Tatiana A Pomelova

Charlene Delacotte

Natalia V Kuratieva

Pierric Lemoine

Stéphane Cordier

Sangjun Park

Thierry Guizouarn

Vincent Pelletier

Régis Gautier

Nikolay G Naumov

Charlène Delacotte

Regis Gautier

Cs 2 Ln 3 CuS 8 (Ln = La-Nd, Sm-Tb): Synthesis, crystal structure, magnetic and optical properties

Keywords: lanthanide sulfide, crystal structure, magnetic properties, magnetocaloric, DFT calculations

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Cs(2)Ln(3)CuS(8) (Ln = La-Nd, Sm-Tb): Synthesis, Crystal Structure, and Magnetic and Optical Properties

Introduction

Rare-earth based chalcogenides containing transition metal are considered as promising functional materials due to their unique structural diversity and their thermal, electrical, magnetic and optical properties. For example, ALnMQ3 compounds (A=Rb, Cs; Ln=rare-earth; M=Mn, Co, Zn, Cd, Hg; Q = S, Se, Te) are semiconductors demonstrating magnetic properties with an optical band gap value depending of chemical composition and crystal orientation, [START_REF] Mitchell | Structure, and Selected Physical Properties of CsLnMnSe3 (Ln= Sm[END_REF][START_REF] Mitchell | The CsLnMSe3 Semiconductors (Ln= Rare-Earth Element, Y; M= Zn, Cd, Hg)[END_REF] AxLn2Cu6-xTe6 (A=K-Cs; Ln=La-Nd 0.65<x<0.77) show thermoelectric properties, [START_REF] Meng | Structures, and Magnetic and Thermoelectric Properties of Double-Tunnel Tellurides: AxRE2Cu6-xTe6 (A= K-Cs; RE= La-Nd)[END_REF][START_REF] Zhao | Strong Kleinman-forbidden second harmonic generation in chiral sulfide: La4InSbS9[END_REF][START_REF] Zhao | crystal structure, and NLO property of the chiral sulfide Sm4InSbS9[END_REF] and ALnMTe4 (A=K, Na; M=Cu, Ag; Ln=La, Ce) exhibits charge density waves. [START_REF] Malliakas | Charge Density Waves in the Square Nets of Tellurium of AMRETe4 (A= K, Na; M= Cu, Ag; RE= La, Ce)[END_REF] A huge number of alkali-metal/rare-earth/transition-metal/chalcogenides (A/Ln/M/Q) synthesized by reactive-flux technique [START_REF] Kanatzidis | Discovery-synthesis, design, and prediction of chalcogenide phases[END_REF] have been discovered over the past decades. [START_REF] Mitchell | Structure, and Selected Physical Properties of CsLnMnSe3 (Ln= Sm[END_REF][START_REF] Mitchell | The CsLnMSe3 Semiconductors (Ln= Rare-Earth Element, Y; M= Zn, Cd, Hg)[END_REF]8,[START_REF] Yao | structures, physical properties, and electronic structures of KLn2CuS4 (Ln= Y, Nd, Sm, Tb, Ho) and K2Ln4Cu4S[END_REF] The low melting points of the AxQy fluxes (433-723 K) and their ability to act as both reagent and reaction medium led to the characterization of kinetically stabilized species that cannot be obtained by the use of traditional high-temperature experimental methods. Most of these chalcogenide compounds are characterized by layered-like (anionic layers + alkali metal cations between them) or tunnel structures. 8 The quaternary A-M-Ln-S system with M = copper was one of those investigated first. Several copper-based systems are reported in literature: ALn2CuS6 family, [START_REF] Sutorik | The First Examples of Alkali Metal/Cu/Ce/Chalcogenides: The Layered Heterometallic Compounds KCuCe2S6 and K2Cu2CeS4[END_REF][START_REF] Sutorik | New quaternary compounds resulting from the reaction of copper and f-block metals in molten polychalcogenide salts at intermediate temperatures. Valence fluctuations in the layered CsCuCeS3[END_REF][START_REF] Bensch | Preparation and Crystal Structure of the New Quaternary Europium-polysulfide KCuEu2S6[END_REF][START_REF] Pomelova | Crystal Structure, and Liquid Exfoliation of Layered Lanthanide Sulfides KLn2CuS6 (Ln= La, Ce, Pr, Nd, Sm)[END_REF] K2CeCu2S4, [START_REF] Sutorik | The First Examples of Alkali Metal/Cu/Ce/Chalcogenides: The Layered Heterometallic Compounds KCuCe2S6 and K2Cu2CeS4[END_REF] CsCeCuS3 [START_REF] Sutorik | New quaternary compounds resulting from the reaction of copper and f-block metals in molten polychalcogenide salts at intermediate temperatures. Valence fluctuations in the layered CsCuCeS3[END_REF] with a layered-like structure and ALn2CuS4, A2Ln4Cu4S9, [START_REF] Yao | structures, physical properties, and electronic structures of KLn2CuS4 (Ln= Y, Nd, Sm, Tb, Ho) and K2Ln4Cu4S[END_REF] as well as CsLn2Cu3S5 [START_REF] Lauxmann | CsCu3Dy2S5 und CsCu3Er2S5: Zwei isotype quaternäre Sulfide der Lanthanoide mit Kanalstrukturen/CsCu3Dy2S5 and CsCu3Er2S5: Two Isotypic Quaternary Sulfides of the Lanthanides with Channel Structures[END_REF] which crystal structures contain tunnels. All known compounds, to the best of our knowledge, are summarized in Table 1. The investigation of the Cs-Ln-Cu-S systems has allowed us to discover the new series of title compounds Cs2Ln3CuS8, which exhibit a new layered-like structure type being hybrid structure of that of the ALn2CuS6 11 series and K2CeCu2S4. [START_REF] Sutorik | The First Examples of Alkali Metal/Cu/Ce/Chalcogenides: The Layered Heterometallic Compounds KCuCe2S6 and K2Cu2CeS4[END_REF] As one can see in Table 1, the small Ln 3+ cations (Gd-Er) tend to favor the formation of tunnel structures, whereas the big ones favor the formation of layered-like structures. From the crystal chemistry point of view, this new Cs2Ln3CuS8 structural type is of prime interest as the number of members of this series (Ln=La, Ce, Pr, Nd, Sm, Eu, Gd, and Tb) is the largest one among all the other related series based on different-sized Ln 3+ cations. In this article we report the syntheses, structural features, optical and magnetic properties of this new Cs2Ln3CuS8 family for which all members crystallize in the same structure-type with Ln=La, Ce, Pr, Nd, Sm, Eu, Gd, and Tb. Red-layered-like crystal structure, grey -tunnel crystal structure, blue -present work materials.

