such studies have mostly focused on establishing individual ancestry with reference to discrete population categories, such as those defined in the US census (e.g. European-Americans and African-Americans). However, to our knowledge, no attempt has so far been reported to infer genetic ancestry proportions from dental data in individuals of mixed continental ancestry.

The population of Latin America has a history of extensive admixture between Native Americans, Europeans and Africans and therefore represents an ideal setting in which to evaluate the informativity of dental traits to estimate genetic ancestry and individual admixture proportions. Here we report an analysis of dental nonmetric trait variation in contemporary Latin Americans and we evaluate the informativity of these dental traits for inferring admixture proportions. Consistent with their historical admixture, Latin Americans present dental nonmetric traits that are common in Native Americans, Europeans and Africans, and some of these traits correlate with genetic ancestry. We observe that although dental traits provide mean ancestry estimates similar to those obtained by genetic data, the informativity of these traits to estimate individual ancestry in the sample examined is relatively low.

MATERIALS AND METHODS

Subjects of study

We studied a sample of 477 individuals of both sexes (women/men = 259/218) aged 18-40 (mean = 23.4) recruited in Medellín, Colombia (the sample is denoted MED in Tables andFigures). This sample is part of the CANDELA cohort (Consortium for the Analysis of the Diversity and Evolution of Latin America, http://www.ucl.ac.uk/silva/candela) [START_REF] Ruiz-Linares | Admixture in Latin America: geographic structure, phenotypic diversity and self-perception of ancestry based on 7,342 individuals[END_REF]. This research was approved by the ethics committees of Universidad de Antioquia (Colombia), Universidad de Tarapacá (Chile), and University College London (UK). All participants provided written informed consent.

Characterization of dental morphology

Intraoral digital photographs were obtained (by LMR) using an IE3 Canon camera (at 12 megapixels resolution) under standardized conditions, including: captures in frontal, lateral and occlusal norms, constant light, proportion and distance. Using these photographs, we examined a total of 34 dental features (corresponding to 86 traits across teeth; Supplementary Table 1) in each individual (by M.D.) following ASUDAS trait definitions [START_REF] Turner | Scoring procedures for key morphological traits of the permanent dentition: the Arizona State University Dental Anthropology System[END_REF] with the exception of elongated mandibular premolars [START_REF] Edgar | Elongated premolar: a new morphological variant[END_REF] and lower premolar accessory ridges [START_REF] Delgado | Variación dental y craneofacial en el Norte de los Andes durante el Pleistoceno y el Holoceno[END_REF] (Supplementary Table 1). This scoring was performed blindly with regards to age, sex or genetic ancestry of the individuals examined. The intra-observer concordance rate for these traits has been shown to be high [START_REF] Delgado | Variación dental y craneofacial en el Norte de los Andes durante el Pleistoceno y el Holoceno[END_REF]. We only scored teeth with no caries, no apparent wear and no dental restorations. We retained the score of the antimere with strongest expression of the trait when asymmetric expression was evident [START_REF] Scott | Populations variation of Carabelli´s trait[END_REF]. Subsequent to scoring, traits with extreme frequencies (<0.3% or >98%), or >5% missing values were excluded. This resulted in 28 traits being retained for subsequent analyses.

