André Nel

Jean Lapeyrie

The first European representative of the South American

family Xenopteraidae (Insecta: Megasecoptera) discovered in the Guadalupian of Lodève (France)

A new genus, Sinitshenkovae gen. nov., is described, comprising the Carboniferous species Sinitshenkovae hueneckeni [START_REF] Pinto | Upper Carboniferous insects from Argentina. 1. Familia Diaphanopteridae (Megasecopteroidea)[END_REF] comb. nov. from South America and new Guadalupian species S. gallica sp. nov. from France. These two species are attributed to the Paleozoic South American family Xenopteraidae, a previously monospecific family only containing Xenoptera riojaensis [START_REF] Pinto | Carboniferous insects from Argentina. 3. Family Xenopteridae Pinto nov. fam. (Megasecoptera)[END_REF]. Sinitshenkovae gallica sp. nov. is therefore the youngest representative of this family and the only record outside South America, which suggests that our current knowledge of the palaeobiogeography of Permian and Carboniferous insects remains incomplete.

André Nel [anel@mnhn.fr] and Romain Garrouste [garroust@mnhn.fr OVER the last 18 years, a number of discoveries from the Guadalupian (locally known as the 'Red' Permian) of southern France have demonstrated the presence of a rich entomofauna, despite previous studies suggesting that these playa outcrops contained only ichnofossils.

Although numerous sites in both the Alpes-Maritimes and Var Departments have yielded a range of fossil insects illustrating trophic relationships between plants, insects and their predators in the Paleozoic [START_REF] Garrouste | Insect mimicry of plants dates back to the Permian[END_REF], those in the Lodève Basin have proven the richest in terms of fossil insect diversity and abundance, with more than 65 different species and 13 orders recorded, most of which were collected by one of the present authors (JL) [START_REF] Prokop | New Middle Permian palaeopteran insects from Lodève Basin in southern France (Ephemeroptera, Diaphanopterodea, Megasecoptera)[END_REF], Prokop et al. 2015a,b, 2017[START_REF] Garrouste | Insects in the Red Middle Permian of Southern France: first Protanisoptera (Odonatoptera) and new Caloneurodea (Panorthoptera), with biostratigraphical implications[END_REF]. Although the Paleozoic orders Palaoedictyoptera and Diaphanopterodea are certainly present, and in the case of the Diaphanopterodea, relatively diverse, within the Lodève Basin, records of the related order Megasecoptera remained unknown until now. Here we describe the first megasecopteran from the Permian of the Lodève Basin, based on an incomplete wing. This wing is noted to be similar to species of the Carboniferous South American family Xenopteraidae [START_REF] Ross | Omaliidae Handlirsch, 1904 (Insecta, Archaeorthoptera) and Xenopteridae Pinto, 1986 (Insecta, Megasecoptera): proposed emendation to Omaliaidae and Xenopteraidae respectively to remove homonymy with Omaliinae MacLeay, 1825 (Insecta, Coleoptera) and Xenopteridae Riek, 1955 (Insecta, Orthoptera)[END_REF].

Material and methods

The fossil was collected by one of the authors (JL) from 'Canals' outcrop in the Guadalupian, Permian Lodève Basin. It is deposited in Lapyerie collection, Musée of Lodève (Ld LaP).

The wing was studied under a NIKON SMZ 1500 binocular microscope, and photographed using a NIKON D800; photographs were processed using the image-editing software Adobe Photoshop CS. Line drawings of the venation were prepared directly with the aid of a camera lucida.

Wing venation nomenclature follows that of [START_REF] Kukalová-Peck | Chapter 6: Fossil history and the evolution of hexapod structures[END_REF], with abbreviations as follows: AA -anal anterior; AP -anal posterior; C -costal vein; CuA -cubitus anterior; CuP -cubitus posterior; MA -media anterior; MP -media posterior; m-cua -basal brace between M and CuA; RA -radius anterior; RP -radius posterior; ScP -subcostal posterior.

Systematic palaeontology

Class INSECTA Linnaeus, 1758 Infraclass PALAEOPTERA Martynov, 1923 Superorder PALAEODICTYOPTEROIDA Goldenberg, 1877 Order MEGASECOPTERA Brongniart, 1885 Family XENOPTERAIDAE Ross, Nicholson & Jarzembowski, 2013 Type genus. Xenoptera Pinto, 1986 Remarks. Xenopteraidae Ross, Nicholson & Jarzembowski, 2013 was proposed as a replacement name for the fossil family 'Xenopteridae Pinto, 1986', as this name was preoccupied by Xenopteridae Riek, 1955 (order Orthoptera;type genus Xenopterum Riek, 1955).

Sinitshenkovae gen. nov.

Etymology. Named after our colleague N.D. Sinitshenkova, specialist of Palaeodictyopterida. [START_REF] Pinto | Upper Carboniferous insects from Argentina. 1. Familia Diaphanopteridae (Megasecopteroidea)[END_REF]) (formerly 'Philiasptilon' hueneckeni [START_REF] Pinto | Upper Carboniferous insects from Argentina. 1. Familia Diaphanopteridae (Megasecopteroidea)[END_REF]; Sinitshenkovea gallica sp. nov.

Species included. Sinitshenkovae hueneckeni

Diagnosis. Fore wing characters only. A rather broader area between RA and C; veinlets between main veins very oblique and distinctly sigmoidal.

Sinitshenkovae gallica sp. nov. (Fig. 1) Diagnosis. Veinlets between RA and C distinctly oblique and long; few veinlets between main veins; three posterior branches of RP.

Etymology. From 'Gallia', the Latin name for France.

Holotype. Specimen Ld LaP 760, (counterprint), Lapeyrie collection, Musée Fleury, Lodève, France.

Locality and age. Guadalupian (mid-Permian) Mérifons Member, Salagou Formation; 'Canals' outcrop (see [START_REF] Garric | Les rigoles fossilifères du Saxonien du bassin de Lodève (Languedoc, France)[END_REF], near Lodève, Hérault, France.

Description

Counterimprint of the distal half of an elongate wing, fragment 15.6 mm long, 4.9 mm wide.

Concave ScP ending on costal margin 7.5 mm from wing apex; subcostal space 0.4 mm wide, one preserved veinlet between ScP and C. Convex RA weakly curved, area between it and C+ScP 0.6 mm wide, with 6-7 hort oblique and simple veinlets; RA ending 1.0 mm from wing apex; base of RP not preserved, but at least 12 mm from wing apex; concave RP with three simple branches. Strongly convex MA simple, strongly approaching RP basally; concave MP forking into two long posterior branches; bases of MA and MP not preserved; area between MP and CuA with a long oblique crossvein partly preserved (brace m-cua?).

Distinctly convex CuA nearly straight and simple, with a broad area between it and CuP, equal in width to area between MA and MP; concave CuP simple and nearly straight. Two convex (AA1 and AA2) and one concave (AP) straight anal veins. Few crossveins between RP, MA, MP, and CuA, all long, oblique and sigmoidally curved; additional 'convex veins' running alongside CuP, AA1, and AA2, and which cross the transverse veinlets between CuA and CuP and CuP and AA1, appear to be fossilization artifacts.

Discussion

Sinitshenkovae gallica sp. nov. does not resemble any of the previously described insects from the Permian Lodève Basin, differing in its forked MP, simple MA and CuA, and sigmoidal crossveins [START_REF] Prokop | New Middle Permian palaeopteran insects from Lodève Basin in southern France (Ephemeroptera, Diaphanopterodea, Megasecoptera)[END_REF], Prokop et al. 2015a,b, Garrouste et al. 2018).

The lack of information on the basal half of the wing makes the fossil difficult to attribute to any particular taxon. Although some 'Grylloblattodea' and 'Eoblattida' share the short ScP, pectinate RA, and simple MA seen in this fossil, they generally also have multi-branched CuA (e.g. Tshekardembia [START_REF] Novokshonov | New fossil insects from the Kungurian of Middle Ural[END_REF], Nestorembia Shcherbakov 2015;[START_REF] Storozhenko | Sistematika, filogeniya i evolyutsiya grilloblattidovykh nasekomykh (Insecta: Grylloblattida) [Systematics, phylogeny and evolution of the grylloblattids (Insecta: Grylloblattida)][END_REF], Aristov 2017a,b), and as a result Sinitshenkovae gallica is excluded from these orders.