Experimental methods

Synthesis

Cs2Sx. A starting mixture of alkali metal polysulfides was prepared by a similar method as that reported for K2Sx [START_REF] Pomelova | Crystal Structure, and Liquid Exfoliation of Layered Lanthanide Sulfides KLn2CuS6 (Ln= La, Ce, Pr, Nd, Sm)[END_REF] from Cs2CO3 (high purity) and NH4SCN vapor as the sulfurization agent. We repeated the sulfurization process at 573 K, and we performed a chemical test with a BaCl2 containing water solution after each iteration for the determination of the moment when all carbonate groups are replaced by polysulfide ones. A red-orange hygroscopic powdered mixture consisting of Cs2Sx (x = 3-6, main fraction is Cs2S6) according to powder X-ray diffraction (PXRD) was obtained.

Cs2Ln3CuS8. 0.6 mmol of Ln2S3 (0.3 mmol EuS) and 0.2 mmol of Cu2S (0.1 mmol of Cu2S in case of Ln=Eu) were ground together in an agate mortar and then placed in a glass ampule with 2 mmol of S and 0.8 mmol of Cs2S6. The ampule was then evacuated to roughly 5 × 10 -2 Torr, sealed, and placed in a programmable furnace. The following temperature profile was used:

heating with a rate of 2 K/min to 673 K, temperature plateau for 120 h, cooling to 423 K with a rate of 10 K/h, and then quenching at 323 K. The orange-yellow (Ln=La, Nd, Sm, Gd, Tb), yellowgreen (Ln=Pr), black (Ln=Eu) or dark red-brown (Ln=Ce) powders were obtained by washing the crude product with distilled water and drying in a vacuum. The yields based on Ln were 95-98%.

The purity of products was confirmed by PXRD. To grow single crystals suitable for crystal structure determination, a large excess of S and Cs2Sx (5-8 mol to 1 mol of Ln2S3) was used.

Characterization Techniques

The PXRD data collections were performed on a Philips PW1820/1710 diffractometer with Philips PW1711/10 Proportional Detector (CuKα radiation, graphite monochromator, 2θ = 5°-70°, measurement time 4sec/point, increment size 0.05 o ). Rietveld analysis including preferred orientation simulation was carried out using GSAS-II software. [START_REF] Toby | GSAS-II: the genesis of a modern open-source all purpose crystallography software package[END_REF] X-ray diffraction data were collected from needle-shaped single-crystals using graphite monochromatized MoKα-radiation (λ = 0.71073 Å) at 293(2) K on a Bruker APEX DUO diffractometer equipped with a 4K CCD area detector. The color of single-crystals was yellow for Ln=La, Pr, Nd, Sm, Gd, Tb) and black for Ln=Eu. The φ-and ω-scan technique was employed to measure the intensities. Absorption corrections were applied empirically using the SADABS program. [START_REF] Bruker | Version 8.18 c), and SADABS (Version 2.11)[END_REF] Structures were solved by the direct methods and further refined by the full-matrix least-squares method using the SHELXTL package. [START_REF] Sheldrick | Crystal structure refinement with SHELXL[END_REF] The diffuse reflectance spectrum of powdered bulk samples was recorded with a UV-3101 PC Shimadzu spectrometer equipped with integrating sphere and BaSO4 as reference in the range of 200-800 nm. The Kubelka-Munk function was used to convert diffuse reflectance data to absorption spectra.

Magnetic and magnetocaloric measurements were performed using a SQUID magnetometer (MPMS XL5, Quantum Design). Zero field cooled (ZFC) measurement was carried out from 1.8

to 300 K at a constant applied magnetic field of 0.1 T. The molar magnetic susceptibilities were corrected from the intrinsic diamagnetism evaluated from Pascal's tables: :

𝜒 𝐷 𝐶𝑠 + = -35 × 10 -6 𝑐𝑚 3 𝑚𝑜𝑙 -1 ,𝜒 𝐷 𝐶𝑒 3+ = 𝜒 𝐷 𝑃𝑟 3+ = 𝜒 𝐷 𝑁𝑑 3+ = 𝜒 𝐷 𝐸𝑢 3+ = 𝜒 𝐷 𝐺𝑑 3+ = -20 × 10 -6 𝑐𝑚 3 𝑚𝑜𝑙 -1 , 𝜒 𝐷 𝑇𝑏 3+ = -19 × 10 -6 𝑐𝑚 3 𝑚𝑜𝑙 -1 , 𝜒 𝐷 𝐶𝑢 + = -12 × 10 -6 𝑐𝑚 3 𝑚𝑜𝑙 -1 and 𝜒 𝐷 𝑆 2-= -30 × 10 -6 𝑐𝑚 3 𝑚𝑜𝑙 -1 . [START_REF] Bain | Diamagnetic corrections and Pascal's constants[END_REF] Note that the chemical bonding encountered in the (S2) 2- dimers as well as the presence of Eu 2+ in Cs2Eu3CuS8 was not considered in the diamagnetism susceptibility correction. Hence, the applied diamagnetic susceptibility corrections were -382 × 10 -6 𝑐𝑚 3 𝑚𝑜𝑙 -1 for Cs2Ln3CuS8 (Ln = Ce, Pr, Nd, Eu, Gd) and -379 × 10 -6 𝑐𝑚 3 𝑚𝑜𝑙 -1 for Cs2Tb3CuS8. The magnetocaloric properties were determined from magnetic entropy change, ΔSM, evaluated using one of the Maxwell relations:

∆𝑆 𝑀 (𝑇) ∆𝐻 = 𝜇 0 ∫ ( 𝜕𝑀(𝑇, 𝐻) 𝜕𝑇 ) 𝐻 𝐻 𝑓 0 𝑑𝐻 (1)
The numerical integration of Eq. ( 1) was carried out using the method proposed by Pecharsky and Gschneidner Jr. [START_REF] Pecharsky | Magnetocaloric effect from indirect measurements: Magnetization and heat capacity[END_REF] , from magnetization isotherms recorded on heating from 2 K to 26 K in applied magnetic fields up to 5 T, with field steps of 0.2 T and temperature increments of 1 K.