Biodistance analysis

We used C. A. B Smith´s mean measure of divergence (MMD) statistic [START_REF] Sjøvold | Nonmetrical divergence between skeletal populations: the theoretical foundation and biological importance of C. A. B. Smith's mean measure of divergence[END_REF][START_REF] Irish | The mean measure of divergence: its utility in model-free and modelbound analyses relative to the Mahalanobis D 2 distance for nonmetric traits[END_REF] to estimate biological distances from the frequency of the dental traits in the Colombian and reference population samples, using the dichotomies of dental traits proposed for ASUDAS (Supplementary Table 1) (Sjøvold 1977, Harris and[START_REF] Harris | Calculation of Smith's mean measure of divergence for intergroup comparisons using nonmetric data[END_REF][START_REF] Irish | The mean measure of divergence: its utility in model-free and modelbound analyses relative to the Mahalanobis D 2 distance for nonmetric traits[END_REF]. The reference population dataset used in these analyses (Appendix 2; [START_REF] Scott | The Anthropology of Modern Human Teeth: Dental Morphology and its Variation in Recent Human Populations, 2 nd Edition[END_REF] consisted of frequencies reported for: Native Americans (American Arctic ). Following [START_REF] Harris | Calculation of Smith's mean measure of divergence for intergroup comparisons using nonmetric data[END_REF] we used Ascombe´s transformation of the MMD since it is slightly better than the Freeman-Tukey formula at asymptotically stabilizing sample variance and is more appropriate for the relatively large sample size examined here [START_REF] Green | The use of inverse sine transformations in the analysis of non-metric cranial data[END_REF]. We excluded traits significantly correlated with sex (since the MMD assumes lack of sexual dimorphism) or with other traits (as the MMD also assumes independence between traits) [START_REF] Nikita | A critical review of the Mean Measure of Divergence and Mahalanobis distances using artificial data and new approaches to the estimation of biodistances employing nonmetric traits[END_REF], and those traits that showed no significant variation between samples. Three traits (SSUI1, DSUI1 and ODOUP1) that have been extensively studied and are highly differentiated between reference population were retained, despite SSUI1 and DSUI1 showing a significant correlation and ODOUP1 a low frequency (<0.3%) in the Colombian sample investigated here. This resulted in 16 traits being retained for this analysis (Supplementary Tables 2 and3). The MMD calculation was performed in R 3.4.3 (R Development Core Team, 2017) using a script written by M.D based on equations presented in [START_REF] Sjøvold | Nonmetrical divergence between skeletal populations: the theoretical foundation and biological importance of C. A. B. Smith's mean measure of divergence[END_REF] and [START_REF] Harris | Calculation of Smith's mean measure of divergence for intergroup comparisons using nonmetric data[END_REF].

Estimation of continental genetic ancestry

The individuals examined here have been previously genotyped on Illumina's HumanOmniExpress chip [START_REF] Adhikari | A genome-wide association study identifies multiple loci variation in ear morphology[END_REF](Adhikari et al., , 2016a,b),b), which includes over 700,000 SNPs. After pruning for Linkage Disequilibrium 93,328 autosomal SNPs were retained.

Genotype data from the admixed samples was combined with genotype data of reference samples from three continental populations to estimate European, African and Native American ancestry proportions using ADMIXTURE [START_REF] Alexander | Enhancements to the ADMIXTURE algorithm for individual ancestry estimation[END_REF].

Reference parental populations included in the ADMIXTURE analyses consisted of Africans and Europeans from 1000 Genomes (The 1000 Genomes Project Consortium, 2015) and selected Native American samples (Reich et al., 2012).

Correlation analyses

For all correlation analyses, the dental trait scores were considered ordinal variables.

The justification for doing so is that we assume an underlying continuous variable [START_REF] Scott | The Anthropology of Modern Human Teeth: Dental Morphology and its Variation in Recent Human Populations, 2 nd Edition[END_REF], and the convention that for an ordinal variable with several categories there is little difference between fitting a linear regression or an ordered probit model [START_REF] Harvati | Human cranial anatomy and the differential preservation of population history and climate signatures[END_REF]. We confirmed that both approaches produced similar results. Simple correlation analysis was performed among dental traits. To evaluate the effect of covariates (genetic ancestry, age, and sex) on the dental traits, we used partial correlation analysis. In these tests, the Bonferroni-adjusted P-value threshold for significance was P <0.001.

Inference of individual genetic ancestry from dental morphology

We explored two approaches to infer individual continental ancestry proportions from dental traits, both implemented in Matlab (R2017b) by K.A.

Using reference population data

Data on full trait distributions was obtained from the literature [START_REF] Scott | The Arizona State University Dental Anthropology System[END_REF] for fourteen reference population samples from areas that contributed extensively to admixture in Latin America: one from Sub-Saharan Africa (West Africa); three from Western Europe (Spain, Netherlands and England) and ten from Central and South America (Native Americans from Mexico, Ecuador, Brazil and Chile). Of the 29 traits described in [START_REF] Scott | The Arizona State University Dental Anthropology System[END_REF], 20 were scored in the Colombian sample. From these 20 we excluded traits that were missing in any reference population or had a low frequency in the Colombian sample (<1%). This resulted in the following 16 traits being retained: WINGUI1, SSUI1, DSUI1, IGUI2, TDUI2, MRUC, ODOUP1, HYPUM2, C5UM2, CTUM1, LCVLP2, GPLM2, CNLM1, CNLM2, PTSLM1 and C7LM1 (see Supplementary Table 1 for trait descriptions and Supplementary Tables 2 and3 for the trait scores in the Colombian sample).

