Maksym Dekhtiarenko

Serhii Krykun

Vincent Carré

Frédéric Aubriet

David Canevet

Magali Allain

Zoia Voitenko

Marc Sallé

Sébastien Goeb

Tuning the structure and the properties of dithiafulvene metalla-assembled tweezers

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

Introduction

The coordination-driven strategy has been successfully used to construct a considerable variety of discrete architectures with very high yields. [START_REF] Cook | Recent Developments in the Preparation and Chemistry of Metallacycles and Metallacages via Coordination[END_REF][START_REF] Sun | Recent developments in the construction and applications of platinum-based metallacycles and metallacages via coordination[END_REF] One reason for this success, lies on the high degree of predictability in the geometry of the resulting selfassembled structures. [START_REF] Chakrabarty | Supramolecular coordination: self-assembly of finite twoand three-dimensional ensembles[END_REF] On this basis, more and more complex systems have been produced, including chiral [START_REF] Chen | Metallomacrocycles: From Structures to Applications[END_REF][START_REF] Chen | Chiral metallosupramolecular architectures[END_REF][START_REF] Liu | Supramolecular Chirality in Self-Assembled Systems[END_REF] , heteroleptic [START_REF] Bardhan | Palladium(II)-Based Self-Assembled Heteroleptic Coordination Architectures: A Growing Family[END_REF][START_REF] Holloway | Controlled selfsorting in self-assembled cage complexes[END_REF][START_REF] Bloch | Integrative self-sorting of coordination cages based on 'naked' metal ions[END_REF] and interlocked [START_REF] Lu | Molecular Borromean Rings Based on Half-Sandwich Organometallic Rectangles[END_REF][START_REF] Huang | Metallacyclic assembly of interlocked superstructures[END_REF][START_REF] Frank | Interpenetrated Cage Structures[END_REF] ones. Those self-assembled discrete structures generally include a cavity, [START_REF] Zarra | Molecular containers in complex chemical systems[END_REF] and their host properties have been widely studied to target various applications (e.g. depollution, [START_REF] Blanco | Complexation and Extraction of PAHs to the Aqueous Phase with a Dinuclear PtII Diazapyrenium-Based Metallacycle[END_REF] drug delivery, [START_REF] Casini | The Promise of Self-Assembled 3D Supramolecular Coordination Complexes for Biomedical Applications[END_REF] catalysis [START_REF] Fang | Catalytic reactions within the cavity of coordination cages[END_REF][START_REF] Guo | Regio-and Enantioselective Photodimerization within the Confined Space of a Homochiral Ruthenium/Palladium Heterometallic Coordination Cage[END_REF][START_REF] Yoshizawa | Functional Molecular Flasks: New Properties and Reactions within Discrete, Self-Assembled Hosts[END_REF] and storage of reactive molecules [START_REF] Mal | White Phosphorus Is Air-Stable Within a Self-Assembled Tetrahedral Capsule[END_REF] ). Nevertheless, for most of these applications, there is an important need for controlling the intensity of the host-guest interaction, [START_REF] Kim | Strategies for Reversible Guest Uptake and Release from Metallosupramolecular Architectures[END_REF] which implies designing stimuli-responsive architectures. [START_REF] Goswami | Nano)mechanical Motion Triggered by Metal Coordination: from Functional Devices to Networked Multicomponent Catalytic Machinery[END_REF][START_REF] Mcconnell | Stimuli-Responsive Metal-Ligand Assemblies[END_REF][START_REF] Li | Mechanistic Interplay between Light Switching and Guest Binding in Photochromic [Pd2Dithienylethene4] Coordination Cages[END_REF][START_REF] Chen | Construction of Stimuli-Responsive Functional Materials via Hierarchical Self-Assembly Involving Coordination Interactions[END_REF] On this basis, we described the preparation and properties of a series of redoxactive rings [START_REF] Goeb | A BPTTF-based self-assembled electron-donating triangle capable of C60 binding[END_REF] and cages [START_REF] Szalóki | Redox-Driven Transformation of a Discrete Molecular Cage into an Infinite 3D Coordination Polymer[END_REF][START_REF] Szalóki | Controlling the Host-Guest Interaction Mode through a Redox Stimulus[END_REF][START_REF] Szalóki | Neutral versus polycationic coordination cages: a comparison regarding neutral guest inclusion[END_REF][START_REF] Goeb | A Self-Assembled Electro-Active M8L4 Cage Based on Tetrathiafulvalene Ligands[END_REF][START_REF] Bivaud | Self-Assembled Containers Based on Extended Tetrathiafulvalene[END_REF][START_REF] Bivaud | A Metal-Directed Self-Assembled Electroactive Cage with Bis(pyrrolo)tetrathiafulvalene (BPTTF) Side Walls[END_REF] constructed from the tetrathiafulvalene (TTF) moieties and some of its derivatives. We also recently depicted the efficiency of the 9-(1,3-dithiol-2ylidene)fluorene (DTF)-based ligands, in generating selfassembled discrete structures, be they rings [START_REF] Krykun | A M2L2 Redox-Active Metalla-Macrocycle Based on Electron-Rich 9-(1,3-Dithiol-2ylidene)Fluorene[END_REF] , tweezers [START_REF] Krykun | Metalla-Assembled Electron-Rich Tweezers: Redox-Controlled Guest Release Through Supramolecular Dimerization[END_REF] or cages. [START_REF] Croué | A self-assembled M2L4 cage incorporating electron-rich 9-(1,3-dithiol-2ylidene)fluorene units[END_REF] The DTF moiety can be oxidized reversibly at low potential to the corresponding radical cation, [START_REF] Perepichka | Combining High Electron Affinity and Intramolecular Charge Transfer in 1,3-Dithiole-Nitrofluorene Push-Pull Diads[END_REF][START_REF] Amriou | The Interplay of Inverted Redox Potentials and Aromaticity in the Oxidized States of New π-Electron Donors: 9-(1,3-Dithiol-2-ylidene)fluorene and 9-(1,3-Dithiol-2-ylidene)thioxanthene Derivatives[END_REF] a species which is prone to form mixed valence or -dimer species under specific conditions. This driving force can be exploited to control, reversibly, the release of a guest compound thanks to a redox driven dimerization process. [START_REF] Krykun | Metalla-Assembled Electron-Rich Tweezers: Redox-Controlled Guest Release Through Supramolecular Dimerization[END_REF] We report herein that the shape, the redox and the binding properties of coordination-driven self-assembled metalla-cycles constructed from ditopic DTF based ligands and the cis-Pd(dppf)(OTf)2 complex (dppf = 1,1'-bis-(diphenylphosphino)ferrocene; OTf = trifluoromethanesulfonate), can be efficiently and readily tuned by a simple change from a 4-pyridyl coordinating unit to a 3-pyridyl one.