Computational details

Spin-polarized band structure and average properties of were computed with the DFT Vienna ab initio Simulations Package (VASP). [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF] The exchange-correlation energy was taken into account using the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional. [START_REF] Perdew | Generalized gradient approximation made simple[END_REF] The energy cutoff in the calculations is 400 eV. The electronic wave function was sampled with 4 × 4 × 4 k-points in the first Brillouin zone using the Monkhorst-Pack method. [START_REF] Monkhorst | Special points for Brillouin-zone integrations[END_REF] Chemical bonding analyses of plane-wave data by Crystal Orbital Hamiltonian Population (COHP) [START_REF] Dronskowski | Crystal orbital Hamilton populations (COHP): energyresolved visualization of chemical bonding in solids based on density-functional calculations[END_REF] were done using LOBSTER. [START_REF] Deringer | Crystal orbital Hamilton population (COHP) analysis as projected from plane-wave basis sets[END_REF][START_REF] Maintz | Analytic projection from plane-wave and PAW wavefunctions and application to chemical-bonding analysis in solids[END_REF][START_REF] Maintz | A tool to extract chemical bonding from plane-wave based DFT[END_REF] . Band-structures, density of states (DOS) and COHP curves were shifted so that the Fermi level lies at 0 eV.

Results and discussion

Synthesis

Eight new quaternary chalcogenides with general formula Cs2Ln3CuS8 (Ln=La, Ce, Pr, Nd, Sm, Eu, Gd, and Tb) were synthesized using the conventional reactive flux method. The reaction of Ln2S3 (or EuS) and Cu2S in melted Cs2Sx results in powder product along with few single-crystals in the shape of needles and plates. Unfortunately, we weren't able to grow Cs2Ce3CuS8 singlecrystal suitable for a crystal structure determination. However, the x-ray powder diffraction pattern of Cs2Ce3CuS8 demonstrated strong similarities with those of the other members of Cs2Ln3CuS8 family in agreement with the stabilization of a unique structure-type. Concerning the syntheses conditions for Ln=Ce a greater excess of Cs2Sx (molar ratio up to 4Cs:1Ln, at least 8Cs:3Ln) is needed to prevent formation of the CsCe2CuS6 as secondary phase. We failed to prepare phase pure Cs2La3CuS8 sample under the applied synthesis conditions, it always contained CsLa2CuS6 (isostructural to CsCe2CuS6 11 ) phase as by-product. Note that admixture of hypothetical CsLn2CuS6 phase was also found for some experiments with Pr, Nd, Sm, and Gd. Thus, for Ln=Ce-Sm, the molar ratio of Ln2S3 to Cu2S seems to determine the product of the reaction. No traces of CsLn2CuS6 phase were found for Eu and Tb samples. In a case of Ln = Tb, for initial loading ratio of Tb2S3:Cu2S = 1:2 a phase isostructural to CsDy2Cu3S5 14 starts to produce as a resulting product.

However, the lack of single crystals prevented further investigation on these samples.

It could be noted, that using stoichiometric amount of Cs2S6 (Ln2S3:Cs2S6 = 3:2, Ln=La-Nd, Sm) in the synthesis leads to mixture of CsLn2CuS6 and Cs2Ln3CuS8 phases despite the initial loading of other sulfides. On other hand, for Ln=Gd, Eu the Cs2Ln3CuS8 phase seems to be preferentially formed in all tested synthesis conditions. All experimental details as well as obtained products are shown in Table 2.

Crystal structure

All crystallographic data and selected calculated bond lengths are summarized in Table 3 and Table S2-S3, respectively. The eight members of the Cs2Ln3CuS8 series all crystallize in the monoclinic space group C2/m (N°12). There are two crystallographically independent Ln positions, one Cu and four S positions in the anionic layer {Ln3CuS8} and one Cs position between these layers. All atoms are located on 4i Wyckoff positions, excepted Ln1 which is located in 2c position. Ln1 is coordinated to six S 2-anions forming a distorted octahedron noted {Ln1S6} with two opposite short Ln-S bonds and four long ones. Ln2 has a bicapped trigonal prism coordination noted {Ln2S4(S2)2}. It is built up from four S 2-(apex and capped positions in prisms) and two (S2) 2-groups forming edges of the prisms (Figure 1A). The S-S interatomic distances within the dimers roughly equal to 2.08 Å. This value is close to ones reported for ALn2CuS6 series [START_REF] Sutorik | The First Examples of Alkali Metal/Cu/Ce/Chalcogenides: The Layered Heterometallic Compounds KCuCe2S6 and K2Cu2CeS4[END_REF][START_REF] Sutorik | New quaternary compounds resulting from the reaction of copper and f-block metals in molten polychalcogenide salts at intermediate temperatures. Valence fluctuations in the layered CsCuCeS3[END_REF][START_REF] Bensch | Preparation and Crystal Structure of the New Quaternary Europium-polysulfide KCuEu2S6[END_REF][START_REF] Pomelova | Crystal Structure, and Liquid Exfoliation of Layered Lanthanide Sulfides KLn2CuS6 (Ln= La, Ce, Pr, Nd, Sm)[END_REF] or CuS2 [START_REF] Will | The bulk moduli of 3d-transition element pyrites measured with synchrotron radiation in a new belt type apparatus[END_REF] Each prism is connected with two neighboring ones by shared triangular faces, forming chains {Ln2S4(S2)2} in a pattern similar to those observed in the CsCe2CuS6 crystal structure type. [START_REF] Sutorik | The First Examples of Alkali Metal/Cu/Ce/Chalcogenides: The Layered Heterometallic Compounds KCuCe2S6 and K2Cu2CeS4[END_REF] The Cs cations are located between the layers in a wavy disposition (Figure 1C). Crystallographic environment of Cs atom could be described as distorted rectangular prism with one cap leading to a coordination number of 9 (Figure S1C in SI). K2CeCu2S4 is also characterized by a layered-like structure but that structure is based on {CeS6} octahedron and {CuS4} tetrahedron. The {CeS6} octahedra are connected through common edges leading to infinite chains of cerium atoms in one direction. The {CuS4} tetrahedra are also connected through common edges leading in that case to zig-zag chains of copper atoms in the same direction. These two kinds of chains are stacked in a second direction to form {CeCu2S4} 2- anionic layers. Finally, potassium cations are located between the layers in a prism formed by seven sulfur atoms. This unusual coordination can be depicted considering a one corner truncated cube, leading to one square face and one triangular face in opposite position.