Like the new fossil described here, the Caloneurodea also have few RP and M branches, and CuA and CuP strongly converging, closely parallel. Although the 'vein' seen alongside CuP in Sinitshenkovae gallica could be interpreted as a CuA closely parallel to CuP, the presence of similar 'veins' along AA1 and AA2, plus the fact that this feature crosses a veinlet between CuA and CuP, strongly suggests it is not a true vein. Furthermore, an attribution to the Caloneurodea is unlikely because in this group the median vein is either simple or has only one or two distal branches; these insects do not have M separating basally into a convex MA and a concave MP, as seen in Sinitshenkovae gallica. An alternative interpretation of the wing venation could be proposed for our fossil that would be more its venation congruent with an attribution to the Caloneurodea; viz., the vein we name MA could be a basal branch of RP, making the forked vein posterior to this (our MP) MA and the vein after that (our CuA) MP+CuA+CuPaα in accordance with [START_REF] Béthoux | The extinct order Caloneurodea (Insecta: Pterygota: Panorthoptera): wing venation, systematics and phylogenetic relationships[END_REF]. However, this alternative hypothesis is in contradiction with the fact that the basal branch of RP (our MA) would then be distinctly convex, which is unlikely as the other branches of RP are concave. This would also indicate a very broad area between the veins 'MP+CuA+CuPaα' (our CuA) and CuP in Sinitshenkovae gallica, whereas this area is very narrow in Caloneurodea. Thus we reject the hypothesis of an attribution to the Caloneurodea for this new species. Some Megasecoptera have a relatively short ScP and a distal area between RA and C with short veinlets (viz. Eubrodia Carpenter, 1967;[START_REF] Prokop | A remarkable insect from the Pennsylvanian of the Joggins Formation in Nova Scotia, Canada: insights into unusual venation of Brodiidae and nymphs of Megasecoptera[END_REF] as seen in the new fossil, and some also share the long and oblique brace m-cua (viz. Calohymen Carpenter, 1947).

Only a small number of megasecopterans share the following combination of characters: simple A, CuP, CuA, and MA; MP with only two branches; presence of few long sigmoidal crossveins. Further, the strong basal convergence of MA and RP seen in Sinitshenkovae gallica is a character also present in the Megasecoptera. Sinitshenkova (2002) divided the Mischopterida Handlirsch, 1906(= Megasecoptera Brongniart, 1893+ Archodonata Martynov, 1932) into four suborders: Eubletina [START_REF] Laurentiaux | Classe des insectes (Insecta Linné, 1758)[END_REF], Mischopterina Handlirsch, 1906 ('essentially the same as that previously called Eumegasecoptera'; Sinitshenkova 2002, p. 121, Aspidothoracina Handlirsch, 1919, and Permothemistina Martynov, 1935. The present fossil is excluded from Sinitshenkova's Permothemistina as insects of this suborder have a pterostigma and a branched CuA. The 'Aspidothoracina' were described as follows:

'Aspidothoracinans are similar to Mischopterina in wings well elongate, costalised and petiolate, but synapomorphic in the wings further costalised (costal space practically lost, and C, SC, and R almost or well touching each other, or else SC lost' (Sinitshenkova 2002, p. 121). As the costal space is rather broad and ScP does not touch R in Sinitshenkovae gallica, an attribution to this group is also excluded. Finally, Sinitshenkova (2002, p. 121) characterized the 'Mischopterina' as 'synapomorphic in having the elongate body lacking paranota, the wings well costalised, homonomous, elongate (rather triangular in Mischopteridae) and usually petiolate, with usually single pectinate A, and crossveins arranged in transverse rows, and plesiomorphic in having well developed costal space and percurrent SC'. Sinitshenkovae gallica therefore differs from this group in the fact that it does not preserve pectinate anal veins, its wing is elongate but not triangular shaped, and in its crossveins being elongate and not clearly arranged into rows.

The Eubletina sensu Sinitshenkova (= Eubleptidae, Namurodiaphidae, Anchineuridae, Engisopteridae, Sphecorydaloididae, and 'Xenopteridae [START_REF] Pinto | Carboniferous insects from Argentina. 3. Family Xenopteridae Pinto nov. fam. (Megasecoptera)[END_REF]', including 'Philiasptilon' hueneckeni Pinto & Pinto de Ornellas, 1978) were characterized by 'the robust body, prothoracic paranota, wide costal space, wide wing base with 3 independent anal veins, and generally rich venation' (Sinitshenkova 2002, p. 121). Within the Eubletina, Sinitshenkovae gallica differs from the Eubletidae, Anchineuridae, Engisopteridae and Namurodiaphidae in having a shorter ScP, sigmoidal crossveins, and simple CuA and CuP (Carpenter 1963a[START_REF] Carpenter | Studies of North American Carboniferous insects. Part 9. A new species of Eubleptidae from Mazon Creek (Palaeodictyoptera)[END_REF][START_REF] Kukalová-Peck | Megasecoptera from the Lower Permian of Moravia[END_REF][START_REF] Kukalová-Peck | Wing folding in pterygote insects, and the oldest Diaphanopterodea from the Early Carboniferous of West Germany[END_REF]. The Sphecorydaloididae share with Sinitshenkovae gallica the short ScP, but differ in the presence of short fusions of MA with RP and CuA with M, plus a forked CuP [START_REF] Pinto | Sphecorydaloides lucchesei, a new Carboniferous megasecopteran insect from Argentina[END_REF].

Overall, the preserved venation of Sinitshenkovae gallica is most similar to the wings of Xenoptera riojaensis Pinto, 1986 and 'Philiasptilon' hueneckeni, sharing features such as the shortened ScP, short veinlets between RA and C, simple MA, single MP fork, and simple CuA, CuP and anal veins. 'Philiasptilon' hueneckeni also shares the presence of long, oblique, sigmoidal crossveins, which are clearly visible in the photograph of the holotype (Pinto & Pinto de Ornellas 1978, fig. 1), although this feature is not seen in Xenoptera (which has straight crossveins). Therefore, we attribute the new fossil to the family Xenopteraidae, but establish a new genus for Sinitshenkovae gallica and 'Philiasptilon' hueneckeni, which differs from Xenoptera primarily in the shape of the crossveins.

The type species of the diaphanopterid Philiasptilon [START_REF] Zalessky | Observations sur les insectes trouvés dans les dépôts à charbons du bassin de Kousnetzk et sur l'âge de ces derniers d'après la faune entomologique[END_REF], Philiasptilon maculosum Zalessky, 1931, differs strongly from 'Philiasptilon' hueneckeni in having CuA with many branches (or perhaps MP with many branches, as following [START_REF] Zalessky | Observations sur les insectes trouvés dans les dépôts à charbons du bassin de Kousnetzk et sur l'âge de ces derniers d'après la faune entomologique[END_REF] original interpretation, the vein M would be simple, which is rather unusual for these insects).

Therefore, as already suggested by Sinitshenkova (2002), 'Philiasptilon' hueneckeni likely corresponds to a very different taxon and should be placed in a different genus, family, and order. We propose that the best place for this species is within the Xenopteraidae with Sinitshenkovae gallica.

Notice that Sinitshenkovae gallica has some similarities with the Brodiopteridae Carpenter, 1963(genus Brodioptera Copeland, 1957), but it differs from Brodioptera in the presence of veinlets between ScP and C, between RA and C+ScP, and a forked MP [START_REF] Copeland | The arthropod fauna of the Upper Carboniferous rocks of the Maritime Provinces[END_REF]Carpenter 1963b;[START_REF] Nelson | Brodioptera stricklani n. sp. (Megasecoptera: Brodiopteridae), a new fossil insect from the upper Manning Canyon Shale Formation, Utah (Lowermost Namurian B)[END_REF][START_REF] Pecharová | A new palaeodictyopteroid (Megasecoptera: Brodiopteridae) from the Early Pennsylvanian of northern China reveals unique morphological traits and intra-specific variability[END_REF].

Conclusion

This new discovery extends the range of the Xenopteraidae into the Permian of Europe for the first time, as xenopteraids were previously only known from the Late Carboniferous of South America. This indicates that this family was more widespread in time and space than previously interpreted. The case of the French 'red' Permian outcrops shows that any new Middle or Late Permian entomofauna contains a majority of new taxa, either genera or species, even families. Important efforts shall be necessary in the next future to improve our vision and understanding of the Permian insect diversity, crucial to better estimate the impact of the Permian-Triassic crisis on this major clade.

  ., LAPEYRIE, J. & GARROUSTE, R., 2018. The first European representative of the South American Xenopteraidae discovered in the Guadalupian of Lodève (France) (Insecta : Megasecoptera). Alcheringa XXX, xxx-xxx.

  Keywords: Palaeodictyopteroida, gen. & sp. nov., Guadalupian, Permian, France.