Results and discussion

We already reported that the self-assembly of the L4Pyr ligand with cis-Pd(dppf)(OTf)2 in dichloromethane at 40 °C converges to a single symmetrical M2L2 discrete species (Scheme 1 left). [START_REF] Krykun | A M2L2 Redox-Active Metalla-Macrocycle Based on Electron-Rich 9-(1,3-Dithiol-2ylidene)Fluorene[END_REF] In the present study, we applied a similar synthetic protocol to L3Pyr (Scheme 1 right). The presence of the 3-pyridyl unit leads to a more complex 1 H NMR spectrum than the one obtained from L4Pyr (Figure 2). Nevertheless, all aromatic signals could be attributed using a COSY experiment (Figure S2). In particular, all signals of pyridyl proton in Pd2L3Pyr2 are upfield shifted compared to the free L3Pyr ligand, except H6 (Figure 1a). This global observation is assigned to the shielding effect promoted by the phenyl rings from the dppf coligand, which is compensated in the case of H6 by coordination to the metal. The presence of only one discrete species is confirmed by [START_REF] Cook | Recent Developments in the Preparation and Chemistry of Metallacycles and Metallacages via Coordination[END_REF] H DOSY NMR experiment (Figure 1c andS3). The latter shows a single set of signals with a diffusion coefficient of D = 4.96 x 10 -10 m².s - 1 , a value which is very similar to the one measured for the Pd2L4Pyr2 metalla-cycle (Figure 1c'). This observation suggests that the self-assembled structure obtained from L3Pyr is similar in size to the one of Pd2L4Pyr2. The corresponding estimated hydrodynamic radius is of ca 10 Å, as extracted from the Stokes-Einstein equation (T = 298 K), [START_REF] Macchioni | Determining accurate molecular sizes in solution through NMR diffusion spectroscopy[END_REF][START_REF] Avram | Diffusion NMR of molecular cages and capsules[END_REF] a value which is consistent with the formation of a M2L2 architectures as in the case of Pd2L4Pyr2. The stoichiometry of the self-assembly Pd2L3Pyr2 was confirmed by high-resolution ESI-FTICR-MS spectrometry (Figure S4). In addition to signals of the expected M2L2 molecular clip [Pd2L3Pyr2 -2OTf] 2+ ; m/z = 1510.667), peaks corresponding to higher molecular masses were observed despite variations carried out on the instrumental conditions, the concentration (10 -5 M < C < 10 -3 M) and the solvent. Taken into account the above DOSY NMR data, these experiments suggest aggregation of the starting M2L2 metalla-cycle upon ESI. Such behavior is known in the literature with soft ionization conditions [START_REF] Ferrer | Self-Assembly of Heterometallic Metallomacrocycles via Ditopic Fluoroaryl Gold(I) Organometallic Metalloligands[END_REF] and was also observed in the case of the Pd2L4Pyr2 analogue. [START_REF] Krykun | A M2L2 Redox-Active Metalla-Macrocycle Based on Electron-Rich 9-(1,3-Dithiol-2ylidene)Fluorene[END_REF] Unfortunately, attempts to grow single crystals of Pd2L3Pyr2 suitable for X-ray analysis were unsuccessful. Theoretical calculations using the MM+ model were undertaken and the results compared to similar experiments carried out for Pd2L4Pyr2 (Figure 2). The calculated Pd2L4Pyr2 structure (Figure 2a) is fully consistent with the one observed in the corresponding by X-ray crystallography (Figure S8c). In particular, a dihedral angle of ca. 80° between both fluorenyl mean planes, and an intramolecular S … S distance between facing dithiole rings of ca. 15 Å, were found, and these values are very close to those observed in the crystal. Importantly, switching from a 4-pyridyl coordinating unit to a 3-pyridyl one, drastically modifies the shape of the metalla-clip. The metal coordination in the meta position of the pyridyl groups in Pd2L3Pyr, results in a significant conformational change with much closer electroactive units. In particular, Pd2L3Pyr shows a dihedral angle between both fluorenyl units of ca. 27° and a S … S distance of ca. 8.5 Å. The electrochemical properties of the metalla-clip Pd2L3Pyr2 were studied by cyclic voltammetry (CV) in CH3CN/CH2Cl2 and compared to the previously described Pd2L4Pyr2 homolog [START_REF] Krykun | A M2L2 Redox-Active Metalla-Macrocycle Based on Electron-Rich 9-(1,3-Dithiol-2ylidene)Fluorene[END_REF] (Figure 3a). Both L4Pyr and L3Pyr ligands exhibit one reversible redox wave, centered on the DTF moiety at E ox = 0.56 and 0.46 V vs Fc/Fc + respectively. One reversible oxidation is also observed for the DTF moieties in Pd2L4Pyr2 (E1 ox = 0.59V vs Fc/Fc + ) which is followed by oxidation of the ferrocene moieties Please do not adjust margins Please do not adjust margins at E2 ox = 0.82V vs Fc/Fc + . This observation indicates that both DTF ligands are electronically equivalent and independent in Pd2L4Pyr2. A striking different behavior is observed for tweezer Pd2L3Pyr2. The CV of the latter exhibits a splitting of the redox wave corresponding to the DTF units, with 2 reversible oxidations occurring at E1 ox = 0.49 V and E2 ox = 0.63 V vs Fc/Fc + , suggesting that both tips of the tweezer do not behave independently. Such splitting has already been reported in the case of molecular tweezers bearing TTF [START_REF] Cotelle | Glycoluriltetrathiafulvalene molecular clips: on the influence of electronic and spatial properties for binding neutral accepting guests[END_REF] and more recently with DTF tips, [START_REF] Krykun | Metalla-Assembled Electron-Rich Tweezers: Redox-Controlled Guest Release Through Supramolecular Dimerization[END_REF] and was ascribed to the formation of mixedvalence and π-dimer species upon oxidation. The abovementioned estimated distance of 8.5 Å between both panels in Pd2L3Pyr2 should in principle allow the sandwiching of a planar aromatic species between both tips, [START_REF] Leblond | Molecular Tweezers: Concepts and Applications[END_REF][START_REF] Hardouin-Lerouge | Molecular clips and tweezers hosting neutral guests[END_REF] including a selfintercalation of two molecular tweezers if no other species is present in solution. This was confirmed by a concentrationdependent CV study of Pd2L3Pyr2, which shows the disappearance of the splitting phenomenon upon diluting the solution from C = 10 -3 M to C = 6.25 x 10 -5 M (Figures 3c,d). Such behavior is similar to the one reported by E. Levillain and P. Hudhomme for TTF-based molecular clips. [START_REF] Cotelle | Glycoluriltetrathiafulvalene molecular clips: on the influence of electronic and spatial properties for binding neutral accepting guests[END_REF] Thanks to the modelling of cyclic voltammetry experiments, these authors could demonstrate that the stepwise oxidation process follows a square scheme involving both neutral and radical cation species, which interact either inside or outside the cavity (Figure S5a). This difference of the CV behavior between Pd2L3Pyr2 and Pd2L4Pyr2, is therefore correlated to the distance separating both tips of the tweezer: whereas Pd2L3Pyr2 can bind a planar guest in the cavity through the simultaneous contribution of both tips (S … S distance 8.5 Å) (Figure S5b), Pd2L4Pyr2 (S … S distance 15 Å) cannot. Based on those electrochemical experiments and geometrical optimizations, it appears that metalla-clip Pd2L3Pyr2 provides a cavity suitable for guest encapsulation. Additional cyclic voltammetry experiments were therefore carried out to monitor the host-guest interaction process, in presence of 9dicyanomethylene-2,4,7-trinitrofluorene (DCTNF), an electrodeficient planar aromatic compound (Figure 3b). Interestingly, the addition of an increasing amount of DCTNF into a solution of Pd2L3Pyr2 shifts the first oxidation process to higher potential with the disappearance of the wave splitting. This suggests the intercalation of the DCTNF unit between both electron-rich DTF tips, which prevents therefore the above-mentioned selfintercalation process of two oxidized metalla-clips to occur. Moreover, the splitting observed during the reduction process of the oxidized molecular tweezer also disappears in the hostguest system (Figure 3b), ruling out a guest release phenomenon upon oxidation, a behavior that we recently This journal is © The Royal Society of Chemistry 20xx

Please do not adjust margins Please do not adjust margins observed for a DTF-based Ruthenium tweezer. [START_REF] Krykun | Metalla-Assembled Electron-Rich Tweezers: Redox-Controlled Guest Release Through Supramolecular Dimerization[END_REF] As expected, similar studies carried out with Pd2L4Pyr2 did not show any significant changes of the cyclic voltammogram, except a very weak anodic shift (Figure S6). To get a better understanding of those interactions we tried to grow single crystals from solutions containing Pd2L4Pyr2 or Pd2L3Pyr2 and DCTNF (2 equiv.). Even though all attempts to get cocrystallized structures were unsuccessful, vapor diffusion of MeOtBu into a mixture of Pd2L4Pyr2 and DCTNF lead to single crystals that does not show presence of DCTNF in the structure. [START_REF] Shtukenberg | Crystal Growth with Macromolecular Additives[END_REF][START_REF] Shtukenberg | Manipulating Crystallization with Molecular Additives[END_REF][START_REF] Jones | Controlling crystal growth with modifiers[END_REF] The latter exhibits a packing mode that differs from the one obtained in absence of DCNTF [START_REF] Krykun | A M2L2 Redox-Active Metalla-Macrocycle Based on Electron-Rich 9-(1,3-Dithiol-2ylidene)Fluorene[END_REF] (Figures S8c) and shows some specific features (Figure 4). It includes three independent M2L2 metalla-clip units interacting through headto-tail π-π stacking between their respective DTF units, with interplanar distances of ca. 3.5 Å. As a result, they form an original discrete architecture constructed from two distinctive supramolecular interactions, i.e. coordination bonds and parallel displaced aromatic-aromatic interactions. Deeper insights related to the interactions mode occurring between DCTNF and Pd2L4Pyr2 or Pd2L3Pyr2 were provided by UV-Vis experiments carried out in CH2Cl2 (Figure 5). Both metalla-clips show absorption spectra close to those of their constitutive ligands (L4Pyr and L3Pyr) with, as expected, molar extinction coefficients which are twice higher. They are characterized by two absorption bands at high energy localized around 300 nm which are ascribed to π-π* transitions located on the pyridine and flurorene units as well as an intense ICT Please do not adjust margins Please do not adjust margins band around 480 nm coming from the HOMODTF -LUMOpyridine transition. [START_REF] Niu | Syntheses, electrochemical behaviors, spectral properties and DFT calculations of two 1,3-dithiole derivatives[END_REF] Job Plot experiments were carried out at λmax = 465 nm (Pd2L3Pyr2, Figure 5b) and 480 nm (Pd2L4Pyr2, Figure 5d), at C = 10 -5 M in CH2Cl2, upon addition of aliquots of DCTNF (C = 5 x 10 -4 M in CH2Cl2). As expected from CV experiments, both metalla-tweezers exhibit highly distinctive behaviors. As clearly seen from Figure 5b, a maximum is observed for a molar fraction of 0.5 in the Job plot titration of Pd2L3Pyr2 with DCTNF. This value is assigned to the formation of a 1:1 host-guest complex, for which both DTF unit cooperatively contribute to the guest binding, according to a sandwich-mode. A binding constant of Ka = 7.8 (± 0.9) x 10 5 was calculated [START_REF] Canevet | Macrocyclic Hosts for Fullerenes: Extreme Changes in Binding Abilities with Small Structural Variations[END_REF] , a value which illustrates the remarkable ability of this tweezer to complex the electro-deficient DCTNF unit. On the other hand, the Job plot titration in the case of Pd2L4Pyr2 (Figure 5d) exhibits a maximum for ca. 0.6-0.7. This value correlates with a 1:2 stoichiometry, meaning that even though the metalla-assembly Pd2L4Pyr2 does not possess a cavity suitable for recognition of planar guests, it is able to interact with two DCTNF units. On this basis, we assume that each DTF fragment can interact independently with one DCTNF unit. This is corroborated by a 1 H NMR experiment, which shows that signals of a mixture of a DTF ligand and DCTNF, are shifted related to the species recorded alone (Figure S7).