The correlation between the crystal structure of Cs2Ln3Cu(S2)2S4 and those of ACe2CuS6 (A = K and Cs) and K2CeCu2S4 is also reflected through the tetrahedral coordination of copper atoms that can be viewed as 'Janus ions'. Indeed, one side of the {CuS4} tetrahedron in Cs2Ln3Cu(S2)2S4

is found in ACe2CuS6 whilst the other side corresponds to that found in K2CeCu2S4 (Figure S4 It also should be noted, that the title Cs2Ln3CuS8 compounds do not belong to any family of the numerous compounds reported in the literature and exhibiting the same stoichiometry A2M 2+ M3' 4+ Q8 (A = alkali metals, Tl, Ag; Q = S, Se, Te, M 2+ = Zn, Cd, Hg.., M' 4+ = Sn, Ge..) 29, 30 , 31, 32 . Indeed, the latter compounds do not exhibit Q-Q bonds due to different metal charges, and their structures is a combination of tetrahedral and/or octahedral {M3M'S8} frameworks. The only structural analogy that can be found with Cs2Ln3CuS8 compounds concerns the layered-like nature of their structures.

As was mentioned above, two compounds among the series slightly differ from the others:

Cs2Ce3CuS8 and Cs2Eu3CuS8. First, the colors of Cs2Ln3CuS8 (Ln=La, Pr, Nd,Sm, Gd, and Tb) sulfides are different shades of yellow, while that of Cs2Ce3CuS8 is dark red-brown and Cs2Eu3CuS8 is black. If for Ce sulfides, such color seems common for other compounds (e.g. Ce2S3 is red, CsCe2CuS6 and KCe2CuS6 are red-brown, CsCeCuS3 is black [START_REF] Sutorik | New quaternary compounds resulting from the reaction of copper and f-block metals in molten polychalcogenide salts at intermediate temperatures. Valence fluctuations in the layered CsCuCeS3[END_REF] ), the black color of europium compound suggests either non-stoichiometric chemical composition or the presence of Eu 2+ cations along with Eu 3+ . Crystal structure refinement of the Cu sites occupancies leads to the following chemical composition: Cs2Eu3Cu1.46S8. From this data, it appears that europium compound is a mixed valence system, suggesting that some Eu ions have a +2 charge. This is supported by the analysis of the averaged Ln-S bond lengths and unit cell volumes along the series (Figure 3 and Figure S5 in SI, respectively) evidencing longer Eu2-S bond lengths than those expected from a linear fit of all Ln1-S and Ln2-S bond lengths. From this analysis, it could be noted that Eu 2+ cations should mostly occupy Ln2 position, in agreement with the fact, that bigger Eu 2+ ions tend to occupy more loose position with complex environment and longer Eu-S bonds.

This hypothesis about the mixed valence Eu 2+ /Eu 3+ is also confirmed by macroscopic magnetic measurements as discussed below.

Optical properties

The optical absorption spectra of Cs2Ln3CuS8 were converted from the diffuse reflectance spectra using the Kubelka-Munk function. Band gaps were calculated as the intersection point between the photon energy axis and the line extrapolated from the linear portion of the absorption edge in a plot of Kubelka-Munk function. Resulting data are summarized in Table 4 and the optical absorption spectra are shown in Figure 4 and Figure S6 in SI. For Ln = Nd and Pr additional peaks on the slope of the spectra were found. These peaks could be explained as f-f (Nd) or 4f-5d (Pr)transitions within the lanthanide ions. [START_REF] Pomelova | Crystal Structure, and Liquid Exfoliation of Layered Lanthanide Sulfides KLn2CuS6 (Ln= La, Ce, Pr, Nd, Sm)[END_REF] For Nd compound these transitions could be assigned to originate from the ground state 4 I9/2 to 2 P1/2 (~2.71 eV), 2 G9/2 (~2.48 eV) and 2 G7/2 (~2 eV) [START_REF] Choudhury | Structure, Magnetic and Optical Properties of Ternary Thio-germanates: Ln4(GeS4)3 (Ln= Ce, Nd)[END_REF] .

Analysis of obtained Eg values revealed that the energy band gap increases as the ionic radii of Ln 3+ increases. For Ce sulfide energy band gap was found to be much lower than ones for other members of the Cs2Ln3CuS8 family. The spectrum of Cs2Eu3Cu1.46S8 compound is difficult to interpret as as it does not content absorption edge. However, due to the black color of the sample, its absorption edge is probably less than that of Cs2Ce3CuS8. Calculated values are consistent with colors of the powders and suggested formula of (Cs + )2 (Ln 3+ )3(Cu + ) (S2 2-)2(S 2-)4.

Magnetic properties

As previously mentioned, the chemical formula of the compounds can be written as (Cs + )2(Ln 3+ )3(Cu + )1(S2 2-)2(S 2-)4. Note that this assumption is incorrect for Cs2Eu3Cu1.46S8 as a mixed valence Eu 2+ /Eu 3+ is strongly suggested. Nevertheless, as copper valence is +1, the only magnetic contribution comes from the rare-earth trivalent cations.

Among the Cs2Ln3CuS8 series, compounds with Ln = Ce, Pr, Nd, Gd and Tb exhibit classical magnetic behaviors, while the magnetic properties of Eu compound is more difficult to interpret due to the mixture of Eu 2+ and Eu 3+ cations (see below).

For the Cs2Ce3CuS8, Cs2Pr3CuS8, Cs2Nd3CuS8, Cs2Gd3CuS8 and Cs2Tb3CuS8 compounds, the magnetic susceptibility curves do not evidence magnetic ordering on the investigated temperature range (1.8K-300K) as illustrated on Supporting Information Figures S7-S11, respectively. This indicates that the five compounds are Curie-paramagnets, which is supported by the magnetization data recorded at 2K (Figure S12). Indeed, the curves profiles are in agreement with a Brillouin function as expected at low temperature for Curie-paramagnets. The inverse susceptibility data were analyzed using the Curie-Weiss law M=C/(T-p) where M is the magnetic susceptibility, C is the Curie constant, T is the absolute temperature and p is the paramagnetic Curie-Weiss temperature. Pr, Nd, Gd and Tb compounds obey the Curie-Weiss law over a wide temperature range while the Ce compound shows a strong deviation below 125K (Insets of Figures S7-S11).