	], Institut Systématique
	Evolution Biodiversité (ISYEB), Muséum national d'Histoire naturelle, CNRS, Sorbonne
	Université, EPHE, 57 rue Cuvier, CP 50, 75005 Paris, France. Jean Lapeyrie

[jean.lapeyrie@orange.fr], Corniche de Fontbonne, F-34700 Lodève, France.

Acknowledgements

We sincerely thank one anonymous referee and the editor of the journal of their helpful comments on the first version of the paper.

Funding

This work was supported by no external funding.

Data access statement

This study did not involve any underlying data. The described specimen is available for restudy at the public institute indicated in the text.


J Schorne-Pinto

A Janghorban

M Lomello-Tafin

A Pisch

G Mikaelian

P Benigni

A Barnabé

L Cassayre

Assessment of thermodynamic data for CuCrO 2 delafossite from calorimetric measurements

Keywords:

A detailed investigation of the thermodynamic properties of delafossite CuCrO 2 was carried out by experimental methods on synthetic CuCrO 2 delafossite samples (differential scanning calorimetry from ambient to 871 K and drop calorimetry from 823 to 1123 K) and theoretical methods (density functional theory). Based on these data and available literature (low temperature heat capacity measurements and calculations, high temperature emf data), we propose, for the first time, a full set of thermodynamic data for the phase CuCrO 2 . Our selection comes to: °H CuCrO ( ) f 298 2 = -670.8 ± 1.3 kJ mol -1 , °S CuCrO ( ) 298 2 = 88.9 J K -1 , and °cp

Introduction

Cuprous delafossite type oxides Cu 1+ M 3+ O 2 with M = (Cr 3+ , Fe 3+ , Al 3+ , among others) have been a topic of intense scientific activity over the last two decades due to their unique physical and chemical properties. Among them, the cuprous chromite CuCrO 2 , also named "Mac Connellite" in its mineral form and sometimes noted as Cu 2 Cr 2 O 4 in older works, is one of the most promising candidates for transparent ptype conducting oxide in optoelectronic devices [START_REF] Barnabé | p-Type conducting transparent characteristics of delafossite Mg-doped 2 thin films prepared by RF-sputtering[END_REF][START_REF] Crêpellière | Transparent conductive CuCrO 2 thin films deposited by pulsed injection metal organic chemical vapor deposition: up-scalable process technology for an improved transparency/conductivity trade-off[END_REF][START_REF] Mahapatra | Low-pressure metal-organic chemical vapor deposition of transparent and p-Type conducting CuCrO 2 thin films with high conductivity[END_REF]. This compound is also of interest for its catalyst/photocatalytic [START_REF] Amrute | Solid-state chemistry of cuprous delafossites: synthesis and stability aspects[END_REF][START_REF] Ketir | Visible light induced NO 2 -removal over CuCrO 2 catalyst[END_REF] and thermoelectric applications [START_REF] Manickam | Double doping induced power factor enhancement in CuCrO 2 for high temperature thermoelectric application[END_REF][START_REF] Sinnarasa | Thermoelectric and transport properties of delafossite CuCrO₂: Mg thin films prepared by RF magnetron sputtering[END_REF][START_REF] Sinnarasa | Influence of thickness and microstructure on thermoelectric properties of Mg-doped CuCrO 2 delafossite thin films deposited by RF-magnetron sputtering[END_REF]. Moreover, the CuCrO 2 phase presents remarkable physical properties such as multiferroic behavior [START_REF] Poienar | Spin dynamics in the geometrically frustrated multiferroic CuCrO 2[END_REF][START_REF] Seki | Spin-driven ferroelectricity in triangular lattice antiferromagnets ACrO 2 (A = Cu, Ag, Li, or Na)[END_REF] at low temperatures.

The CuCrO 2 delafossite crystallizes with the rhombohedral structure (space group R 3m) composed of alternating layers of linearly co- ordinated O-Cu 1+ -O and Cr 3+ O 6 edge-shared octahedra. In air, this phase is stable from 1073 K [START_REF] Amrute | Solid-state chemistry of cuprous delafossites: synthesis and stability aspects[END_REF] up to a temperature higher than 1833 K based on observations of a quenched sample by Gadalla et al. [START_REF] Gadalla | The system CuO-Cu 2 O-Cr 2 O 3 and its bearing on the performance of basic refractories in copper-melting furnaces[END_REF]. This phase is one of the three mixed oxide (together with the CuCr 2 O 4 spinel and CuCrO 4 copper chromate [START_REF] Kale | Thermal decomposition of CuCrO 4 •2CuO•2H 2 O and phase relations in the Cu-Cr-O system[END_REF][START_REF] Jacob | Gibbs energy of formation of CuCrO 4 and phase relations in the system Cu-Cr-O below 735 K[END_REF]) composing the Cu-Cr-O ternary system, in which Hamuyuni and Taskinen recently performed liquidus measurements [START_REF] Hamuyuni | Liquidus experimental data for the system Cu-O-Cr 2 O 3 in air[END_REF].

However, limited thermodynamic data for CuCrO 2 are available in the literature. As evidenced by Perrot in his review of the Cu-Cr-O system in 2010 [START_REF] Perrot | Chromium -copper -oxygen[END_REF], there is a strong lack of experimental information such as heat capacity, entropy, and enthalpy for CuCrO 2 , at room temperature and above. At high temperature, two systematics studies were performed on the Cr-Cu-O system by emf method. Jacob et al. [START_REF] Jacob | Oxygen potentials, Gibbs' energies and phase relations in the Cu-Cr-O system[END_REF] reported information on mixed oxides CuCrO 2 and CuCr 2 O 4 in addition to the single oxides Cr 2 O 3 , CuO, and Cu 2 O in the 900-1350 K temperature range. The same year, Vlach et al. [START_REF] Vlach | A thermodynamic study of the Cu-Cr-O system by the EMF method[END_REF] performed similar measurements, and included an extensive review of Gibbs energy values for the formation reaction of CuCrO 2 . Among the twelve studies they reported for the CuCrO 2 phase, their emf values, the values of Jacob et al. [START_REF] Jacob | Oxygen potentials, Gibbs' energies and phase relations in the Cu-Cr-O system[END_REF] and the derived function obtained by Schmahl and Minzl [START_REF] Schmahl | Ermittlung thermodynamischer Daten Von Doppeloxidbildungen aus Gleichgewichtsmessungen[END_REF] are in good agreement. The applicative interest of the CuCrO 2 phase also favored studies of the low-temperature heat capacity, magnetization, and resistivity. Indeed, Okuda et al. [START_REF] Okuda | Specific heat of delafossite oxide CuCr 1-x Mg x O 2 (0 ≤ x ≤ 0.03)[END_REF] made estimations of the heat capacity between 0 to 150 K, and Poienar et al. [START_REF] Poienar | Structural and magnetic properties of CuCr 1-x Mg x O 2 by neutron powder diffraction[END_REF] carried out heat capacity measurements between 2.5 and 50 K. Finally, a value for the enthalpy of formation of the phase at 0 K was proposed by Scanlon & Waston [START_REF] Scanlon | Understanding the p-type defect chemistry of CuCrO 2[END_REF], based on density functional theory (DFT) calculations.

Due to some lack of experimental data, especially for the heat https://doi.org/10.1016/j.tca.2019.178345

⁎ Corresponding author.

E-mail address: laurent.cassayre@ensiacet.fr (L. Cassayre).

Cuboid samples of around 40 mg (≈3 × 3 × 3 mm 3 ) were obtained by cutting the initial pellet using a wire saw.

Drop calorimetry: apparatus and procedure

An isothermal Multi-HTC calorimeter from Setaram Instrumentation was used for this study. The calorimetric cell was heated by a vertical furnace and connected to an atmosphere controlled-tight container, loaded alternately with alumina pieces and CuCrO 2 cuboid samples. The experiments were done in an alumina crucible containing a onecentimeter-thick bed of HfO 2 powder in order to ensure the best reproducibility of heat transfers. The drop measurements were performed in flowing argon (99,999% N50) having an impurity of O 2 less than 2 ppm, that leads to a maximal value of oxygen partial pressure of 2.10 -6 atm. The temperature was calibrated with respect to pure standard metals (Al, Ag, Au). Their melting temperature was recorded at three heating rates (1, 2.5 and 5 K min -1 ) and were linearly extrapolated to zero heating rate. The calibration of the calorimeter was achieved by dropping an alumina sample into the crucible before and after each drop of CuCrO 2 sample. The sensitivity of the calorimetric cell was determined by comparing the calorimetric signals with tabulated data for Al 2 O 3 [START_REF] Ditmars | Enthalpy and heatcapacity standard reference material: synthetic sapphire (a-Al 2 O 3 ) from 10 to 2250 K[END_REF]. The temperature of the Ar-tight container was measured using an individual thermometer prior to each drop. The cell temperature had a fluctuation range between ± 0.01 K and ± 0.03 K as the isotherms increased from 823 K to 1123 K. The thermopile fluctuations for all isotherms was found to be less than ± 1.6 μV. The baseline treatment and the peak integration were done with the CA-LISTO Setaram software.