To obtain estimates of ancestry in the Colombian sample based on these traits we followed the approach described below.

For a trait (j) with possible states 1, 2, …, c, the trait frequencies (f) in reference population r (with values a, e or n for African, European and Native, respectively) can be represented by: (𝑓 1 𝑗𝑟 , 𝑓 2 𝑗𝑟 , ⋯ , 𝑓 𝑐 𝑗𝑟 ), where the frequencies in each reference population sum up to one. These continental frequencies can be combined with ancestry proportions to construct a trait frequency distribution in individuals (i) of mixed ancestry (m) as:

𝑓 𝑘𝑖 𝑗𝑚 = 𝑝 𝑖 𝑎 • 𝑓 𝑘 𝑗𝑎 + 𝑝 𝑖 𝑒 • 𝑓 𝑘 𝑗𝑒 + 𝑝 𝑖 𝑛 • 𝑓 𝑘 𝑗𝑛 for any trait value k from 1 to c.
Where (𝑝 𝑖 𝑎 , 𝑝 𝑖 𝑒 , 𝑝 𝑖 𝑛 ) refer to the proportions of African, European and Native American ancestries in the admixed individuals (i). These 'mixed' trait frequencies also sum to one for any trait.

For a given ancestry proportion, a score can be constructed for each trait indicating how probable or improbable the observed trait value is, given the frequency distribution of this trait. For example, the score 𝑆 𝑖𝑗 of an individual i of mixed ancestry with value 𝑡 𝑖 for a trait j when compared to the frequency distribution (𝑓 𝑖 𝑗𝑚 ) for this trait can be calculated as:

𝑆 𝑖𝑗 = ∑|𝑡 𝑖𝑗 -𝑘| • 𝑓 𝑘 𝑗𝑚 𝑐 𝑘=1
This score represents the mean absolute deviation [START_REF] Rao | Linear statistical inference and its applications[END_REF] of the trait value in an individual relative to a frequency distribution. For any individual i, and any trait j, these scores can be calculated for each trait given ancestry proportions (𝑝 𝑖 𝑎 , 𝑝 𝑖 𝑒 , 𝑝 𝑖 𝑛 ). A composite score can then be constructed by summing across traits. For example, the composite score for person i over all T traits is:

𝑆 𝑖 = ∑ √ 𝑤 𝑗 • 𝑆 𝑖𝑗 𝑇 𝑗=1
To adjust for correlation between traits included in the analysis, we use weights (𝑤 𝑗 ) inversely proportional to their total correlation with other traits. As correlation values from the reference data was not available, correlation values in the Colombian dataset were used for this step. A commonly used weight [START_REF] Zou | Quantification of population structure using correlated SNPs by shrinkage principal components[END_REF] to scale the contribution of trait j is

𝑤 𝑗 = 1 ∑ 𝑟 𝑗𝑘 2 𝑇 𝑘=1
where 𝑟 𝑗𝑘 is the correlation between traits j and k.

To estimate ancestry for individual i we find the ancestry proportions (𝑝 𝑖 𝑎 , 𝑝 𝑖 𝑒 , 𝑝 𝑖 𝑛 )

which minimize the composite score 𝑆 𝑖 using a grid search over all possible ancestry proportions and evaluating the score at each combination. The individual ancestry estimates obtained with genetic and dental data were compared using intraclass correlations [START_REF] Shrout | Intraclass correlations: Uses in assessing rater reliability[END_REF]. The squared correlations, estimating the proportion of variance explained, were taken as estimates of the accuracy of estimation of genetic ancestry from dental morphology.

Estimation within the Colombian sample data

In the second approach we regressed genetic ancestry on each dental trait separately, or on multiple traits simultaneously, solely within the Colombian dataset. In the regression models we examined prediction accuracy based on 10-fold cross-validation (CV) [START_REF] Hastie | The elements of statistical learning[END_REF]. Thus, for each of 10 random subsets of these data, we trained models based on 90% of the subset and predicted genetic ancestry values in the remaining 10%. Prediction accuracy was evaluated by the fraction of trait variance explained by a model (R 2 CV), averaged over the 10 CV sets.

