G Picot

O Adam

M Bergounioux

H Glotin

F-X Mayer

Automatic prosodic clustering of humpback whales song

We automatically segmented a humpback whale song using the Roger Payne's principle of sound unit and we patterned and automatically classified intonations of sound units thanks to an unsupervised algorithm to describe recurrent patterns. We determined 6 different patterns of intonation. Some different sound units present the same pattern of intonation and one sound unit can be submitted to different patterns of intonation. Intonation could be related to information's transmission between humpback whales while they are singing.

I. INTRODUCTION

Humpback whale songs are long cyclical sequences produced by males during the reproduction season which follows their migration from high-latitude to low-latitude waters. Singers of one geographical population share parts of the same song. This leads to the idea of dialect [1,2,3]. Different hypotheses of these songs were emitted [START_REF] Medrano | Sex identificationd of humpback whales, Megaptera novaeangliae, on the wintering grounds of the pacific ocean[END_REF][START_REF] Frankel | Spatial distribution, habitat utilization and social interactions oh humpback whales, Megaptera novaeangliae, off Hawaii, determined using acoustic and visual techniques[END_REF][START_REF] Baker | Aggressive behavior between humpback whale (Megaptera novaeangliae) wintering in Hawaiian waters[END_REF], even as used as sonar [START_REF] Mercado | A sonar model for humpback whale song[END_REF][START_REF] Au | Against the humpback whale sonar hypothesis[END_REF][START_REF] Mercado | Humpback Whale Song or Humpback Whale Sonar? A Reply to Au et al[END_REF].

In 1982, in a handmade work without using any software, Roger Payne exhibited a hierarchical structure of humpback whales songs. Defining a sound unit as any continuous sound between two silences, he showed that a song is an ordered sound units sequence. A so called subphrase is a particular sequence of 4 to 6 sequences. Subphrases compose phrases that compose themes. A song is composed of 3 to 9 themes and its length is about 20 to 40 minutes. Variations of songs perpetually occur; they are related to modifications of sound unit (duration, frequency) or to modifications of the vocalizations order. The explanation of this evolution remains unknown but it seems that one modification is shared by all the singers of of a population. Some long-term similarities between songs of neighbors populations exist that refutes any hypothesis of random modification [2,3,[START_REF] Winn | Song of the Humpback Whale-Population comparison[END_REF].

We studied acoustic characteristics of songs by developing signal processing automatic methods. We present recurrent distinctive features of humpback whales songs and put forward new hypothesis about syntax or semantic content. We look for an automatic classification of specific intonations of different sound units of a same song. This goal is not new [START_REF] Mercado | Classification of Humpback Whale Vocalizations Using a Self-Organising Neural Network[END_REF] but the originality of our work is to focus on prosody of humpback whale songs that is the role of intonation in the transmission of information via acoustic communication between different speakers.

II. METHODS

Using MATLAB© software, we have implemented an automatic segmentation algorithm based on Payne's principle to build up a database of sound units of a song. To analyze these vocalizations, we focus on the frequency range [0-10kHz] and set the minimal duration of a vocalization to 0.1s. Songs were sampled at 44.1kHz and encoded with a vectorial form. We calculate the spectrogram matrix using samples of 4096 coefficients and a shifting window of 2048 samples [START_REF] Gasquet | Analyses de Fourier et Applications[END_REF]. We kept the frequency curve corresponding to the maximal energy level in each column of the spectrogram matrix. We called it the characteristic frequency curve denoted F0. It is important to note that F0 is a priori different from the fundamental frequency f (Fig. 1).

Fig. 1 Algorithm for the HW vocalizations analysis

We extracted indexes of F0 corresponding to values superior to the 20Hz threshold of minimal frequency and distinguished sound units by listing couples of difference superior to 0.1sec. Vocalizations with too oscillating characteristic frequency or too weak energy or characteristic frequency were deleted to improve the algorithm accuracy.

We obtained a pattern of the intonation of a vocalization, assuming that humpback whales songs are harmonic and considering evolution of characteristic frequency. We listed frequency corresponding to each tenth of the total duration of a unit sound to approximate characteristic frequency with a piece-wise linear function. Then we calculated the slope of the segment joining collected frequencies to get an estimate of the "derivative curve" of the characteristic frequency (Fig. 2). The time evolution of the characteristic curve is an acceptable pattern of the intonation of vocalization. Thus we constituted the matricial database of intonations.

An automatic classification of intonations was performed using the unsupervised algorithm k-means which splits a database in k distinct clusters. We used the predefined function of Matlab© called Kmeans_clusters [START_REF] Guillaume | Musique et acoustique, de l'instrument à l'ordinateur[END_REF][START_REF] Escudier | La parole, des modèles cognitifs aux machines communicantes[END_REF][START_REF] Duda | Pattern Classification[END_REF][START_REF] Haton | Reconnaissance automatique de la parole,du signal à son interprétation[END_REF]. The number of clusters was varying between 1 and 20. The accuracy of an estimate was computed with the corresponding Davies-Bouldin index that gives information on the ratio between intra-clusters and inter-clusters similarity [START_REF] Davies | A cluster separation measure[END_REF].

Let note the k th classes of the set E: E 1 , E 2 ,…, E k with their respective kernel: x 1 , x 2 ,…, x k . For 1≤i≤k, the diameter of E i is defined by eq. 1:

( ) ( ) 2 1 2 2 1       - = ∆ ∑ ∈ i E x i i i x x E card E (1)
The distance between 2 classes is given by eq. 2:

( )

2 , j i j i x x E E - = δ (2)
We use the Davies-Bouldin criterion for the classification. This criterion is:

( ) ( ) ( ) ∑ = ≤ ≠ ≤           ∆ + ∆ = k i j i j i k i j E E E E k DB 1 1 , max 1 δ (3)
A low criterion (eq. 3) means a strong similarity intra-classes. Thus we deduced an optimal classification.

III. RESULTS

The automatic segmentation and classification of intonations algorithms were tested on a 24 minutes long song. 505 sound units were detected. The time reference points for silences and vocalizations were compared and turned out to be perfectly complementary. The listening of discerned sound units turned out to be satisfactory. The intonations of the 505 sound units were modeled, pooled under matricial form and classified. The table I reports the Davies-Bouldin indexes of the different classifications.

We determined 13 clusters. The figure 3 reports the temporal organization of intonations.

72% of sound units are submitted to one intonation pattern. 5 other patterns gather more than 2.5% of the sound units. The last 7 patterns are too poorly represented to be significant and often seem to be very similar to main patterns. The surrounding marine noise may have induced a perturbation for the performed classification. We report below the 6 types of the listed intonations. They correspond to the 4, 7, 13, 12, 8 and 2 clusters classes.

The main pattern is the number 4 which gathers different sound units of frequencies between 0 and 5 kHz (Fig. 4). The characteristic frequency first slightly decreases; then it increases slowly showing a slight intonation. Modulations of rhythm and variations of the amplitude are picked out but global shapes of the 4 listed characteristic frequencies are similar. Below the characteristic frequency of each unit sound is juxtaposed to the spectrogram with a continuous line thanks to the software Praat (http://www.fon.hum.uva.nl/praat/). Its values depends on the [0-500Hz] range at the right-hand of the picture. Pattern 7 gathers 7.5% of sound units. It is characterized by an increasing of the slope of the characteristic frequency starting at the half of the sound unit; it is followed by a sharp readjustment of the height of the note. The corresponding spectrum of unit sounds seems to be large in view of the 3 examples below (Fig. 5).

Pattern 13 describes a brutal falldown of the characteristic frequency at the half of the sound unit after a phase of frequency modulation of variable amplitude. It remains constant, falls again then remains constant before increasing. 2 models of sound units have this particularity which gathers 5.5% of the sound units of the song (Fig. 6).

The characteristic frequencies of vocalizations of the class 12 show a quick jump followed by a slow increasing ended by a sharp speeding up. 2 distinct sound units are thus identified (Fig. 7); it gathers 5% of total sound units. Note the likeness with the class 2. Moreover it seems that the first example of vocalizations of the class 4 is similar to the first example of vocalizations of the class 2. This makes us believe that the singer has changed the intonation of this sound unit during the song. Pattern 8 gathers 2.5% of the sound units (Fig. 7). There is one unique example of vocalization characterized by a sudden reduction of the characteristic frequency before a long phase of frequency modulation as in the class 4. The difference between the two patterns shows the importance of a slight modification of intonation of a sound unit.

Let us have a look on one of the unit sound that belongs to the class 11 (Fig. 8). It is very similar to vocalizations of the former class but with slightly different intonation: the duration before the fall of the characteristic frequency is longer. This observation gives a good illustration that one vocalization can be associated to distinct intonations. Pattern 2 shows several similarities with t pattern 7. There is a frequency peak at the half of the unit sound. The distinction between the two patterns is hard to establish but it could be explained by the less important increasing of the characteristic frequency in the pattern 2 than in the number 7. It gathers 2.5% of the sound units.

The table II gives the mean durations of vocalizations of each class of intonation.

The mean duration of sound units associated to intonation 4 is the only one inferior to 1sec. The shortest vocalizations are associated to the same pattern of intonation. The modulations of intonation are mainly applied on long vocalizations. The table below gives the probability that one pattern of intonation is followed by another. The way goes from intonation in the row to intonation in the column (Table III).

It is delicate to identify a coherent organisation of intonations. It appears that patterns of intonations 2, 7, 8, 12, and 13 phrase irregularly the song and that pattern 4 is the basic intonation. A more accurate pattern is required to try to explicit a structure of the song related to intonations.

IV. . CONCLUSION

Automatic segmentation of the song was successfully tested. The characterization by the so-called characteristic frequency is useful to distinguish sound unit and ambient marine noise. This may be a good base to implement more efficient automatic segmentation algorithm. The study of the characteristic frequency of unit sound gave pertinent patterns of sound units. 6 distinct and recurrent patterns have been distinguished. We can note that this number also corresponds to the different vocalizations that Roger Payne distinguished in a whole song. Humpback whales seem to use as many vocalizations as intonations. Different vocalizations (duration, frequency, fundamental frequency, harmonics) showed similarities and we obtained examples of vocalizations occurring several times but with different intonations. Intonation could have a structural importance and transmit information. The signification of a sound unit could be altered with intonation. The mean duration of sound units of each class seems to be relevant that modifications of intonations affect the longest vocalizations. We can suppose that differences of intonation are more perceptible when they are related to long vocalizations. Correlations between intonation and duration of the vocalization have to be statistically studied. Moreover accurate patterns of intonation have also to be obtained. Other clustering methods will be tested as far as k-means is known to be quite dependant to the initial conditions. It will be also interesting to study the role of silences in the song and the energy of the vocalizations.