Conclusions

In summary, the properties of two M2L2 metalla-clips, Pd2L4Pyr2 and Pd2L3Pyr2, constructed from the same cis-blocked Pd(dppf)(OTf)2 complex and two isomeric DTF-based ligands differing by the position of the nitrogen atom on the pyridyl coordinating units, are compared. While the molecular tweezer built from L4Pyr shows an intramolecular distance of ca. 15 Å between both redox-active tips, the one obtained from ligand L3Pyr features a cavity in which both DTF units are separated by 8.5 Å. The latter structural organization is favorable for promoting i) a tweezer dimerization upon oxidation, through formation of intercalated cationic dimeric species ii) formation of a host-guest complex with an electro-deficient DCTNF unit, with a remarkable association constant of 7.8 x 10 5 in methylene chloride. These results illustrate at which extent minor structural changes led on the starting ligand, may drastically impact the geometry and host properties of the resulting metalla-species prepared through a coordinationdriven self-assembled processes.

Fig. 1 1 H

 1 Fig. 1 1 H NMR spectra (aromatic region) of ligands L3Pyr (a) and L4Pyr (a') in CDCl3, metalla-macrocycles Pd2L3Pyr2 (b) and Pd2L4Pyr2 (b') in CD2Cl2, and corresponding 1 H NMR DOSY spectra (c and c') related to (b) and (b').

Fig. 2

 2 Fig. 2 Molecular force field (MM+) model of tweezers Pd2L4Pyr2 (a) and Pd2L3Pyr2 (b).

Fig. 3

 3 Fig. 3 Cyclic voltammograms (CH3CN/CH2Cl2 (v/v 1/1), 0.1 M nBu4NPF6, 100 mV•s -1 , CG, V vs. Fc/Fc + ) of a) L3Pyr, L4Pyr, Pd2L4Pyr2 and Pd2L3Pyr2 at C = 10 -3 M, b) Pd2L3Pyr2 at C = 10 -3 M in presence of DCTNF, c) Pd2L3Pyr2 at different concentrations and d) the deconvoluted CV corresponding to (c).

Fig. 4

 4 Fig. 4 Crystal packing of Pd2L4Pyr2 crystallized by slow diffusion of MeOtBu in a solution of CHCl3 containing 2 equiv. of DCTNF (dppf phenyl rings omitted for clarity).

Fig. 5

 5 Fig. 5 UV-Vis spectra of ligands L3Pyr, L4Pyr and metalla-tweezers Pd2L3Pyr2 and Pd2L4Pyr2 recorded in CH2Cl2 (a), Job plots for complexation of receptor Pd2L3Pyr2 (b) and Pd2L4Pyr2 (d) with DCNTF determined by UV-Vis spectroscopy at respectively 465 and 480 nm (CH2Cl2, C = 10 -5 M), and plots of absorbance of a UVvis titration for complexation of receptor Pd2L3Pyr2 (CH2Cl2, C = 10 -5 M) with DCNTF (CH2Cl2, 5 x 10 -4 M) at 465 nm (c).

This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-3 | 3

This journal is © The Royal Society of Chemistry 20xx J. Name., 2013, 00, 1-3 | 5

Acknowledgements

The authors gratefully acknowledge the French Embassy in Kiev (Ukr) for PhD grants (SK and MD). They also acknowledge the ASTRAL platform (SFR MATRIX, Univ. Angers) for their assistance in spectroscopic analyses. Finally, the financial support from the National FT-ICR network (FR 3624 CNRS) for conducting the research is gratefully acknowledged.

Conflicts of interest

There are no conflicts to declare


Serhii Kryhun

Maksym Dekhtiarenko

David Canevet

Vincent Carré

Frédéric Aubriet

Eric Levillain

Magali Allain

Zoia Voitenko

Marc Sallé

Sébastien Goeb

Metalla-Assembled Electron-Rich Tweezers: Original Redox-Controlled Guest Release through Supramolecular Dimerization

Keywords: Host-guest systems, Molecular tweezers, Selfassembly, Sulfur-heterocycles, Supramolecular chemistry

Developing methodologies to control on demand the release of a molecular guest requires the rational design of stimuliresponsive hosts bearing functional cavities. While a substantial number of responsive metalla-cages have been described so far, the case of coordination-tweezers has been less explored. Herein, we report the first example of a redox-triggered guest release from a metalla-assembled tweezer. The latter incorporates two redox-active panels facing each other and constructed from the electron-rich 9-(1,3-dithiol-2-ylidene)fluorene unit. The tweezer dimerizes spontaneously in solution and the resulting interpenetrated supramolecular structure is able to dissociate in presence of an electron-poor planar unit, forming a 1:1 host-guest complex. The latter can be dissociated upon tweezer oxidation/dimerization, offering an original redox-triggered molecular delivery pathway.

Designing functional supramolecular materials requires a fine control over the relative spatial organization and stoichiometry of the constitutive elements. The coordination driven self-assembly methodology may lead to highly predictable geometries, by using complementary metal complexes and organic ligands. For instance, this strategy has been used to produce discrete supramolecular structures in very high yields. [1] In particular, important efforts have been devoted to devise molecular hosts in order to target applications such as drug delivery, [2] catalysis, [1b, 3] or sequestration of pollutants/reactive molecules. [3a] A step further has been reached with the design of functional cavities able to release on-demand an encapsulated guest, in response to an external stimulus. [4] In the course of our recent investigations in designing functional redox-active rings and cages [5] inspired from the tetrathiafulvalene (TTF) framework, [6] we recently depicted a redox-triggered guest releasing from electron-rich coordination cages. [7] Beside the widely described family of coordination rings and cages, i.e. featuring a closed cavity, molecular tweezers constitute a class of acyclic host molecules prone to bind various guest systems. [8] In this case, the cavity is geometrically defined by two panels facing each other and maintained in a more or less parallel conformation by a linker. Their guest binding capacities depend on the inherent properties (e.g. electronic) of their panels and on the distance separating them. For instance, a distance of ca. 7 Å is considered to facilitate the binding of a planar aromatic molecule, the resulting host-guest system being possibly stabilized in this case through -, CH- or donor-acceptor noncovalent interactions. Some molecular tweezers constructed from the electron-rich tetrathiafulvalene family have already been described, [9] but none has been constructed from the coordination-driven self-assembly strategy to our knowledge, though the latter has been extensively used to reach various supramolecular objects. [1b, 10] We report herein the one-pot synthesis of two ruthenium-based self-assembled molecular tweezers OxM4L2 and NaphM4L2 featuring the electron-rich 9-(1,3-dithiol-2-ylidene)fluorene unit. These complexes differ by the respective distances separating both dithiafulvenyl (DTF) tips, a parameter which is tuned depending on the length of the bis-ruthenium complex spacer (OxRu or NaphRu) (Figure 1). Whereas the smaller tweezer (OxM4L2) is observed as an individual unit, the larger one spontaneously forms the interpenetrated supramolecular dimer (NaphM4L2)2 in solution and in the solid state. This dimer can be dissociated either upon dilution to C < 10 -3 M, or upon addition of an electron-poor aromatic guest (i.e. 9-dicyanomethylene-2,4,7trinitrofluorene (DCTNF)), affording the NaphM4L2 monomer or the DCTNF⸦NaphM4L2 host guest complex respectively. Remarkably, the latter can be reversibly shifted to a tweezer dimer upon oxidation, with concomitant guest release (Figure 1). The synthesis of tweezer OxM4L2 was achieved in one-step from a stoichiometric mixture of redox active ligand 4PyrDTF [11] and arene ruthenium acceptor OxRu [12] in MeOH at C = 10 -3 M (15 h, 50°C). After precipitation with Et2O, the resulting solid exhibits a 1 H NMR spectrum (MeOD) with / pyridyl and fluorenyl signals upfield shifted in comparison with starting 4PyrDTF, as a result of the metal-ligand coordination (Figure 2a-b). A 1 H NMR DOSY experiment (Figure S5) revealed the presence of only one discrete species in solution with a diffusion coefficient (D) of 3.31 x 10 -10 m² s -1 in MeOD at C = 10 -3 M. The corresponding calculated Stokes radius of 12 Å, is in good agreement with the formation of the expected M4L2 species. [13] Interestingly, the 1 H NMR spectrum (MeOD) obtained from the reaction of 4PyrDTF with the NaphRu [14] acceptor (Figure 2c), shows a splitting of each signal, indicating the possible formation of a dimer structure. In particular, the large upfield shifts of fluorenyl aromatic protons (ac) in the 5.5-7.0 ppm region suggests an association driven by - interactions. The formation of a dimeric structure is further confirmed by the Stokes radius of 19 Å calculated from a 1 H DOSY NMR experiment (Figure S8), a value which is significantly larger than the one observed with OxRu. One will note that no discrete structure could be reached from the larger TetraRu acceptor. [14] High-resolution ESI-FTICR-MS spectrometry experiments were carried out on the isolated OxM4L2 and (NaphM4L2)2 selfassembled complexes in CH3CN at C = 10 -3 M (Figure 3 and Figures S15,S16). While the metalla-tweezer obtained from OxRu exhibits only signals resulting from the monomeric OxM4L2 species at m/z = 1325.0751 and 833.3996 (main contributions, Figure 3a), the self-assembly isolated from the reaction between 4PyrDTF and the larger NaphRu acceptor shows one isotopic pattern at m/z = 1949.4623 corresponding to the dimeric (NaphM4L2)2 species (main contribution, Figure 3b). It is worth nothing that no signal corresponding to the monomeric tweezer is observed, highlighting the stability of the supramolecular dimer, even in the gas phase. Eventually, all experimental isotopic distributions are in good agreement with calculated theoretical ones (Figures S15 andS16).