In the case of single-trait regression, ordinary multivariate linear regression was used.

Values of one ancestry component were regressed on age, sex, and one dental trait. In the case of regression involving multiple traits, we explored reducing overfitting and collinearity (which could affect prediction performance, [START_REF] Chatterjee | Regression analysis by example[END_REF], by applying the LASSO approach, which selectively includes only a few covariates in the regression model [START_REF] Hastie | The elements of statistical learning[END_REF]. We also used two dimension-reduction techniques on the set of all dental traits: Principal Component Analysis (PCA) and Independent Component Analysis (ICA), which summarize the total dental trait variation into a reduced number of independent variables, each capturing a substantial fraction of the total variation [START_REF] Hastie | The elements of statistical learning[END_REF]. In the case of PCA we retained for the regression analyses 20 PCs with relatively high eigenvalues and explaining 86% of the total variance. For ICA we retained 3 or 6 components, explaining 31.3% and 52.5% of the total variance, respectively.

We performed simulations to assess the performance of this prediction methodology under two scenarios. In the first scenario, we simulated a uniform ancestry distribution (between 0 to 100%) by sampling with replacement individuals from the Colombian data [START_REF] Fuller | Sampling statistics[END_REF], so as to obtain a simulated dataset with the same sample size and the same relationship between all variables and covariates as in the original dataset. We generated 100 simulated samples and obtained the average R 2 across samples to calculate prediction accuracy.

In the second scenario we divided the Colombian data into two subsets: one highly European (>95% European ancestry) and one highly Native (>95% Native American ancestry). We then sampled with replacement from these two subsets to create a simulated sample in which half of the individuals are highly European and the other half highly Native.

As before, this resampling maintains the same relationship between all variables and covariates. We generated 100 simulated samples. Since here the regression model is predicting dichotomous group labels, we used classification accuracy (% of correctly predicted group label) as an indicator of prediction accuracy [START_REF] Hastie | The elements of statistical learning[END_REF].

RESULTS

Distribution of individual genetic ancestry

Average estimates of genetic ancestry in the Colombian sample investigated were:

63% European, 28% Native American and 9% African. Individual estimates of Native ancestry show a relatively sharp peak at around 30% (Figure 1). As expected (since ancestry proportions are constrained by having to add up to 1) there is a strong negative correlation between European and non-European (Native or African) ancestry (r < -0.65). African ancestry presents a highly skewed distribution, with few individuals presenting >20% of African ancestry and no individual with >80% of such ancestry.

Correlation between dental traits and covariates

The frequencies of the dental traits examined in the Colombian sample are presented in Supplementary Tables 23. This sample shows low to moderate frequencies of traits common in Native Americans (e.g., WINGUI1, SSUI1, SSUI2, DSUI1, DSUI2, C5LM2; C6LM1), whereas traits with high frequencies in Africans (MRUC, DIASUI1 and C7LM1) presented low frequencies in the Colombians. Several features characterizing the Eurasian dental complex are also present in the Colombian sample (e.g., high frequencies of CTUM1, LCVLP2, 3CUM2 and CNLM1 and low frequencies of WINGUI1, DSUI1, GPLM2, C6LM1, C7LM1 and DWLM1). Overall, the frequency of dental traits in the sample examined reflects its mixed ancestry.

Moderate to strong positive, and significant, correlations (r>0.5, p-value <1. 29E-31) were observed between several of the traits examined. These usually represent the same trait scored in different teeth, including: SSUI1, SSUI2, SSLI1, SSLI2, DSUI1, DSUI2, DSLI1, DSLI2, DTUI1, DTUI2, ARUP1, ARUP2, AMTUP1, AMTUP2, AFLM1 and AFLM2.

Across traits, several significant positive correlations were observed, with the strongest occurring between SS and DS, in both upper and lower incisors. Possible explanations for these correlations include admixture linkage disequilibrium (particularly for traits present with high frequencies in parental populations) and pleiotropic effects of certain genetic variants influencing dental development [START_REF] Townsend | Genetic and environmental influences on human dental variation: a critical evaluation of studies involving twins[END_REF][START_REF] Hughes | Twin and family studies of human dental crown morphology: genetic, epigenetic and environmental determinants of the modern human dentition[END_REF][START_REF] Hillson | Tooth development in human evolution and bioarchaeology[END_REF]Dhamo et al., 2018).