This phenomenon has been reported for other Ce 3+ compounds and has been attributed to crystal field splitting of the 2 F5/2 ground state [START_REF] Lueken | Magnetic properties of NaCeS2 between 3.7 and 297 K. J. less-common met[END_REF][START_REF] Duczmal | The crystal field influence on magnetic susceptibilities of TlCeSe2 and TlCeTe2[END_REF] . Note that the Cs2Ce3CuS8 curve profile is similar to the one observed for CsCe2CuS6 and CsCeCuS3 11 . Results of Ce, Pr, Nd, Gd and Tb inverse susceptibility fits are summarized in Table 5. The obtained effective magnetic moment µeff are 2.95(1) µB/Ce 3+ , 3.93(4) µB/Pr 3+ , 3.70(3) µB/Nd 3+ , 7.41(1) µB/Gd 3+ and 9.69(1) µB/Tb 3+ . These experimental values are consistent with theoretical ones for Cs2Nd3CuS8 and Cs2Tb3CuS8, they are significantly different for others compounds suggesting the presence of uncharacterized paramagnetic impurities in the samples. For Cs2Ce3CuS8, the higher value of µeff than that excepted is associated with a large negative p value. Such effective magnetic moment deviation and large negative p value has been also observed in CsCeCuS3. The authors reported that the nature of the Ce oxidation state remains unclear and that valence fluctuations might occur in the compound. [START_REF] Sutorik | New quaternary compounds resulting from the reaction of copper and f-block metals in molten polychalcogenide salts at intermediate temperatures. Valence fluctuations in the layered CsCuCeS3[END_REF] For each compound, fitting parameters indicate negative paramagnetic Curie-Weiss temperatures p (Table 5) suggesting local antiferromagnetic interactions. The temperature dependent magnetic susceptibility of Cs2Eu3CuS8 is shown in Figure 4A. Two anomalies are visible at about 3K and 17 K (Figure 4B) and can be related respectively to the presence of ferromagnetic Eu3S4 (TC = 3.1 K 36 ) and EuS (TC = 16.6 K 37 ) as secondary phases.

This is supported by the magnetization data recorded at low temperature (Figure S13). Note that the weakness of impurities signal on PXRD data (Figure S3 cations in the material, which is in agreement with the single crystal structural refinement that leads to the following composition: Cs2Eu3Cu1.46S8. However, from these magnetic measurements we cannot unambiguously conclude on the Eu 2+ :Eu 3+ ratio because of the ferromagnetic impurities that contain both species. Following our investigation on magnetocaloric properties of Gd sulfides, [START_REF] Delacotte | NaGdS2: A Promising Sulfide for Cryogenic Magnetic Cooling[END_REF] those of the Cs2Gd3CuS8 member were analyzed. Indeed, one can expect interesting magnetocaloric properties due to the large spin quantum number of Gd 3+ ion (S=7/2) favoring a large magnetic entropy change. The magnetic entropy change determined from isothermal magnetization curves (Figure 5A) increases upon cooling down to 2.5 K for applied magnetic field changes of 1 and 2 T, and presents a maximum at 3.5 K for higher magnetic field variations (Figure 5B). Cs2Gd3CuS8 is characterized by relatively large values of magnetic entropy change, reaching 6.7 J kg -1 K -1 (or 33 mJ cm -3 K -1 ) at 2.5 K for 0ΔH = 2 T and 19.5 J kg -1 K -1 (or 95 mJ cm -3 K -1 ) at 3.5 K for 0ΔH = 5 T. These values are comparable to those reported for Gd-based oxides [START_REF] Dong | Structural, magnetic and magnetocaloric properties in perovskite RE2FeCoO6 (RE= Er and Gd) compounds[END_REF][START_REF] Palacios | Effect of Gd polarization on the large magnetocaloric effect of GdCrO4 in a broad temperature range[END_REF][START_REF] Dey | Cryogenic magnetocaloric effect in zircon-type RVO4 (R= Gd, Ho, Er, and Yb)[END_REF] including the reference material Gd3Ga5O12, [START_REF] Hamilton | Enhancement of the magnetocaloric effect driven by changes in the crystal structure of Al-doped GGG, Gd3Ga5-xAlxO12 (0≤ x≤ 5)[END_REF] and superior, near liquid helium temperature, to those reported for Gd-based intermetallics [START_REF] Rawat | Heat capacity and magnetocaloric studies of RPd2Si (R= Gd, Tb and Dy)[END_REF][START_REF] Pakhira | Large magnetic cooling power involving frustrated antiferromagnetic spin-glass state in R2NiSi3 (R= Gd, Er)[END_REF][START_REF] Pakhira | Magnetic and magnetocaloric properties of (Gd1-xYx)2NiSi3 compounds (x= 0[END_REF][START_REF] Pani | RNi8Si3 (R= Gd, Tb): Novel ternary ordered derivatives of the BaCd11 type[END_REF] , borides [START_REF] Li | Giant reversible magnetocaloric effect in antiferromagnetic GdCo2B2 compound[END_REF] , carbides, [START_REF] Meng | Magnetic properties and giant reversible magnetocaloric effect in GdCoC2[END_REF] and borocarbides. [START_REF] Zhang | Magnetic properties and magneto-caloric performances in RECo2B2C (RE= Gd, Tb and Dy) compounds[END_REF][START_REF] Li | Low field giant magnetocaloric effect in RNiBC (R= Er and Gd) and enhanced refrigerant capacity in its composite materials[END_REF] Nevertheless, the magnetocaloric effect of Cs2Gd3CuS8 is significantly weaker than the one of NaGdS2. [START_REF] Delacotte | NaGdS2: A Promising Sulfide for Cryogenic Magnetic Cooling[END_REF] This can be explained by the fact that, (i) Cs2Gd3CuS8 suffers from a weak magnetic/non-magnetic mass ratio and (ii) the magnetization isotherms at low temperature are far from saturation even under an applied magnetic field of 5 T (Figure 5A), indicating non-negligible antiferromagnetic interactions between Gd centers. Moreover, the shape of the magnetization curve recorded at 2 K exhibits a metamagnetic-like transition that might be correlated to some kind of short-range magnetic ordering, thus supporting the existence of interactions between Gd 3+ ions.