Fig. 2 :

 2 Fig. 2: Variation of the characteristic frequency F0.F0Estimate of F0 Derivative of F0

Fig

  Fig. 3: time repartition of the intonations

1Fig

  Fig. 6 Intonation 13. Vocalizations 1 and 2

ACKNOWLEDGMENT

  This work was supported in part by Association Megaptera (France), Association Dirac (France) and by University of Orléans (France).REFERENCES[1] D.A Helweg, D.H Cato, P.F Jenkins, C. Guarrigue and R.R McCauley, "Geographic variation in south pacific humpback whales songs," Behavior, 135, pp. 1-27, 1997. [2] R.S. Payne, "Behavior and vocalizations of humpback whales (Megaptera sp)" pp. 56-78. In: K.S.Norris and R.R. Reeves (eds) Report on a workshop on problems related to humpback whales (Megaptera novaeangliae) in Hawaii, NTIS, PB-280794, Report No. MMC-77/03. Springfield, VA. 90pp. , 1978 [3] K. Payne, P. Tyack and R. Payne, "Progressive changes in the songs of humpback whales (Megaptera novaeangliae) : a detailed analysis of two seasons in hawaii", in Communication and behavior of whales, pp. 9-58, Westview Press, Boulder, 1983.

TABLE III TRANSITION

 III MATRIX BETWEEN THE 6 MOST VISITED CLUSTERS (IN %). CLUSTER 4 IS DOMINANT.

				TABLE II
			DURATION OF VOCALIZATIONS OF EACH CLASS
	Intonation	2	4	7	8	12	13
	Duration (sec)	1.85	0.84	1.83	2.1	1.8	1.1
	From \ To	2	4	7	8	12	13
	2	8	69	2	8	0	0
	4	2	79	6	2	4	3
	7	0	68	5	3	13	3
	8	0	27	27	0	27	18
	12	8	44	12	4	0	16
	13	0	66	4	4	7	18


I. INTRODUCTION

Electronic properties of semiconductor nano-structures are strongly influenced by their strain state, and many examples have already shown that strain engineering was an efficient tool to boost the microelectronics technologies. [START_REF] Dunstan | Strain and strain relaxation in semiconductors[END_REF][START_REF] Lee | Strained Si, SiGe, and Ge channels for high-mobility metal-oxide-semiconductor field-effect transistors[END_REF][START_REF] Bedell | Strain scaling for CMOS[END_REF] For example, the introduction of strain in the channel of highly efficient transistors (Metal Oxide Semiconductor Field-Effect Transistors, MOSFETs) since the 65 nm technology node allowed the pursuit of Moore's law and enhancing performance in logic gates. [START_REF] Paul | Silicon-Germanium Strained Layer Materials in Microelectronics[END_REF] The latest developments have led to a high-performance 14 nm-technology using Fully Depleted Silicon On Insulator (FDSOI) transistors and the integration of a strained SiGe channel in p-type MOSFETs. [START_REF] Baudot | Electrical and diffraction characterization of short and narrow MOSFETs on fully depleted strained silicon-on-insulator (sSOI)[END_REF][START_REF] Casse | Experimental Investigation of Hole Transport in Strained $\hbox{Si}_{1 -x}\hbox{Ge}_{x}/\hbox{SOI}$ pMOSFETs-Part I: Scattering Mechanisms in Long-Channel Devices[END_REF][START_REF] Weber | 14nm FDSOI upgraded device performance for ultra-low voltage operation[END_REF] The choice of strained SiGe as a channel was driven by two factors : firstly, hole mobility in Germanium is higher than in Silicon and secondly, heteroepitaxy of SiGe on Si yields a biaxial compressive stress in the layer, which also enhances the hole mobility of a SiGe p-MOS channel. [START_REF] Cheng | High performance extremely thin SOI (ETSOI) hybrid CMOS with Si channel NFET and strained SiGe channel PFET[END_REF] In general, the mechanical loading of the transistor channel can be performed by four basic methods by using a: (i) Contact-Etch Stop Layer (CESL), e.g. an amorphous layer typically made of Silicon nitride to precisely control a chemical etching (and elastic relaxation) process, (ii) Stress Memorization Technique (SMT), depositing a high tensile stressed silicon nitride (called SiN x hereafter) on top of the source and drain, the whole structure is then recrystallized and finally, the SiN x removed, (iii) Pseudomorphic Epitaxy of the source and drain in a material with different lattice parameter than the Silicon substrate, and ultimately (iv) Substrate Engineering which aims to use a modified substrate by epitaxy or bonding transfer of a set of non-matching materials, such as the SiGe-on-insulator (SGOI) studied in this letter. [START_REF] Baudot | Fully Depleted Strained Silicon-on-Insulator p-MOSFETs With Recessed and Embedded Silicon-Germanium Source/Drain[END_REF] For such devices, the characterization and understanding of the strain evolution along the transistors integration flow for different design layout/geometries is key to guarantee the predictability of the electrical models and to finally achieve the maximum performance of the circuits. As the size of functional nanostructures is reduced, the ability to map strain at the nanoscale has become essential.

While Transmission Electron Microscopy allows measuring high spatial-resolution strain maps on single objects, it involves destroying the sample and changing the strain state with sample preparation. Also due to sample thinning, it cannot analyze a large number of nano-structures. Raman spectroscopy is based on the knowledge of the phonon mode dependence on composition and strain tensor [START_REF] Pezzoli | Raman spectroscopy determination of composition and strain in heterostructures[END_REF] and a precise determination of phonon shift coefficients [START_REF] Wong | Determination of Raman Phonon Strain Shift Coefficient of Strained Silicon and Strained SiGe[END_REF][START_REF] Nakashima | Raman investigation of strain in Si/SiGe heterostructures: Precise determination of the strain-shift coefficient of Si bands[END_REF] . This method has been extensively used for the measurement of SiGe nanostructures, e.g. stripes and patterns [START_REF] Jain | Stresses in strained GeSi stripes: Calculation and determination from Raman measurements[END_REF][START_REF] Dietrich | Raman investigations of elastic strain relief in Si 1-x Ge x layers on patterned silicon substrate[END_REF] . This technique is also limited by both; the low excitation probability of the Raman process leading to heating effects, and by its resolution related to the optical limit [START_REF] Takei | Channel strain analysis in high-performance damascene-gate p-metal-oxide-semiconductor field effect transistors using high-spatial resolution Raman spectroscopy[END_REF] .

X-ray diffraction is also a choice method for strain determination in nano-structures: it is for example possible to determine the average strain field in an assembly of identical nano-objects, using phase retrieval techniques 16,[START_REF] Minkevich | Inversion of the diffraction pattern from an inhomogeneously strained crystal using an iterative algorithm[END_REF] . Using modern X-ray focusing optics, micro-diffraction has been increasingly used for strain determination in individual heterostructures [START_REF] Murray | High-resolution strain mapping in heteroepitaxial thin-film features[END_REF][START_REF] Murray | Nanoscale silicon-on-insulator deformation induced by stressed liner structures[END_REF] . Recently, an optimized Scanning X-Ray Diffraction Microscopy (SXDM) technique has been developed at the ESRF ID01 beamline, [START_REF] Chahine | Imaging of strain and lattice orientation by quick scanning X-ray microscopy combined with three-dimensional reciprocal space mapping[END_REF][START_REF] Zoellner | Imaging Structure and Composition Homogeneity of 300 mm SiGe Virtual Substrates for Advanced CMOS Applications by Scanning X-ray Diffraction Microscopy[END_REF] which enables the quantitative determination of strain in nanostructures down to about 100 nm with a strain sensitivity below 10 -4 . SXDM takes advantage of the Bragg diffraction condition to yield information with different resolution levels: the beam size defines the real-space resolution of the scanning probe, while the beam divergence defines the reciprocal space resolution, and thus the strain resolution. Note that while X-ray Bragg Ptychography [START_REF] Hruszkewycz | Quantitative Nanoscale Imaging of Lattice Distortions in Epitaxial Semiconductor Heterostructures Using Nanofocused X-ray Bragg Projection Ptychography[END_REF][START_REF] Hruszkewycz | Efficient modeling of Bragg coherent x-ray nanobeam diffraction[END_REF][START_REF] Hruszkewycz | High-resolution three-dimensional structural microscopy by single-angle Bragg ptychography[END_REF] can be used to yield a higher resolution strain map, it requires isolating the coherent X-ray scattering from the studied nano-structure, which is not always possible due to the proximity of the substrate diffraction peak.

II. SAMPLES

While SOI is anticipated to become a major substrate for future electronics, most of the expected improvements will depend on the CMOS process and in particular on the epitaxy of defect-free ultra-thin Si and SiGe layers. Up to now, two main techniques which will be illustrated in this paper, have become more interesting to produce thin SiGe layers with high crystalline quality. The first approach consists of growing an epitaxial relaxed SiGe layer on Si (involving for example composition and strain gradients) and uses a combination of implantation and wafer bonding processes to transfer this SiGe layer to an SOI substrate. [25][START_REF] Gu | Size and Thickness Effect on the Local Strain Relaxation in Patterned Strained Silicon-on-Insulator[END_REF][START_REF] Moutanabbir | Multiwavelength micro-Raman analysis of strain in nanopatterned ultrathin strained silicon-on-insulator[END_REF] The second technique to produce SGOI involves the so-called Germanium condensation process (see Figure S1 in the supplementary materials for schematic of the condensation process and a sample description). [START_REF] Tezuka | A Novel Fabrication Technique of Ultrathin and Relaxed SiGe Buffer Layers with High Ge Fraction for Sub-100 nm Strained Silicon-on-Insulator MOSFETs[END_REF][START_REF] Tezuka | High-mobility strained SiGe-on-insulator pMOSFETs with Ge-rich surface channels fabricated by local condensation technique[END_REF][START_REF] Tezuka | Strained SOI/SGOI dual-channel CMOS technology based on the Ge condensation technique[END_REF][START_REF] David | Kinetics and Energetics of Ge Condensation in SiGe Oxidation[END_REF][START_REF] Boureau | Strain/composition interplay in thin SiGe layers on insulator processed by Ge condensation[END_REF] The initial substrate results from the epitaxial growth by Reduced Pressure-Chemical Vapor Deposition of a 20-nm thick Si 0.76 Ge 0.24 alloy layer on SOI (6 nm-thick Si layer on 20 nm-thick SiO 2 layer). The first step of the condensation process consists of a Rapid Thermal Oxidation performed at 1050 • C for 230 s. [START_REF] Boureau | Déformations introduites lors de la fabrication de transistors FDSOI : une contribution de l'holographie électronique en champ sombre[END_REF] This process leads to the preferential oxidation of Si atoms and due to the very small miscibility of Ge in SiO 2 , the remaining Ge atoms are rejected into the underlying Si layer. Then, thermal oxide is removed before the deposition of 4 nm-thick tetraethyl orthosilicate (TEOS). Then, when applicable, 55 nm-thick silicon nitride is deposited by low pressure chemical vapor deposition (LPCVD). It is continued by a temperature annealing at 1050 • C during a longer time (30 min.) that allows Si and Ge interdiffusion and homogenisation of the SiGe alloy.