A number of weak, but significant, correlations were observed between dental traits and covariates (r values 0.12-0.23) (Supplementary Table 4). Nine traits showed a negative correlation with age (DARUC, ARUP1, ARUP2, AMTUP1, AMTUP2, METUM2, HYPUM1, ARLP2, AFLM2), and one trait (PTSLM1) was positively correlated with age.

With the exception of PTSLM1 all dental traits correlated with age are related to cusps, ridges and foveae, which are structures that are very susceptible to wear. The relevance of dental wear as a proxy of biological age has been highly exploited in bioarchaeology [START_REF] Lovejoy | Dental wear in the Libben population: its functional pattern and role in the determination of adult skeletal age[END_REF]. Our findings suggest that in contemporary humans, despite the consumption of soft and processed foods, the effect of age on dental wear is considerable [START_REF] Faillace | The applicability of dental wear in age estimation for a modern American population[END_REF]. Finally, we found that five traits were correlated with sex: TDUI1, TDUC, MRUC, DARUC and DARLC. Four of these traits represent features of the canines, the most sexually dimorphic teeth in humans, hominins and non-human primates [START_REF] Plavcan | Sexual size dimorphism, canine dimorphism, and male-male competition in primates: where do humans fit in?[END_REF]. These observations underline the utility of canine morphology in the assignment of sex in undetermined samples from contemporary human populations [START_REF] Tardivo | Three-dimensional modeling of the various volumes of canines to determine age and sex: a preliminary study[END_REF].

Positive correlations were observed between African ancestry and three traits: C5UM2, CNLM1 and C7LM1. In addition, fourteen additional traits showed positive correlations with Native American ancestry (and, correspondingly, negative correlations with European ancestry): SSUI1, SSUI2, DSUI1, DSUI2, METUM1, METUM2, SSLI1, SSLI2, DSLI1, DSLI2, AFLM2, CNLM2, C5LM2, C7LM2.

Inter-population differentiation based on dental trait frequency

Table 1 shows the MMD matrix between nine reference population samples and the sample from Colombia calculated on the basis of the frequency of 16 dichotomous dental traits. Figure 2 displays the frequency of the 16 dental traits used in calculating the MMD matrix in the samples investigated and Figure 3 shows a principal coordinate analysis (PCoA) of the MMD matrix. All MMD distances except the pairs WE-NE, NE-NA and AA-NWNA, NWNA-NSA were significant (p<0.025). In Figure 3 PCo1 differentiates Native Americans from Europeans, North Africans and Sub-Saharan Africans, while PCo2

discriminates Sub-Saharan Africans from Europeans, North Africans and Native Americans.

Consistent with its mainly Native American-European but predominantly European ancestry, the Colombian sample lies on the European-Native American axis and is closest to Europeans.

Estimation of ancestry from dental traits

We explored two approaches to estimating ancestry from dental data. In the first approach, based on the frequency of dental traits in reference population samples, we estimated (as described in the Materials and Methods) average African, European and Native ancestry proportions as: 0.09, 0.59 and 0.32, respectively (with standard deviations of 0.26, 0.49, 0.47, respectively). These average ancestry estimates are similar to those obtained with genetic data (respectively, 0.09, 0.63, 0.28), although the values estimated from the dental data show more variation than the genetic estimates (which have standard deviations of 0.10, 0.13, 0.10, respectively). When contrasting individual genetic and dental ancestry estimates, the squared correlations (R 2 ) were low for the three ancestries: 0.7%, 0.7% and 0.5% (for African, European and Native American ancestries, respectively).