DSC: apparatus and procedure

The DSC 111 instrument and the procedure used for measuring the heat capacity of CuCrO 2 are the same as used for ZnSb and described in [START_REF] Benigni | Measurement of the heat capacity of ZnSb by DSC between 300 and 673 K[END_REF]. Further relevant experimental details are described in this section.

A mass of 114.220 mg of CuCrO 2 powder was weighed with a microbalance ( ± 1 μg), and hermetically sealed in a first stainless steel crucible under argon within a glovebox. Then, a mass of 68.345 mg of Standard Reference Material SRM720 α-Al 2 O 3 [START_REF] Ditmars | Enthalpy and heatcapacity standard reference material: synthetic sapphire (a-Al 2 O 3 ) from 10 to 2250 K[END_REF] was sealed in a second stainless steel crucible, and finally, two other similar crucibles were sealed empty. The four crucibles of equal weights were all sealed inside the glovebox, in which the oxygen level was lower than 2 ppm, and the water level was measured at 53 ppm using a cermet hygrometer.

The heat capacity was measured between 300 and 871 K using the small temperature step method. The three parameters of the temperature program were as follows: temperature step of 2.5 K, heating rate of 1.5 K min -1 between each step and stabilization time of 800 s after each temperature step.

The heat capacity measurement by DSC requires three consecutive heating runs: the so-called zeroline, calibration, and sample runs as detailed in [START_REF] Benigni | Measurement of the heat capacity of ZnSb by DSC between 300 and 673 K[END_REF]. To protect the steel crucibles from possible oxidation during these runs, the experiments were performed under a flow of argon gas, Alphagaz 1 commercial grade (purity > 99.999% vol., O 2 < 2 ppm, H 2 O < 3 ppm, C n H m < 0.5 ppm) supplied by the Air Liquide company. Before starting the temperature program, the two tubes of the differential calorimeter were flushed with an argon flowrate of approximately 0.5 L min -1 during 1 h. This argon flowrate was maintained during the whole duration of the experiments.

The temperature measurement within the DSC device was calibrated with respect to the melting temperature of pure In, Sn, Zn, and Al.

Theoretical methods

The ground state properties of CuCrO 2 were calculated using DFT [START_REF] Hohenberg | Inhomogeneous electron gas[END_REF][START_REF] Kohn | Self-consistent equations including exchange and correlation effects[END_REF]. The calculations were performed using the VASP software package [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF][START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmentedwave method[END_REF] in its most recent version (5.4.4).

The many-body exchange semi-local density functional SCAN (Strongly Conditioned and Appropriately Normed) [START_REF] Sun | Strongly Constrained and appropriately normed density functional[END_REF] was used to compute the ground state properties of Cu 2 O, Cr 2 O 3, and CuCrO 2 . For Cu and Cr, the 3d and 4s orbitals and for O the 2s and 2p orbitals are considered as valence states in the calculations. The energy cut-off for the projector augmented plane-wave bases was set to 800 eV. An automatically generated, gamma centred grid of k-points in the irreducible part of the Brillouin zone was used following the Monkhorst-Pack scheme [START_REF] Monkhorst | Special points for Brillouin-zone integrations[END_REF]. The k-point grid for Cu 2 O was 11 × 11 × 11, for Cr 2 O 3 7 × 7 × 7 and for CuCrO 2 11 × 11 × 2. The magnetic properties for Cr 2 O 3 (antiferromagnetic) and CuCrO 2 (ferromagnetic) were taken into account.

The lattice parameters for all three solids as well as the internal atomic coordinates were fully relaxed. The linear tetrahedron method with Blöchl corrections [START_REF] Blöchl | Improved tetrahedron method for Brillouinzone integrations[END_REF] was used to calculate the electronic Density of States (DOS). The relaxations were performed with a convergence criterion of 10 -8 eV Å -1 for the total energy and 10 -6 eV Å -1 for the forces to avoid any kind of residual stress in the Hellman-Feynman forces.

The energy of formation at 0 K for CuCrO 2 with respect to the simple oxides was calculated using the relation:

ΔE(CuCrO 2 , 0 K) = E(CuCrO 2 , 0 K) -0.5 x E(Cu 2 O, 0 K) -0.5 x E(Cr 2 O 3 , 0 K) (1)
capacity between 150 and 1000 K, no thermodynamic functions were proposed so far for the CuCrO 2 delafossite phase. In this work, we performed heat capacity measurements with differential s canning calorimetry (DSC) from ambient temperature to 871 K and drop calorimetry from 823 to 1123 K on synthetic CuCrO 2 delafossite samples, as well as DFT calculations at 0 K. Then, we assessed a full set of refined thermodynamic data from 298.15 K (which will be noted 298 K in the rest of the paper) to 1300 K, based on a third law analysis of our data and literature data, following a similar procedure as presented by Jacob et al. [START_REF] Jacob | Gibbs energy of formation of MnO: measurement and assessment[END_REF] for the MnO phase.

Materials and methods

Preparation and characterization of CuCrO 2 samples

Polycrystalline powder synthesis

CuCrO 2 was prepared by high-temperature solid-state reaction in nitrogen atmosphere as described elsewhere [START_REF] Lalanne | Synthesis and thermostructural studies of a CuFe 1-x Cr x O 2 delafossite solid solution with 0 ≤ x ≤ 1[END_REF]. The Cu 2 O (Alfa Aesar 99%) and Cr 2 O 3 (Acros Organics, 99+%) powders were mixed in stoichiometric quantities in a mortar and then treated at 900 and 1000 °C for 30 h, with intermediate grindings to ensure good homogeneity.

Sintering & pellets preparation

Resulting powder was mixed with an organic binder (Rhodoviol ® ) and uniaxially pressed into a pellet of 2 cm in diameter. The debinding was carried out under air at 400 °C, and the sintering at 1050 °C with a dwell time of 10 h under Ar atmosphere.

Composition analysis

The cationic molar ratio of the CuCrO 2 product was checked by Field Emission Gun -Electron Probe Microanalysis FEG-EPMA (SX Five FE, CAM ECA) before and after drop calorimetry. X-Ray Fluorescence spectroscopy (XRF) (S2 Ranger, Bruker) was also performed to confirm the composition.

Structural analysis

The pellets were characterized before and after drop calorimetry by room-temperature X-Ray Diffraction ( Bruker D 4 d iffractometer, λCu Kα1 = 1.54056 Å and Kα2 = 1.54443 Å radiation).

Cutting samples 2.5. Selected thermodynamic data and functions

Thermodynamic data and functions for all pure compounds considered in this work (Cu(fcc), Cr(bcc), O 2 (g), Cr 2 O 3 (s) and Cu 2 O(s)) are compiled in Table 1. We have selected tabulated or experimental data for heat capacity below 298 K, and polynomial functions above 298 K. For Cr 2 O 3 (s), the low temperature heat capacity was taken from recent measurements from [START_REF] Gurevich | Thermodynamic functions of eskolaite Cr2O3(c) at 0-1800 K[END_REF]. For Cu 2 O(s), according to the recommendations of NIST-JANAF [START_REF] Chase | NIST-JANAF thermochemical tables[END_REF], we selected the data from [START_REF] Hu | Low temperature heat capacities of inorganic solids. IX. Heat capacity and thermodynamic properties of cuprous oxide from 14 to 300 K[END_REF] for 0 < T < 120 K and from [START_REF] Mah | Thermodynamic Data for Cuprous and Cupric Oxides[END_REF] for 120 < T < 298 K. For these two single oxides, the polynomial regression are from FTOxid [START_REF] Bale | FactSage thermochemical software and databases[END_REF], which reproduces tabulated data recommended by NIST-JANAF [START_REF] Chase | NIST-JANAF thermochemical tables[END_REF] for T > 298 K.

Results

Structural and chemical characterizations

The sintered sample was checked by room temperature XRD that confirmed the presence of the CuCrO 2 single phase, without any secondary phase, with rhombohedral structure (3R polytype with the space group R 3m) as illustrated on Fig. 1. Based on Rietveld refinement (R factor of 4.54), the lattice parameters are a = 2.9730(3) Å and c = 17.086(2) Å.