Due to this thermal budget, the initial thin Si layer of the SOI substrate can be completely transformed, leading to a quasi-homogeneous Ge enriched SiGe layer directly on an insulator.

It explains why the remaining Ge atoms are rejected into the underlying SiGe layer and how a quasi-homogeneous Ge-enriched SiGe layer can be obtained. [START_REF] David | Kinetics and Energetics of Ge Condensation in SiGe Oxidation[END_REF][START_REF] Roze | Comparative Analysis of Growth Rate Enhancement and Ge Redistribution during Silicon-Germanium Oxidation by Rapid Thermal Oxidation[END_REF] The crystallization process maintains the strain imposed by the initial Si/SiO 2 interface and does not increase the number of structural extended defects. Hence, the condensed SiGe layer has a very good crystallinity with a high degree of control of the strain and composition. [START_REF] Casse | Experimental Investigation of Hole Transport in Strained $\hbox{Si}_{1 -x}\hbox{Ge}_{x}/\hbox{SOI}$ pMOSFETs-Part I: Scattering Mechanisms in Long-Channel Devices[END_REF][START_REF] David | Kinetics and Energetics of Ge Condensation in SiGe Oxidation[END_REF][START_REF] Boureau | Strain/composition interplay in thin SiGe layers on insulator processed by Ge condensation[END_REF][START_REF] Zhang | Strain Relaxation in Ultrathin SGOI Substrates Fabricated by Multistep Ge Condensation Method[END_REF][START_REF] Suh | Highly strained-SiGe-oninsulator p-channel metal-oxide-semiconductor field-effective transistors fabricated by applying Ge condensation technique to strained-Si-on-insulator substrates[END_REF][START_REF] Boureau | Strain evolution of SiGe-oninsulator obtained by the Ge-condensation technique[END_REF] From the bottom thick Si substrate, the complete stacking of the samples studied in this paper consists of 20 nm-thick SiO 2 Buried-Oxide (the initial BOX of the SOI), 20 or 13 nm-thick Si 0.76 Ge 0.24 , 4 nm-thick SiO 2 and an optional 55 nm-thick SiN x layer.

In this letter, we study the individual strain relaxation of square patterns obtained by UV-lithography from strained SGOI layers. Three samples were synthesized at CEA-Leti and STMicroelectronics using a mask including SiGe lines and square or rectangular SiGe islands of lateral size 0.25, 0.5, 2 and 5 µm, with an inter-spacing of the order of the object sizes (see Figure S2 Note that such thickness for single SiGe nanostructures represents a challenge for X-ray measurements due to their quite small atomic scattering factors (Z Si =14, Z Ge =32). [START_REF] Mastropietro | Time-Dependent Relaxation of Strained Silicon-on-Insulator Lines Using a Partially Coherent X-Ray Nanobeam[END_REF]

III. EXPERIMENT

We carried out the high resolution x-ray micro-diffraction measurements at the ID01 beamline (ESRF) [START_REF] Leake | The Nanodiffraction beamline ID01/ESRF: a microscope for imaging strain and structure[END_REF] . To be able to measure very thin nanostructures with a high lateral resolution, a specific setup has been used with a multilayer monochromator, but with a 0.31% bandwidth pink-beam illumination centered at 8 keV. The x-ray beam was then focused down to a 170 nm (vertical) x 220 nm (horizontal) spot size using a Kirkpatrick-Baez mirror (KB) in order to reach 3.5x10 6 photons/sec/nm 2 . Such a high flux is made possible because of the pink-beam illumination and enables unprecedented imaging of ultra-thin layer. The diffracted intensity is recorded by a fast readout two-dimensional photon counting detector with 516 x 516 pixels of 55 µm size positioned at 96 cm from the sample. [START_REF] Ponchut | MAX-IPIX, a fast readout photon-counting X-ray area detector for synchrotron applications[END_REF] The sample was mounted on a fast scanning piezoelectric stage with a 2 nm resolution (see Figure S3 in the supplementary materials for the SXDM description and sketch of the experimental setup).

A rough alignment was first carried out by mapping out the etched patterns with an optical microscope mounted vertically on top of the sample. Then, a finer alignment was made possible by recording the diffracted intensity on the detector with the fast three dimensional SXDM at the Bragg peak: while raster scanning a zone of the sample, the intensity on the detector is summed for each scan point leading to an intensity map which gives a clear location of the features of interest. The real space scans were typically made over areas of about 10 µm x 10 µm with a 100 nm step size in both in-plane directions. The SiGe and Si Bragg angles were determined by making standard radial scans, taking advantage of slightly different SiGe and Si crystal orientations, both .

The 004 reflection of the buried Si (incidence angle of 34.8 • ) provides an absolute reference value for the further calculated lattice parameters. By identifying the coordinates of the center of mass of the Si Bragg peak on the detector, combined with the knowledge of the position of the direct beam and of the angles of the diffractometer, we measured a Si = 4λ/(2 sin(θ)) = 5.441Å which is within 0.19% relative error compared to the Si bulk lattice parameter tabulated at room temperature (a Si = 5.431Å). Note that the approximation made by rounding the pixel coordinate corresponds to an accuracy of 0.005% relative to the tabulated Si lattice parameter. The 004 SiGe Bragg peak, which has a larger lattice parameter than Si (a Ge = 5.658Å), appears at a lower incident angle, i.e. at a lower scattering vector value (Q = 4.589Å

-1 ). The two-dimensional scan around this reciprocal space point gives a real space distribution of the scattered intensity for the (004) SiGe planes, but to separate strain and tilt, we need to identify the position of the Bragg peak in the 3D reciprocal space.

Taking into account the spectral divergence of the pink-beam, this is achieved by a 0.4 • rotation of incident angles between 34.28

• (Q = 4.568 Å -1
) and 34.68

• (Q = 4.614 Å -1 )
with a 0.01 • angular step. The same method was used to analyze the asymmetric SiGe (113) reflection, which is better separated from the contribution of the Si substrate compared to the (004) reflection, and has also the advantage to be almost tangential to the Ewald sphere (i.e. the information about the displacement field is contained in a single image). In order to acquire strain and tilt information from the 113 reflection, 3D scanning is performed for incident angles varying between 53.99 • and 54.39 • with a 0.01 • angular step, collecting the diffracted beam at 2θ = 55.7 • . Note that the 113 reflection also presents the advantage of being closer to a normal incidence on the sample, hence providing a smaller beam footprint (212 nm at 54 • against 300 nm at 34.5 • ) yielding higher spatial resolution in the vertical direction.

IV. RESULTS AND DISCUSSION

A. Comparison of growth methods

As a reference used in further lithographic processes, the full-sheet strain corresponding to the initial SiGe layer obtained by condensation is measured on 50 µm-wide lines with 10 µm x 10 µm area scan. The lateral scale of this pattern is indeed much larger than the usual elastic relaxation length induced by the edge boundaries as it will be demonstrated later. This measurement can be also compared to results gathered on a 70 nm-thick SiGeon-SOI layer obtained by implantation, splitting and wafer transfer, corresponding to a completely different technological solution. parameter -and hence closely related to the (004) lattice parameter as a full-sheet layer can be modeled with a biaxial approach:

d 113 = (2/a [100] 2 + 9/a [001] 2 ) -1/2 (1)
where a corresponding to the most intense slice of the SiGe Bragg peak. Note that the integration procedure includes masking the areas where the substrate peak is diffraction (including its crystal truncation rod), which is essential as the intensity is very low for each individual frame, as depicted in supplementary figure S4.

This maximum intensity map is taken as reference to determine a threshold, which enables to separate the squared islands from the substrate underneath, generating the white masks of the other maps. Note that the squares appear less sharp for the 004 measurements as compared with the ones from 113 measurements, because for this data acquisition geometry: (i) the silicon substrate peak is closer to the SiGe (i.e. the overlap is higher) and (ii) the beam footprint on the sample is wider (it causes a blurring effect because the incident angles are respectively 54 • and 34.5 • ). It is also important to stress that the quality of the results is poorer in the vertical (Y) direction due to the asymmetry of the incoming beam , reducing the spatial resolution in this direction.

The consequence of which was the expected four-fold symmetry of deformation and tilt is reduced to a two-fold horizontal symmetry. Indeed, the lattice tilts of the SiGe layer are due to the elastic relaxation at the free boundary conditions introduced by sidewall etching, considering that the bottom of this layer is still compressed by the substrate. Maps at the middle of Figure 2 show the root mean square (RMS) of both azimuthal and planar tilts. The sidewall relaxation of the squares induces up to 0.26 • RMS tilt for the (113) lattice planes, and 0.18 • RMS tilt for the (004) lattice planes. Furthermore, the out-of-plane (004) deformation ( (004) ) and the (113) deformation -mixing in-plane and out-of-planeare depicted in the right-hand side of Figure 2. In this paper, deformation 42 is defined with respect to the Si lattice parameter, i.e., for a given (hkl) reflection:

hkl = a hkl √ h 2 + k 2 + l 2 a Si -1 (2)
We observe a good homogeneity of both deformations at the center of the squares and a small variation at the edges of the squares due to sidewall relaxation.