In the second approach, we predicted genetic ancestry values using regression models incorporating dental trait variation solely in the Colombian sample. Based on results from a 10-fold CV approach, we find that predictions of genetic ancestry from single dental traits have low R 2 values for all ancestries ( We also evaluated prediction of genetic ancestry from regression models incorporating all dental traits examined or components from two dimension-reduction methods (ICA and PCA) (Table 3). When including all traits, R 2 value were 0.8% for African, 2.1% for European and 3.4% for Native American ancestry. Although still low, prediction accuracy improved somewhat when using ICA or PCA. For ICA, using 3 components we obtain R 2 of 1.8%, 4.5% and 3.4% for African, European and Native American ancestry, respectively. Using 6 ICA components we obtain R 2 of 2.5%, 4.2% and 3.4% for African, European and Native American ancestry, respectively. When using 20 PCs we obtained R 2 of 0.8%, 4.1% and 4.6% for African, European and Native American ancestry, respectively. Finally, for the combined analysis using both ICs and PCs we obtained the R 2 of 1.2%, 4.1% and 4.9% for African, European and Native American ancestry, respectively.

DISCUSSION

The diversity in dental morphology observed in the Colombian sample studied here is consistent with the history of admixture between Native Americans, Europeans and Africans that characterizes Latin Americans. Traits common in those three continental populations are prevalent in the Colombian sample. Furthermore, the biodistance analysis and the average estimates of ancestry in the Colombian sample obtained from dental morphology data are consistent with the genetic estimates of ancestry: a predominant European ancestry, with substantial Native American ancestry and a relatively small African contribution. The correlation of certain dental features with specific genetic ancestries suggests that aspects of tooth morphology are likely to be influenced by alleles differentiated in frequency between continental populations (see [START_REF] Hubbard | Do nuclear and dental nonmetric data produce similar reconstructions of regional population history? An example from modern coastal Kenya[END_REF][START_REF] Rathmann | Reconstructing human population history from dental phenotypes[END_REF], probably involving loci impacting on tooth development [START_REF] Edgar | Dominance in dental morphological traits: implications for biological distance studies[END_REF]Dhamo et al., 2018). The three traits correlated with African ancestry detected here (C5UM2, CNLM1 and C7LM1) have been reported to show markedly higher frequencies in Sub-Saharan Africans relative to other continental populations [START_REF] Irish | Characteristic high-and low-frequency dental traits in Sub-Saharan African populations[END_REF][START_REF] Irish | Afridonty: "the Sub-Saharan African dental complex" revisited[END_REF][START_REF] Scott | The Anthropology of Modern Human Teeth: Dental Morphology and its Variation in Recent Human Populations, 2 nd Edition[END_REF][START_REF] Scott | The Arizona State University Dental Anthropology System[END_REF]. However, certain traits that have been described as characterizing a "Sub-Saharan African dental complex" (such as DIASUI1, MRUC, LCUI2 and GPLM2; [START_REF] Irish | Afridonty: "the Sub-Saharan African dental complex" revisited[END_REF] showed no significant correlation with genetic estimates of African ancestry. Similarly, most of the 14 traits showing positive correlation with Native American ancestry have been extensively documented as common in East Asians and Native Americans (Scott and Turner, 1997 and references therein). Noticeably, we did not detect any dental trait positively correlated with European ancestry. However, the distribution of dental traits in the Colombian sample shares some common features with the so-called "Western Eurasian dental complex" (sensu [START_REF] Scott | Basque dental morphology and the "Eurodont" dental pattern[END_REF], that is, low frequencies of WINGUI1, GPLM2, C6LM1, C7LM1 and DWLM1 and moderate to high frequencies of CTUM1, LCVLP2, 3CUM2 and four-cusped LM2 (CNLM2). So-called "Classic" European traits, such as the Carabelli tubercle, showed positive although not significant correlations (r<0.05) with European genetic ancestry. The lack of a significant correlation with ancestry of certain dental traits could be related to a lack of power to detect such effects, for instance due to the relatively low Sub-Saharan African ancestry and the rather narrow spread of individual ancestry estimates in the Colombian sample studied here (Figure 1). Furthermore, the difference in frequency of some traits between the parental populations involved in resulted in an increase in R 2 for prediction based on SSUI1 from 2.4% to 61.9%. In a second simulation we replicated the setting usually examined in the literature, which evaluates prediction of ancestry as pertains to discrete population categories to which individuals are assigned [START_REF] Edgar | Estimation of ancestry using dental morphological characteristics[END_REF][START_REF] Irish | Dental nonmetric variation around the world: using key traits in populations to estimate ancestry in individuals[END_REF]. Using the Colombian data-set we generated simulated sets of individuals either with high (>95%) European or Native American ancestry and then tested how accurately SSUI1 can assign individuals to these two sets. Classification accuracy was very high, at 93.5%.