Magnetocaloric properties were also investigated for the other members of the Cs2Ln3CuS8 family, but the effect is weaker, i.e. values of magnetic entropy change < 1.5 J kg -1 K -1 excepted for the Tb compound where -SM reaches 8 J kg -1 K -1 at 5.5K. Results for the whole family are summarized in Table 6.

T (K) -SM (J kg -1 K -1 -SM (mJ cm -3 K -1 )  (g cm -3 ) 0-2 T 0-5 T 0-2 T 0-5 T Cs2Ce3CuS8 -- -- -- -- -- Cs2Pr3CuS8

Theoretical considerations

DFT calculations were carried out for Cs2La3CuS8. Since copper positions are half-occupied, several models had to be considered for the crystal structure of this compound. Assuming the unitcell resulting from X-ray diffraction studies, three of them can be considered; they are sketched in The top of the valence band shows an antibonding S-S character; this is consistent with a single  S-S bond as expected considering their distance close to 2.10 Å. It is noteworthy to mention that La-S bonds are optimized for hexacoordinated La atoms. This is not the case for octa-coordinated La atoms as shown by the corresponding COHP curves. The top of the valence band also exhibits an antibonding Cu-S character. This is often the case for Cu-S bonds in CuS4 tetrahedron.

Conclusions

In this work, we have demonstrated that the crystal structure of the new quaternary semiconducting sulfides Cs2Ln3CuS8 is hybrid of those of ACe2CuS6 compounds (A = K and Cs) and that of K2Cu2CeS4 compound. The singularity of this structure is based on a complex framework built-up from two types of chains of rare earths generated by the two types of coordination polyhedrons of Ln 3+ ions, the {Ln2S4(S2)2} bicapped trigonal prims and the {Ln1S6} octahedrons, and their interconnections modes. It was found Cs2Gd3CuS8 demonstrates a relatively large magnetocaloric effect near liquid helium temperature comparable with other effective Gdbased materials. This work highlights the route of lanthanide sulfides as a promising magnetocaloric materials for magnetic refrigeration at cryogenic temperature either for gas liquefaction or ultra-low temperature applications.

Table of Content

Novel compounds Cs2Ln3CuS8 (Ln=La-Nd,Sm-Tb) has been prepared by reactive flux method from mixture of component sulfides. These compounds have layered-like structure lies between CsCe2CuS6 and K2CeCuS4 structural types. Optical band gaps of the compounds decrease with Ln radii increasing from 2.62 eV for Tb compound to 2.29 for La one with exceptions for Ln=Ce, Eu which band gap is lower. Magnetic measurements reveal that the Cs2Gd3CuS8 displayed considerable magnetocaloric effect near liquid helium temperature.

  Two of the latter chains of {Ln2S4(S2)2} are connected together via shared capping edges of the prisms. Considering one {Ln2S4(S2)2} prism involved in the connection of the chains, each opposite capping edge is shared with two edges of two {Ln1S6} octahedra. This second type of capping edge of {Ln2S4(S2)2} shared with {Ln1S6} octahedron is longer than the first type of capping edge shared between two {Ln2S4(S2)2} prims described above. At the end, second type of chain is formed by the sharing of common edges between {Ln1S6} octahedra. The singularity of this structure is that it is based on two types of chains of rare earth atoms generated by the two types of coordination polyhedrons, the {Ln2S4(S2)2} prims and the {Ln1S6} octahedrons, and their interconnections modes. Several magnetic interactions are thus expected: within each of the two types of chains and between the chains. The Cu atoms lie in tetrahedral voids located between prisms and octahedron (FigureS1in SI), formed by two edges of two adjacent {Ln1S6} octahedra and two cape edges of two neighboring {Ln2S4(S2)2} prisms. The occupancy of Cu positions was found to be 50% except for Eu. In the case of Eu, the refinement of the Cu position occupancy deviates from 50% within the estimated standard deviations. The consequence on the oxidation state of Eu will be discussed below. The alternation of {Ln2S4(S2)2}-{Ln2S4(S2)2} and {Ln1S6} fragments (Figure1B) lead to distorted {Ln1(Ln2)2CuS8} 2-of anionic layers staked along c-axis.

Figure 1 .

 1 Figure 1. Crystallographic environment of Ln 3+ cations (A), {Ln2S4(S2)2}-{Ln2S4(S2)2}-

Figure 2 .

 2 Figure 2. Correlations between Cs2Ln3CuS8, CsCe2CuS6 and K2CeCu2S4 crystal structures.

  in SI). The {CuS4} tetrahedron in Cs2Ln3Cu(S2)2S4 shares three edges with three Ln2S4(S2)2 bicapped trigonal prisms, two edges with two {LnS6} octahedron and the last edge with one Cs(S2)2(S2)3/2S2 prism. Hence, Cu + ions act as linkers between the Ln1 chain and Ln2 double chains to form {Ln3Cu(S2)2S4}

Figure 3 .

 3 Figure 3. Averaged bond lengths for different Cs2Ln3CuS8 compounds versus the Ln 3+ ion radii.

Figure 4 .

 4 Figure 4. Optical absorption spectra of Cs2Sm3CuS8 (black) and Cs2Nd3CuS8 (red).

  in SI, only EuS is visible) suggests that they are both contained as traces in the sample. At high temperature (T>100K), the Cs2Eu3CuS8 compound follows the Curie-Weiss law as illustrated on the inset of Figure 4A. The fit resulted in an effective magnetic moment of 4.77(3) µB per Eu atom and a paramagnetic Curie-Weiss temperature of -203.4(5) K (

Figure 5 .

 5 Figure 5. Temperature dependence of the molar magnetic susceptibility (M) of Cs2Eu3CuS8

Figure 6 .

 6 Figure 6. Magnetization isotherms of Cs2Gd3CuS8 recorded from 2 K to 26 K in applied magnetic

Figure 7 .

 7 Figure 7. Their crystal structures have lower symmetry than the parent compound. Assuming a

Figure 7 .