Secondly, smaller patterns with 500x500 nm 2 13 nm-thick SGOI squares without SiN x on top (sample C) have been analyzed. Although this sample contains a very low amount of SiGe, we were still able to discern the patterns and isolate their diffraction spots. Figure 3 shows the intensity, RMS tilt and deformation maps from a 8 x 8 µm 2 area scan at the 113 Bragg reflection condition. One can note a RMS tilt of 0.07 • on the edges of the patterns and especially an homogeneous deformation across the area, with variations smaller than 0.05%. This suggests that the scanned area is made of patterns that are all close to their completely relaxed state and also provides an estimation of the relaxation length of the compressive in-plane deformation that must be at least of the same order of magnitude as half the width of the measured patterns (> 250 nm).

C. Statistical information

SXDM allows us not only to study the homogeneity of the sSGOI patterns, but also to gather statistical information. For instance, an interesting feature that can be extracted from the data is the mean value of deformation at the center of each pattern. By defining an integration zone of 300x300 nm 2 centered on each pattern, corresponding to 3x3 points of the map, one can compare the mean deformation over multiple patterns. These central areas are supposed to be homogeneous unlike the edges, where the introduction of free boundaries by etching modifies the strain state.

Figure 4 shows the histograms extracted from the 2x2 µm deformation distribution, both calculated with respect to the bulk Si lattice parameter. For these small islands, the 170 nm (v) x 220 nm (h) size of the beam limits the resolution, so we focused the quantitative analysis to the deformation at the center of the islands, as shown in Fig. 4 and from the 500x500 nm 2 patterns of sample C. It is striking that there is a very small deviation around the mean value for samples A & B, calculated as the RMS of the statistical distribution of extracted deformation: ±0.004% for sample A and ±0.007% for sample B.

Then, sample C presents a RMS of ±0.03%. This increase is likely to be a consequence of the smaller thickness of the sample, making the growth process more sensitive. Note also that the initial wafer is different for every sample. Overall, these small variations outline the very good homogeneity over one given wafer. Next, the tensile role of the nitride cap is shown by comparing sample A and sample B. For the same 2x2 µm 2 pattern, the mean (113) deformation is lower in the absence of SiN x (1.125% without, 1.227% with). As the (113) deformation is mainly proportional to the out-of-plane strain, and the layers supposed to be biaxially strained, a lower (113) deformation is linked to a larger relaxation of the inplane strain. Hence, the intrinsically stressed SiN x layer helps maintaining the compressive in-plane strain. The mean value and RMS for each sample are the following: 1.125% ± 0.004% for sample A (2x2 µm 2 ), 1.227% ± 0.007% for sample B (2x2 µm 2 ) and 1.224% ± 0.03% for sample C(0.5x0.5 µm 2 ).

D. Relaxation lengths

Finally, it is possible to assess the relaxation at the edges of the patterns. To do so, we extracted the deformation profiles of the largest patterns from the 13 nm-thick sSGOI sample. The choice of sample was driven by the fact that the mean value of the 113 is the same for the 2x2 µm 2 patterns and the 5x5 µm 2 patterns. Figure 5 presents the deformation profiles (dots symbols) along with an empirical model (straight lines) adapted from Ref. 43 in order to derive a typical relaxation length. The fit function, based on an exponential decay, is the following:

f relax = f min + (f max -f min ) 1 -e -x λ -e x-L act λ (3)
where f min and f max are the minimum and maximum deformation values, L act the width of the pattern and λ the relaxation length (see Table T1 in the supplementary materials for the fitted values of the four parameters). The 2x2 µm 2 patterns has an average value of λ of about 384 nm with a variation from 333 to 430 nm, whereas the relaxation length of the 5x5 µm 2 patterns has smaller variation and is close to 301 nm.

We have also included in Fig. 5 the relaxation curves simulated using Finite Element Modeling (FEM): the main results from this elasticity modeling are that the relaxation lengths are slightly smaller for the FEM data -which could be due to the broadening due to the beam size -, and that the relaxation on the island borders is significantly larger experimentally compared to the elastic model. 44

Such relaxation determined from X-ray diffraction has the same order of magnitude as what has been determined by electron microscopy on similar samples. An xx profile has been determined by both; nano-beam electron diffraction (NBED) to extend spatially up to 400 nm [START_REF] Berthelon | Strain integration and performance optimization in sub-20nm FDSOI CMOS technology[END_REF] , and Dark-Field Electron Holography (DFEH) up to more than 300 nm. [START_REF] Boureau | Strain evolution of SiGe-oninsulator obtained by the Ge-condensation technique[END_REF] Note also that these techniques have also to take into account carefully the lattice rotations to get precise measurements of the deformations. An interface glide at the edge of the pattern has been proposed that could result from the two of the main steps of the technological process: the heteroepitaxy of SiGe on an SOI substrate and the rapid thermal oxidation condensation and annealing. This interface gliding could explain the larger relaxation in the experimental data compared to the elastic model.

V. CONCLUSION

In conclusion, we showed that the SXDM technique yields accurate and precise quantitative deformation measurements of ultra-thin SiGe layers whose diffraction can be shadowed by intense substrate scattering. From these quantitative deformation maps, we were able to evaluate the reliability of the condensation technique used to integrate strain in FDSOI. In comparison with the traditional implantation, smart-cut, and bonding technique, it appears that the condensation process not only removes the cross-hatch patterning but also yields less disoriented layers.

Furthermore, we observed that the strain over the central area of patterns with a given width is homogeneous, with relative variations of less than 1.2% for the 20 nm-thick samples, and of 4.9% for the 13 nm-thick sample. Also, by measuring that the (113) strain of the 20 nm-thick sample with SiN x on top is larger than the one of the 20 nm-thick sample without SiN x , we showed that a tensile stressed SiN x cap layer helps to maintain the compressive in-plane strain of the SiGe layer.

Finally, this study also gave insights on the typical lattice rotation and relaxation length of the in-plane strain, caused by the introduction through etching, of free boundaries on the side of the patterns. A comparison with elasticity models shows that while the measured relaxation lengths are generally between 300 and 400 nm, the simulated ones are slightly smaller. The most striking difference is that the amplitude of the measured relaxation on the border is much larger than predicted by the simulations, probably due to non-elastic processes. Indeed, the fact that the mean strains on the central area of all patterns with width above 500 nm are equal and higher than the ones from all patterns with width below 500 nm, demonstrates that the smallest patterns are not fully strained. Moreover, estimated relaxation lengths were extracted from strain profiles along the width of several patterns.

Interestingly, these estimated values are in agreement with recent electron holography measurements which tend to validate the assumption of an interface glide at the boundary between the SiGe and the BOX. This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0033494

  in the supplementary materials for examples giving some examples of scanning electron microscopy images). The thickness of the SiGe patterns was: • sample A: 20 nm-thick SGOI with 55 nm SiN x on top • sample B: 20 nm-thick SGOI without SiN x • sample C: 13 nm-thick SGOI without SiN x

  Figure 1 shows the comparison of the different tilts measured from the 113 Bragg reflection on 50 µm-wide lines of 13 nm-thick SiGe grown by condensation, i.e. sample C (first row: (a) to (c)), and on the 70 nm-thick SiGe-on-SOI layer grown by smart-cut molecular bonding (second row: (a') to (c')). The displacement of the Bragg peak in the 2θ direction is directly related to the variation of the SiGe 113 lattice

Figure 1 .

 1 Figures1(b) and 1(c) (resp. 1(b') and 1(c')) show for the 13 nm-thick SiGe layer (resp. 70 nm-thick SiGe layer) the tilt distributions taken at maximum intensity in the directions perpendicular and parallel to the scattering planes. The first row of Figure1shows that the tilt maps are very homogeneous with a standard deviation of both azimuthal and in-plane angle variations of about σ az.&plan. = 0.004 • . It demonstrates that the growth-condensation process achieves dislocation and tilt-free layers. The same type of analysis performed with the 70 nm-thick layer obtained by layer bonding and transfer is completely different. The mosaicity is about 0.10 • and the standard deviation of both azimuthal and planar tilt is σ az.&plan. = 0.08 • . This is explained by the occurrence of both horizontal and vertical stripes resulting from the standard cross-hatch pattern induced by the SiGe growth on Si created by 60 • misfit dislocations along the <110> directions (a/2 [101] Burgers vector).[START_REF] Zoellner | Imaging Structure and Composition Homogeneity of 300 mm SiGe Virtual Substrates for Advanced CMOS Applications by Scanning X-ray Diffraction Microscopy[END_REF][START_REF] Chen | Crosshatching on a SiGe film grown on a Si(001) substrate studied by Raman mapping and atomic force microscopy[END_REF]

Figure 2 .

 2 Figure 2. Map of a 12x12 µm 2 area of strained SiGe-on-insulator 2x2 µm 2 islands of thickness 20 nm (sample A), for both 113 (a-c) and 004 (d-f) Bragg reflections. (a,d) Maximum of intensity integrated on the whole detector for each pixel. (b,e) RMS tilt angle, considering both the perpendicular and parallel angular deviation with respect to the scattering plane showing a clear evidence of the side relaxation of the islands. (f) zz out-of-plane deformation distribution, (c) 113 deformation distribution, both calculated with respect to the bulk Si lattice parameter. The incident and diffracted beams are in the XZ plane. The slightly smaller size of the islands for the (004) reflections in (d-f) is due to the larger relative deformation, which reduces the intensity on the borders. Some interface defects may explain the differences in the middle horizontal island sizes.

Figure 3 .

 3 Figure 3. Mapping of a 8x8 µm 2 area of strained SiGe-on-insulator 500×500 nm 2 square islands of thickness 20 nm (sample A) for the 113 Bragg reflection. (Left) Maximum of intensity integrated on the whole detector for each pixel. (Center) RMS tilt angle, taking into account both the perpendicular and parallel angular deviation with respect to the scattering plane. (Right) 113

Figure 4 .

 4 Figure 4. Distribution of (113) deformation from the central areas of all the probed patterns on each sample. The dotted lines depict the average deformation over the entire distribution. The bar histograms represent the density of the distribution, i.e., a number of counts by deformation value.

Figure 5 .

 5 Figure 5. (113) deformation profiles from (a) 2x2 µm 2 patterns (6 islands) and (b) 5x5 µm 2 (two different islands) of 13 nm-thick SGOI (sample C) and corresponding curves from the empirical model (see equation 3). The typical relaxation lengths λ obtained with the analytical model (lines) are in agreement with the data (dots) and are between 234 nm and 377 nm. Uncertainties on deformations values are estimated to ±0.002%. The red curves correspond to FEM elasticity models, which present slightly smaller relaxation lengths, but significantly less relaxation on the border of the islands.