In conclusion, our study shows that the dental characteristics of Latin Americans reflect their history of admixture involving Native Americans, Europeans and Africans.

However, despite dental morphology reflecting past admixture, the use of dental traits for inferring genetic ancestry components in admixed Latin Americans is a considerably more difficult task than the ancestry assignments usually performed in studies using discrete categories, such as those often used in US study samples. The correlation of certain dental traits with genetic ancestry suggests that aspects of tooth morphology could be influenced by specific alleles differentiated in frequency between continental populations. Further study of Latin American populations could provide a fruitful approach to the identification of such dental morphology loci.

Tables

[

  AA, N=1,022], North-South America [NSA, N=3,276] and Northwest North America [NNA, N=741); Africans (West Africa [WA, N=92], Khoisan [K, N=155] and South Africa [SA, 531]) and Europeans (Western Europeans [WE, N=371], Northern Europeans [NE, N=319] and North Africans [NA, N=545]

  admixture in Latin America might have been lower than what has been documented in available reference population data.Despite dental data providing relatively good estimates of average genetic ancestry in the Colombian sample, our prediction analyses indicate that the dental traits examined are relatively poor predictors of individual genetic ancestry in this sample. The prediction accuracy estimated is likely influenced by a range of factors, including: (i) the differentiation in trait frequency between the populations contributing to the admixture, (ii) the genetic architecture of the traits used (i.e., number of loci and allele frequencies at these loci, additive/dominant/recessive genetic effects), (iii) categorization of the traits in the ASUDAS system, including how it relates to the underlying dental morphology, (iv) the magnitude of the ancestry components being estimated, and (v) the distribution of individual ancestry values in the study sample.As an illustration of the importance of the distribution of individual genetic ancestry on prediction accuracy, we examined data for the SSUI1 trait characterized in the CANDELA sample from Chile (N=1,792; MFG unpublished). This sample is on average 49.4% European, 48.3% of Native American and 2.2% African[START_REF] Ruiz-Linares | Admixture in Latin America: geographic structure, phenotypic diversity and self-perception of ancestry based on 7,342 individuals[END_REF] and shows a wider individual ancestry distribution than the sample from Colombia (s.d. of 0.10 and 0.16, in Colombia and Chile, respectively, Supplementary Figure1). Consistent with the relatively larger spread of individual ancestry along the European-Native American axis, the Chilean sample shows both a stronger correlation of Native American ancestry with SSUI1 than seen in the Colombian sample (r of 0.33 v. 0.16, respectively) and higher ancestry prediction scores: 2.3%, 12.8% and 12.4% for African, European and Native American ancestry, respectively. For comparison, we evaluated the impact of the distribution of ancestry values on the accuracy of individual genetic ancestry prediction using SSUI1 by simulations based on resampling the Colombian data. A simulation changing the Colombian ancestry distribution to uniform (resulting in ancestry s.d. increasing from 0.10 to 0.29)

Table 2

 2

	: median R 2 of ~ 1% (range 0.7% -1.4%)

TABLE 1 .

 1 Mean Measure of Divergence (MDD) matrix showing distances between the Colombian and reference population samples based on dichotomized trait frequencies.

TABLE 2 .