Single crystals suitable for X-ray diffraction analyses were obtained for both ruthenium-based tweezers, by liquid diffusion of methyl tert-butyl ether into a solution of the self-assembled structures in methanol at room temperature (Figure 4). The monomeric structure of OxM4L2 consists in two DTF electro-active units facing each other thanks to - interactions, with a distance of 3.47(1) Å (Figure 4a). Consequently, both OxRu spacers, in which the ruthenium atoms are separated by 5.49(1) Å, are twisted by 19.55 and 32.65° respectively from the ideal perpendicular conformation with the dithiafulvenyl fragments (Figure S20).The X-ray crystal structure of (NaphM4L2)2 reveals that two metalla-tweezers are partially stacked and stabilized byintermolecular - interactions with distances in the range of 3.44-3.56(1) Å (Figure 4b). No additional stabilization forces such as CH- interactions between the DTF ligands and the hydroxynaphthoquinonato units are observed, while these have been described as the main driving forces for interlocking carbazolebased ligands. [15] The stability of the dimer arrangement has been investigated by performing variable-concentration NMR experiments in deuterated methanol at 298 K (Figures 5a-c andS10). Diluting the solution from C = 10 -3 M to C = 3 x 10 -5 M results in a drastic simplification of the NMR spectrum and to the disappearance of all signals in the 6-7 ppm region. Dissociation of the dimer is further supported by a 1 H DOSY NMR experiment recorded at C = 3 × 10 -5 M from which a diffusion coefficient D = 3.63 × 10 -10 m².s -1 has been extracted (Figure S11), a value similar to that observed for the monomer OxM4L2 tweezer (D = 3.31 × 10 -10 m².s -1 , Figure 2 and S5). The slow equilibrium between the monomer and the dimer species at the NMR timescale, allowed a straightforward determination of the dimerization constant Kdim(MeOD) = 4416 ± 246 (Figure S12). [16] In order to study further the stability of the dimeric (NaphM4L2)2 species, we investigated its behavior in presence of DCTNF, such electron-poor unit being known to interact strongly with electronrich derivatives. [17] Interestingly, upon addition of 4 equivalents of DCTNF into a solution of (NaphM4L2)2 (C = 10 -3 M, MeOD), the 1 H NMR spectrum appeared significantly simplified (Figure 5d), illustrating the dissociation of the dimeric species. Moreover, the resulting  and  protons show chemical shifts similar to those of the NaphM4L2 monomer (Figure 5c), while signals corresponding to the DTF core are upfield shifted. Such observation suggests the intercalation of the electron-poor DCTNF plan between both DTF tips of the NaphM4L2 monomer. A 1 H NMR DOSY experiment from which diffusion coefficients of 3.07 x 10 -10 m².s -1 and 3.73 x 10 -10 m².s -1 could be extracted for the host and the guest respectively (Figure 5d and Figure S15) confirms i) the drastic decreasing of the self-assembly radius size, which is now comparable to the one of NaphM4L2 monomer and ii) the strong host-guest interaction. Finally, the formation of the DCTNF⊂NaphM4L2 complex is unambiguously demonstrated by an ESI-FTICR mass analysis of a mixture of (NaphM4L2)2 and 2 equivalents of DCTNF in acetonitrile, for which a characteristic signal of the doubly charged species is found at m/z = 1606.6168 (Figure 3c andS17).

The electrochemical properties of both OxM4L2 monomer and (NaphM4L2)2 dimer were studied by cyclic voltammetry in CH3CN at C = 10 -3 M and compared to those of ligand 4pyrDTF (Figure 6a). The latter exhibits one reversible oxidation wave at E1 ox = 0.56 V vs Fc/Fc + that is ascribed to the formation of a radical cation. [18] This value is in good accordance with the one reported for the analogous SHexyl functionalized ligand. [11] Interestingly, both self-assembled structures OxM4L2 and (NaphM4L2)2 show a significant splitting of the oxidation wave, providing evidence of electronic interactions between DTF units. A similar splitting was already reported in the case of TTF-based molecular tweezers and was ascribed to the formation of mixed valence and -dimer species. [9e] From a mechanistic point of view the electrochemical process observed for the (NaphM4L2)2 dimer consists of two successive oxidations, each involving two electrons (Figure 7a). Cyclic voltammetry was also considered in order to monitor the recognition process of DCTNF by (NaphM4L2)2 (Figure 6b). Addition of increasing amount of DCTNF leads to a shift of the binding equilibrium the host-guest complex formation, resulting in the disappearance of the oxidation process splitting according to the square scheme shown in Figure 7b. The DCTNF⊂NaphM4L2 host-guest complex exhibits a unique oxidation process at E1 ox = 0.58 V vs Fc/Fc + (Figure 6b). Interestingly, two reduction waves remain during the reduction scan, which occur at potentials very similar to those of the dimeric (NaphM4L2)2 self-assembly (Figure 6a). The reduction event may therefore be ascribed to the (NaphM4L2)2 4+ species that is recovered while releasing the encapsulated DCTNF (Figures 1 and7). One will note that the release process is reversible since the voltammogram remains identical after several cycles (Figure S19). In order to get a deeper understanding of the release/uptake mechanism, theoretical voltammograms were simulated both in absence and presence of the guest, taking into account equilibria illustrated in Figure 7c. Those electrochemical simulations fit nicely with the experimental CVs (Figure 6c) and confirm that this redox-triggered release process is driven by the highly favorable dimerization process of oxidized NaphM4L2 2+ tweezers (see SI).

In summary, two novel self-assembled metalla-tweezers were designed from an electron-rich DTF-based ligand and hydroxyquinonato diruthenium complexes. The larger NaphM4L2 tweezer shows a distance of ca 7 Å between both redox-active tips. Such geometry proves to be favourable for a spontaneous dimerization ((NaphM4L2)2), which could be characterized in solution, in the gas phase and in the solid state. Remarkably, this interpenetrated arrangement can be dissociated in presence of an electron-poor DCTNF unit, leading to a 1:1 host-guest complex (DCTNF⊂NaphM4L2) as shown by NMR and HRMS-FTICR experiments. Finally, electrochemical oxidation of the latter hostguest complex allows for regenerating the dimeric structure thanks to favourable interactions between the oxidized tweezerlike molecules, resulting in a concomitant original redox-controlled delivering of the DCTNF guest molecule. Work is underway to extend this new efficient approach in guest delivering, to new redox-active molecular tweezers.

COMMUNICATION Entry for the

Figure 1 .

 1 Figure 1. Synthesis of self-assembled tweezers oxM4L2 and (NaphM4L2)2 from ligand 4PyrDTF and complexes OxRu and NaphRu respectively, and supramolecular transformations occurring from (NaphM4L2)2.

  . Krykun, M. Dekhtiarenko, Dr. D. Canevet, Dr. E. Levillain, M. Allain, Dr. S.

Figure 2 .

 2 Figure 2. 1 H NMR (298 K, C = 10 -3 M, downfield region) of a) ligand 4PyrDTF in CDCl3, b) OxM4L2 in MeOD and c) (NaphM4L2)2 in MeOD. See Figure 1 for 1 H NMR assignments. D corresponds to the diffusion coefficient extracted from a 1 H DOSY NMR experiment and R to the corresponding hydrodynamic radii calculated from the Stokes-Einstein equation.

Figure 3 .

 3 Figure 3. ESI-FTICR mass spectra recorded in CH3CN at C = 10 -3 M of a) OxM4L2, b) (NaphM4L2)2 and c) (NaphM4L2)2 with 2 equiv. of DCTNF.

Figure 4 .

 4 Figure 4. X-Ray crystal structures of a) OxM4L2 and b) (NaphM4L2)2. Propyl chains have been omitted for clarity.

Figure 5 .

 5 Figure 5. a-c) 1 H NMR spectra evolution in MeOD of (NaphM4L2)2 from C = 10 - 3 M to C = 3 x 10 -5 M and d) 1 H NMR spectrum recorded from a solution at C = 10 -3 M of (NaphM4L2)2 containing 4 equiv. of DCTNF.

Figure 6 .

 6 Figure 6. Cyclic voltammogram at C = 10 -3 M in 0.1 M TBAPF6 (CH3CN, 100 mV.s -1 , vs Fc/Fc + ) of a) 4PyrDTF, OxM4L2 and (NaphM4L2)2, b) (NaphM4L2)2 in presence of DCTNF; c) Simulated Cyclic voltammogram of (NaphM4L2)2 in presence of DCTNF.