37

 37

  VI. SUPPLEMENTARY MATERIALSee supplementary material for the (i) description of the samples with a schematic of the condensation process (S1), scanning electron microscopy images of patterned samples (S2), a sketch of the experimental setup (S3), an example of diffraction frame exhibiting the low intensity counts (S4), and the results of the fits of Figure5 (T1).VII. ACKNOWLEDGEMENTSAuthors would like to acknowledge the ESRF ID01 beamline for the beamtimes MA2625 and MA2242, as well as STMicroelectronics for the preparation of samples. The PhD scholarship of GG has been partially granted by the French ANR Labex LANEF (10-LABX-0051).

  This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5004 = (a -a Si )/a Si 113 = (a -a Si )/a Si 1.00%

  This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

	Y (µm)	98 100 102			I Obs		4000 6000 8000 10000 12000 14000 16000		RMS tilt		0.04 • 0.06 • 0.08 • 0.10 • 0.12 • 0.14 •		113 = (a -a Si )/a Si	1.28% 1.29% 1.30% 1.31% 1.32%
		96	96	98	100	102	0 2000	96	98	100	102	0.00 • 0.02 •	96	98	100	102	1.26% 1.27%
				X (µm)				X (µm)				X (µm)
	PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0033494

2 patterns of sample A & B 10

  This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

			1.40 1.42	(a)
			1.38
			1.36
		113 (%)	1.26 1.28 1.32 1.34 1.30			Symbols: exp. data or FEM Lines: model =363nm =627nm =440nm =321nm =367nm =380nm	=414nm FEM 2 m [ =229nm]
	PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0033494	113 (%)	1.26 1.28 1.30 1.32 1.34 1.36 1.38 1.40 1.42	(b) -1	-0.75	Symbols: exp. data or FEM Lines: model FEM 5 m [ =338nm] =301nm =301nm -0.5 -0.25 0 0.25 X ( m)	0.5	0.75	1
					-2	-1	0 X ( m)	1		2

CITE THIS ARTICLE AS DOI: 10.1063/5.0033494

  This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.PLEASE Si )/a Si This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. PLEASE

	Y (µm)	98 100 102			I Obs		4000 6000 8000 10000 12000 14000 16000		RMS tilt		0.04 • 0.06 • 0.08 • 0.10 • 0.12 • 0.14 •					1.04% 1.08% 1.12% 1.16% 1.20% 1.24% 1.28% 1.28% 1.29% 1.30% 1.31% 1.32%
		96	96	98	100	102	0 2000	96	98	100	102	0.00 • 0.02 •	96	98	100	102	1.26% 1.27%
				X (µm)				X (µm)				X (µm)

113 = (aa

CITE THIS ARTICLE AS DOI: 10.1063/5.0033494

  This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. PLEASE

		70
							A: 20nm w/ SiN
		60					(500x500 nm)
	Count/deformation	20 30 40 50					B: 20nm w/o SiN (2x2 µm) C: 13nm w/o SiN (2x2 µm)
		10
		0	1.10	1.15	1.20	1.25	1.30
					113 (%)

CITE THIS ARTICLE AS DOI: 10.1063/5.0033494

		1.40 1.42
		1.38
		1.36
	113 (%)	1.30 1.32 1.34			Symbols: exp. data or FEM Lines: model
		1.28
		1.26
		1.40 1.42	(b) -1	-0.75	-0.5	-0.25	0 X ( m)	0.25	0.5	0.75	1
		1.38
		1.36
	113 (%)	1.26 1.28 1.32 1.34 1.30			Symbols: exp. data or FEM Lines: model FEM 5 m [ =338nm] =301nm =301nm
				-2	-1		0 X ( m)	1		2

This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0033494

VIII. DATA AVAILABILITY STATEMENT

Raw data were generated at the European Synchrotron Radiation Facility (ESRF). Derived data supporting the findings of this study are available from the corresponding author upon reasonable request.


Ang Li

Jérémy Forté

Yanling Li

Yves Journaux

Laurent Lisnard
email: laurent.lisnard@sorbonne-universite.fr

Synthesis, structure and magnetic properties of an oxamate

Keywords: Oxamate ligand, multi-polydentate ligand, solvothermal synthesis, coordination polymer, heterobimetallic compound

Introduction

Oxamate ligands are attractive synthetic tools with a rich coordination chemistry that facilitates the design and preparation of molecular materials. [START_REF] Kahn | Chemistry and Physics of Supramolecular Magnetic Materials[END_REF][START_REF] Grancha | Oxamato-based coordination polymers: recent advances in multifunctional magnetic materials[END_REF][START_REF] Castellano | Metallosupramolecular approach toward multifunctional magnetic devices for molecular spintronics[END_REF][START_REF] Castellano | Dicopper(II) Metallacyclophanes as Multifunctional Magnetic Devices: A Joint Experimental and Computational Study[END_REF][START_REF] Fortea-Pérez | The MOF-driven synthesis of supported palladium clusters with catalytic activity for carbene-mediated chemistry[END_REF][START_REF] Mon | Metal-organic framework technologies for water remediation: towards a sustainable ecosystem[END_REF][START_REF] Viciano-Chumillas | Metal-Organic Frameworks as Chemical Nanoreactors: Synthesis and Stabilization of Catalytically Active Metal Species in Confined Spaces[END_REF] While phenyl-based oxamate ligands, [START_REF] Ruiz | Coordination chemistry of N,N′bis(coordinating group substituted)oxamides: a rational design of nuclearity tailored polynuclear complexes[END_REF][START_REF] Pardo | Ligand design for multidimensional magnetic materials: a metallosupramolecular perspective[END_REF][START_REF] Dul | Supramolecular coordination chemistry of aromatic polyoxalamide ligands: A metallosupramolecular approach toward functional magnetic materials[END_REF][START_REF] Journaux | Design of Magnetic Coordination Polymers Built from Polyoxalamide Ligands: A Thirty Year Story[END_REF] and amino-acid-based oxamate ligands now represent the bulk of the investigations, [START_REF] Grancha | Structural Studies on a New Family of Chiral BioMOFs[END_REF][START_REF] Mon | Selective Gold Recovery and Catalysis in a Highly Flexible Methionine-Decorated Metal-Organic Framework[END_REF][START_REF] Mon | Selective and Efficient Removal of Mercury from Aqueous Media with the Highly Flexible Arms of a BioMOF[END_REF][START_REF] Grancha | Tuning the selectivity of light hydrocarbons in natural gas in a family of isoreticular MOFs[END_REF][START_REF] Mon | Postsynthetic Approach for the Rational Design of Chiral Ferroelectric Metal-Organic Frameworks[END_REF][START_REF] Grancha | Rational Synthesis of Chiral Metal-Organic Frameworks from Preformed Rodlike Secondary Building Units[END_REF][START_REF] Grancha | Toward Engineering Chiral Rodlike Metal-Organic Frameworks with Rare Topologies[END_REF][START_REF] Mon | Lanthanide Discrimination with Hydroxyl-Decorated Flexible Metal-Organic Frameworks[END_REF][START_REF] Mon | Crystallographic snapshots of host-guest interactions in drugs@metal-organic frameworks: towards mimicking molecular recognition processes[END_REF][START_REF] Mon | Efficient Capture of Organic Dyes and Crystallographic Snapshots by a Highly Crystalline Amino-Acid-Derived Metal-Organic Framework[END_REF][START_REF] Mon | Synthesis of Densely Packaged, Ultrasmall Pt02 Clusters within a Thioether-Functionalized MOF: Catalytic Activity in Industrial Reactions at Low Temperature[END_REF][START_REF] Mon | Efficient Gas Separation and Transport Mechanism in Rare Hemilabile Metal-Organic Framework[END_REF] a sub-class of aromatic oxamate ligands that are substituted with additional -non-oxamic-coordinating groups starts to gain attention. [START_REF] Paul-Roth | Synthesis and characterization of a new bis-oxamide copper(II) complex incorporating a pendant carboxylate function[END_REF][START_REF] Yoneda | A Homometallic Ferrimagnet Based on Mixed Antiferromagnetic and Ferromagnetic Interactions through Oxamato and Carboxylato Bridges[END_REF][START_REF] Oliveira | Cobalt(II) and copper(II) assembling through a functionalized oxamate-type ligand[END_REF][START_REF] Fernandes | Dicopper(II) Metallacyclophanes with N,N′-2,6-Pyridinebis(oxamate): Solution Study, Synthesis, Crystal Structures, and Magnetic Properties[END_REF][START_REF] Rühlig | CuII bis(oxamato) end-grafted poly(amidoamine) dendrimers[END_REF][START_REF] Conte-Daban | Link between Affinity and Cu(II) Binding Sites to Amyloid-β Peptides Evaluated by a New Water-Soluble UV-Visible Ratiometric Dye with a Moderate Cu(II) Affinity[END_REF][START_REF] Fernandes | 2D and 3D mixed MII/CuII metalorganic frameworks (M = Ca and Sr) with N,N′-2,6-pyridinebis(oxamate) and oxalate: preparation and magneto-structural study[END_REF][START_REF] Da Cunha | Slow magnetic relaxation in mononuclear gadolinium(III) and dysprosium(III) oxamato complexes[END_REF][START_REF] Hou | Structural Diversity of CPs Induced by Coordinating Modes of a New Bis(oxamate) Ligand: Luminescent and Magnetic Properties[END_REF][START_REF] Maciel | New Metal-Organic Systems with a Functionalized Oxamate-Type Ligand and MnII, FeII, CuII and ZnII[END_REF] Like the amino-acid-based oxamate ligands, such multi-polydentate ligands bearing additional carboxylato, hydroxido or N-donor groups offer diverse coordination modes with metal ions, which give access to new structural types. Recently, this led us to investigate the reactivity of the 2-hydroyphenyloxamate ligand and we have observed the formation of two atypical structures for phenyloxamate-related chemistry: a hexametallic macrocyclic coordination ring and of a chiral coordination polymer. [START_REF] Li | A Bis-Polydentate Oxamate-Based Achiral Ligand That Can Stabilize a Macrocyclic Mixed Valence Compound or Induce a 1D Helical Chain[END_REF] To further this reactivity investigation, we have also decided to revisit solvothermal reactions. Indeed, prior attempts by others and us at using this technique for reacting oxamate ligands highlighted difficulties in obtaining a fully deprotonated, i.e. fully coordinating, form of the oxamate ligand. [START_REF] Hou | Structural Diversity of CPs Induced by Coordinating Modes of a New Bis(oxamate) Ligand: Luminescent and Magnetic Properties[END_REF][START_REF] Lisnard | Solvothermal Synthesis of Oxamate-Based Helicate: Temperature Dependence of the Hydrogen Bond Structuring in the Solid[END_REF] Nevertheless, the use of solvothermal reactions for the 2hydroyphenyloxamate ligand was successful, and we were able to isolate a 1D coordination polymer. [START_REF] Li | Solvothermal synthesis, structure and magnetic properties of heterometallic coordination polymers based on a phenolato-oxamato co-bidentate-tridentate ligand[END_REF] To continue our study, we have extended the use of solvothermal conditions to the ortho-substitued carboxylatophenyloxamate ligand (2-(ethyloxamate)benzoic acid, H 2 Et-oaba) in the presence of copper(II) and cobalt(II) ions. It has resulted in the formation of a novel 1D coordination polymer, [Cu 4 Co 3 (oaba) 4 (OH) 2 (DMF) 6 ]•2(DMF)•1H 2 O, [START_REF] Kahn | Chemistry and Physics of Supramolecular Magnetic Materials[END_REF], where the hexadentate ligand generates pentametallic building blocks. We present here the synthesis, structural and magnetic characterizations of 1.