EPMA analysis was also carried out on a cross section of a polished sample. The average composition determined by ten random point analyzes is 24.0(7) mol% of copper, 24.5(5) mol% of chromium and 51.4(6) mol% of oxygen, which corresponds to the stoichiometric composition CuCrO 2 .

DSC data

The DSC data are plotted vs. temperature on Fig. 2 (numeric values are provided in the supplementary Excel file). The data are compared to an estimation of the heat capacity using the Neumann-Kopp additivity Rule (NKR) [START_REF] Leitner | Application of Neumann-Kopp rule for the estimation of heat capacity of mixed oxides[END_REF] established with the Cr 2 O 3 and Cu 2 O heat capacities reported in Table 1. The heat capacity at room temperature was also estimated by Dulong-Petit limit (99.77 J mol -1 K -1 ), defined as 3nR, where n is the number of atoms by molecule (n = 4) and R is the gas constant. The molar heat capacity at constant volume c V calculated with Einstein's relation (see for instance the recent work of Zienert and Fabrichnaya [START_REF] Zienert | Prediction of heat capacity for crystalline substances[END_REF] for mathematical expression) is also reported.

The calculated NKR curve shows a kink around 320 K which is a pure artefact resulting from the magnetic transition of Cr 2 O 3 . Indeed, the delafossite CuCrO 2 phase only exhibits a magnetic transition at around 24 K according to [START_REF] Maignan | On the strong impact of doping in the triangular antiferromagnet CuCrO 2[END_REF] and no other transition is expected at 320 K.

Hence, the reason for the increased scattering of the experimental data points between 300 and 400 K is not fully understood. It is possibly due to vaporization of residual water, as the atmosphere of the glovebox contained 53 ppm of water when the DSC crucibles were sealed. In the 400-770 K, the DSC signal is smoother. Some scattering above 770 K might be related to the slow decomposition of CuCrO 2 caused by the low oxygen partial pressure in the crucible.

Drop calorimetry data

An example of heat flow recorded at 872 K is provided on Fig. 3.

Table 1

Selected thermodynamics functions and data.

As indicated in the Guide to the Expression of Uncertainty in Measurement (GUM) [START_REF]Working Group 1 of the Joint Committee for Guides in Metrology, Evaluation of Measurement Data -Guide to the Expression of Uncertainty in Measurement[END_REF], which remains the reference document related to uncertainty measurement, the nature of certain measurement procedures or tests can make the rigorous application of the GUM difficult. In our case, several sources of uncertainty contribute to a global component when enthalpy increments are measured by drop calorimetry. Then, all effects can be regarded as being addressed by estimating the overall uncertainty of the experimental values. However, each experiment must include sampling, accuracy of the instrument, preparation and analysis. Here, the standard uncertainty (u) is generally evaluated from the experimental standard deviation (s) on the data set, assuming that the increment enthalpy values follow a normal distribution. Typically, in that case, the standard uncertainty (u = s/ √n) is multiplied by a coverage interval factor k = 2 to express the expanded uncertainty (U) with a confidence level of 95%. But it should be noted that this treatment is valid for an infinite number of trials only. Because our values are obtained from the average of a maximum of four measurements, we have applied the Student's coverage factor (t p ), which depends on the degree of freedom (ν = n-1) for a number of n tests and on the confidence level (p) of the coverage gap taken at 95%.

The values of the enthalpy increments at fixed temperature T ( °°H H )

T 298 compiled in Table 2 are thus given with a confidence interval (U) of the mean value ( H ¯) defined by:

°°= ± H H H t s n ¯. T 298 , (2)
The values of the factors t

, and the details of the estimation of the expanded uncertainties are provided in the Supplementary Excel file.

Between 823 and 1023 K, the values of the confidence intervals reported in Table 2 are about 5% of the enthalpy increments, which is fully acceptable. As illustrated in Fig. 4a, SEM-FEG characterization in BSE mode of the external part of the pellets after drop calorimetry did not evidence any modification of the pristine delafossite phase (not shown here), the presence of HfO 2 being attributed to some residual powder stuck to the samples.

Conversely, the confidence intervals reach 20% for the two highest temperatures (1073 and 1123 K). The XRD diffractograms of the pellets after drop calorimetry did not show any noticeable change compared to the initial material. However, SEM-FEG analyses (Fig. 4b) showed the presence of Cu metal nodules, attributed to a partial reduction of the phase during measurement caused by the low oxygen partial pressure imposed in the calorimeter. Consequently, these data were discarded in the assessment of the thermodynamic functions.

DFT calculations

The ground state properties (lattice parameters, total energy and magnetic moments) calculated by DFT are compiled in Table 3. The magnetic structure of Cr 2 O 3 is antiferromagnetic with a spin sequence of +-+-along the [111] direction in the rhombohedral setting, in The resulting polynomial functions are:

= + < < °c T T T ( ) 0.
The two functions are plotted in Fig. 5 together with available data. The integral of °c T ( )

p 2
is plotted in Fig. 6 and compared to our two set of experimental data (integrated DSC data and enthalpy increments).

Entropy of CuCrO 2 at 298 K

The entropy of CuCrO 2 is obtained from Eq. [START_REF] Manickam | Double doping induced power factor enhancement in CuCrO 2 for high temperature thermoelectric application[END_REF].

°= CuCrO c CuCrO T T dT ( ) ( )( ) p 298 2 0 298 2 (6)
We performed direct numerical integration of the experimental values from [START_REF] Poienar | Structural and magnetic properties of CuCr 1-x Mg x O 2 by neutron powder diffraction[END_REF] between 0 and 40 K (contribution of 9.95 J K -1 ) and analytic integration of the °c T ( ) p 1 function (Eq. ( 4)) between 40 and 298 K (contribution of 78.94 J K -1 ). Our recommended value for the entropy of CuCrO 2 comes to: °S CuCrO ( ) 298 2 = 88.89 J K -1 . This value is significantly higher than the value (85.2 J K -1 ) proposed by Vlach et al. [START_REF] Vlach | A thermodynamic study of the Cu-Cr-O system by the EMF method[END_REF], which was evaluated by the structural analog method using the entropy of formation of the CuFeO 2 delafossite. It is also slightly higher than the value (86.73 J K -1 ) obtained from ideal mixing of Cu 2 O and Cr 2 O 3 (integration of Neumann-Kopp function).

Enthalpy of formation of CuCrO 2 at 298 K

The enthalpy of formation of CuCrO 2, °H CuCrO ( )

f 298
2 , is related to Eq. [START_REF] Sinnarasa | Thermoelectric and transport properties of delafossite CuCrO₂: Mg thin films prepared by RF magnetron sputtering[END_REF].

+ + = Cu fcc Cr bcc O g CuCrO s ( ) ( ) ( ) ( ) 2 2 (7)
Our assessment of °H CuCrO ( ) f 298 2 takes into account high temperature emf data from [START_REF] Hamuyuni | Liquidus experimental data for the system Cu-O-Cr 2 O 3 in air[END_REF][START_REF] Perrot | Chromium -copper -oxygen[END_REF], from which we derived values of Gibbs energy of formation °G CuCrO ( )

f T
2 . The 14 emf data of [START_REF] Hamuyuni | Liquidus experimental data for the system Cu-O-Cr 2 O 3 in air[END_REF][START_REF] Perrot | Chromium -copper -oxygen[END_REF] are related to the following electrochemical cell:

+ = Cu O Cr O CuCrO 2 2 2 3 2 (8)
with agreement with experimental data from the literature [START_REF] Corliss | Magnetic structure of Cr 2 O 3[END_REF]. The ground state for CuCrO 2 is ferromagnetic with an overall magnetic moment of 8.64 Bohr.

°= G cell F emf ( ) 2. . r T and °= °+ °+ °G CuCrO G cell G Cu O G Cr O ( ) ( ( ) ( ) ( )) f T r T f T f T 2 1 2 2 2 3 °G Cu O ( )
The values of the cell parameters calculated at 0 K (a = 2.980 Å and c = 17.019 Å) are very close to the ones refined f rom o ur r oom temperature XRD pattern (a = 2.973 Å and c = 17.086 Å). The difference is respectively +0.10% and -0.02%, and could be attributed to the temperature dependence of the cell parameters. Indeed, these small variations are consistent with those reported by [START_REF] Poienar | Structural and magnetic properties of CuCr 1-x Mg x O 2 by neutron powder diffraction[END_REF] from the refinement of high-resolution neutron powder diffractograms o f CuCrO 2 , which showed a deviation of +0.25% of a and -0.16% of c between 10 and 300 K. As a consequence, the formation energy calculated at 0 K (-20.2 kJ mol -1 ) provides an additional data that will be considered in the assessment of the thermodynamic functions of CuCrO 2 .