 7 Figure 7. The valence band is mainly centered on sulfur and copper. The bottom of the conduction

Figure 7 .

 7 Figure 7. Different structural models considered for DFT calculations.

Figure 9 .

 9 Figure 9. COHP computed for Cu-S contacts (ranging from 2.271 Å to 2.408 Å), S-S contacts

Table 1 .

 1 Formula and structure motif of compounds in the A-Ln-Cu-S systems

	Series	Ref.

La Ce Pr Nd Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

	KLn2CuS6	10-13
	K2Ln2CuS4	10
	CsLnCuS3	11
	CsLn2CuS6	11
	Cs2Ln3CuS8 This work
	KLn2CuS4	9
	K2Ln4Cu4S9 9
	RbLn2CuS4	15
	RbLn2Cu3S5 15
	Rb2Ln4Cu4S9 15
	CsLn2Cu3S5 15
	Cs2Ln4Cu4S9 14

Table 2 .

 2 Ratio of components and main products in Cs2Ln3CuS8 synthesis.

	Cs-Ln-Cu-S	La	Ce	Nd-	Eu	Gd	Tb
				Sm
	2Ln2S3+Cu2S+4Cs2S6		CsLn2CuS6		Cs2Ln3CuS8	CsTb2Cu3S5(?)
	3Ln2S3+Cu2S+4Cs2S6		CsLn2CuS6+			Cs2Ln3CuS8
			Cs2Ln3CuS8
	3Ln2S3+Cu2S+8Cs2S6 CsLn2CuS6+				Cs2Ln3CuS8
		Cs2Ln3CuS8
	2Ln2S3+Cu2S+2Cs2S6		CsLn2CuS6+		Cs2Eu3CuS8 Cs2Gd3CuS8	No reaction
						+CsGd2CuS6
	3Ln2S3+Cu2S+2Cs2S6		Cs2Ln3CuS8			(traces)

Table 3 .

 3 Structure data and refined parameters for Cs2Ln3CuS8 (Ln = La-Nd, Sm-Tb)

	Ln	La	Ce*	Pr	Nd	Sm	Eu	Gd	Tb
	Crystal system			monoclinic
	Space group			C2/m(No12)
	a, Å	16.904(2)	16.78	16.709(3)	16.678(2)	16.535 (1)	16.4383(8)	16.443(1)	16.352(2)
	b, Å	4.2482(4)	4.203	4.1811(5)	4.1578(6)	4.1110(2)	4.1047(2)	4.0703(2)	4.0451(4)
	c, Å	11.997 (1)	11.97	11.9516(19)	11.9499(17)	11.9041(8)	11.9340(6)	11.8808(7)	11.8505(12)
	β,deg	115.209(4)	115.41	115.228(5)	115.201(3)	115.177(2)	114.582(4)	115.098(2)	115.183(3)
	V, Å 3	779.48	762.84	755.32	749.78	732.34	732.26	720.09	709.39
	Z						2
	ρcalc, g/cm 3	4.272	4.33	4.435	4.512	4.702	5.013	4.878	4.975
	μ, mm -1	15.035	-	16.707	17.471	19.280	21.516	21.191	22.441
	crystal size,	0.100 x 0.020	-	0.180 x 0.030	0.190 x 0.030	0.200 x 0.020	0.110 x 0.020	0.100 x 0.020	0.100 x 0.005
	mm 3	x 0.005		x 0.010	x 0.005	x 0.020	x 0.005	x 0.010	x 0.002
	θ range, deg.	2.521 -28.272 -	1.884 -28.312 1.883 -30.709 1.890 -30.742 2.587 -27.507 1.893 -30.622 2.595 -27.484
	R1 (wR2) for I	0.0447(0.093	-	0.0515	0.0176	0.0154	0.0369	0.0228	0.0386
	≥ 2σ(I)	3)		(0.0903)	(0.0395)	(0.0365)	(0.0932)	(0.0399)	(0.0691)
	R1 (wR2)	0.0726	-	0.0774	0.0217	0.0170	0.0432	0.0307	0.0663
		(0.0996)		(0.0969)	(0.0404)	(0.0370)	(0.0953)	(0.0411)	(0.0746)
	*Structural data based on PXRD refinement (figure S2 in SI)

Table 4 .

 4 Optical band gap of Cs2Ln3CuS8 compounds

	Cs2Ln3CuS8 color	Band gap
	Ce	red-	1.2 eV
		brown
	Pr	yellow-	2.37 eV
		green
	Nd	yellow-	2.42 eV
		orange
	Sm	yellow-	2.48 eV
		orange
	Gd	yellow-	2.56 eV
		orange
	Tb	yellow 2.62 eV

Table 5 .

 5 Fitted paramagnetic Curie-Weiss temperatures p and effective magnetic moments µeff of

	the Cs2Ln3CuS8 series
			µeff (µB/Ln 3+ )	µeff (µB/Ln 3+ )	∆(μeff )(%)
	Compound	p (K)
			this study	theoretical
	Cs2Ce3CuS8	-142.9(7)	2.95(1)	2.54	+16

Table 5 )

 5 . The negative p value indicates predominant antiferromagnetic interactions and the effective magnetic moment µeff lies in between Eu 2+ and Eu 3+ expected values. On the one hand, Eu 2+ has a large spin quantum number S=7/2 and an orbital angular momentum L=0 which leads to a theoretical effective magnetic moment of 7.94 µB. On the other hand, Eu 3+ has a spin quantum number S=3 and an orbital angular momentum L=3 that cancel each other, thus giving theoretically no effective magnetic moment. However, because of the narrow energy separation between its ground state 7 F0 and the successive excited states, at high temperature, Eu 3+ ions give rise to Van Vleck paramagnetism with a magnetic moment μeff = 3.4 μB[START_REF] Takikawa | Vleck paramagnetism of the trivalent Eu ions[END_REF] . This means that both Eu 2+ /Eu 3+ cations contribute to the effective magnetic moment deduced from our Curie-Weiss fit. Outcomes from this fit thus confirm the existence of both Eu 2+ and Eu 3+

Table 6 .

 6 Magnetocaloric properties of the Cs2Ln3CuS8 series Compound

Table 7 .