Experimantal section

Materials and methods

All reagents were used as purchased with no further purification. The ester proligand 2-(ethyloxamate)benzoic acid (H 2 Et-oaba) was prepared here according to the general procedure for oxamate ligand, [START_REF] Cervera | Stabilization of copper (III) complexes by substituted oxamate ligands[END_REF] which differs from the previously reported synthesis for H 2 Et-oaba. [START_REF] Yoneda | A Homometallic Ferrimagnet Based on Mixed Antiferromagnetic and Ferromagnetic Interactions through Oxamato and Carboxylato Bridges[END_REF] Elemental analysis was performed in the "service de microanalyse" at ICSN (CNRS, Gif/Yvette, France) and via the PARI program at the IPGP (Paris, France). ATR/FT-IR spectra were collected on a Bruker TENSOR 27 equipped with a simple reflexion ATR diamond plate of the Harrick MPV2 series. The thermogravimetric analysis (TGA) was performed on a TA Instruments SDTQ600 under air or nitrogen with a heating rate of 5 °C/min. 1 H and 13 C NMR spectra were collected on 300 and 400 MHz Bruker Avance spectrometers at 298 K.

Synthesis

Ligand preparation, ester proligand: 2-(ethyloxamate)benzoic acid, H 2 Et-oaba.

To 6.0 g of anthranilic acid (M=137.14 gmol -1 , 43.75 mmol) in 250 mL of THF were added dropwise 5.5 mL of ethyloxalyl chloride (98%; 1eq.) under strong stirring. The mixture was refluxed for 120 min and filtered on paper while hot (some white residue is filtered off). Removal of the solvent under reduced pressure yields a white powder. The powder was washed with 700 mL of water under stirring for 30 min and then collected on a sintered glass filter. Further washing was done with cold 50 % ethanol and the solid was dried in air. The final product was collected as a white powder (9.15 g, Yield: 88.17 %, M=237.2 gmol -1 ).

Synthesis of [Cu 4 Co 3 (oaba) 4 (OH) 2 (DMF) 6 ]•2(DMF)•1H 2 O, (1).

H 2.5 Na 0.5 -oaba•0.5(H 2 O) (0.5 mmol, 0.115g) Cu(OAC) 2 .H 2 O (0.5 mmol, 0.099g), and Co(OAC) 2 .4H 2 O (0.5 mmol, 0.124 g) were placed in a 23 mL Teflon-lined autoclave reactor filled with DMF (4 mL). The reactor was heated to 80°C in 2 h, kept at this temperature for 72 h and then cooled down to room temperature in 24 h. Dark purple crystals of 1 were collected and washed by sonication in EtOH. Yield: 0.123 g, 51% (based on copper; M=1889 gmol -1

X-Ray crystallography

A single crystal of 1 was selected, mounted onto a MiTeGen MiroGripper loop using Paratone-N oil and transferred into a cold nitrogen gas stream produced with an Oxford cooler. Intensity data were collected with a Bruker Kappa-APEXII diffractometer using graphite-monochromated Mo-Kα radiation (λ = 0.71073 Å). Data collection was performed with the Bruker APEXII suite.[38] Unit-cell parameters determination, integration and data reduction were carried out with SAINT program.[38] SADABS was used for scaling and absorption correction. [38,[START_REF] Blessing | An empirical correction for absorption anisotropy[END_REF] The structure was solved with SHELXT-2014, [START_REF] Sheldrick | SHELXT -Integrated space-group and crystal-structure determination[END_REF] and refined by full-matrix least-squares methods with SHELXL-2014, [START_REF] Sheldrick | Crystal structure refinement with SHELXL[END_REF] using the Olex2 software package. [START_REF] Dolomanov | OLEX2: a complete structure solution, refinement and analysis program[END_REF] It was refined as a 2-component twin (twin law -1 0 1 0 -1 1 0 0 1). All non-hydrogen atoms, except an oxygen atom of a water molecule, were refined anisotropically. The main crystallographic parameters and data refinement results are presented in Table 1. The structure was deposited at the Cambridge Crystallographic Data Centre with number CCDC 1984798 and can be obtained free of charge via www.ccdc.cam.ac.uk/structures.

β [°]
105.923 [START_REF] Viciano-Chumillas | Metal-Organic Frameworks as Chemical Nanoreactors: Synthesis and Stabilization of Catalytically Active Metal Species in Confined Spaces[END_REF] γ [°] 98.564( 7)

V [Å 3 ]
2035.9( 13)

Z 1 T [K] 200(2) λ [Å] 0.71073 ρ calc [g cm -3 ] 1.593 µ (Mo Ka ) [mm -1 ] 1.
€ R 1 = F o -F c / F o ∑ ∑ € ωR 2 = ω F o 2 -F c 2 ( ) 2 $ % & ' ( ) ∑ ω F o 2 ( ) 2 $ % & ' ( ) ∑ + , - . / 0 1 2

Magnetic measurements

Magnetic measurements in dc mode were performed on a polycrystalline sample of 1 restrained within a capsule with a Quantum Design MPMS SQUID. Magnetic susceptibility data were corrected for the diamagnetism of the constituent atoms using the Pascal's constants. The diamagnetism of the sample holder was measured and subtracted from the raw data.

Results and discussion

Synthesis and structure of 1

The neutral 1D compound 1 (Figure 1) was synthesized solvothermally in DMF at 80 °C with a 1:1:1 stoichiometry (ligand:Cu:Co) and in the lack of base. 4-, that consist of two fused lacunary coordination cubane (Figure 2). This complex then acts as a tetrakis-bidentate ligand and its coordination to Co2 (in a cis fashion)

generates the 1D arrangement of compound 1 (Figure 3). In comparison to the [Cu{Cu(oaba)(H 2 O)(py)} 2 ] and [Cu{Cu(oaba)(MeOH)} 2 ] 2D compounds, [START_REF] Yoneda | A Homometallic Ferrimagnet Based on Mixed Antiferromagnetic and Ferromagnetic Interactions through Oxamato and Carboxylato Bridges[END_REF] the (oaba) 3-ligand in 1 binds one extra metal ions, thus acting as a bridge for three metallic pairs, instead of two (Scheme 1). The dimensionality is however lowered, yet the observed morphology contrasts drastically with the linear and zig-zag arrangements commonly observed with phenyloxamate bridging ligands. [START_REF] Journaux | Design of Magnetic Coordination Polymers Built from Polyoxalamide Ligands: A Thirty Year Story[END_REF] Scheme 1. Representation of the (oaba) 3-

Magnetic properties of 1.

The magnetic properties of compound 1 in the form of the χ M T versus T plot (χ M is the magnetic susceptibility per {Cu 4 Co 3 } unit) is shown in Figure 4, as well as the magnetic behavior of a hypothetical uncoupled {Cu 4 Co 3 } system. The value of χ M T at room temperature is of 9.0 cm 3 mol -1 K, a value which is lower than the smallest value expected for a sum of four Cu II and three Co II noninteracting ions (≈10.1 cm 3 mol -1 K; S Cu = ½ with g = 2.12, χ M T (Cu II ) = 0.421 cm 3 mol -1 K; octahedral Co II with orbitally degenerate 4 T 1g ground state, 2.7 < χ M T(Co II ) < 3.4 cm 3 mol -1 K [START_REF] Lloret | Magnetic properties of sixcoordinated high-spin cobalt(II) complexes: Theoretical background and its application[END_REF]), indicating a strong antiferromagnetic coupling between the ions. Upon cooling, the χ M T product steadily decreases down to a value of 2.12 cm 3 mol -1 K at 2 K. The shape of this curve is typical of the combination of an antiferromagnetic interaction between the magnetic centers with the effect of spinorbit coupling on the Co II ions. No maximum of χ M is observed in the temperature range investigated.

With a magnetic ordering that cannot be observed in a 1D compound, [START_REF] Palacio | From Ferromagnetic Interactions to Molecular Ferromagnets : An Overview of Models and Materials[END_REF] this shows the absence of a magnetic ordering between the well isolated chains in the crystal. Oe (T < 200K). The theoretical curve for an uncoupled {Cu 4 Co 3 } system is calculated taking into account the spin-orbit coupling on the cobalt ions with λ = -180 cm -1 , α = 0.9, Δ = -800cm -1 (λ, α and Δ being respectively the spin orbit coupling constant, the orbital reduction factor and the distortion parameter), and for copper ions an average g factor of 2.12 and a TIP contribution of 60 10 -6 cm 3 mol -1 .

The M versus H plot for compound 1 at 2 K (M is the magnetization per {Cu 3 Co 4 } unit and H is the applied magnetic field) is depicted on Figure 5. The observed value of 2.4 Nβ for M at 7 T is well below the magnetization saturation value for an uncoupled {Co 3 Cu 4 } system that would reach 10.5

Nβ.