Figure 7 .

 7 Figure 7. Scheme illustrating equilibria occurring during a) the redox process involving the (NaphM4L2)2 dimer, b) the redox-triggered guest release process involving the NaphM4L2 monomer and c) the complete redox mechanism involved in the guest release process.

Table of Contents

	COMMUNICATION
	A redox-active coordination tweezer	Serhii Kryhun, Maksym Dekhtiarenko,
	constructed from the dithiol-fluorene	David Canevet Vincent Carré, Frédéric
	(DTF) framework spontaneously	Aubriet, Eric Levillain, Magali Allain,
	dimerizes in solution thanks to	Zoia Voitenko, Marc Sallé* and
	favourable geometric and electronic	Sébastien Goeb*
	parameters. The interconnected
	dimer can be dissociated upon
	forming a 1:1 host-guest complex in
	presence of an electron-poor guest.
	The latter can be reversibly released
	upon oxidation, through an original
	exchange process.

Page No. -Page No. Metalla-Assembled Electron-Rich Tweezers: Original Redox- Controlled Guest Release through Supramolecular Dimerization

Acknowledgements

The authors gratefully acknowledge the French Embassy in Kiev (Ukr) for PhD grants (SK and MD). They also acknowledge the ASTRAL platform (SFR MATRIX, Univ. Angers) for their assistance in spectroscopic analyses.


domain: phys spi

text:
K Pantzas

G Patriarche

Experimental quantification of atomically-resolved HAADF-STEM images using EDX

Atomically-resolved mappings of the indium composition in InGaN/GaN multi-quantum well structures have been obtained by quantifying the contrast in HAADF-STEM. The quantification procedure presented here does not rely on computation-intensive simulations, but rather uses EDX measurements to calibrate the HAADF-STEM contrast. The histogram of indium compositions obtained from the mapping provides unique insights into the growth of InGaN: the transition from GaN to InGaN and vice versa occurs in discreet increments of composition; each increment corresponds to one monolayer of the interface, indicating that nucleation takes longer than the lateral growth of the step. Strain-state analysis is also performed by applying Peak-Pair Analysis to the positions of the atomic columns identified the quantification of the contrast. The strain mappings yield an estimate of the composition in good agreement with the one obtained from quantified HAADF-STEM, albeit with a lower precision. Possible improvements to increase the precision of the strain mappings are discussed, opening potential pathways for the quantification of arbitrary quaternary alloys at atomic scales.

I. INTRODUCTION

Optoelectronic semiconductor devices are complex heterostructures that rely on multiple layers of semiconductor alloys. Tailoring these alloys to meet increasingly demanding designs for modern applications requires a thorough understanding of alloy formation and of the distribution of compositions within individual atomic monolayers and at the interfaces between different materials. A wide variety of characterization techniques can be used to measure the composition of alloys. Few, however, are capable of probing composition with an atomic resolution, such the one achieved in transmission electron microscopy (TEM).

In TEM, the composition of semiconductor alloys can be assessed quantitatively using strain-state analysis [START_REF] Bartel | A quantitative procedure to probe for compositional inhomegeneities in InGaN alloys[END_REF][START_REF] Gerthsen | Indium distribution in epitaxially grown InGaN layers analyzed by transmission electron microscopy[END_REF], cathodoluminescence [START_REF] Seguin | Multi-excitonic complexes in single InGaN quantum dots[END_REF][START_REF] Zagonel | Nanometer scale spectral imaging of quantum emitters in nanowires and its correlation to their atomically resolved structure[END_REF], energy-filtered TEM [START_REF] Lin | Quasiregular quantum-dot-like structure formation with postgrowth thermal annealing of InGaN/GaN quantum wells[END_REF][START_REF] Davies | Optical and microstructural studies of InGaN/GaN quantum dot ensembles[END_REF], and energy-dispersive X-ray spectroscopy [START_REF] Jinschek | Local Indium Segregation and Band-Gap Variations in High-Efficiency Green Light-Emitting InGaN/GaN Diodes[END_REF][START_REF] Pantzas | Investigation of a Relaxation Mechanism Specific to InGaN for Improved MOVPE Growth of Nitride Solar-cell Materials[END_REF]. These techniques either provide high chemical precision or high resolution. Only scanning transmission electron microscopy (STEM) in the high-angle annular dark field (HAADF) mode has been shown to combine high chemical precision with ultimate resolution. Indeed, in HAADF-STEM, the integrated intensity is a function of the atomic number Z of atomic columns scanned by the electron probe [START_REF] Pennycook | Chemically sensitive structure-imaging with a scanning transmission electron microscope[END_REF][START_REF] Pennycook | Z-contrast Imaging in an Aberration-corrected Scanning Transmission Electron Microscope[END_REF]. This integrated intensity can be simply modeled using Rutherford scattering. In practice, however, several additional factors need to be taken into account and the contrast of a HAADF-STEM micrograph alone can only be interpreted qualitatively [START_REF] Lebeau | Quantitative Atomic Resolution Scanning Transmission Electron Microscopy[END_REF][START_REF] Lebeau | Experimental quantification of annular dark-field images in scanning transmission electron microscopy[END_REF][START_REF] Rosenauer | Measurement of specimen thickness and composition in algan/gan using high-angle annular dark field images[END_REF][START_REF] Rosenauer | Composition mapping in ingan by scanning transmission electron microscopy[END_REF][START_REF] Walther | A new experimental procedure to quantify annular dark field images in scanning transmission electron microscopy[END_REF][START_REF] Atif | Modified qhaadf method for atomic column-by-column compositional quantification of semiconductor heterostructures[END_REF]. A quantitative interpretation of this contrast requires an external calibration. Rosenauer et al. [START_REF] Rosenauer | Composition mapping in ingan by scanning transmission electron microscopy[END_REF] showed that this calibration can be obtained by comparing normalized experimental intensities to intensities obtained from frozen-lattice simulations. Nonetheless, these simulations tend to be computationally intensive, and adapting them to a variety of material systems can prove prohibitively time consuming.

An alternative means of calibrating the contrast was proposed by the present authors, where the HAADF-STEM contrast is calibrated using energy-dispersive x-ray diffraction spectroscopy (EDX) measurements. This calibration procedure yielded reliable composition mappings from HAADF-STEM images for two families of semiconductor alloys (InGaN, InAlGaAs), although at magnifications not high enough to resolve individual atomic columns [START_REF] Pantzas | Nanometer-scale, quantitative composition mappings of ingan layers from a combination of scanning transmission electron microscopy and energy dispersive x-ray spectroscopy[END_REF][START_REF] Pantzas | Role of compositional fluctuations and their suppression on the strain and luminescence of ingan alloys[END_REF][START_REF] Pantzas | Sub-nanometrically resolved chemical mappings of quantum-cascade laser active regions[END_REF].

In the present contribution we adapt this procedure to the quantification of atomically resolved HAADF-STEM images. The alloy under investigation is indium gallium nitride (InGaN). Indium gallium nitride is an alloy that is nowadays ubiquitous in our daily life, with applications in light emitting diodes (LEDs), laser diodes and high-power electronics [START_REF] Nakamura | High-power gan p-n junction blue-light-emitting diodes[END_REF][START_REF] Nakamura | The Blue Laser Diode[END_REF][START_REF] Mishra | Gan-based rf rf power devices and amplifiers[END_REF][START_REF] Gil | Physics of Wurtzite Nitrides and Oxides -Passport to Devices[END_REF][START_REF] Rajan | Gallium nitride electronics[END_REF]. Among III-V semiconductors, this alloy holds a particular place, as LEDs based on InGaN/GaN quantum wells exhibit record high internal quantum efficiencies, well beyond 80 % [START_REF] Nippert | Temperature-dependent recombination coefficients in ingan light-emitting diodes: Hole localization, auger processes, and the green gap[END_REF], despite threading dislocation in the 1 × 10 8 cm -2 to 1 × 10 9 cm -2 range [START_REF] Ponce | Nitride-based semiconductors afor blue and green light-emitting devices[END_REF], i.e. four orders of magnitude higher than those typically observed in indium phosphide or gallium arsenide. Chichibu et al. [START_REF] Chichibu | Origin of defect-insensitive emission probability in in-containing (al,in,ga)n alloy semiconductors[END_REF] attributed this robustness to defects to the presence of localized radiative centers, related to the short diffusion length of holes in III-nitrides comparatively to other III-V semiconductors. These localized radiative centers were linked, in theory, to the presence of indium-rich clusters that potentially form quantum dots. Microscopic evidence of their presence has been the subject of intense debates: samples investigated in TEM were shown to form clusters due to damage by the electron beam [START_REF] Humphreys | Does in really form in-rich clusters in ingan quantum wells?[END_REF]; indium-rich quantum dots were unambiguously observed in one case in HAADF-STEM [START_REF] Rosenauer | Measurement of specimen thickness and composition in algan/gan using high-angle annular dark field images[END_REF]; InGaN wells investigated using atom-probe tomography (APT) [START_REF] Rigutti | Atom probe tomography of nitride semiconductors[END_REF][START_REF] Cerezo | Atom probe tomography today[END_REF], on the other hand, showed that InGaN is a random alloy. As a result of these investigations, a wealth of information is available for this alloy, making it a suitable test vehicle for the algorithm presented here.