 7 P2/m model is significantly energetically unfavored compared to the two other models. P21/m model is slightly more stable than the Bm model (+0.05 eV / unit cell). It is interesting to mention than the most stable model corresponds to the most compact unit cell.Optimized bond distances are comparable for both models: Cu-S bond distances range from 2.27 to 2.45 Å, S-S bond distances range from 2.07 to 2.12 Å and La-S bond distances range from 2.72 to 3.02 Å.The total and atom-projected DOS computed for the P21/m model of Cs2La3CuS8 is sketched in

Table 7 .

 7 Optimized cell parameters and selected bond lengths of used models

	Models	P2/m	Bm	P21/m
	Energy (eV /u.c.) +0.24	+0.05	0
	a (Å)	15.611	16.345	15.726
	b (Å)	11.743	15.754	11.657
	c (Å)	4.159	4.151	4.138
	 ()	107.65	137.31	107.32
	V (Å 3 )	726.47	724.81	724.17

Funding Sources

The research was supported by the Ministry of Science and Higher Education of the Russian Federation, N 121031700315-2.

AUTHOR INFORMATION

Corresponding Author *naumov@niic.nsc.ru Present Addresses †Institut Jean Lamour, UMR 7198 CNRS, Université de Lorraine, 54011 Nancy, France

Author Contributions

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

Supporting Information: Details of crystal structures for all compounds(selected bonds lengths, atomic parameters, anisotropic displacements parameters, additional figures of crystal structure), powder diffraction patterns of all compounds, optical absorption spectra of Cs2Ln3CuS8 (Ln = Ce, Pr, Gd,Tb), temperature dependences of the molar magnetic susceptibility for Cs2Ln3CuS8 Ce, Pr, Gd,Tb) and magnetization isotherms of all the Cs2Ln3CuS8 series.


PIV measurements and POD analysis as a tool to study mixing of non-Newtonian fluids in stirred vessels

J.-C. Gabelle 1,2,3,5 , A. Liné 1,2,3 , J. Morchain 1,2,3 , D. Anne-Archard 3,4 , F. Augier 5 1 Université de Toulouse, INSA, UPS, INP; LISBP; 135 Avenue de Rangueil, F-31077 Toulouse, France. tel. +33 (0)5 6155 9786, e-mail: alain.line@insa-toulouse.fr; fax: +33 (0)5 6155 9776. 2 INRA UMR792 Ingénierie des Systèmes Biologiques et des Procédés, F-31400 Toulouse, France.

3 CNRS ; Fédération de Recherche FERMAT ; F-31400 Toulouse, France. 4 Université de Toulouse ; INPT, UPS ; IMFT (Institut de Mécanique des Fluides de Toulouse), Allée Camille Soula, F-31400 Toulouse, France. 5 IFP Energies nouvelles, Rond-point de l'échangeur de Solaize, BP3, 69360 Solaize, France.

In bioprocess, the stirred tank reactor is often chosen to perform reaction operations or blending because it offers high mixing and mass transfer capacities. Most of the previous works on this topic are concerned with Newtonian fluids. But industrial fluids such as fermentation broths are hardly ever Newtonian. Although there has been recent progress, there are still a lot to understand about physical mechanism, especially with non-Newtonian fluids. This lack of knowledge can lead, sometimes, to erroneous design and scale-up. 2D-PIV measurements were performed in a 70 L stirred tank equipped with four equally spaced baffles. A Rushton turbine (D/T = 0.33) was used and driven at three volumetric power draws (82, 212 and 384 W•m -3 , corresponding to Reynolds numbers 85, 145 and 200). Measurements were successively performed on four rectangular areas (9x7 cm 2 ): one in the impeller stream, one under the stirrer and two above. The yield stress shear thinning fluid Carbopol 980 (0.08 %) (Noveon Canada Inc., Waterloo, ON) was used. It offers good transparency even at high polymer concentration.

Rheological parameters of the Herschel-Bulkley model were identified using a Haake Mars III rheometer (Thermo Scientific, Germany). A serrated plates geometry (P60/Ti L) was used to avoid wall slip effect at low shear rate.

The PIV system used in this study consisted of a laser and an image acquisition system provided by LaVision (LaVision GmbH, Goettingen, Germany). The system includes a Nd-Yag laser (Quantel, 10 Hz, 2 × 200 mJ), a synchronization system and a CCD camera (Imager Intense, 12 bits, 1376×1040 pixels 2 ). Fast Fourier transform (FFT) cross correlation was used to examine the two images, which are divided into interrogation area (16×16 pixels 2 ). For all experiments, 400 -1000 image pairs are recorded and statistical convergence of the velocity is checked. In order to study the influence of spatial resolution in the vicinity of the impeller, two spatial resolutions Δx were tested (0.7-1 mm). The delay between each frame in an image pair Δt was chosen in relation to the agitation speed and the medium (range: 200 to 3000 μs).

A Proper Orthogonal Decomposition (POD) was used. It is a linear procedure which decomposes a set of signals into a modal base (Lumley 1967). POD is proven to be a complementary analysis tool to identify organized motion in a stirred tank (Doulgerakis et al. 2011;Moreau & Liné 2006;Tabib & Joshi 2008). This tool allows separating the different motions without the necessity to collect angular phased data (Moreau & Liné 2006). POD is carried out using snapshot method with 700 "non-conditioned" instantaneous velocity fields directly calculated from the measurements. The result is then an orthonormal basis of eigenfunctions and the associated eigenvalues. Moreover the energy brought by the three first modes is about 92% to 97% of the total energy. Mode 1 is structurally closed to the average velocity field (Figure 1.a, classical result with the instantaneous velocity fields containing mean contribution). The second and third eigenvalues are almost equal thus involving that the energy brought by these modes is the same. These two modes reveal large scale rotating structures (Figure 1.b).

The instantaneous velocity field is projected on each POD modes. The value of this projection gives a good evaluation of the square root of the energy of the instantaneous flow contained in the corresponding mode. From these projections it is possible to reconstruct the velocity field. As shown in the presentation, three modes seem to be sufficient to reproduce the hydrodynamics of Carbopol 980 flow.

Finally, the velocity field is then post processed to determine the size of the cavity, characteristic of such flow pattern (Elson et al. 1986).

Figure 1 :

 1 Figure 1: Vector plot of the velocity field associated with: a) 1 st mode, b) reconstructed field based on 2 nd and 3 th modes (Re = 85, in the impeller steam).