μ 0 H / Tesla M / Nβ
This confirms the presence of a strong antiferromagnetic coupling between the magnetic ions. The polymeric nature of compound 1 and the composition of the repeating unit that includes four Cu II ions and three Co II ions make it impossible to model the magnetic properties, especially with Co II ions that have first-order orbital momentum. However, the analysis of the structure in correlation with the results published in the literature and the value of 2.4 Nβ found for the magnetization at high field allows us to speculate on the configuration of the spins in the ground state. First, the pentametallic cores bind to Co II ions via oxamato bridges. The interaction between a Co II ion and a Cu II ion across an oxamato bridge is in the -45 to -20 cm -1 range. [START_REF] Van Koningsbruggen | Magnetism of A-copper(II) bimetallic chain compounds (A = iron, cobalt, nickel): oneand three-dimensional behaviors[END_REF][START_REF] Pardo | Ligand design for heterobimetallic single-chain magnets: synthesis, crystal structures, and magnetic properties of MIICuII (M = Mn, Co) chains with sterically hindered methyl-substituted phenyloxamate bridging ligands[END_REF] Therefore at low temperature the spins of the Co II ions that link the pentametallic units have a direction opposite to that of the neighboring Cu II ions. Within the pentametallic entity, the topology of the interaction is formed by two opposite triangles sharing the central Co II ion as a vertex. If all interactions are antiferromagnetic, this arrangement creates a frustration. The spin configuration will depend on the relative values of the interaction between the Cu II ions and that of the interaction between the Cu II and Co II ions. There are many examples of Cu-Co interaction reported in the literature with either phenoxo [START_REF] O'connor | Relation between structure and magnetic exchange interactions in bis(hexafluoroacetylacetonato){N,N'-ethylenebis[2hydroxypropiophenone iminato-N,O(2-)]copper(II)}M'(II), Cu((prp)2en)M'(hfa)2, where M' = Cu, Ni, and Mn. Crystal structures of the complexes(M((prp)2en)M'(hfa)2)[END_REF][START_REF] Mikuriya | Binuclear Metal Complexes, XXIII. Molecular Structure of a Heterometal Binuclear Complex, CuCo(fsaen)•3H2O(C18H18N2O9CoCu)[END_REF][START_REF] Galy | Crystal and molecular structure of CuCo(fsa)2en.6H2O(H4[END_REF][START_REF] Branzea | New heterometallic coordination polymers constructed from 3d-3d′ binuclear nodes[END_REF][START_REF] Ghosh | The Impact of Anion-Modulated Structural Variations on the Magnetic Coupling in Trinuclear Heterometallic CuII-CoII Complexes Derived from a Salen-Type Schiff Base Ligand[END_REF][START_REF] Ghosh | Structural and Magnetic Analysis of Retrosynthetically Designed Architectures Built from a Triply Bridged Heterometallic (CuL)2Co Node and Benzenedicarboxylates[END_REF][START_REF] Verani | Exchange coupling in a bis(heterodinuclear) [CuIINiII]2 and a linear heterotrinuclear complex CoIIICuIINiII. Synthesis, structures and properties[END_REF][START_REF] Hari | Syntheses, crystal structures, magnetic properties and ESI-MS studies of a series of trinuclear CuIIMIICuII compounds (M = Cu[END_REF] or alkoxo bridges, [START_REF] Martin | Heterometallic CoII-CoIII-MII alkoxido-bridged heptanuclear motifs (M=Cu, Zn). Syntheses, crystal structures and magnetic properties[END_REF][START_REF] Nesterov | An unprecedented heterotrimetallic Fe/Cu/Co core for mild and highly efficient catalytic oxidation of cycloalkanes by hydrogen peroxide[END_REF][START_REF] Nesterov | Assembling Novel Heterotrimetallic Cu/Co/Ni and Cu/Co/Cd Cores Supported by Diethanolamine Ligand in One-Pot Reactions of Zerovalent Copper with Metal Salts[END_REF][START_REF] Hamid | Synthesis of Isostructural Cage Complexes of Copper with Cobalt and Nickel for Deposition of Mixed Ceramic Oxide Materials[END_REF][START_REF] Nakajima | Systematic Synthesis of Di-, Tri-, and Tetranuclear Homo-and Heterometal Complexes Using a Mononuclear Copper Synthon with a Tetradentate Amino Alcohol Ligand[END_REF][START_REF] Sultan | Hexanuclear coppernickel and copper-cobalt complexes for thin film deposition of ceramic oxide composites[END_REF] but very few examples are described with of a µ 3 -hydroxo bridge such as in compound 1. [START_REF] Hamid | Synthesis of Isostructural Cage Complexes of Copper with Cobalt and Nickel for Deposition of Mixed Ceramic Oxide Materials[END_REF][START_REF] Makhankova | Novel polynuclear CuII/CoII complexes constructed from one and two Cu2Co triangles with antiferromagnetic exchange coupling[END_REF] Actually, the geometry of the triangle in compound 1 is close to the one observed by Vassilyeva et al, [START_REF] Makhankova | Novel polynuclear CuII/CoII complexes constructed from one and two Cu2Co triangles with antiferromagnetic exchange coupling[END_REF] except that the second bridge between the Cu II and Co II ions is not a µ-κO-carboxylato but a µ-alkoxo bridge. Due to its molecular nature and the fact that the Co II ions do not exhibit an orbital moment in their trigonal bipyramid environments, the magnetic properties of Vassilyeva's compound was modeled and all the interactions were found antiferromagnetic. This, along with the analysis of the geometry of the pentametallic entity as well as the other results from the literature, allows us to predict that in compound 1 this should also be the case. The antiferromagnetic interaction is approximately proportional to the square of the overlap of the magnetic orbitals [START_REF] Kahn | Molecular Magnetism[END_REF] and in the case of monoatomic bridges, such as in compound 1, the overlap will strongly depend on the angle of the bridge. In particular, this has been well established for hydroxo-bridged Cu(II) ions where the smaller angle, the weaker the coupling. [START_REF] Crawford | Relation between the singlet-triplet splitting and the copper-oxygen-copper bridge angle in hydroxo-bridged copper dimers[END_REF][START_REF] Hay | Orbital interactions in metal dimer complexes[END_REF][START_REF] Ruiz | Toward the Prediction of Magnetic Coupling in Molecular Systems: Hydroxo-and Alkoxo-Bridged Cu(II) Binuclear Complexes[END_REF][START_REF] Ruiz | Structural Modeling and Magneto-Structural Correlations for Hydroxo-Bridged Copper(II) Binuclear Complexes[END_REF] For values slightly higher than 90°, the magnetic orbitals are accidentally orthogonal and the coupling is ferromagnetic. In compound 1 the Cu1-O-Cu2

angle is equal to 117.2° and is smaller than that observed in Vassilyeva's compound (119.8°), but it is largely superior than 90°. It excludes ferromagnetic interaction between the two copper ions. The value of the antiferromagnetic Cu-Cu interaction in 1 is therefore probably less than the -86.2 cm -1 found in the Vassilyeva's compound but is certainly of one or two tens of wave numbers in absolute value. The geometrical arrangement in 1 also allows a good interaction between the magnetic orbitals of the Co II ion with the magnetic orbital of the Cu II ions. In the literature, {CuCo} compounds with a double bridge consisting of oxygen atoms overwhelming present antiferromagnetic interactions. [START_REF] Aono | Diphenoxobridged NiCo and CuCo complexes of macrocyclic ligands:synthesis, structure and electrochemical behaviour[END_REF][START_REF] Nayak | Syntheses, Structures, and Magnetic Properties of Mononuclear CuII and Tetranuclear CuII3MII (M = Cu, Co, or Mn) Compounds Derived from N,N'-Ethylenebis(3-ethoxysalicylaldimine): Cocrystallization Due to Potential Encapsulation of Water[END_REF][START_REF] Tao | Synthesis, characterization, crystal structures and magnetic properties of dissymmetrical double schiff base heterotrinuclear complexes: [CuL(H2O)CoCuL]•H2O•CH3OH and [(CuL)2Ni]•2H2[END_REF][START_REF] Sunatsuki | Synthesis, Structure, and Properties of Di-μ-phenoxo-bridged Dinuclear CuIINiII and CuIICoII Complexes and Cyclic Di-μ-phenoxo-μ-amido-bridged Tetranuclear Cu2IIZn2II and Cu4IIComplexes Derived from the 1,2-Bis(2-oxidobenzamidato)benzenecuprate(II) Dianionic Ligand-Complex[END_REF][START_REF] Yonemura | Coordination-Position Isomeric MIICuII and CuIIMII (M = Co, Ni, Zn) Complexes Derived from Macrocyclic Compartmental Ligands[END_REF] The only examples of ferromagnetic interactions are found when bridges' angles are less than 93°. [START_REF] Nesterov | Self-assembly of the unique heterotrimetallic Cu/Co/M complexes possessing triangular antiferromagnetic {Cu2CoPb}2 and linear ferromagnetic {Cu2CoCd2} cores[END_REF][START_REF] Matsumoto | μ-Acetatodi-μ-phenolato-metal(II)cobalt(II) (Metal = Fe, Co, Ni, Cu, Zn) Complexes with Low-Spin Co(II): Synthesis, Structures, and Magnetism[END_REF] With Cu-O-Co angles comprised between of 95.7 and 97.1°, the coupling is certainly antiferromagnetic as in the reported compounds with angle in the same range. [START_REF] Ghosh | The Impact of Anion-Modulated Structural Variations on the Magnetic Coupling in Trinuclear Heterometallic CuII-CoII Complexes Derived from a Salen-Type Schiff Base Ligand[END_REF][START_REF] Ghosh | An adaptable heterometallic trinuclear coordination cluster in the synthesis of tailored one-dimensional architecture: Structural characterization, magnetic analysis and theoretical calculations[END_REF][START_REF] Parreiras | Solvent effects on the dimensionality of oxamato-bridged manganese(II) compounds[END_REF] The two triangles are therefore frustrated, and assumptions must be made to predict the configuration of the spins. If the coupling between the Cu II ions dominates, the spins of the Cu II ions will be antiparallel and so will the spins of the two Co II ions that link the pentametallic units. Under these conditions, the overall behavior should be reminiscent to that of a single Co II ion. The fit of the magnetization curve taking into account only one Co II ion does not give a good result but gives magnetization values that are compatible with the experimental curve (see Figure 5). To go further, the experimental magnetization curve was modeled by taking into account only the pentametallic entity and an acceptable model was obtained. To avoid overparametrization, the spin orbit constant and the orbital reduction factor for the Co II ions were set to standard values (λ = -180cm -1 ; α = 0.9). The model gives a value for the interaction between the Cu II ions, J CuCu = -8.7 cm -1 , that is higher than that between the Cu II ions and the central Co II ion, J CuCo = -2.25 cm -1 . In the opposite situation, where the Cu-Co interaction is the strongest, the three spins of the Co II ions will point in the same direction and will be antiparallel to those of the Cu II ions. In this case, the magnetization value at 7 T would be much higher than the observed 2.4 Nβ, reaching 5 to 6 Nβ, depending on the distortion parameters of the Co II ions (see Figure S3). In light of this analysis, the configuration of the spins at low temperature is dictated by the dominant Cu-Cu interaction, leading to a magnetization behavior reminiscent to that of a single Co II ion.