Discussion

Temperature evolution of heat capacity from 0 to 1300 K

We have chosen to divide the evolution of the heat capacity into three temperature domains. At low temperature (T < 40 K), we selected experimental data from [START_REF] Poienar | Structural and magnetic properties of CuCr 1-x Mg x O 2 by neutron powder diffraction[END_REF], which are consistent with simulation from [START_REF] Okuda | Specific heat of delafossite oxide CuCr 1-x Mg x O 2 (0 ≤ x ≤ 0.03)[END_REF]. Due to the occurrence of the magnetic transition, and since our major objective was to obtain an accurate entropy value at 298 K, we did not perform any fit o f t he e xperimental d ata i n this temperature range.

°=

The enthalpy value comes to °H r Ox 298 = -21.9 ± 1.3 kJ mol -1 . Ab initio calculations from [START_REF] Scanlon | Understanding the p-type defect chemistry of CuCrO 2[END_REF] provide another value of enthalpy of formation of CuCrO 2 at 0 K, from pure metals (Eq. ( 7)):

Comparison to DFT calculations

As reported in

°= H f DFT 0 2
-660.9 kJ mol -1 . Their value computed at 0 K is compared to our assessed value of °H f 298 by extrapolation to 298 K according to:

°= °+ °H H c dT ( ) f DFT f DFT p R 298 2 0 2 0 298 2 (12)
with

°= °°°°c c CuCrO c Cu fcc c Cr bcc c O g ( ) ( ) ( ( )) ( ( )) ( ( )) p R p p p p 2 2 2
°c CuCrO ( ) p 2 : same as Eq. ( 11) °cp data for Cu(fcc), Cr(bcc) and O 2 (g) from Table 1 The resulting value for °H f DFT 298 2 is -665.6 kJ mol -1 . As illustrated in Fig. 7, this value is not in full accordance with our assessment, however, the relative difference remains lower than 1%.

Conclusions

We performed heat capacity measurements with DSC (from ambient to 871 K) and drop calorimetry (from 823 to 1123 K) on synthetic CuCrO 2 delafossite samples, as well as DFT calculations at 0 K. Our two sets of experimental data are very consistent. Combined with low temperature literature data, the heat capacity is described from 0 to 1300 K, from which we derive the standard enthalpy at 298 K. A "third law" analysis of 14 emf data points provides a mean value for the enthalpy of formation of CuCrO 2 at 298 K, which is very consistent with our value calculated at 0 K by DFT and extrapolated to 298 K.

Based on this assessment, we propose, for the first time, a full set of thermodynamic data for the delafossite phase CuCrO 2 . These data, tabulated in Table 5, present a great interest for research and development activities linked to the application of the delafossite materials on a very large range of temperature.

T (K)

°cp T (J K -1 mol -1 ) °°H H T 298 (J mol -1 ) °S T (J K

Fig. 1 .

 1 Fig. 1. a) Crystal structure of CuCrO 2 , octahedron occupied by Cr 3+ and Cu 1+ in linear coordination. b) X-ray diffractogram of the sintered CuCrO 2 sample.

Fig. 2 .

 2 Fig. 2. Heat capacity obtained from DSC measurements on CuCrO 2 sample compared to NKR, Cv from Einstein relation and the Dulong-Petit limit.

Fig. 3 .

 3 Fig. 3. Heat flow measured during successive drops of Al 2 O 3 and CuCrO 2 samples at 872 K.

Fig. 4 .

 4 Fig. 4. BSE micrographs of external part of samples recovered after drop calorimetry at 1023 K (a) and 1123 K (b).

Above 40 K 2 (

 402 , we established two polynomial expressions, °c T ( ) T < 1300 K based on the least square method. The polynomial regression of °c T ( ) the data from [19] for 40 < T < 150 K. The polynomial regression of combined our experimental DSC data for 300 < T < 870 K and our experimental drop calorimetry data for 823 < T < 1023 K. The experimental drop calorimetry data °°H H T 298 are the reference values for the integrated °c T ( ) was constrained according to:(i) the continuity of the two functions at 298 K : ii) the continuity of the derivative of the two functions at 298 K :

Fig. 5 .

 5 Fig. 5. Temperature evolution of heat capacity derived from DSC (this work), drop calorimetry (this work), low temperature calculations[START_REF] Okuda | Specific heat of delafossite oxide CuCr 1-x Mg x O 2 (0 ≤ x ≤ 0.03)[END_REF] and experimental data[START_REF] Poienar | Structural and magnetic properties of CuCr 1-x Mg x O 2 by neutron powder diffraction[END_REF].

Fig. 6 .

 6 Fig. 6. Comparison of

  to -1.00 kJ mol -1 . The resulting value for °H f DFT 298 1 is 21.2 kJ mol -1 , which is fully consistent with °H r Ox 298 .

Fig. 7 .

 7 Fig. 7. Results of third-law analysis of Gibbs energy of formation of CuCrO 2 ; comparison to DFT calculations.

Table 2

 2 Experimental data from drop calorimetry of CuCrO 2 samples.

	T (K)	°°H	T	H	298 (J)	Mean (J mol -1 )	U (J mol -1 )
	823	46 960.1		47 989	2219
	823	48 571.3
	823	48 436.4
	873	51 913.1		54 286	3555
	873	53 552.3
	873	54 423.2
	873	57 254.2
	923	57 856.7		58 621	1032
	923	59 319.7
	923	58 346.3
	923	58 962.8
	973	60 342.4		61 032	4806
	973	65 208.9
	973	60 594.2
	973	57 983.7
	1 023	66 552.2		68 676	4646
	1 023	70 081.8
	1 023	69 394.9
	1 073	70 354.9		69 792	14 019
	1 073	63 884.1
	1 073	75 135.5
	1 123	85 848.0		81 445	16 352
	1 123	84 614.7
	1 123	73 872.8

Table 3

 3 Ground state properties of Cu 2 O, Cr 2 O 3 and CuCrO 2 .

	Phase		Cu 2 O	Cr 2 O 3	CuCrO 2
	Lattice parameter	Å	a = 4.228	a = 5.362	a = 2.980
				α = 54.991°c = 17.019
	Magnetic moment	Bohr	-	0 (AFM)	8.64 (FM)
	Ground state energy	eV fu -1	-37.999340 -68.468135 -53.443067
	Formation energy at	eV fu -1			-0.209330
	0 K	kJ mol -1			-20.2

Table 1 .

 1 The set of 14 assessed data for

	f dynamic functions compiled in °G CuCrO 2 and °G Cr O ( f T 2 3 come from the selected thermo-) ( ) f T 2 is provided in Table 4. For each data, a value of °H CuCrO ( )

f 298 2 is obtained from Eq. (

9

):

  , which are plotted as a function of the temperature of measurements in Fig.7. Based on the average of these 14 values, our recommended value for the enthalpy of formation of CuCrO 2 is

	f		298		f	G	°°°+ H H ( ) T T 298	T	(	f		S	°+ 298	S (	°°H S )) T 298 (9) °= °°°H H CuCrO ( ) r Ox f 298 298 2	1 2	f	H	298	(	Cu O 2	)	1 2	f	H	298	(	Cr O 2 3	)
	with
	f	°= T	r	°G G CuCrO ( T	2	)
	(	°°= H ) T 298	T 298	°°°°H c T c Cu fcc [ ( ) ( ( )) p p 2	c Cr bcc ( ( )) p
											c O g dT ( ( ))] p 2
	f	°°°°°S 298	=	S 298	CuCrO (	2	)			S	298	Cu fcc ( ( ))		S 298	Cr bcc ( ( ))	S 298	O g ( ( )) 2
	(	°°= S ) T 298	T 298	°°°°S c T c Cu fcc c Cr bcc 1 [ ( ) T ( ( )) ( ( )) p p p 2
										c O g dT ( ( ))] p 2
		The determination of		f	°H	298	CuCrO (	) 2 is then built from (i) our
	assessments of °c T ( ) p 2		(Eq. (5)) and °S	298	(	CuCrO	) 2 , (ii) the thermo-
	dynamic functions compiled in Table 1 and (iii) the assessed values of
	f	°G CuCrO ( T	) 2 compiled in Table 4. As a result, we obtained 14 values
	of f	f	°H 2 °H CuCrO ( 298 CuCrO ( ) 298 2 = -670.8 ± 1.3 kJ mol -1 . )
		From this value of		f	°H	298 , we also derived an enthalpy of reaction
	corresponding to the formation of CuCrO 2 from the pure oxides (Eq.
	(8)):

Table 3 ,

 3 our computed enthalpy of formation of CuCrO 2 at K from single oxide (1/2 Eq. (8)) is data for Cu 2 O and Cr 2 O 3 from Table1The integral of

	r	H	°= DFT 0 1	-20.2 kJ mol -1 . This value is compared to our assessed
	value at 298 K (	r	°H	Eq

°cp

Table 4

 4 from emf data of[START_REF] Jacob | Oxygen potentials, Gibbs' energies and phase relations in the Cu-Cr-O system[END_REF] and[START_REF] Vlach | A thermodynamic study of the Cu-Cr-O system by the EMF method[END_REF], with selected Cu 2 O and Cr 2 O 3 thermodynamic functions from Table1.