The paper is structured as follows: the experimental setup is first described. The quantification algorithm is then explained and applied to an atomically-resolved HAADF-STEM image of InGaN quantum wells in GaN barriers. The distribution of indium in the wells and at the interfaces is discussed. Finally, the distribution of indium obtained from the quantification HAADF-STEM contrast is compared against that derived from strain mappings from the same image, as well as EDX measurements.

II. EXPERIMENTAL SETUP

The InGaN sample consists of ten 3 nm thick InGaN wells separated by 8 nm thick GaN barriers. The sample was provided by Novagan. X-ray diffraction measurements confirm that the wells are pseudomorphically accommodated on the GaN substrate and contain 17 at. % indium.

Lamellae for STEM observation were prepared from the sample using Focused Ion Beam (FIB) ion milling and thinning. Prior to FIB ion milling, the sample surface was coated with 50 nm of carbon to protect the surface from the platinum mask deposited used for the 3 ion milling process. Ion milling and thinning were carried out in a FEI SCIOS dual-beam FIB-SEM. Initial etching was performed at 30 keV, and final polishing was performed at 5 keV.

All samples were observed in an aberration-corrected FEI TITAN 200 TEM-STEM operating at 200 keV. The convergence half-angle of the probe was 17.6 mrad and the detection inner and outer half-angles for HAADF-STEM were 69 mrad and 200 mrad, respectively.

The lamella was imaged along the 1 1 2 0 zone axis. All micrographs where 2048 by 2048 pixels. The dwell time was 8 µs and the total acquisition time 41 s.

The EDX calibration of the HAADF-STEM contrast is the same as that used in Rereferences [START_REF] Pantzas | Nanometer-scale, quantitative composition mappings of ingan layers from a combination of scanning transmission electron microscopy and energy dispersive x-ray spectroscopy[END_REF][START_REF] Pantzas | Role of compositional fluctuations and their suppression on the strain and luminescence of ingan alloys[END_REF]. Additional EDX measurements were performed in the Titan microscope featuring the Chemistem system, that uses a Bruker windowless Super-X four-quadrant detector and has a collection angle of 0.8 sr. During EDX acquisition, the sample was also aligned along 1 1 2 0 . The acquisition time for the linescans was 10 min, during which no significant drift occurred.

The computer code for the quantification procedure described below has been written for the 64-bit version of Igor Pro 7 (WaveMetrics, Lake Oswego, OR, USA) 1 . In particular, the code uses the Igor Pro Image Processing library for image-processing operations, including particle analysis. Computation-intensive steps, such as extracting the average intensity for each atomic column, have been optimized for multithreaded execution. On a laptop equipped with a quad-core, dual-thread Intel i7 from 2015, i.e. running a total of 8 threads, the most demanding steps take about 15 min to process.

III. QUANTIFICATION PROCEDURE

The quantification procedure is based on References [START_REF] Pantzas | Nanometer-scale, quantitative composition mappings of ingan layers from a combination of scanning transmission electron microscopy and energy dispersive x-ray spectroscopy[END_REF][START_REF] Pantzas | Role of compositional fluctuations and their suppression on the strain and luminescence of ingan alloys[END_REF], where HAADF-STEM and EDX were combined to quantify the composition of InGaN alloys in STEM micrographs acquired at magnifications too low to resolve individual atomic columns. In these references, the composition x of indium in an In x Ga 1-x N alloy was shown to relate to the Z-contrast in the image, R, following2 :

x = Z α Ga + Z α N Z α In -Z α Ga (R -1) . (1)
Here, Z i is the atomic number of element i and α a scattering exponent. The contrast R is computed from the HAADF-STEM image intensity I following:

R = I -I 0 I ref -I 0 , (2)
where I 0 is the HAADF detector background intensity and I ref is a reference intensity. This reference is evaluated in a region of known composition, for instance in a region of GaN, then linearly extrapolated to the remainder of the image. Correctly defining I ref is a crucial step, as it also corrects for small variations in the thickness of the lamella. Energy-dispersive X-ray spectroscopy was used to estimate the scattering exponent α, and a value of 1.7 was found to yield the best fit.

While at low magnifications it is the intensity of each pixel that is quantified, in atomically-resolved HAADF-STEM micrographs pixels need to be grouped together into domains, each domain encompassing one atomic column. The HAADF-STEM micrograph needs, therefore, to be partitioned prior to applying the quantification procedure described above. Partitioning follows four steps: the original image is first filtered; atomic columns are then identified in the filtered image; the positions of the atomic columns are used to create a partition of the image into domains; finally, the average intensity over one domain of the partition is attributed to that domain's atomic column. These four steps are formally similar to those described by Rosenauer et al. [START_REF] Rosenauer | Composition mapping in ingan by scanning transmission electron microscopy[END_REF], however the specifics of the implementation differ. Using the computed reference intensity and by estimating the polarization current following the procedure in Reference [START_REF] Pantzas | Nanometer-scale, quantitative composition mappings of ingan layers from a combination of scanning transmission electron microscopy and energy dispersive x-ray spectroscopy[END_REF], the normalized contrast R is computed for each domain of the HAADF-STEM image. The average ratio R at the core of the InGaN wells is 1.23. Using this value and a scattering exponent of 1.7 yields an average concentration of 17.2 at. % indium, i.e. the nominal of the InGaN wells. Furthermore, the results from frozen lattice simulations in Reference [START_REF] Rosenauer | Composition mapping in ingan by scanning transmission electron microscopy[END_REF] also give a ratio of 1.23 for a lamella that is 80 nm thick and contains 17.2 at % indium. This indicates that the calibration used in References [START_REF] Pantzas | Nanometer-scale, quantitative composition mappings of ingan layers from a combination of scanning transmission electron microscopy and energy dispersive x-ray spectroscopy[END_REF][START_REF] Pantzas | Role of compositional fluctuations and their suppression on the strain and luminescence of ingan alloys[END_REF] is valid in the present case also.

Using the vector of ratios, Equation (1), and a scattering exponent of 1.7, the composition mapping presented in Figure 1 To obtain a good fit to the histogram, a total of six more peaks needs to be added to the sum of Gaussian curves used to fit the peaks of the cores of the GaN barriers and the InGaN wells. Gaussian curves are used as the distribution of compositions in InGaN is expected to follow a normal distribution. As stated above, InGaN is a random alloy and the composition in a single atomic column follows by a binomial distribution. By virtue of the central-limit theorem, this binomial distribution is well approximated by a normal distribution. Given that each frequency maps back to several monolayers and that each monolayer contains more than one hundred atomic columns, the conditions for the central-limit theorem apply here. Mappings (c) through (h) reveal that each peak corresponds to monolayers of distinct composition in the transition from GaN to InGaN and, symmetrically, from InGaN to GaN.

These monolayers are not necessarily contiguous, but on average extend laterally to about 25 nm, a value that is consistent with the typical step size in the layer. This indicates that the nucleation time is significantly shorter than the propagation time of a step. The composition of each layer in the transition is fixed at the time of its nucleation relative to the concentration of the indium precursor in the vapor phase. This concentration varies briefly in the time it takes to commute the indium source between the growth and vent manifolds in the MOCVD reactor.

IV. COMPARISON WITH ALTERNATE METHODS FOR MEASURING THE

COMPOSITION

The composition of alloys in an atomically resolved HAADF-STEM image can also be deduced from strain mappings computed from the image, albeit with a lower precision. Several algorithms have been developed over the years to compute such strain mappings, including geometric-phase analysis (GPA) [START_REF] Hÿtch | Quantitative measurement of displacement and strain fields from hrem micrographs[END_REF], peak-pairs analysis (PPA) [START_REF] Galindo | The peak pairs algorithm for strain mapping from hrtem images[END_REF], and template matching (TeMa) [START_REF] Zuo | Lattice and strain analysis of atomic resolution z-contrast images based on template matching[END_REF]. Of the three, the PPA algorithm can be straightforwardly implemented in the present case: in PPA, strain is computed from the real-space positions of atomic columns.

These positions have already been retrieved in the process of quantifying the HAADF-STEM contrast. The algorithm has been modified slightly from the one in Reference [START_REF] Galindo | The peak pairs algorithm for strain mapping from hrtem images[END_REF], in an attempt to improve its precision. In reference, the displacement is calculated between a given point and it's nearest neighbor along one of the two base vectors that have been chosen. Here, the displacement is instead computed as half the sum of the displacements from a given point to it's nearest neighbor along a base vector and from the same point to it's nearest neighbor in the direction opposite of the chosen base vector. This second definition is tantamount to using central differences to compute the displacement, which are well known to yield more precise results than forward or backward differences for the same number of grid points 3 .

Furthermore, it is well established that in HAADF-STEM there is a small amount of distortion that is related to sample drift during acquisition [START_REF] Zuo | Lattice and strain analysis of atomic resolution z-contrast images based on template matching[END_REF]. To obtain precise results, this drift has to be taken measured and corrected for. The correction is based on the assumption that overall drift is slow and does not change in direction during the acquisition.