Conclusion

A new heterometallic oxamate-based 1D coordination polymer has been synthesized from a phenyloxamate ligand ortho-substituted with a carboxylato group. This compound illustrates the potential of the solvothermal synthetic method to ease the preparation and crystallization of compounds based on complex multi-polydentate oxamate ligands. Indeed, a fully coordinating mode has been observed, thus addressing the deprotonation issues that may occur on the bench with this type of oxamate ligands. The presence of copper ions and its binding affinity for the κN,κO chelating site of the oxamate group undoubtedly facilitate the one-pot solvothermal synthesis of heterometallic compounds. However, if the additional coordinating group successfully yields novel morphologies, even for 1D compounds, it comes at a cost over the predictability of the magnetic interactions and behavior.

  1635(s), 1571(s), 1433(w), 1383(w), 1347(m), 1251(w), 1184(m), 1095(m), 1051(m), 883(w), 852(w), 804(m), 767(m), 716(w), 678(m), 619(w), 580(w), 495(m), 374 (m), 323(m).

Figure 1 .

 1 Figure 1. View of the bimetallic chain compound 1. H atoms and non-coordinated solvent molecules have been omitted for clarity.

Figure 2 .

 2 Figure 2. (top) View of the asymmetric unit in the crystal structure of compound 1. (symmetry codes: #: 1-x,2-y,1-z; *: 1-x,1-y,1-z). (bottom) representation of the lacunar bis-cubane pentametallic core. H atoms and non-coordinated solvent molecules have been omitted for clarity.

Figure 3 .

 3 Scheme 1. Representation of the (oaba) 3-coordination mode in (a) the [Cu{Cu(oaba)(H 2 O)(py)} 2 ] and [Cu{Cu(oaba)(MeOH)} 2 ] 2D compounds,[25] and (b) in compound 1.

Figure 4 .

 4 Figure 4. Thermal dependence of χ M T for compound 1 in an applied field of 1 T (T ≥ 200K) and 250

Figure 5 .

 5 Figure 5. M v. H for compound 1 at 2 K (blue triangles). The solid green line represents a fit of M v.H taking into account only one Co(II) ion (λ = -130 cm -1 , α = 0.82, Δ = 241 cm -1 ), the orange solid line represents a fit taking into account the {Cu 4 Co} pentametallic unit (λ = -180 cm -1 , α = 0.9, Δ = 42.7 cm -1 , J CuCu = -8.7 cm -1 , J CuCo = -2.1 cm -1 )

  1 H-NMR (400 MHz, DMSO) δ (ppm): 12.56 (s, 1H), 8.57 (d, J = 8.4

	Hz, 1H), 8.02 (d, J = 7.9 Hz, 1H), 7.67 (t, J = 8.6 Hz, 1H), 7.26 (t, J = 8.6 Hz, 1H), 4.29 (q, J = 7.1 Hz,
	2H), 1.30 (t, J = 7.1 Hz, 3H). 13 C-NMR (75 MHz, DMSO) δ (ppm): 169.20 (s, -COO-), 159.76 (s, -
	COO-), 154.32 (s, -CONH-), 139.27 (s, -PhNH-), 134.34 (s, Ph), 131.37 (s, Ph), 123.98 (s, Ph),
	119.56 (s, Ph), 116.90 (s, PhCOOH), 62.82 (s, -CH 2 -), 13.74 (s, -CH 3 ). FTIR (cm-1): 3501 (m), 3416
	(m), 2982 (w), 2481 (w), 1755 (s), 1689 (s), 1663 (s), 1589 (m), 1519 (s), 1466 (m), 1452 (w), 1428 (w),
	1297 (m), 1248 (s), 1188 (s), 1092 (w), 999 (m), 929 (w), 858 (m), 822 (w), 789 (s), 762 (s), 698 (m),
	660 (m), 602 (m), 510 (m), 356 (m), 320 (m), 275 (m). Elemental analysis (%): calc. for C 11 H 11 NO 5 . C,
	55.70; H, 4.67; N, 5.90 Found: C, 55.46; H, 4.59; N, 5.96.
	2.2.2. Ligand preparation, acid form: 2-(oxamato)benzoic acid hydrate, mixed sodium salt, H 2.5 Na 0.5 -
	oaba•0.5(H 2 O).
	To 2.7 g of H 2 Et-oaba (M = 237.2 gmol -1 ; 11.38 mmol) suspended in 300 mL of water were slowly
	added 11.3 mL of 2M NaOH (2eq). The solution was stirred for 30 min and filtered on paper. Under
	stirring, 5.7 mL of 4M HCl (3eq.) were added dropwise and a precipitate formed gradually. The stirring
	was maintained for another 30 min and the solid was collected on a sintered glass filter, and dried in
	an oven at 70 °C overnight. (2.34 g, Yield: 89.75 %, M= 229.1 gmol -1 ). 1 H-NMR (400 MHz, DMSO) δ
	(ppm): 12.53 (s, 1H), 8.65 (d, J = 8.4 Hz, 1H), 8.03 (d, J = 7.9 Hz, 1H), 7.64 (t, J = 7.7 Hz, 1H), 7.22
	(t, J = 7.7 Hz, 1H). 13 C-NMR (101 MHz, DMSO) δ (ppm): 169.41 (s, -COOH), 161.96 (s, oxamaic -
	COOH), 157.41 (s, -CONH-), 139.96 (s, -PhNH-), 134.64 (s, Ph), 131.84 (s, Ph), 124.16 (s, Ph),
	119.98 (s, Ph), 117.55(s, -PhCOOH). FTIR (cm-1): 3213 (w), 1689 (s), 1601 (m), 1586 (m), 1531 (m),
	1452 (w), 1375 (m), 1290 (m), 1213 (s), 1190 (s), 1140 (m), 1078 (w), 903 (w), 837 (w), 780 (s), 751
	(s), 651(m), 557 (m), 484 (m), 379 (s), 276 (m). Elemental analysis (%): calc. for C 9 H 7.5 NO 5.5 Na 0.5 . C,
	47.17; H, 3.30; N, 6.11 Found: C, 47.95; H, 3.29; N, 6.15.

  ). Elemental analysis (%): calc. for C 60 H 76 Co 3 Cu 4 N 12 O 31 : C, 38.11; H, 4.05; N, 8.89; Co, 9.36; Cu, 13.32 (wt. Cu/Co=1.42). Found: C, 36.97; H, 3.97; N, 8.70; Co, 9,27; Cu, 12,79 (wt. Cu/Co=1.38). Selected IR data (cm -1 ): 2934(w),

Table 1 .

 1 Crystallographic parameters and data refinement for compound 1.

		1
	Formula	C 48 H 46 Co 3 Cu 4 N 8 O 26 •5(C 3 H 7 N O),0.3(H 2 O)
	FW [g mol -1 ]	1952.76
	Crystal system	Triclinic
	Space group	P-1
	a [Å]	11.192(4)
	b [Å]	13.437(5)
	c [Å]	15.800(6)
	α [°]	111.817(6)

  Co1 lies on an inversion center and binds the two {Cu(oaba)} metalloligands of the asymmetric unit in a facial manner via the µ 3 -hydroxide group (O1) and two carboxylate oxygen atoms (O2, O4). Co2 is cis-coordinated to the remaining carbonyl groups of two metalloligands (O6*, O7*, O9 and O11) and has two DMF molecules to complete its coordination sphere. The Co-O distances are quite narrowly distributed, and range from 2.081(6) to 2.135(9) Å.

	Some distortion is however apparent looking at O-Co-O angles that vary from 78 to 102°, and deviate
	on average from orthogonality by 6°. Overall, Co1, Cu1 and Cu2 describe a pentametallic sub-unit,
	[Co{Cu(oaba)} 4 (OH) 2 (DMF) 2 ]

). The Cu-O and Cu-N bond lengths are similar to the previously reported [Cu{Cu(oaba)(H 2 O)(py)} 2 ] and [Cu{Cu(oaba)(MeOH)} 2 ] 2D compounds.

[START_REF] Yoneda | A Homometallic Ferrimagnet Based on Mixed Antiferromagnetic and Ferromagnetic Interactions through Oxamato and Carboxylato Bridges[END_REF]

They range from 1.946(7) to 1.976(7) Å for the equatorial positions and from 2.500(9) to 2.529(5) Å for the apical ones. Co1 and Co2 are both six-coordinate with an octahedral geometry.

Acknowledgements

This work was supported by the Ministère de l'Enseignement Supérieur, de la Recherche et de l'Innovation (MESRI), the Centre National de la Recherche Scientifique (CNRS) and the China Scholarship Council (CSC) in the form of M. Ang Li's PhD fellowship. Elemental analysis was supported by the IPGP multidisciplinary program PARI, and by Paris-IdF region SESAME Grant no.

12015908. We thank the staff of the low temperature physical measurement MPBT technical platform at Sorbonne Université.

Supplementary material

Supplementary material is available for this article.

Supplementary Material for:

Synthesis, structure and magnetic properties of an oxamate-based 1D coordination polymer built on pentametallic links.

Ang Li (李昂), a Jérémy Forté, a Yanling Li, a Laurent Lisnard,* a Yves Journaux* a a. Sorbonne Université, CNRS, Institut Parisien de Chimie Moléculaire, IPCM, F-75252, Paris, France. *Corresponding author: laurent.lisnard@sorbonne-universite.fr