	Reassessment of 2 Data source °G CuCrO ( f T T (K)	)	emf (mV)	r	°G cell ( ) T	(J mol -1	f	°G Cu O ( T 2	)	(J mol -1 )	f	°G Cr O ( T 2 3 (J mol -1 ) )	f	°G CuCrO ( T	) 2 (J mol -1 )
	[16]	950.1		196.36	-37 889		-99 034			-879 473	-508 197
		953.5		194.08	-37 449		-98 788			-878 628	-507 433
		1000.0		192.71	-37 185		-95 439			-867 091	-499 858
		1068.9		189.07	-36 482		-90 504			-850 042	-488 514
		1143.0		184.51	-35 603		-85 233			-831 757	-476 296
		1237.8		179.50	-34 636		-78 546			-808 418	-460 800
		1339.4		174.03	-33 581		-71 449			-783 448	-444 239
	[17]	1074.7		198.4	-38 283		-90 069			-848 535	-488 443
		1122.4		195.88	-37 797		-86 723			-836 934	-480 727
		1125.6		195.74	-37 770		-86 439			-835 948	-480 078
		1179.3		193.59	-37 355		-82 686			-822 888	-471 465
		1228.2		191.76	-37 002		-79 234			-810 829	-463 532
		1230.4		191.65	-36 981		-79 094			-810 337	-463 205
		1275.4		189.72	-36 608		-75 939			-799 272	-455 909

Table 5

 5 -1 mol -1 ) °H Assessed thermodynamic data for CuCrO 2 .

	f	T (kJ mol )	f	°G	T (kJ mol -1 )

Acknowledgments

The authors from Laboratoire de Génie Chimique and CIRIMAT thank the Région Occitanie for the PhD funding of J. Schorne Pinto.

All authors also wish to thank the GDR CNRS n°3584 TherMatHT for the financial contribution to experimental drop calorimetry measurements and for fruitful discussions and collaborative work on the present project.

The help of Prof. Xavier Joulia (Laboratoire de Génie Chimique) for the implementation of the numerical method used in the establishment of the heat capacity functions was greatly appreciated.

Appendix A. Supplementary data

Supplementary material related to this article can be found, in the online version, at doi:https://doi.org/10.1016/j.tca.2019.178345.


M Mathian
email: mariemathian@hotmail.com

F Muller
email: fmuller@ansoft.com

M Grzeskowiak

O Picon

LMDS BASE STATION ANTENNA DESIGN

The design of a feed network for a 24 x 2 stratified linearly polarized patch array is presented in this article. This design is a candidate for an LMDS Base Station antenna and complies with ETSI Standard requirements such as polarization, bandwidth, gain, -3 dB beamwidths and Side lobe levels. The feed network has been designed to produce appropriate unequal power excitation for each patch and a match condition at the feed point. Unequal distribution of the power improves the side lobe level. From simulation, the array antenna yields -23 dB return loss in the LMDS band, narrow -3 dB beamwidths of 2.9° and 46° in the elevation plane and azimuth plane respectively, high gain of 23 dB and 7.5 % bandwidth satisfying with ETSI Standard.

Introduction

Millimeter wave communication systems in the 24 GHz to 30 GHz band are being developed in the United States for use in a Local Multipoint Distribution Service (LMDS). These systems with large usable bandwidth are envisioned to support full duplex, high data rate applications such as high-speed Internet, interactive video, broadcast voice and digital television channels [START_REF] Izadpanah | LMDS Technologies For Broadband Wireless Local Loop Applications[END_REF]. To bring LMDS to the masses, certain technical hurdles will have to be overcome, including the development of low cost, small size, high-gain and narrow beam antenna [START_REF] Izadian | Considering antenna options for LMDS[END_REF]. Because of their low profile, low weight, low cost and easy manufacturing, microstrip antenna are the best candidates for the design of LMDS Base Station antennas [3]. This article describes the design of a antenna array that must satisfy with ETSI Standard for LMDS application [4].

LMDS Base Station Antenna Design

Array synthesis

Antenna array consisting of an appropriate number of patches, patch weight and distance between two neighboring elements must comply with the ETSI Standard requirements. The side lobe level and -3 dB beamwidth are dictated by the weight and the number of patches respectively. The distance between two neighbor patches allows both parameters to vary. All parameters have been determined using 1D Array Analysis Software. 24 patches in the elevation plane and 2 in the azimuth plane satisfied beamwidth as prescribed by ETSI Standard. Ideal weights for 12 elements (use of symmetrical network) with two neighboring elements distanced by 0.75l 0 (360° phase shift) are described in Table 1 giving side lobe level of -30 dB. Element 1 2 3 4 5 6 7 8 9 10 11 12 Weights Magnitude 0.2 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.8 0.9 1 1

Table 1 : Ideal weight for 12 elements

Design of a single element Figure 1(a) shows a single-feed arrangement for a rectangular patch antenna to produce linear polarization and an input impedance Z inp = 400 W. shows the computer-predicted return loss as function of frequency, using Ensemble ' v.8 [START_REF]Ansoft Ensemble® v8 -Software Based on Full Wave Analysis[END_REF].

Study of element coupling

The study of the coupling effect between elements in large antenna array is a very important step in the spatial positioning of the array elements. Since the distance between two successive patches in the azimuth plane is critical (half l 0 ), the coupling effect will affect either the frequency parameters and the radiation pattern if the two patches are collinear in the E-plane. To overcome this effect, the two patches are separated spatially by an adequate distance l g /2 corresponding to 180°. To avoid physical overlapping and coupling between patches and feed network, a 180° phase difference between the electromagnetic field vectors of two successive patches in the E-plane has been introduced.

Feed network

An hybrid (parallel-series) feed network is well suited for a planar array antenna, each-fed element antenna phase is the same (see figure 2).

Figure 2 : Ideal feed network

The power splitters used in the feed network consist of 44 quarter-wave transformers; consequently, it is not possible to obtain closed form solutions for the design. The design is therefore based on the required power split for each patch, the maximum realizable impedance values for the microstrip lines to reduce spurious radiation and coupling by the feed network, and to obtain a match at the feed point [START_REF] Hall | Coplanar Corporate Feed Effects on Microstrip Patch Array Design[END_REF]. The equivalent input impedance at each junction is dictated by the weight of the patches as illustrated in Figure 3. For instance, At junction V 10 :

W = ¥ = 300 4 . 0 3 . 0 10 in in Z Z (1) the equivalent input Z inJ impedance is W = + ¥ = 4 . 171 10 10 in in in in inJ Z Z Z Z Z (2)
The same procedure has been applied to calculate the equivalent input impedance at the junctions. Two neighbor patches are separated by 360° phase shift (0.75l 0 ) of the order of l g . Four quarter wave transformers have been introduced between two neighbor patches, and their characteristic impedances determined as illustrated in Figure 4 for patch 12 and 11. Assumptions have been made for three of these characteristic impedances considering that the highest characteristic impedance that can be practically realized using Teflon (e r = 2.2, h = 0.762 mm, tand = 0.002) is Z 0 = 210 W. Z 44 , Z 43 , Z 42 have been assumed in order to calculate the characteristic impedance Z 41 .

Figure 4 : Patch 12 and 11

The same technique has been used to calculate the characteristic impedance of all 44 quarter wave transformers. There is not a unique solution, but it has been considered that further the patch is from the array center, lesser the weight of the patch and highest the characteristic impedance. The array is illustrated in Figure 5.