 2 R 2 and weight values from regression analysis of genetic ancestry on each dental trait in the Colombian sample.

	Trait code	Africa	Weight	Europe	Weight	America	Weight
	SSUI1	0.009	0.002	0.013	0.896	0.024	1
	SSUI2	0.009	0.004	0.019	0.992	0.029	1
	DSUI1	0.008	0.538	0.009	0.134	0.025	1
	DSUI2	0.008	0.122	0.010	0.746	0.033	1
	CAUI2	0.008	0.156	0.010	0.876	0.009	0.112
	PSUI2	0.009	0.008	0.008	0.5	0.018	0.994
	WINUI1	0.009	0.004	0.009	0.148	0.009	0.256
	LCUI1	0.009	0.002	0.010	0.042	0.009	0.032
	LCUI2	0.008	0.120	0.011	0.874	0.009	0.608
	DIASUI1	0.009	0.012	0.009	0.14	0.009	0.628
	IGUI1	0.009	0	0.010	0.058	0.009	0.068
	IGUI2	0.009	0	0.009	0.002	0.009	0
	TDUI1	0.009	0.02	0.009	0.016	0.009	0.002
	TDUI2	0.008	0.208	0.009	0.296	0.010	0.018
	TDUC	0.016	0.972	0.008	0.652	0.009	0
	MRUC	0.009	0.044	0.008	0.416	0.008	0.278
	DARUC	0.009	0.006	0.009	0.128	0.009	0.112
	ARUP1	0.008	0.34	0.010	0.756	0.009	0.126
	ARUP2	0.008	0.13	0.009	0.014	0.009	0.002
	ODOUP1	0.008	0.006	0.010	0.022	0.009	0.006
	AMTUP1	0.009	0	0.009	0.01	0.009	0.006
	AMTUP2	0.007	0.228	0.010	0.008	0.009	0.002
	CAUP2	0.008	0.528	0.011	0.824	0.009	0.258
	X3CUP1	0.008	0.008	0.010	0.02	0.009	0.01
	MetUM1	0.008	0.556	0.015	0.96	0.008	0.454

Note: Boldfaced values denote higher weights (> 0.1). Trait codes as in Supplementary Table

1

TABLE 3 .

 3 R 2 values from a regression analysis of continental genetic ancestry on components obtained from Independent Components Analysis (ICA) or Principal Components Analysis (PCA) of the dental traits examined. Distribution of individual African (A), European (B) and Native American (C) ancestry obtained using genome-wide SNP data in the Colombian sample examined here. Frequency of the 16 dental traits used in the biodistance analysis in the Colombian and reference population samples. Sample codes: MED: Colombia; WA: Western Africans; KHO; Khoisan; SA: Southern Africans; WE: Western Europeans; NE: Northern Europeans; NA: Northern Africans; AA: American Artic; NWNA: Northwest North America; NSA: North and South Native Americans. Trait codes are as in Supplementary Table 1. Figure 3. Principal Coordinate Analysis (95.1% of the variance explained) of the MMD matrix (Table 1) displaying the relatedness of the population samples examined. MED: Colombia;

	Variables used	African	European	Native
				American
	All traits	0.008	0.021	0.034
	ICA, 3 Components	0.018	0.045	0.034
	(31.3% of total variance)
	ICA, 6 Components	0.025	0.042	0.037
	(52.5% of total variance)
	PCA, 20 Components	0.008	0.041	0.046
	(86% of total variance)
	ICA+PCA combined	0.012	0.041	0.046

WA: Western Africans; KHO; Khoisan; SA: Southern Africans; WE: Western Europeans; NE: Northern Europeans; NA: Northern Africans; AA: American Artic; NWNA: Northwest North America; NSA: North and South Native Americans.

ACKNOWLEDGMENTS

We thank the volunteers for their enthusiastic support for this research. We are very grateful to Universidad de Antioquia, Medellín, Colombia and Universidad de Tarapacá, Arica, Chile for kindly providing facilities for the assessment of volunteers. We are indebted to Lina Maria Parra (Universidad Libre de Colombia, Cali), Bernardo Salazar and Camilo Preciado (Facultad de Odontología, Universidad de Antioquia, Medellín) for their support during sample collection. We thank G.R Scott and J.D. Irish for their clarifications on the reference population data used in the present research. We thank Peter Ellison (AJPA Associate Editor) and two anonymous reviewers for their helpful comments provided during the reviewing process. Work leading to this publication was funded by grants from the: Leverhulme Trust (F/07 134/DF), BBSRC (BB/I021213/1) (to ARL), Excellence Initiative of Aix-Marseille University -A*MIDEX (a French "Investissements d'Avenir" programme) (to ARL), National Natural Science Foundation of China (31771393) (to ARL), Wenner-Gren Foundation for Anthropological Research (to MD), Universidad de Antioquia (CODI 2014-1124 to MD and LMR), and UCL Global Engagement Fund (to KA). KA was also supported by a Wellcome Investigator Award WT107055AIA (to Prof. C.D. Stern).

Supplementary Figure 1. Distribution of individual African (A), European (B) and Native

American (C) ancestry obtained using genome-wide SNP data in the Chilean sample examined.