The drift velocity is evaluated in regions of GaN, where no strain is expected. This velocity is then used to correct the positions in vector X before applying the modified PPA algorithm.

The end result are the four mappings shown in Figure 3, that were obtained from the HAADF-STEM micrograph in Figure 1 (a). In Figure 3, strain mapping (a) represents the in-plane strain, ε 1 100 , mapping (b) the strain along the growth direction, ε 0002 , mapping (c) the rotation and mapping (d) the shear strain. Of the four, only mapping (b) shows the presence of strain, i.e. the InGaN wells are pseudomorphically accommodated on GaN. The average strain in the core of the wells is 5.3 %, a value in good agreement with that expected for an InGaN alloy with an average indium composition of 17.2 %. The precision of the mappings, measured as the standard deviation in the GaN areas is 0.4 %.

Using the strain mappings of Figure 3 and the method for determining the composition from strain described in Reference [35], a second estimate of the composition is obtained from the same image. The composition measured in this manner is compared against the one obtained by quantifying the contrast in the HAADF-STEM micrograph in the plot of Figure 4. The plot graphs the average indium concentration per monolayer, i.e. the average over columns that belong to the same (0 0 0 2) plane. The red solid curve represents the composition determined by quantifying the HAADF-STEM contrast and the blue dashed curve the composition determined from the strain-state analysis. The two curves are in remarkable agreement. Nevertheless, the composition from HAADF-STEM is shown to be more precise: fluctuations in GaN are less than 0.1 at. %, as each monolayer groups more than 100 atomic columns. In the case of the strain-state analysis, though GaN on average is close to 0 at. %, the standard deviation in GaN from strain analysis is closer to 1.5 at. %.

Indeed, quasi-periodic oscillations are visible in GaN. Such fluctuations are the result of a small residual magnetic field present in the microscope's room, that affects the electron-beam 3 For further information please refer to Appendix B 9 during acquisition, and that despite the presence of a magnetic compensation loop. Having such a residual is unavoidable, but there have been recent successful attempts to correct for it [START_REF] Sanchez | An approach to the systematic distortion correction in aberration-corrected haadf images[END_REF][START_REF] Sanchez | Quantitative strain mappings applied to aberration-corrected haadf-stem images[END_REF]. In the present case, however, applying the method described in these references, was not possible, as fluctuations appear across both axes of the image. A few workarounds have been proposed in the literature. One approach consists in acquiring a single image at 45 • angle to the scanning direction, thereby allowing one to fit and correct for these fluctuations in both directions in a fashion similar to the one proposed in Reference [START_REF] Sanchez | An approach to the systematic distortion correction in aberration-corrected haadf images[END_REF]. A second approach consists in acquiring image pairs with orthogonal scan directions, allowing a better estimate of distortion [START_REF] Ophus | Correcting nonlinear drift distortion of scanning probe and scanning transmission electron microscopies from image pairs with orthogonal scan directions[END_REF]. Finally, revolving STEM, where a series of images acquired at several scanning angles was proposed to correct drift and distortions without prior knowledge [START_REF] Sang | Revolving scanning transmission electron microscopy: Correcting sample drift distortion without prior knowledge[END_REF]. In these methods increased precision comes at the cost of increased complexity of the acquisition. Alternatively, newer acquisition modes implemented in state of the art microscope where the microscope automatically acquires a series of rapid images, corrects for drift between them and sums them are now becoming available and are a promising way to decrease the residual errors in strain analysis. Such improvements would increase the precision of composition estimates based on strain-state analysis. The threshold for the precision of strain-state analysis to yield composition estimates comparable to that of quantified HAADF-STEM is a few tens to a hundred ppm, i.e. at least an order of magnitude better than the current precision. Reaching such precision is highly desirable, as it would allow one to quantify arbitrary quaternary alloys, where strain-state analysis or the intensity alone would not suffice to access both compositions of the alloy.

Finally, the third curve in the plot of Figure 4 graphs the results of an EDX linescan across the same area. The measured composition is in excellent agreement with that measured in quantified HAADF-STEM, although the noise floor is higher: the residual average in GaN is 0.4 at. % with a standard deviation of 0.2 at. %. No broadening of the wells is observed, indicating that at this magnification convolution with the electron beam is minimal. This is an encouraging result that shows that it is possible to use EDX to precisely measure the composition even in thin wells. It does not, however, provide quantitative information on the composition on the level of the atomic column, making it as of yet impossible to evaluate the distribution of compositions in an image and the insights that distribution provide regarding the growth mechanism of the layers in the image.

Using Equations (B9)-(B12) instead of Equations (B1)-(B4) is equivalent to using central finite differences instead of forward finite differences when one computes the strain fields.

Indeed, the strain fields are defined as the partial derivatives of the displacement versus the position:

ε xx = ∂U ∂x , ε xy = ∂U ∂y , ε yy = ∂V ∂x , ε yx = ∂V ∂y , (B13)
and, in the original PPA paper, the strain fields are computed by solving the following set of linear equations:

a x ε xx + a y ε xy = u x a y ε yy + a x ε yx = u y b x ε xx + b y ε xy = v x b y ε yy + b x ε yx = v y . (B14)
As a result, Equations (B1)-(B4) and (B14) compute the strain fields from the positions using forward differences, whereas Equations (B9)-(B12) and (B14) compute the strain fields from the positions using central differences. Forward differences are O(h) accurate, whereas central differences are O(h 2 ) [START_REF] Press | Numerical Recipes 3rd Edition: The Art of Scientific Computing[END_REF], hence, the second set of equations yields more accurate values for the strain fields from the same vector of positions. with a measurement error in GaN of less than 0.1 at. %. Although strain-state analysis yields a composition in good agreement with quantified HAADF-STEM, fluctuations are higher as a result of the magnetic environment of the microscope's room. Finally, the EDX linescan is shown to provide a good estimate as well, with a residual error of about 0.5 at. %. The wells do not show significant broadening.

Figure 1

 1 Figure1 (d) shows the result of this extrapolation. A gradient from the bottom left to the top right corner is visible in the surface plot. As mentioned above, this gradient is due to variations in the thickness of the lamella. The total variation of thickness accounts for 10 % of the intensity of GaN, and about 5 % of the maximum intensity in the image, highlighting how important it is to correct for it. Indeed, without the correction, the thickness gradient would account for an additional variation of 8.5 at. % of indium in the final composition mapping.

  (e) is finally computed. The mapping reveals the presence of three types of variations of the indium composition: grading along [0 0 0 2], at the interfaces between the GaN barriers and the InGaN wells, long-range variations of the indium composition in the InGaN wells along [1 1 0 0], and short-range fluctuations both in InGaN and GaN layers. To better analyze these variations, the histogram of indium compositions is shown in Figure 2 (a). In addition to the histogram, Figure 2 also presents mappings(b-i)of the spatial distribution of the mean indium concentration for each peak identified in the the GaN barriers as shown in mapping (b). The standard deviation for GaN is 0.5 at. %, and can be attributed to detector noise[START_REF] Rosenauer | Composition mapping in ingan by scanning transmission electron microscopy[END_REF][START_REF] Pantzas | Nanometer-scale, quantitative composition mappings of ingan layers from a combination of scanning transmission electron microscopy and energy dispersive x-ray spectroscopy[END_REF][START_REF] Pantzas | Role of compositional fluctuations and their suppression on the strain and luminescence of ingan alloys[END_REF][START_REF] Pantzas | Sub-nanometrically resolved chemical mappings of quantum-cascade laser active regions[END_REF]. The noise accounts for the fluctuations observed in the GaN barriers. The second-highest peak is centered at 17.2 at. %, at the opposite end of the histogram. Mapping (i) reveals that the second peak corresponds to the core of the InGaN wells. The standard deviation of this second peak is 1.5 at. %, larger than the standard deviation in GaN. This broadening of the distribution of indium in InGaN is due to random-alloy disorder[START_REF] Rosenauer | Composition mapping in ingan by scanning transmission electron microscopy[END_REF][START_REF] Rigutti | Atom probe tomography of nitride semiconductors[END_REF], although it is lower than the value expected for InGaN that contains 17.2 at. % indium and for a lamella thickness of 80 nm. Indeed, for a random alloy the distribution of compositions is binomial, and the standard deviation, σ alloy , is 2.4 at. %. Taking into account broadening due to detector noise, measured in GaN, the total standard deviation becomes 2.5 at. %. Rosenauer et al.[START_REF] Rosenauer | Composition mapping in ingan by scanning transmission electron microscopy[END_REF] attributed this discrepancy to averaging of the intensity from contribution of neighboring. An alternate interpretation, however, is possible. Indeed, given the thickness of the lamella, a single column can cross several atomic steps. The composition in each step is expected to vary slightly due to random alloy disorder. Therefore, the intensity measured for each column will represent an average over N steps, and the standard deviation is reduced by a factor 1/N . Using the values cited above, averaging would need to occur over 2.6 atomic steps, a reasonable estimate of atomic steps crossing the atomic column under observation in an 80 nm thick lamella. Given this standard deviation, what may appear to be indium clusters fall well within compositions expected for an InGaN alloy with an average indium content of 17.2 at. %. In fact, atomic columns with compositions as far apart as 6 at. % are likely to be observed, as they lie within the [µ In + 2σ In , µ In -2σ In ] interval. Examples of such clusters can be seen in the areas pointed out by white arrows in mapping (i) of Figure 2. The clusters in the same well are far apart enough to create localized emission centers, given the low hole diffusion lengths typically observed in InGaN alloys [27, 31], without any other phase separation or clustering mechanism to have to be taken into account. Between the two aforementioned peaks of GaN and InGaN, the histogram in Figure 2 (a) is not typical of homogeneously graded interfaces between InGaN and GaN. Instead of continuous tail, the histogram displays additional peaks at distinct indium compositions.