Figure 5 : 24¥2 antenna array

To match Z inA to 200 W (see Figure 3 and Figure 5), two-quarter wave transformers have been introduced. The 12 element network has been simulated using Serenade® v8.7 [START_REF]Ansoft Serenade® v8.7 -Circuit and system Package[END_REF] in order to determine the real weights of the patch as well as the real input impedance of the network. Black boxes have been introduced representing the simulated single patch (using Ensemble®). At 28 GHz, an input impedance of 214 W has been determined for 12 elements, agreeing with predicted value of 200 W. The real weights of the patches are illustrated in Table 2.

Table 2 : Real weights of the patches

Since coupling has appeared between parallel feed network and patches at the center of the array, a stratified configuration has been used. The infinite ground plane is sandwiched between two substrates (Teflon). The series feed network containing the patch has been designed on Substrate 1 and the parallel feed network on Substrate 2. The two substrates are connected to the centers of the two series feed network by two via. The 24 ¥ 2 patch array (illustrated in Figure 9) has been designed and simulated using Ensemble ' v8. A first simulation has proved that the array was unmatched with a return loss of -12 dB at 27.3 GHz. To improve matching network, a stub designed at 28 GHz has been introduced in the design. The 24 ¥ 2 antenna array is illustrated in Figure 8. The computer predicted results polar

Figure 1 :

 1 Figure 1 : (a) Single Patch Element, (b) Return loss referenced to 400 W Figure 1(b)shows the computer-predicted return loss as function of frequency, using Ensemble ' v.8[START_REF]Ansoft Ensemble® v8 -Software Based on Full Wave Analysis[END_REF].

Figure 3 :

 3 Figure 3 : 12 element network

  0.36 0.36 0.46 0.54 0.61 0.68 0.71 0.79 0.79 0.86 0.93 1

  as a function of angle are illustrated in Figure 7(a) and Figure 7(b) respectively, Figure 8(a) represents return loss and Figure 8(b) represents VSWR.

Figure 6 :

 6 Figure 6 : Radiation Pattern and gain at 27.7GHz

Figure 7 :Figure 8 :

 78 Figure 7 : Return loss and VSWR referenced to 50W Figure 8 : 24¥2 antenna arrayConclusionA microstrip single patch antenna has been developed and yields linear polarization and high input impedance. A parallel-series feed network was utilized to improve radiation pattern, gain and bandwidth. A series-feed network was designed from Dolph-Chebyshev method for a -35 dB side lobe level while the simulated side lobe level shows -23 dB due to the feed network. The array antenna producing matching at the feed point provides 23 dB gain and 2.9° and 46° -3 dB beamwidth in the elevation plane and azimuth plane respectively, satisfying with ETSI Standard. The bandwidth has been slightly reduced for the array antenna due to the use of series feed network, achieving 2.6 GHz bandwidth (10 %) for single patch and 2.1 GHz bandwidth (7.5 %) for the array. Since the use of via has been shown to be detrimental to manufacturing yield at LMDS band, this work has been restricted to the design and simulation of an array prototype for LMDS system.


Je fais de la bouillie pour mes petits cochons.

Pour un cochon, pour deux cochons, pour trois cochons, pour quatre, puis pour cinq, pour six, pour sept, pour huit, pour neuf, boeuf!

Commentaires

Et pour une poule sur un mur qui picoterait du pain dur? c'est bien beau de nourrir les petits cochons mais qu'en est-il des autres? Emma, 22 ans, Limoges Je vois que vous êtes, telle la petite poule rousse, bien aimable. Avez-vous pu compter sur l'aide du chat et du canard (et des cochons eux-mêmes!) pour semer vos 5 grains de blé? Les cochons se sont-ils régalés? html_nodes(html,"div") %>% html_attrs() Extract data and make it into a table:

## [[1]] ## class ## "ingredients" ## ## [[2]] ## class ## "right" ## ## [[3]] ## class ## "image" ## ## [[4]] ## class ## "comment" ## ## [[5]] ## class ## "comment-

Rectangular format, and function-ization

It is actually a good idea to make all this into a fonction that would have the page's url as intput and the tibble as output: We would like to apply extract_comments() iteratively to all these pages.

Iteration

The purrr package enables us to apply a function iteratively to all elements of a list or of a vector (… of course this is just a more straightforward way to loop through a for structure…). For instance, to detect all voyels in the string:

Iteration with purrr

str_view_all("youp la boum", "[aeiou]") youp la boum

Regexp: character classes and groups

See the difference:

A132-f445-e34-C308-M9-E18 A132-f445-e34-C308-M9-E18
Any character can be noted ..

For instance, the pattern "any character followed by a letter" can be searched through For instance, all numbers between 1 and 5:

  right">
<im
 Je fais de la bouillie pour mes petit
 Pour un cochon, pour deux cochons, po comments
Et pour une poule su

Emma, 22 ans,
Je vois que vous ête
Michel, right">
<im
 Je fais de la bouillie pour mes petit
 Pour un cochon, pour deux cochons, po comments
Et pour une poule su

Emma, 22 ans,
Je vois que vous ête
Michel, 56 an Extract the content of some elementsExtract the content of nodes or nodesets:

<im
 Je fais de la bouillie pour mes petit
 Pour un cochon, pour deux cochons, po comments
Et pour une poule su

Emma, 22 ans,
Je vois que vous ête
Michel,

  right">
<im
 Je fais de la bouillie pour mes petit
 Pour un cochon, pour deux cochons, po comments
Et pour une poule su

Emma, 22 ans,
Je vois que vous ête
Michel,

  /blog_de_jean-marc.htm Tout ça ## data/blog_de_jean-marc.htm Je préf ## data/blog_de_jean-marc.htm On ne c ## data/blog_de_jean-marc.htm Et pend Now, let's imagine that we actually have to deal with several pages with a common structure.

  /blog_de_jean-marc.htm Les th ## 4 data/blog_de_jean-marc.htm Pourqu ## 5 data/blog_de_jean-marc.htm Tout ç ## 6 data/blog_de_jean-marc.htm Je pré ## 7 data/blog_de_jean-marc.htm On ne #

right">
<im
 Je fais de la bouillie pour mes petit
 Pour un cochon, pour deux cochons, po comments
Et pour une poule su

Emma, 22 ans,
Je vois que vous ête
Michel, 56 an  Read an html page

 MA VIE A LA FERME

  INGREDIENTS

 >1 cochon(s)

 >1 légume(s)

 MA VIE A LA FERME

  INGREDIENTS

 >1 cochon(s)

 >1 légume(s)

 <div class="Read html page in R:

<im
 Je fais de la bouillie pour mes petit
 Pour un cochon, pour deux cochons, po comments
Et pour une poule su

Emma, 22 ans,
Je vois que vous ête
Michel, 56 an  library(rvest) html=read_html("data/blog_de_ginette.ht html ## {xml_document} ##  ## [1] \n<meta http-equiv="Conten ## [2] \n
 MA VIE A LA FERME < Extract some elements in the html page

	Extract some
	elements ("nodes" or
	"nodesets"):

html_nodes(html,"b") ## {xml_nodeset (2)} ## [1]  INGREDIENTS ## [2] Commentaires html_nodes(html,".comment-author") html_nodes(html,".ingredients") %>% html_children()
 MA VIE A LA FERME

  INGREDIENTS

 >1 cochon(s)

 >1 légume(s)

 <div class="

str_view_all("turlututu chapeau pointu", "[^aeiou ]") turlututu chapeau pointu Regexp: excluded characters, character ranges

	So that the pattern Regexp: special characters passed to the function
	A character class can be defined as all characters excluding	is actually . (as we saw before), "[\\.\\?\\!]". as well as ? and ! are special characters. So, to point out actual dots or Ranges of characters are noted [...-...]
	the ones listed. This	interrogation/exclamation
	To find dots, question is noted as [^...]:	the escape character marks, one has to use
	marks, exclamation For instance, all	\. The regular
	marks: characters that are	expression hence
	neither a vowel nor a	becomes [\.\?\!]
	blank space:	…
	But it does not end Allô, John-John? Ici Joe la frite. Surprise! here… as it is not
	Note that we don't write "[.?!]", but "[\\.\\?\\!]".	directly the regular expression that is passed to the function, but a string
		that is interpreted as a
		regular expression.
		Thus each escape
		character \ has to be
		escaped through a \.

str_view_all(c("Allô, John-John? Ici Joe "[\\.\\?\\!]")

Some character classes are predefined for instance digits, punctuation characters, lowercase alphabetical characters, etc.

Regexp: predefined classes

Quantifiers are used to specify how many consecutive times a particular class or group occurs.

zero or one: the pattern of interest is followed by ?.

Xpath

XPATH is another way to query the DOM, it's very powerfull, but also a little complex. Use some cheatsheet to remember principal operators. A and game (1)