Figure 1 .

 1 Figure 1. (a) The input to the quantification procedure: an atomically-resolved HAADF-STEM image of the sample. Three InGaN quantum wells in GaN barriers are visible in the image. The inset is focused on the second InGaN well to GaN barrier interface. Dumbbells appear a disks, given that nitrogen has a much lower atomic number than gallium and indium. (b) Power spectral density (PSD) of the micrograph in (a). The first step in the algorithm consists in filtering in the Fourier space. The red circles indicate the crystal reflections that are selected. The remainder of the PSD is filtered out. (c) Bragg-filtered image of the micrograph in (a), obtained from the filtered PSD in (b). Compared to the original micrograph, this image does not contain variations due to composition, and only holds information regarding the position of the disks. This image is used to run a particle analysis and identify the atomic columns present in the image. These positions are in turn used to obtain a partition of the original micrograph using Voronoi tessellation. The image in (d) shows the result of the particle analysis and the tessellation. In the image a magnified portion of the (c) is superimposed with the identified positions of the centers of mass of atomic columns (blue crosses) and the vertices that are the result of the Voronoi tessellation. The identified domains closely resemble the intersection of the Wigner-Seitz cell for InGaN and the [1 1 2 0] planes[START_REF] Rosenauer | Composition mapping in ingan by scanning transmission electron microscopy[END_REF]. The partition obtained at this step allows one to measure the average HAADF intensity for each atomic column and associate it with the corresponding position. From this point on, the algorithm introduced in Reference[START_REF] Pantzas | Nanometer-scale, quantitative composition mappings of ingan layers from a combination of scanning transmission electron microscopy and energy dispersive x-ray spectroscopy[END_REF] can be applied to quantify the contrast. A crucial step in this quantification procedure is the establishment of a reference intensity in the GaN barriers, i.e. a region of known composition. The intensity measured in GaN is fitted using a plane and extrapolated to the whole image. The result is shown in (e). Using this reference intensity and Equations 1 and 2, one can now compute the composition mapping in (f).

Figure 2 .

 2 Figure 2. (a) Histogram of the indium compositions from Figure 1 (e), represented by the red solid line. The green dashed lines represent peaks identified in the histogram and the blue double-dashed line their sum, fitted to the histogram. Residuals of the fit are also given (orange line with round markers). The residuals show the overall fit is accurate to within 0.5 at. %, a value lower than the precision of the algorithm. (b-i) are mappings of the composition one standard deviation away from the mean of each peak identified in the histogram. The leftmost peak, centered at 0.1 at. % corresponds to the core of the GaN barriers (b). The standard deviation is 0.8 at. % and correspondsto detector noise. The rightmost peak, centered at 17.2 at. % corresponds to the core of InGaN wells (i). The standard deviation of this peak is 1.7 at. %. It is higher than that of GaN due to random alloy disorder, leading to the appearance of columns that can have composition as far apart 6 at. % (white arrows). Between these two, six additional peaks can be identified. The mappings (c-h) show that this distinct compositions each correspond to sets of monolayers between the GaN barriers and the InGaN wells. Such monolayers of distinct compositions can only occur during at the interface between GaN and InGaN if the propagation time of an atomic step is significantly lower than the layer's nucleation time. The composition is then fixed to that of the nucleus during nucleation.

Figure 3 .

 3 Figure 3. Deformation mappings, computed from the HAADF-STEM in Figure1(a), using the modified PPA algorithm described in the text. The mappings show that there is strain in InGaN only along {0}002, i.e. the growth direction. The average strain in the core of the InGaN wells is 5.2 %, a value in good agreement with an indium composition of 17.2 at. % in InGaN layers that are pseudomorphically accommodated on GaN. The error, measured in the GaN barrier, is 0.3 %. It is mainly due to fluctuations that are the result of a small residual magnetic field in the environment of the microscope. Such fluctuations can, in certain case be corrected for, increasing the precision of the strain-state analysis, and, as a result that of composition estimates derived from it[START_REF] Sanchez | An approach to the systematic distortion correction in aberration-corrected haadf images[END_REF].

Figure 4 .

 4 Figure 4. Plot comparing the indium composition per [1 1 0 0] monolayer, measured using three different techniques: the red solid line corresponds to quantified HAADF-STEM, the blue dashed curve to the composition deduced from strain-state analysis, and the green dot-dashed curve an EDX linescan. Of the three, quantified HAADF-STEM is shown to provide the most precise measurement,

The code can be used on a collaboration basis. A request should be sent by e-mail to the authors.

For a full derivation see Appendix A

ACKNOWLEDGMENTS

The authors would like to thankfully acknowledge funding from the CNRS Renatech network, the ANR Labex TEMPOS (ANR-10-EQPX-0050), and the ANR project LIGNEDEMIR (ANR-18-CE09-0035).

V. CONCLUSIONS

In the present contribution, atomically-resolved, quantitative mappings of the indium composition in InGaN/GaN multi-quantum well structures have been computed from HAADF-STEM micrographs. The quantification procedure does not rely on simulations, but rather a calibration through comparison with EDX measurements, a method that can be straightforwardly applied to a variety of semiconductor and other alloys. The resulting mapping contains a wealth of information regarding the distribution of indium in the structure, providing a wealth of insights as to its growth mechanism. The histogram of compositions in the mapping reveals that the transition from GaN to InGaN and vice occurs over monolayers of distinct compositions, a fact that shows that the composition is fixed at the nucleation, i.e. that the nucleation time of a layer is significantly higher than the subsequent lateral growth. Strain-state analysis was also performed by applying a modified version of the PPA algorithm to the position vector of identified atomic columns, obtained during the quantification. The composition deduced from the strain mappings is in good agreement with that from quantified HAADF-STEM. The precision is, however, at the moment lower. Increasing the precision of the strain-state analysis would open the path for the precise quantification at the atomic scale of arbitrary quaternary alloys.

Appendix A: Relationship between HAADF contrast and composition

The HAADF-STEM annular detector detects electrons scattered to high angles through Rutherford scattering. The detected intensity I can be expressed as follows:

where I 0 is the background intensity, and depends on the brightness settings used to acquire the HAADF-STEM image. K is a constant, d the thickness of the lamella under observation, (x i , Z i ) the concentration and atomic number of scattering element i in the lamella, and α the scattering exponent. Following Equation (A1), the intensity of In x Ga 1-x N alloy is:

the contrast R is defined as the ratio of the intensity in Equation (A1) to a reference intensity I ref :

If the reference intensity is taken in GaN, and linearly extrapolated to the whole image, one can show that R is linked to the composition x through:

or, equivalently:

Using EDX and this equation, one can estimate the scattering exponent α. In the case of InGaN, we have shown that a value of 1.7 yields the best fit [START_REF] Pantzas | Nanometer-scale, quantitative composition mappings of ingan layers from a combination of scanning transmission electron microscopy and energy dispersive x-ray spectroscopy[END_REF][START_REF] Pantzas | Role of compositional fluctuations and their suppression on the strain and luminescence of ingan alloys[END_REF].

In Peak-Pair Analysis (PPA), the strain fields ε xx , ε xy , ε yy , and ε yx are computed from the displacements (U, V) between nearest neighbors. Four nearest neighbors to a given position (x, y) in the vector of atomic-column positions X are identified using two non-colinear base vectors a, b . In the following, the index pair (n, m) is used to denote the position at which the displacements (U, V) are computed. The nearest neighbor in the direction of base vector a is denoted using the index pair (n + 1, m) and the nearest neighbor in the direction of base vector b the index pair (n, m + 1). Using this notation, Galindo et al. [START_REF] Galindo | The peak pairs algorithm for strain mapping from hrtem images[END_REF] define the deformation U with respect to base vector a at position X n,m as:

Similarly, deformation V with respect to base vector b at position X n,m is defined as:

Given, however, that the nearest neighbors (n -1, m), and (n, m -1), along the directions of vectorsa andb, respectively, have also been identified, the displacements (U, V)

can also be defined as:

and

To increase the precision of the strain mappings, the deformation in the present contribution is taken as the average between Equations (B1)-(B4) and Equations (B5)-(B8), i.e.

(U, V) are expressed as follows:

and

Appendix C: Corrections for drift in the STEM image

In STEM, images are acquired by scanning the probe over a region of interest in the sample. Even in the most stable environments, small sample drift still occurs. This results in slight distortions in the image that need to be corrected for when one computes strain from a given HAADF-STEM image. Using the same notation as in Section B and assuming small drift in an arbitrary direction, the position of an atomic column in the image can be expressed as follows: Here . denotes the floor function. Equations (C3) and (C4) express the drift as the drift velocity multiplied by the time it took the beam to reach the pixel where the atomic columns was identified. Based on these expressions, the displacements (U, V) become: