Hugo Bouteiller

Bruno Fontaine

Takao Mori

Franck Gascoin

Jean-François Halet

David Berthebaud

Jean- François Halet

Synthesis, Crystal and Electronic Structure, and Thermal Conductivity Investigation of the Hollandite-like Cs x Cr 5 Te 8 Phases (0.73 < x < 1)

Keywords: Synthesis, Crystal and Electronic Structure, and Thermal Conductivity Investigation

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INTRODUCTION

Transition metal chalcogenides (TMCs) have been extensively studied for their wide range of properties and potential applications, including superconductivity, 1 optoelectronics, [START_REF] Carrig | Transition-Metal-Doped Chalcogenide Lasers[END_REF][START_REF] Kagkoura | Transition-Metal Chalcogenide/Graphene Ensembles for Light-Induced Energy Applications[END_REF] photocatalysis, [START_REF] Munonde | Review on Metal Chalcogenides and Metal Chalcogenide-Based Nanocomposites in Photocatalytic Applications[END_REF] and energy storage. [START_REF] Yadav | Transitional Metal Chalcogenide Nanostructures for Remediation and Energy: A Review[END_REF] One of the key factors contributing to their diverse properties is their complex structural diversity, which often manifests as low-dimensional arrangements. [START_REF] Guo | Chemical Intercalations in Layered Transition Metal Chalcogenides: Syntheses, Structures, and Related Properties[END_REF][START_REF] Dai | Synthesis and Applications of Nanostructured Hollow Transition Metal Chalcogenides[END_REF] These structures can be characterized by the presence of two-dimensional (2D) sheets or onedimensional (1D) infinite channels, often featuring spacious voids as observed in compounds like AgCrSe2 [START_REF] Hahn | Untersuchungen Über Ternäre Chalkogenide. XII. Über Ternäre Chalkogenide Des Chroms Mit Einwertigem Kupfer Und Silber[END_REF][START_REF] Gautam | Magnetic and Transport Properties, and Electronic Structure of the Layered Chalcogenide AgCrSe2[END_REF] or Nb3Se4. [START_REF] Smeggil | Void Channels in the Nb3Te4, Ta2S, and Nb2Se Structure Types; the Structure of Nb3Se4[END_REF] Such structural features are particularly attractive in the field of thermoelectricity where a very low thermal conductivity is required. [START_REF] Hendricks | Keynote Review of Latest Advances in Thermoelectric Generation Materials, Devices, and Technologies[END_REF] Indeed, the lattice component (kl) of the thermal conductivity is primarily governed by phonon scattering which is generally large in highly complex structures. [START_REF] Slack | Semiconductors and Semimetals[END_REF][START_REF] Mark | Ultralow Thermal Conductivity in the Mixed-Anion Solid Solution Sn2SbS2-xSexI3[END_REF] Consequently, an efficient strategy to reach low thermal conductivity is to aim at synthesizing low-dimensional structures containing large scattering centers in order to reduce effectively the phonon mean free path. [START_REF] Hébert | Searching for New Thermoelectric Materials: Some Examples among Oxides, Sulfides and Selenides[END_REF][START_REF] Takahashi | Transport Properties of an Intermetallic with Pseudo-Hollandite Structure as a Potential Thermoelectric Material: The Example of TlxCr5Se8[END_REF][START_REF] Lefèvre | Polar Transition-Metal Chalcogenide: Structure and Properties of the New Pseudo-Hollandite Ba0.5Cr5Se8[END_REF][START_REF] Lefèvre | Magnetic and Thermoelectric Properties of the Ternary Pseudo-Hollandite BaxCr5Se8 (0.5 < x < 0.55) Solid Solution[END_REF][START_REF] Maier | The Solid Solution Series Tl(V1-xCrx)5Se8: Crystal Structure, Magnetic and Thermoelectric Properties[END_REF] This is the case for instance of the chromium chalcogenide compounds TlxCr5Se8 [START_REF] Takahashi | Transport Properties of an Intermetallic with Pseudo-Hollandite Structure as a Potential Thermoelectric Material: The Example of TlxCr5Se8[END_REF] and Ba0.5Cr5Se8, [START_REF] Lefèvre | Polar Transition-Metal Chalcogenide: Structure and Properties of the New Pseudo-Hollandite Ba0.5Cr5Se8[END_REF] which exhibit remarkably low thermal conductivities of 0.7 W.m -1 .K -1 and 0.8 W.m -1 .K -1 at 300 K, respectively.

Motivated by these findings, we have conducted a complete study on related compounds possessing similar structural features, with the aim of exploring their potential in thermoelectric applications.

The two aforementioned compounds belong to the family of hollandite derivatives materials, characterized by the general formula AM5X8 (A = Li-Cs, Sr, Ba, Cd, In, Tl, Sn, and Pb; M = Sc, Ti, V, Cr; and X = S, Se, Te). The structure of these compounds is somewhat related to that of the hollandite mineral oxide BaMn8O16. First described by Byström and Byström, [START_REF] Byström | The Crystal Structure of Hollandite, the Related Manganese Oxide Minerals, and α-MnO2[END_REF] the hollandite structure consists of interconnected chains of MnO6 octahedra, where the chains share corners, forming a quasi-one-dimensional framework. This arrangement gives rise to two distinct channels along the same axis direction. Barium cations, sitting in the largest channels, counterbalance the charge of the anionic framework and stabilize the structure (Figure 1a). octahedra corresponding to equivalent Cr1, Cr2 and Cr3 chromium atoms are depicted in blue, red and green, respectively. The same color scheme is used for all hollandite and hollandite derivatives structures to emphasize their related structural features. The size of the chalcogenide atoms is reduced for clarity.

Pseudo-hollandite compounds, such as TlCr5Se8, [START_REF] Klepp | Channel Structures Based on Octahedral Frameworks: The Crystal Structure of TlTi5Se8, TlV5Se8, and TlCr5Se8 and Its Relationships to TlCr3S5, Hollandites, and Psilomelane[END_REF] derive from this parent hollandite mineral.

Their structure involves the stacking of two dimensional CdI2-like layers, where MX6 octahedra share edges. These layers are interconnected by double chains of edge-and face-sharing MX6 octahedra. The resulting framework forms large infinite channels along the monoclinic b-axis, with the cation A located at the center. Consequently, the small channels formed by the empty octahedral sites at the intersection of the double chains are absent in the pseudo-hollandite structure. These voids are filled with MX6 octahedra, forming a continuous two-dimensional layer. This feature explains the stoichiometry difference between hollandite and pseudo-hollandite compounds. Furthermore, the filled octahedral sites involve face-sharing octahedra at the junction between the CdI2-type layers and define the mode of connection between each layer in these hollandite derivatives (Figure 1b).

Boucher et al. demonstrated by investigating Rb0.73Cr5Te8 the existence of another structural type referred to as "hollandite-like", which also originates from the parent hollandite. [START_REF] Boucher | Synthesis and Crystal Structure of the Pseudo-Hollandite Rb0.62Cr5Te8 and Analysis of the Electronic Band Structures of the RbxCr5Te8 Phases[END_REF] This structure is still built up from 2D layers of CrTe6 edge-sharing octahedra interconnected by pillaring double chains of face-and edge-sharing CrTe6 octahedra, resulting in the same chemical formula as pseudo-hollandites. However, the way in which the two-dimensional layers interconnect differs. The "hollandite-like" structure can be described as a hollandite structure with a CrTe6 octahedra occupying the octahedral voids present at the intersection of the double chains (Figure 1c). Yamazaki and Ueda 32 confirmed the existence of this second structural 'hollandite-like' arrangement and proposed the designations "A-type" for pseudo-hollandite compounds and "B-type" for the "hollandite-like" structures. This nomenclature is adopted in our study.

It is worth noting that among the extensive range of hollandite derivative compounds reported to date, only Rbx-and Csx-inserted chromium tellurides (x > 0.73) adopt the 'hollandite-like' Btype structure, while all others crystallize in the 'pseudo-hollandite' A-type structure. Furthermore, deviations from stoichiometry are commonly observed in most of the hollandite derivatives, regardless of the A or B structure type. [START_REF] Takahashi | Transport Properties of an Intermetallic with Pseudo-Hollandite Structure as a Potential Thermoelectric Material: The Example of TlxCr5Se8[END_REF][START_REF] Lefèvre | Polar Transition-Metal Chalcogenide: Structure and Properties of the New Pseudo-Hollandite Ba0.5Cr5Se8[END_REF][START_REF] Lefèvre | Magnetic and Thermoelectric Properties of the Ternary Pseudo-Hollandite BaxCr5Se8 (0.5 < x < 0.55) Solid Solution[END_REF][START_REF] Schramm | Nonstoichiometric Channel Chalcogenides TlxV5S8: Topotactic Redox Reactions and NMR Studies[END_REF][START_REF] Quint | On the Crystal Chemistry of Hollandite-like Phases with TlV5S8 Structure: The Crystal Structures of TlxTi5S8, TlxV5S8 and TlCr5S8[END_REF][START_REF] Gareh | Synthesis and Crystal Structure of the New Hollandite-like Channel Phase Rb0.73Cr5Te8[END_REF][START_REF] Boucher | Synthesis and Crystal Structure of the Pseudo-Hollandite Rb0.62Cr5Te8 and Analysis of the Electronic Band Structures of the RbxCr5Te8 Phases[END_REF][START_REF] Bensch | Evidences for the Formation of Chromium in the Unusual Oxidation State Cr(IV): I. Chemical Reactivity, Microhomogeneity, and Crystal Structures of the Nonstoichiometric Channel Compounds TlxCr5Se8 (0 ≤ x ≤ 1)[END_REF][START_REF] Saßmannshausen | Thermal Motion of the Univalent Metal Ions in KCr5S8-Type Chalcogenides, Ternary Chromium Selenides MxCr5Se8 (M = Rb, Cs)[END_REF][START_REF] Petricek | A Study of the Cation Order in Hollandite-like MxT5S8 Phases[END_REF][START_REF] Waki | Physical Properties of Ba1.09V8O16 with Hollandite Structure[END_REF][START_REF] Maignan | Metal to Insulator Transition in the n-Type Hollandite Vanadate Pb1.6V8O16[END_REF][START_REF] Bronsema | One-, Two-, and Three-Dimensional Order in and Four-Dimensional Description of KxV5S8 (0.5 ≦ x ≦ 0.7)[END_REF] In the case of chromium tellurides, the amount of A cations inside the channels influences the observed structural type and the determination of the tipping stoichiometry for the formation of one or the other structure type proves to be challenging. For instance, Rb0.62Cr5Te8 crystallizes in the A-type structure whereas Rb0.73Cr5Te8 adopts the B-type structure. Conversely, the non-stoichiometric chromium selenides Rb0.75Cr5Se8 and Cs0.76Cr5Se8 were reported to crystallize in the A-type structure. [START_REF] Saßmannshausen | Thermal Motion of the Univalent Metal Ions in KCr5S8-Type Chalcogenides, Ternary Chromium Selenides MxCr5Se8 (M = Rb, Cs)[END_REF] This suggests that the B structural type is favored by (i) extended channels formed by large anions such as tellurium and (ii) large size cations such as Rb and Cs. Consistently, Yamazaki and Ueda 32 stated that the larger the amount of Rb, the more favored the B-type structure. However, no detailed structural determination was performed concerning the Cs-inserted chromium tellurides, nor the influence of the stoichiometric deviation on the structural features of these compounds. In this study, we report for the first time a complete crystal structure determination of a range of CsxCr5Te8 compounds (x = 0.73; 0.91; 0.97) synthesized as single crystals by two different routes.

The impact of non-stoichiometry on the structural features is explored and compared through electronic structure calculations and crystal structure determination, enabling a discussion on the structural stability of specific compositions. Subsequently, the transport properties of these compounds are assessed and compared with those of other compounds.

EXPERIMENTAL SECTION

Synthesis and Preparation. Single crystals of CsxCr5Te8 with different compositions were grown using the self-flux method in fused silica tubes. The series of compounds was synthesized using two different routes. On the one hand, Cs0.73Cr5Te8 and Cs0.97Cr5Te8 single crystals were obtained by loading the CsCr5Te8 nominal composition from Cs2CO3 (powder, 99.9%), Cr (powder, 99.9%), and Te (shots, 99.999%) reagents under Ar atmosphere in a fused silica tube. After the tubes were flame-sealed under dynamic vacuum, temperature was raised to 500 °C over 8 hours, then to 800 °C over 8 hours and kept constant for 48 hours. Samples were then cooled to 200 °C over 8 days. On the other hand, Cs0.91Cr5Te8 single crystals were grown from a different Cs precursor. CsTe4 was first synthesized in a niobium tube by mixing appropriate amounts of Cs (metal, 99.8%) and Te (shots, 99.999%) within a glovebox. The niobium tube was then sealed under high purity argon within an arc furnace set up and placed inside a fused silica tube which was subsequently flame-sealed under dynamic vacuum. The sample was then heated over 10 hours at 300 °C for 96 hours, and cooled to room temperature over 10 hours. Mixture of CsTe4, Cr (powder, 99.9%), and Te (shots, 99.999%) were loaded in a fused silica tube with the CsCr5Te8 nominal composition and sealed in a similar manner. The temperature was raised to 500 °C over 8 hours and kept constant for 8 hours. After this plateau, temperature was raised again over 8 hours at 800 °C and maintained for 24 hours, before cooling down the sample to 200 °C over a period of 96 hours. Black metallic-like needles were obtained by both synthesis routes.

Bulk samples of CsxCr5Te8 were prepared by mixing Cs2CO3 (powder, 99.9%), Cr (powder, 99.9%), and Te (shots, 99.999%) in a glovebox with appropriate amounts to obtain the Cs0.73Cr5Te8 stoichiometry. The mixture was introduced in a 65-cm 3 stainless steel jar with two balls (Ø 12.6 mm) and underwent a run of 10 hours under argon atmosphere in a vibratory ball milling equipment (SPEX). The obtained powder was subsequently sintered by Spark Plasma Sintering (SPS) at 700 °C and the densified pellet was annealed at 700 °C during 24 hours. The relative density of the densified bulk material was 96 %. Powder X-ray diffraction pattern refinement was carried out by the Le Bail method using the Fullprof Suite, [START_REF] Rodriguez-Carvajal | Fullprof: A Program for Rietveld Refinement and Pattern Matching Analysis[END_REF] yielding Rp = 11.3 %, Rwp = 15.3 % and χ² = 1.81 agreement factors (14 parameters). Thermal conductivity measurements were performed under N2 atmosphere using a Netzsch 467 HyperFlash Laser-Flash Apparatus (LFA) on 10-mm diameter and 1-mm thick sample coated with graphite. Heat capacity was estimated according to the Dulong-Petit law and density was measured by the Archimede method in high purity ethanol. Single Crystal Characterization. Single crystals of appropriate size for X-ray investigation were picked up in air and isolated in silicon oil, before being loaded on the goniometric head of a fourcircle Rigaku XtaLAB Synergy-S diffractometer equipped with a molybdenum radiation source (λMo = 0.71073 Å). The CrysAlis-Pro software [START_REF] Crysalis | Oxford Diffraction[END_REF] was used to analyze the collected data. Threedimensional peak hunting was made before the subsequent data reduction corrected for absorption.

Only reflections with I > 3σ(I) were used for the charge-flipping structure resolution from SUPERFLIP [START_REF] Palatinus | SUPERFLIP -A Computer Program for the Solution of Crystal Structures by Charge Flipping in Arbitrary Dimensions[END_REF] alongside the following refinement performed with Jana2006 software. [START_REF] Petrícek | Crystallographic Computing System JANA2006: General Features[END_REF] All parameters were refined with an instability factor of 0.025. Atomic displacement parameters (ADP) were refined anisotropically. Electronic Structure Calculations. Periodic spin-polarized density functional theory (DFT) calculations were carried out in order to gain insight into the structural and electronic properties of the CsxCr5Te8 phases. Geometry optimizations were first performed on the stoichiometric CsCr5Te8 and non-stoichiometric Cs0.75Cr5Te8 compounds using the Vienna ab initio Simulation (VASP) code, [START_REF] Kresse | Ab Initio Molecular Dynamics for Liquid Metals[END_REF][START_REF] Kresse | Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set[END_REF][START_REF] Kresse | Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set[END_REF] with the Perdew-Burke-Ernzerhof (PBE) functional. [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] VASP-relaxed structures were then used to compute the electronic density of states (DOS) with the WIEN2k code using the full-potential linearized augmented plane wave (FLAPW) approach, [START_REF] Blaha | 2k: An APW+lo Program for Calculating the Properties of Solids[END_REF] employing the modified Becke-Johnson (mBJ) exchange-correlation potential. [START_REF] Tran | Accurate Band Gaps of Semiconductors and Insulators with a Semilocal Exchange-Correlation Potential[END_REF]

RESULTS AND DISCUSSION

CsxCr5Te8 (x = 0.73, 0.91, 0.97) Structures. All CsxCr5Te8 compounds (x = 0.73, 0.91, 0.97) were found to adopt the hollandite-like B-type structure with the space group C2/m (Figure 1c). Initially, the structures were solved by structure visualization, assuming a stoichiometric composition of CsCr5Te8 based on the nominal composition. However, akin to the structure resolution of Rb0.73Cr5Te8 conducted by Gareh et al., [START_REF] Gareh | Synthesis and Crystal Structure of the New Hollandite-like Channel Phase Rb0.73Cr5Te8[END_REF] Fourier difference maps revealed large electronic residues on the Cs 2a site, accompanied by high atomic displacement parameters. These observations suggested a possible deviation from stoichiometry, similar to RbxCr5Te8 compounds (x = 0.5, 0.62, and 0.73). [START_REF] Yamazaki | New Ferromagnetic Chromium Chalcogenides, ACr5Te8 (A = K, Cs and Rb)[END_REF][START_REF] Gareh | Synthesis and Crystal Structure of the New Hollandite-like Channel Phase Rb0.73Cr5Te8[END_REF][START_REF] Boucher | Synthesis and Crystal Structure of the Pseudo-Hollandite Rb0.62Cr5Te8 and Analysis of the Electronic Band Structures of the RbxCr5Te8 Phases[END_REF] Subsequent refinement of the Cs site occupancy significantly reduced the electronic residues and improved the reliability factors for all crystals. Detailed crystallographic data collected for Cs0.73Cr5Te8, Cs0.91Cr5Te8 and Cs0.97Cr5Te8 are given in Table 1. Pertinent interatomic distances of the investigated compounds are displayed and compared to those of Rb0.73Cr5Te8 (B-type structure) in Table 2. The refined coordinates and atomic displacement parameters (ADPs) of the three compounds, along with their estimated standard deviation (esd), are available in the Supporting Information (Tables 3, 4 and 5, respectively). The B-type structural feature found for this range of composition CsxCr5Te8 (x = 0.73, 0.91, 0.97) is consistent with the results of Yamazaki and Ueda 32 which state from powder X-ray diffraction analysis a B-type structure for Cs-inserted chromium telluride hollandite derivatives. The cells parameters of all compounds, except β, show a linear-like evolution with the increase of the b axis and a decrease of the a and c axes upon an increasing amount of Cs (Figure 2). This supports the existence of a solid solution ranging from the Cs0. The atomic displacement parameters (ADPs) of the investigated compounds show notable characteristics. Indeed, the anisotropic ADP U22 along the b axis is significantly larger in Cs0.73Cr5Te8 compared to the higher Cs-filled chromium tellurides (0.0853(5), 0.0347(5), 0.0246(2) Å 2 for x = 0.73, 0.91, and 0.97, respectively). This observation clearly indicates a high degree of disorder in the Cs distribution within the channels of the non-stoichiometric Cs0.73Cr5Te8 compound. In contrast, the channel axis-oriented Cs ADP U22 rapidly decreases for Cs0.91Cr5Te8

and becomes similar to other directional ADPs in Cs0.97Cr5Te8, suggesting an isotropic ADP and reduced cationic disorder for the nearly fully occupied CsxCr5Te8 compound. These findings are consistent with the highly anisotropic ADP observed for the inserted cations in other nonstoichiometric hollandite derivatives, [START_REF] Quint | On the Crystal Chemistry of Hollandite-like Phases with TlV5S8 Structure: The Crystal Structures of TlxTi5S8, TlxV5S8 and TlCr5S8[END_REF][START_REF] Saßmannshausen | Thermal Motion of the Univalent Metal Ions in KCr5S8-Type Chalcogenides, Ternary Chromium Selenides MxCr5Se8 (M = Rb, Cs)[END_REF][START_REF] Petricek | A Study of the Cation Order in Hollandite-like MxT5S8 Phases[END_REF] including the B-type Rb0.73Cr5Te8. 34

Stability of the B Structural Type.

A noteworthy feature of the B-type structure, adopted by all investigated CsxCr5Te8 compositions, is the interaction between Cr atoms from the octahedra situated at the intersection between the layers and the pillaring double chain of octahedra (Figure 3). As previously mentioned, the distinction between the A-and B-types is the configuration of the face-sharing bridging double chain of octahedra between the CrTe2 sheets positioned in the ab plane. In the A-type structure exemplified by Rb0.62Cr5Te8, the junction consists of two distinct face-sharing octahedra (depicted in red in Following the discussion of Boucher, Gareh and co-workers, [START_REF] Gareh | Synthesis and Crystal Structure of the New Hollandite-like Channel Phase Rb0.73Cr5Te8[END_REF][START_REF] Boucher | Synthesis and Crystal Structure of the Pseudo-Hollandite Rb0.62Cr5Te8 and Analysis of the Electronic Band Structures of the RbxCr5Te8 Phases[END_REF] the weakly antibonding nature of the Cr-Cr interactions must explain the slight off-centering of the chromium atoms within their respective octahedra, as they somewhat repel each other. In the case of the A-type structure, the octahedra junction arrangement does not impose significant geometric restrictions on the chromium atoms, allowing them to have more freedom to repulse each other. However, this is not the case in the B-type structure, where the octahedron formed by Cr1 shares two faces with upper and lower pillaring octahedra, thereby restricting the freedom of Cr1 despite the antibonding nature of its interaction with both the upper and lower Cr3 atoms. This crucial observation helps to elucidate why the B-type hollandite-like structure is not as commonly stabilized compared to the much more frequently encountered A-type pseudo-hollandites.

In the case of CsxCr5Te8 compounds reported in this work, the Cr-Cr distances are all longer than in Rb0.73Cr5Te8. In particular, the Cr-Cr distance reaches 3.1037(3) Å in Cs0.73Cr5Te8 to be compared to the somewhat shorter one (3.069(2) Å) in Rb0.73Cr5Te8. It appears that this Cr-Cr distance decreases with increasing Cs content, with values of 3.101(2) Å and 3.0925(6) Å for Cs0.91Cr5Te8 and Cs0.97Cr5Te8, respectively. As the Cr-Cr interaction is overall weakly antibonding, the longer the Cr-Cr distance, the more stable the compound is expected to be. Hence, Cs0.73Cr5Te8 should be more stable than higher Cs-filled chromium tellurides.

Periodic density functional theory (DFT) calculations were carried out on stoichiometric CsCr5Te8 and non-stoichiometric Cs0.75Cr5Te8 compounds in order to elucidate their electronic and conducting properties. The computed total and Cs and Cr atom-projected spin-polarized electronic DOS are sketched in that the optimal preparative conditions for Cs0.73Cr5Te8 and CsCr5Te8 are highly similar, rendering difficult the control of the stoichiometry. Low-intensity reflections could be attributed to an unfilled Cr5Te8 impurity (space group P3 " m). However, since Cr5Te8 exhibits metallic behavior, [START_REF] Fu | Redetermination the Basic Cell Trigonal Cr5Te8 Single Crystal Structure and Its Temperature Dependence Raman Spectra[END_REF] as expected for CsxCr5Te8 as well, the presence of this impurity in the bulk is not believed to have a significant impact on the transport properties. It should be noted that the densified specimen showed sensitivity to oxidation and humidity, resulting in its degradation after a few days under ambient conditions. Nevertheless, thermal conductivity measurements were successfully performed on the sample before degradation occurred. hollandite compounds: TlV5Se8 (green), 18 Ba0.5Cr5Se8 (blue), 16 TlCr5Se8 (red) [START_REF] Takahashi | Transport Properties of an Intermetallic with Pseudo-Hollandite Structure as a Potential Thermoelectric Material: The Example of TlxCr5Se8[END_REF] and TlIn5Se8 (purple). [START_REF] Lefèvre | Ultra-Low Thermal Conductivity of Tl0.98In5Se8 and Structure of the New Complex Chalcogenide Tl0[END_REF] Assuming an approximate lattice thermal conductivity of 0.8 W.m -1 .K -1 for chromium hollandite derivatives of this kind, [START_REF] Lefèvre | Polar Transition-Metal Chalcogenide: Structure and Properties of the New Pseudo-Hollandite Ba0.5Cr5Se8[END_REF] the expected resistivity for CsxCr5Te8 using the Wiedemann-Franz law and the standard Lorenz factor for metals (L0 = 2.44•10 -8 J 2 .K -2 .C -2 ) would be around ρ = 1.2 mΩ.cm at 300 K. This resistivity value is comparable to the reported value of ρ = 0.45 mΩ.cm measured for highly conductive TlV5Se8 at the same temperature. [START_REF] Maier | The Solid Solution Series Tl(V1-xCrx)5Se8: Crystal Structure, Magnetic and Thermoelectric Properties[END_REF] It is worth mentioning, however, that Yamazaki and Ueda reported a value of ρ ~ 1•10² mΩ.cm for ACr5Te8 (A = K, Rb, Cs) at 300 K. [START_REF] Yamazaki | New Ferromagnetic Chromium Chalcogenides, ACr5Te8 (A = K, Cs and Rb)[END_REF] Furthermore, considering that the lattice thermal conductivity is expected to slightly decrease with temperature, the increase observed for the total thermal conductivity suggests a significant rise in the electronic contribution upon increasing temperature. Assuming a rise in resistivity with temperature, which is consistent with a metallic conductive behavior, this observation suggests a dominant temperature-dependent electronic thermal conductivity contribution over that of resistivity, resulting in a gradual increase in resistivity with temperature.

However, that eventuality must be confirmed through direct resistivity measurements.

The title compounds show a substantial sensitivity to oxidation and moisture, degrading after a few days under ambient conditions. Therefore, it did not allow us to measure the resistivity and Seebeck coefficient. The latter is expected to be quite low, similar to TlV5Se8, given the metallic character of these compounds.

CONCLUSION

The synthesis of single crystals of Cs-filled chromium tellurides revealed the existence of a solid solution within the CsxCr5Te8 composition range (x = 0.73, 0.91 and 0.97). All compositions were found to crystallize in the hollandite-like B-type structural form. A detailed crystallographic investigation showed unambiguously that the presence of Cs atoms inside the channels helps in stabilizing the B-type structure. Density functional theory calculations performed on Cs0.75Cr5Te8 indicated that the non-stoichiometric ACr5Te8 compounds (A = Rb, Cs) should be metallic in character with hardly any participation of the alkaline element around the Fermi level. A substantial electronic thermal conductivity can then be expected. As a result, due to an enhanced participation of charge carriers in the thermal transport mechanism, the presence of Cs cations within the channels does not result in a reduction of thermal conductivity compared to that of other A-type hollandite derivative compounds.

Figure 1 .

 1 Figure 1. Structural representations of a) hollandite mineral, 43 b) pseudo-hollandite Rb0.62Cr5Te8 (A-type,

  73Cr5Te8 composition -identical to that observed for the B-type Rb0.73Cr5Te8 -to the almost completely filled Cs0.97Cr5Te8 composition. The decrease of a and c cell parameters with the Cs amount is caused by a slight distortion of the CrTe6 octahedra in the vicinity of the Cs inserted cations, contracting the cell along these axis directions. This is illustrated by the increased distances between Cs and Te atoms as well as Te-Te distances in the channels (Te3 and Te4) (Table2). On the other hand, the increase of b stems from the increase of the Cs-Cs distances upon Cs insertion inside the channels and gives rise to an increased cell volume overall. Between compositions x = 0.73 and x = 0.91, the cell volume experiences a 0.66% increase. While the cell volumes of the highly Cs-filled compositions (x = 0.91 and x = 0.97) are closely similar (753.70(16) and 752.74(12) Å 3 , respectively), the slight decrease observed with increasing Cs content can be attributed to a further contraction of the unit cell along the a and c axes.

Figure 2 .

 2 Figure 2. Evolution of cell parameters of the series of compounds CsxCr5Te8 (x = 0.73, 0.91, and 0.97)

Figure 3 )

 3 originating from the CrTe2 layer, resulting in two Cr2-Cr3 pairs of Cr-Cr interactions. Conversely, in the B-type structure, only one octahedron (represented in blue in Figure 3) is involved in the face-sharing octahedra junction with the upper and lower pillaring double chains. As a consequence, a linear three-atom chain Cr3-Cr1-Cr3 is formed in this structure type, with shorter Cr-Cr distances compared to the A-type structure. For instance, Cr-Cr distances in A-type Rb0.62Cr5Te8 are somewhat longer than in B-type Rb0.73Cr5Te8: 3.161(2) Å and 3.069(2) Å, respectively. As the preparative conditions were invoked to synthesize either A-or B-type Rb-inserted RbxCr5Te8, 34 no occurrence of any A-type CsxCr5Te8 compound was found in our work, regardless of the synthesis routes.

Figure 3 .

 3 Figure 3. Description of the Cr-Cr interactions within the frameworks of Rb0.62Cr5Te8 (A-type) 35 and

Figure 4 .

 4 As discussed before for the RbxCr5Te8 phases,[START_REF] Boucher | Synthesis and Crystal Structure of the Pseudo-Hollandite Rb0.62Cr5Te8 and Analysis of the Electronic Band Structures of the RbxCr5Te8 Phases[END_REF] spin-up and spin-down total and atom projected DOS strongly differ, suggesting magnetic properties which, unfortunately, have never been confirmed experimentally up to now. Interestingly, a favorable semiconducting behavior is computed for the stoichiometric CsCr5Te8 (Cs + [Cr5Te8] -) composition -this is almost reached for CsxCr5Te8 with x = 0.97 -with a strong participation of the Cr atoms and hardly any participation of the Cs cations. However, Boucher et al. have shown that for the RbxCr5Te8 phases,[START_REF] Boucher | Synthesis and Crystal Structure of the Pseudo-Hollandite Rb0.62Cr5Te8 and Analysis of the Electronic Band Structures of the RbxCr5Te8 Phases[END_REF] Rb vacancies were expected to lower the Fermi level and to depopulate Cr-Cr non-bonding and antibonding states, favoring the structural stability of nonstoichiometric RbxCr5Te8 phases. The same situation occurs here for the non-stoichiometric CsxCr5Te8 compounds, i.e., partial depopulation of antibonding Cr-Cr states which enable to somewhat stabilize the structure. As a consequence, the compounds are expected to show metallic properties with the Fermi level positioned in a substantial peak of DOS. It is interesting to mention that the interactions between chromium atoms appear to be crucial for the stabilization of B-type hollandite-like, as neither the stoichiometric RbSc5Te8, 41 CsSc5Te8 58 nor CsTi5Te8 40 compounds have been reported to crystallize in this structural form.

Figure 4 .

 4 Figure 4. Spin-polarized total and atom-projected density of states of CsCr5Te8 (left) and Cs0.75Cr5Te8

Figure 5 . 6 .

 56 Figure 5. Le Bail refinement of the X-ray diffraction pattern of a densified and annealed CsxCr5Te8 sample.Low intensity additional reflections were attributed to a Cr5Te8 (space group P3 " m) phase.

Figure 6 .

 6 Figure 6. Thermal conductivity of B-type CsxCr5Te8 bulk material (black) and other A-type pseudo-

Table 1 . Crystallographic Data of CsxCr5Te8 Compounds (x = 0.73, 0.91, and 0.97)

 1

	Formula	Cs0.73(1)Cr5Te8	Cs0.91(1)Cr5Te8	Cs0.97(1)Cr5Te8
	Structural type	B	B	B

Table 2 . Interatomic Distances of CsxCr5Te8 (x = 0.73, 0.91 and 0.97) and comparison with isostructural Rb0.73Cr5Te8. 34

 2

		Rb0.73Cr5Te8 34	Cs0.73Cr5Te8	Cs0.91Cr5Te8	Cs0.97Cr5Te8
	CrTe2 layer (ab plane)	Cr1-Te1	2.724(1) x 2	Cr1-Te1	2.7349(2) x 2	Cr1-Te1	2.7260(7) x 2	Cr1-Te1	2.7272(4) x 2
		Cr1-Te2	2.766(1) x 4	Cr1-Te2	2.7683(1) x 4	Cr1-Te2	2.7829(6) x 4	Cr1-Te2	2.7801(3) x 4
		Cr2-Te1	2.726(2) x 2	Cr2-Te1	2.7289(1) x 2	Cr2-Te1	2.733(2) x 2	Cr2-Te1	2.7306(5) x 2
		Cr2-Te2	2.752(2)	Cr2-Te2 2.7568(2) Cr2-Te2	2.759(2)	Cr2-Te2 2.7572(7)
		Cr2-Te3	2.709(2) x 3	Cr2-Te3	2.7070(1) x 2	Cr2-Te3	2.709(2) x 2	Cr2-Te3	2.7093(5) x 2
				Cr2-Te3 2.7094(2) Cr2-Te3	2.710(2)	Cr2-Te3 2.7088(6)
	Bridging
	Cr-Te	Cr3-Te1	2.730(3)	Cr3-Te1 2.7474(1) Cr3-Te1	2.746(2)	Cr3-Te1 2.7456(9)
	octahedra
		Cr3-Te2	2.775(1) x 2	Cr3-Te2	2.7777(1) x 2	Cr3-Te2	2.7853(7) x 2	Cr3-Te2	2.7795(4) x 2
		Cr3-Te4	2.695(3)	Cr3-Te4 2.7017(1) Cr3-Te4	2.699 (2)	Cr3-Te4 2.702 (1)
		Cr3-Te4	2.715(2) x 2	Cr3-Te4	2.7133(1) x 2	Cr3-Te4	2.7198(7) x 2	Cr3-Te4	2.7198(3) x 2

ACKNOWLEDGMENTS

The authors are grateful to the Agence Nationale de la Recherche (ANR -Project HIGHTHERM -Ref ANR-18-CE05-0037) and the Japan Society for the Promotion of Science (JSPS -PE21708) for financial support. Support from JST Mirai Program JPMJMI19A1 is also acknowledged.

Notes

The authors declare no competing financial interest.

AUTHOR INFORMATION Corresponding Authors

Jean-François Halet -orcid.org/0000-0002-2315-4200; Email: jean-francois.halet@univ-rennes1.fr David Berthebaud -orcid.org/0000-0002-2892-2125; Email: david.berthebaud@cnrs.fr

Authors

Hugo Bouteiller -orcid.org/0009-0004-2132-2962; Email: hugo.bouteiller@univ-poitiers.fr Bruno Fontaine -Email: bruno.fontaine@ensc-rennes.fr Takao Mori -orcid.org/0000-0003-2682-1846; Email: mori.takao@nims.go.jp Franck Gascoin -orcid.org/0000-0002-9791-1358; Email: franck.gascoin@ensicaen.fr

Author Contributions

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


Volodymyr Babizhetskyy
email: volodymyr.babizhetskyy@lnu.edu.ua

Reinhard K Kremer

Régis Jardin

Régis Gautier

Bruno Fontaine
email: bruno.fontaine@ensc-rennes.fr

Jean-François Halet

Boron-induced phase transformation of ternary cerium boron silicides

Keywords: Crystal structure, Density functional calculations, Electronic structure, Magnetism, Rare-earth metal silicide boride, Silicide boride

Samples of the alloys CeSi2-хBх (x = 0, 0.1, 0.2, 0.4, and 0.5) were prepared and their crystal structures, electrical and magnetic properties were determined. Depending on the amount of boron, x, the phases CeSi2-хBх crystallize in the α-ThSi2 structure type (x = 0, 0.1), or in the α-GdSi2 structure type (x = 0.2, 0.4). Interestingly, as determined by means of X-ray single crystal diffraction crystallizes, CeSi1.5B0.5 crystallizes in the AlB2 structure type (space group P6/mmm, a = 3.9922(2), c = 4.3053(4) Å, 191 reflections with Io ≥ 2σ(Io), R1 = 0.019, wR2 = 0.042).

Measurements of the electrical and magnetic properties indicate that phases CeSi2-xBx (x = 0, 0.1, 0.2, 0.4, 0.5) are metallic in character and that phases with B substitution x ³ 0.2 exhibit correlated magnetic behavior, typically below ~15 K. Density functional theory calculations were performed to elucidate the change of electronic and physical properties upon boron substitution.

Introduction

A first systematic study of the ternary phase diagrams of the RE-Si-B (RE = Y, La, Ce, Er) phases was reported by Kuz'ma and co-workers some time ago [START_REF] Kuz'ma | Binary and Ternary Systems Containing Boron[END_REF][START_REF] Chaban | Phase equilibria in the Er-Si-B system[END_REF][START_REF] Chaban | Kuz'ma, X-ray Diffraction Study of the RMB (R= Y, La, Ce; M= Al, Si) Systems[END_REF]. At that time, the existence of ternary phases was not evidenced, with the exception of narrow homogeneity ranges of some specific binary compositions. More recently, in the progress of our ongoing investigation of structural and physical properties of ternary RE-Si-B phases (RE = rare earth metals), different preparation techniques were explored (sealed silica tubes, arc melting, high frequency furnace, and tin flux synthesis), resulting in the synthesis and characterization of several new binary and ternary rare-earth metal boron silicides [START_REF] Jardin | Crystal structure of the rare earth borosilicide Er8Si17B3[END_REF][START_REF] Babizhetskyy | Rare-earth metal borosilicides R9Si15-xB3 (R = Tb, Yb): new ordered structures derived from the AlB2 structure type[END_REF][START_REF] Babizhetskyy | Flux synthesis, crystal structure and electronic properties of the layered rare earth metal boride silicide Er3Si5-xB. An example of a boron/silicon-ordered structure derived from the AlB2 structure type[END_REF]. For example, using arc melting techniques on the isothermal sections of the ternary systems RE-Si-B (RE = Y, Nd, Gd, Dy, Ho, Er) at 1270 K [START_REF] Roger | The ternary RE-Si-B systems (RE = Dy, Ho, Er and Y) at 1270 K: Solid state phase equilibria and magnetic properties of the solid solution REB2-xSix (RE = Dy and Ho)[END_REF][START_REF] Roger | Solid state phase equilibria in the ternary Nd-Si-B system at 1270 K[END_REF][START_REF] Babizhetskyy | Solid state phase equilibria in the Gd-Si-B system at 1270 K[END_REF] we found that, except for Nd, a few new ternary phases could be synthesized, namely the stoichiometric compound RE5Si2B8 (Gd5Si2B8 structure type) [START_REF] Babizhetskyy | Gd5Si2B8: A Ternary Rare-Earth-Metal Silicide Boride Compound[END_REF][START_REF] Roger | Crystal structures, physical properties and NMR experiments on the ternary rare-earth metal silicide boride compounds RE5Si2B8 (RE=Y[END_REF], the boron-inserted 'Nowotny phase' RE5Si3Bx (Mn5Si3-type structure) [START_REF] Roger | Mn5Si3-type host-interstitial boron rare-earth metal silicide compounds RE5Si3: Crystal structures, physical properties and theoretical considerations[END_REF], and the solid solution REB2-xSix (AlB2type structure) [START_REF] Kuz'ma | Binary and Ternary Systems Containing Boron[END_REF]. For the Nd-Si-B system, only Nd5Si3Bx (Mn5Si3-type structure) could be ascertained [START_REF] Roger | Solid state phase equilibria in the ternary Nd-Si-B system at 1270 K[END_REF]. Using flux techniques [START_REF] Kanatzidis | The metal flux: a preparative tool for the exploration of intermetallic compounds[END_REF] with tin as the metal flux a novel series of binary silicides of composition RESi1.7 (RE = Dy, Ho) [START_REF] Roger | Tin flux synthesis of rare-earth metal silicide compounds RESi1.7 (RE = Dy, Ho): a novel ordered structure derived from the AlB2 type[END_REF] were obtained, as well as new layered ternary boride silicides in the silicon-rich part of the RE-Si-B phase diagram, namely RE8Si17B3 (RE = Ho, Er) [START_REF] Kuz'ma | Binary and Ternary Systems Containing Boron[END_REF], RE9Si15-xB3 (RE = Tb, Yb) [START_REF] Chaban | Phase equilibria in the Er-Si-B system[END_REF] and Er3Si5-xB (x = 1.17) [START_REF] Hofmann | Der Strukturtyp von Aluminiumborid (AlB2)[END_REF]. It turned out that the insertion of boron atoms into the silicon slabs in these new ternary structures generates ordered commensurate arrangements in the c direction, which can be derived from the AlB2 structure type [START_REF] Hofmann | Der Strukturtyp von Aluminiumborid (AlB2)[END_REF].

In 2002, Bulanova et al. investigated and constructed the phase diagram of the Ce-Si binary system [START_REF] Bulanova | Cerium-silicon system[END_REF]. In the region of ~66 at. % Si they identified two cerium disilicides namely CeSi2-a1 (0.43 > a1 > 0.3) crystallizing with the α-GdSi2 structure type (space group (SG) Imma) and CeSi2-a2 (0.3 > a2 > 0) crystallizing with the α-ThSi2 structure type (SG I41/amd)). According to these authors, the phases with the α-GdSi2 and the α-ThSi2 structures seem to correspond to individual compounds rather than polymorphous modifications of the same compound CeSi2-a. This statement was made on the basis of the absence of thermal effects in the range CeSi + CeSi2-a1 at temperatures lower than the solidus, and also by analogy with the La-Si and Pr-Si systems [START_REF] Bulanova | Cerium-silicon system[END_REF]. The boundaries of the two-phase field CeSi2-a1 and CeSi2-a2 are located between 62.6 and 64.1 at % Si and they shift towards Si-poorer compositions when the temperature decreases. CeSi2-a1 in the α-GdSi2 structure type exists between 62 and 65 at. % Si whereas CeSi2-a2 (α-ThSi2 structure type) covers the range between 65.0 and 66.7 at. % Si [START_REF] Bulanova | Phase diagram and the phases thermodynamics in binary systems of rare earths and silicon[END_REF]. Later, an incommensurately modulated structure of CeSi2-x (x = 1.82) with reduced monoclinic symmetry was reported by Leisegang et al. [START_REF] Leisegang | [END_REF]. Modulated crystals and crystals without satellite reflections were found simultaneously in the same macroscopic sample showing composition changes of about 4 % (1.87 < x < 1.91) [START_REF] Leisegang | [END_REF].

It turns out that the compounds CeSi2-a1 and CeSi2-a2 or more generally CeSi2-x, exhibit a strong variation of physical properties when changing the composition from a1 to a2 (x). Long range ferromagnetic ordering of the Ce atoms due to a Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction was observed at temperatures Tm ≈ 12 to 1 K and for compositions with x varying from 0.40 to 0.18. For values x = 0.40 to 0.18, Kondo behavior (Kondo temperature TK = 2 -22 K) leads to the absence of magnetic ordering. These properties arise from an exchange interaction between the conduction electrons and the Ce 4f electrons [START_REF] Shaheen | Ferromagnetism of CeSix at ambient and high pressure[END_REF][START_REF] Lee | Competition between the Kondo effect and exchange interactions in the system CeSix[END_REF][START_REF] Pierre | Anisotropy of the magnetic and electrical properties of CeSix[END_REF][START_REF] Yashima | Nonmagnetic-magnetic transition in Ce-Si system[END_REF][START_REF] Yashima | Ferromagnetic dense Kondo behaviour of Ce-Si system[END_REF].

Due to the wide homogeneity region of x = 0 -0.4, CeSi2-x is indeed an interesting system to study in order to elucidate the influence of the non-magnetic Si deficiency on the structural and physical properties. Additionally, we may wonder if insertion of a third element such as boron, for example, would also modify the structural arrangement and consequently alter in some ways the physical properties.

Here we report on a detailed investigation of structural, electrical and magnetic properties of samples with composition CeSi2-хBх (x = 0, 0.1, 0.2, 0.4, and 0.5) prepared by arc melting techniques. In particular, the novel ternary boride silicide CeSi1.5B0.5 was synthesized and characterized. The structure determination from single-crystal X-ray diffraction data indicates that CeSi1.5B0.5 adopts the AlB2 type structure [START_REF] Hofmann | Der Strukturtyp von Aluminiumborid (AlB2)[END_REF][START_REF] Burkhardt | On the electronic and structural properties of aluminum diboride Al0.9B2[END_REF] with a mixed Si/B site occupation.

Moreover, the presence or absence of inserted boron atoms in CeSi2-хBх is discussed on the basis of difference Fourier syntheses, structural analysis, electrical and magnetic behavior and density functional theory (DFT) calculations.

Experimental section

Synthesis

The samples with compositions CeSi2-хBх (x = 0, 0.1, 0.2, 0.4, and 0.5) were prepared from commercially available elements: Ce-sublimed bulk pieces, 99.99 at. % (Alfa Aesar, Johnson Matthey Company), powders of elemental silicon and boron (Strem Chemicals, purity > 99.99 at. %). Cerium metal was filed to coarse powders with beryllium bronze files (Dönges GmbH, Germany). Mixtures of the components were compacted in stainless steel dies and the resulting pellets of ~1 g were arc-melted under purified argon atmosphere on a water-cooled copper hearth, turned over and re-melted typically three times to improve homogeneity. The samplebuttons were then wrapped in a molybdenum foil enclosed in an evacuated silica tube, annealed at 1070 K for one month, and then the tube was quenched in cold water.

Diffraction and sample characterization

An initial metallographic inspection and complementary qualitative and quantitative phase analysis, energy dispersive X-ray spectroscopy (EDX) was employed. The samples were embedded in Wood's metal (melting point of 75 °C, Fluka Chemie). The embedded samples were polished on a nylon cloth using diamond paste with grain sizes 1-5 μm. Quantitative and qualitative composition analyses of the polished samples were performed by EDX on a TESCAN VEGA 3 LMU scanning electron microscope with an Oxford Instruments Aztec ONE detector X-Max N 20. For the chemical microprobe, the polishing procedure had to be performed or repeated just before the measurements. This method was further used to determine the Ce:Si ratios of the synthetized specimen (standard deviations estimated less than 1 at.%).

Unfortunately, no boron content could be determined by a quantitative microanalysis. The surface of the phases CeSi2-хBх (x = 0, 0.1, 0.2, 0.4, and 0.5) appears to be quite stable in air.

Powder X-ray diffraction (PXRD) patterns of CeSi2-хBх (x = 0, 0.1, 0.2, 0.4, and 0.5) were collected on a STOE STADI P powder diffractometer with monochromated Mo-Ka1 radiation (3° £ 2q £ 60°, step size 0.1°, measurement time per step: 120 s) to check the homogeneity of the samples. The lattice parameters and the atomic positions the PXRD were fitted by a Rietveldtype profile refinement using the WinCSD program package [START_REF] Akselrud | WinCSD (version 4), Software Package for Crystallographic Calculations[END_REF]. The PXRD pattern of the alloy with nominal compositions CeSi2-хBх (x = 0, 0.1, 0.2, 0.4, and 0.5) confirmed the presence of three phases: the α-GdSi2, α-ThSi2 and AlB2 structure types, respectively (details see Table 1).

Table 1

Crystal structure parameters from XRD powder data for CeSi2-хBх (x = 0, 0. Small and irregular platelet-shaped single crystals for single-crystal X-ray investigation were selected from the crushed arc-melted sample with the nominal composition CeSi1.5B0.5. Singlecrystal XRD data of a representative single-crystalline specimen were collected at room temperature on a Bruker D8 Venture diffractometer with monochromated Mo-Kα radiation (l = 0.71073 Å). The raw frames data were integrated using the Bruker APEX3 software package.

The integrated intensities were corrected for absorption effects using the multiscan method (SADABS) [START_REF] Blessing | An empirical correction for absorption anisotropy[END_REF]. The symmetry check of the E statistics indicated centrosymmetry of the crystal structure and an analysis of high versus lower indices Laue classes was performed. The starting atomic parameters were initially derived via direct methods using the program Sir97 [START_REF] Altomare | SIR97: a new tool for crystal structure determination and refinement[END_REF] and subsequently refined with the program SHELXL97 employing the WinGX program package [START_REF] Sheldrick | Shelxt -integrated space-group and crystal-structure determination[END_REF][START_REF] Farrugia | WinGX suite for small-molecule single-crystal crystallography[END_REF] (full-matrix least-squares on F 2 ) allowing anisotropic displacements parameters. The refinement confirmed the CeSi1.5B0.5 composition. All relevant details concerning the data collection are listed in Table 2. The program Diamond was used for the drawing of the crystal structure [START_REF] Brandenburg | Diamond (version 2.1c), Crystal and Molecular Structure Visualization, Crystal Impact[END_REF].

R1(F 2 ) = [(|Fo|-|Fc|)]/|Fo|. b wR2(F 2 ) = [w(Fo 2 -Fc 2 ) 2 /[w(Fo 2 ) 2 ]] 1/2 ; [w -1 = σ 2 (Fo) 2 +(0.0104P) 2 ]
, where P = (Fo 2 +2Fc 2 )/3.

Low temperature physical properties

Temperature and field dependent magnetic measurements were performed on a SQUID MPMS, (Quantum Design, San Diego, CA) magnetometer (from 2 K to room temperature) applying static magnetic fields up to 6 T. Four-point electrical resistances as a function of temperature were measured with the ac option available in a PPMS device (Quantum Design) using current between 1 and 10 mA and frequencies of 19 Hz and 119 Hz.

Electronic structure calculations

Spin-polarized density functional theory (DFT) calculations were carried out in order to gain insight into the structural and electronic properties of the alloys CeSi2-хBх (x = 0 and 0.5).

Starting from the experimental lattice parameters and atomic positions published in the literature for x = 0 and our data for x = 0.5, the crystal structures were optimized. Full occupation of the Si positions was assumed. The full-potential linearized augmented plane wave (FLAPW) approach, as implemented in the WIEN2K code [START_REF] Schwarz | Electronic structure calculations of solids using the WIEN2k package for material sciences[END_REF][START_REF] Blaha | WIEN2K: An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties[END_REF][START_REF] Blaha | 2k: An APW+lo program for calculating the properties of solids[END_REF] was employed. The Perdew, Burke and Ernzerhof (PBE) functional [START_REF] Perdew | Generalized gradient approximation made simple[END_REF] and a plane wave cut-off corresponding to RMTKmax = 7 were used. The radial wave functions inside the non-overlapping muffin-tin spheres were expanded up to lmax = 12. The charge density was Fourier expanded up to Gmax = 12 Å -1 . The muffin-tin radii were set to 1.94, 2.50, and 1.94 a.u. for B, Ce, and Si atoms, respectively. Total energy convergence was achieved with a Brillouin Zone (BZ) integration mesh of 500 k-points, generating 144 k-points in the irreducible part of the BZ. For a better description of the localized 4f states of the rare-earth element Ce, all electronic densities of states (DOS) were computed using the PBE0 hybrid functional [START_REF] Tran | Hybrid exchange-correlation energy functionals for strongly correlated electrons: applications to transition-metal monoxides[END_REF] and including spin-orbit coupling (SO) [START_REF] Susilo | Magnetic structures of R2Fe2Si2C intermetallic compounds: Evolution to Er2Fe2Si2C and Tm2Fe2Si2C[END_REF], with a magnetization confined along the [001] direction. Electronic density of states (DOS) were plotted considering the Fermi level as the energy reference.

When possible, two approaches were used to probe the thermodynamical stability of CeSi2-хBх (x = 0 and 0.5) in the three structure types (α-GdSi2, α-ThSi2 and AlB2): i) The theoretical phonon spectra were calculated using density functional perturbation theory (DFPT) [START_REF] Gonze | Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory[END_REF] as implemented in the PHONOPY package [START_REF] Gonze | Dynamical matrices, Born effective charges, dielectric permittivity tensors, and interatomic force constants from density-functional perturbation theory[END_REF], and ii) The PBE+U [START_REF] Liechtenstein | Density-functional theory and strong interactions: orbital ordering in Mott-Hubbard insulators[END_REF] energies were used as the fitness function of the evolutionary algorithm USPEX [START_REF] Stokes | FINDSYM: program for identifying the space-group symmetry of a crystal[END_REF]. A fixed-composition calculation was applied for the CeSi2 and CeSi1.5B0.5 phases (12 atoms per unit cell), and up to 1200 and 2000 structural optimizations were performed, respectively. PBE+U calculations were carried out since they are much faster that PBE0 calculations that could not be envisioned for so many structural optimizations. The first-generation structures were created randomly, and a population of 60 was employed in this work. The best 70% of each generation were used to produce the next generation structures by heredity. Global optimizations were performed for at least 15 generations after the minimum energy was found. In any mode, no initial assumption about the crystal structure of the known phases was implied. All phases were calculated with the same Ueff value, which allowed for direct comparison of the calculated enthalpies of formation. The final structural parameters reported were obtained from the FINDSYM algorithm [START_REF] Glass | USPEX -evolutionary crystal structure prediction[END_REF], using a tolerance of 0.10 Å. Thus, periodic DFT calculations were performed on these different structures of these compounds using the VASP code [START_REF] Kresse | Ab initio molecular dynamics for liquid metals[END_REF][START_REF] Kresse | Norm-conserving and ultrasoft pseudopotentials for first row and transition elements[END_REF]. Because of the presence of localized 4f-electrons, an additional Hubbard-like term was introduced for Ce. The simplified Dudarev approach [START_REF] Dudarev | Electron-energy-loss spectra and the structural stability of nickel oxide: an LSDA+U study[END_REF] was employed with Ueff = U -J = 5 eV for the Ce 4f atomic orbitals. The exchange-correlation interaction was described within the generalised gradient approximation in the parametrisation of the PBE functional [START_REF] Tran | Hybrid exchange-correlation energy functionals for strongly correlated electrons: applications to transition-metal monoxides[END_REF]. Projector augmented wave potentials were used for all atoms [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF] and calculations were performed with a cut-off energy of 400 eV. The electronic wave functions were sampled on dense densities in the irreducible BZ using the Monkhorst-Pack method [START_REF] Monkhorst | Special points for Brillouin-zone integrations[END_REF]. Structure relaxations including cell parameters and atomic positions were carried out without any symmetry constraints.

Results and discussion

Structural characterization

The X-ray powder patterns of the boron-containing alloys CeSi2-хBх (x = 0, 0.1, 0.2, 0.4, and 0.5) were indexed on the basis of tetragonal, orthorhombic and hexagonal symmetry of the α-ThSi2, α-GdSi2 and AlB2 type structures, respectively. Partial substitution of Si by B changes the initial structure. In order to check the homogeneity of the sample, Rietveld profile refinements of the X-ray powder patterns were performed using the program WinCSD [START_REF] Akselrud | WinCSD (version 4), Software Package for Crystallographic Calculations[END_REF]. The PXRD patterns collected of CeSi2 and CeSi1.9B0.1 indicated homogeneous phases of α-ThSi2-type structure. For the CeSi1.8B0.2 and CeSi1.6B0.4 compositions, the α-GdSi2-type structure was found, whereas for CeSi1.5B0.5, the AlB2-type structure was observed. The stoichiometric compositions of the binary and Ce/Si ratio for ternary compounds were confirmed by EDX analysis. Crystallographic data for the CeSi2-хBх (x = 0, 0.1, 0.2, 0.4, and 0.5) are given in Table 1. Fig. 1 illustrates the final Rietveld refinement obtained between the calculated and observed patterns of the sample CeSi1.5B0.5 which crystallizes in the AlB2-type of structure. Small traces of CeB4 [START_REF] Babizhetskyy | Single crystal investigation and physical properties of the binary compound CeB4[END_REF] were detected in the alloy CeSi1.5B0.5 by means of EDX and PXRD analysis. A high-quality single crystal could be obtained via mechanical fragmentation of the sample with nominal composition CeSi1.5B0.5. Details of the single crystal X-ray analysis and crystal data are compiled in Table 2. The atomic coordinates and the thermal displacement factors are listed in Table 3.

Table 3

Atomic coordinates and displacement parameters a (in Å 2 ) for CeSi1.5B0.5.

Atom

U23 = U13 = 0.
An attempt to refine the structure with complete occupation of both positions (cerium and silicon) led to R1(iso) = 0.025 in the isotropic and R1(aniso) = 0.023 for the anisotropic approximation of atomic displacement. Despite quite acceptable values of the residual factors, our results indicate large values of the anisotropic displacement parameters for U11 for Si atoms.

A refinement of the site occupancy for the silicon position (SOF(Si)) and subsequent refinement of the atomic displacement parameters led to slightly smaller residual values (R1(iso) = 0.022 and R1(aniso) = 0.019) and an occupation factor SOF(Si) = 0.843(1), but with a more reasonable ratio of Ueq(Ce)/Ueq(Si). Taking this into account, the presence of boron leads to a mixed Si/B occupied position 2d with a Si/B ratio of 75(2)/25 [START_REF] Chaban | Phase equilibria in the Er-Si-B system[END_REF]. Consequently, the refined composition of the investigated phase indicates the formula CeSi1.5B0.5. The corresponding Ce/Si ratio of the latter of 40/60 matches with the nominal composition ratio found by of EDX analysis which is 39.1/60.9.

The lattice parameter a = 3.9922(2) Å reflects the nearest Ce-Ce distances (see Fig. 2). Ce-Si/B distances are found to be 3.154(1) Å. With the covalent radii of silicon (1.17 Å) and boron (0.85 Å) [START_REF] Pyykkö | Molecular single-bond covalent radii for elements 1-118[END_REF], the interatomic distances for Si/B-Si/B (2.3049(1) Å) measured within the hexagon clearly indicates the presence of boron in the structure.

Magnetic and electrical properties

The molar magnetic susceptibilities measured in an external magnetic field of 100 Oe exhibit a hysteresis between the field cooled (fc) and the zero-field cooled (zfc) susceptibility for samples with a B content x > 0.5, typically below ~15 K, indicating correlated magnetic behavior. For the sample CeSi1.8B0.2 (Fig. 3 (c)), the fc susceptibility exhibits the characteristics of a ferromagnet with a Curie temperature of ~14 K. The phases with x = 0 and x = 0.1 (Fig. 3

𝐶 = ! ! " # " $ % " &'' % $% $ ('( Q () ) + 𝜒 * eq. ( 1
)
where NA is the Avogadro constant, µB the Bohr magneton, kB the Boltzmann constant, µeff the effective magnetic moment and QCW the Curie-Weiss temperature, the latter two quantities being fit parameters.

For the temperature independent susceptibility, 𝜒 * , we used the diamagnetic increments of Ce 3+ and Si 4+ listed by Bain and Berry [START_REF] Bain | Diamagnetic Corrections and Pascal's Constants[END_REF]. The Curie-Weiss temperatures (see Table 4) are of the order of ~-100 K. At low temperatures, the inverse susceptibilities gradually bend in and vanish towards lowest temperatures. This temperature dependence is typical for crystal field

2.305Å

Ce B/Si splitting effects which in the case of Ce 3+ split the 2 F5/2 Russel-Saunders ground state of the 4f 1 electronic configuration into three Kramers doublets. By further substituting boron and entering the α-GdSi2 structure-type, the inverse susceptibilities become less curved (Fig. 3 (c), (d)), indicating a reduction of the crystal electric field splitting, possibly also due to a random variation of the Si/B environment to the Ce atoms. The fits of a Curie-Weiss law to the inverse susceptibilities resulted in effective magnetic moments of ~2.7 -~2.9 µB (see Table 4), somewhat higher than expected for Ce 3+ with electronic configuration 4f 1 (2.54 µB) [START_REF] Kremer | Rare Earth Magnetism -Condensed Matter[END_REF]. Table 4. Effective magnetic moments, µeff, Curie-Weiss temperatures, QCW, and magnetic entropies (see text) of the phases CeSi2-xBx obtained from fits to the high-temperature (T ³ 200 K) magnetic susceptibilities according to eq. ( 1) and the integration of Cmag(T)/T. The temperature independent diamagnetic susceptibility contribution, c0, in eq. ( 1) arising from the electrons in the closed shells was calculated from Pascal's increments and fixed to -22´10 -6 cm 3 /mol [START_REF] Bain | Diamagnetic Corrections and Pascal's Constants[END_REF].

Fig. 3 phase The low-field susceptibilities of the phases with x > 0.2 (Fig. 3(c) -(e)) exhibit anomalies associated to cooperative magnetic behavior at low temperatures. Especially well developed is the anomaly for the phase CeSi1.6B0.4 (see the low-temperature specific heat displayed in the left inset in Fig. 3d. It exhibits a slight splitting, also visible in the field-cooled magnetic susceptibility, which may be ascribed to a random environment of the magnetic entities. The specific heat of the AlB2 phase CeSi1.5B0.5 (not shown) shows a rounded peak centred at 2.6 K, coinciding well with the low temperature peaks in the magnetic susceptibilities. Integrating the magnetic contributions to the heat capacities Cmag(T)/T of the phases CeSi1.6B0.4 and CeSi1.5B0.5 obtained after a subtraction of an appropriate lattice contribution to the heat capacity, results in a magnetic entropy contained in the anomaly of ~80 % of R ln2, with R being the molar gas constant (see Table 4). This result implies ordering of a Kramers doublet ground state resulting from the crystal electric field splitting of the 6-fold degenerate 2 F5/2 Russel-Saunders multiplet expected for the 4f 1 electronic configuration [START_REF] Lea | The Raising of Angular Momentum Degeneracy of f-Eelectron Terms by Cubic Crystal Fields[END_REF][START_REF] Grewe | Heavy Fermions[END_REF]. For the phase CeSi1.8B0.2, Cp/T (not shown) increases towards lowest temperatures indicating that magnetic correlation energies are well below ~2 K and the magnetic entropy amounts to only 47 % of the entropy R ln2 expected for a Kramers doublet.

µeff (µB) QCW (K) Smag/R ln2 (%) (a) CeSi2
Measurements of the electrical resistance indicate metallic conductivity for all phases with typical resistivities of the order of 100 µWcm, except for the phase CeSi1.6B0.4 for which the resistivity was found to be an order of magnitude larger (Fig. 4). The temperature dependences of the resistivities, especially of the phases with x ³ 0.2 exhibit anomalies at low temperatures which we ascribe to magnetic scattering of the electrons with the Ce magnetic moments. For the phase CeSi1.6B0.4, the resistivity shows a sharp spike with maximum at 14 K, coinciding well with the magnetic ordering anomalies found in the magnetic susceptibility measurements. The resistivities of the phases with x < 0.2 after an almost flat plateau above ~200 K decrease continuously. The resistivity of CeSi2 exhibits a step-like feature at about 260 K, the origin of which is unclear at present.

Summarizing the electrical and magnetic properties, the phases CeSi2-xBx (x = 0, 0.1, 0.2, 0.4, 0.5) are metallic and phases with B substitution x ³ 0.2 exhibit magnetic correlated behavior, typically below ~15 K. The magnetic contributions to the specific heat indicate Kramers doublets as the crystal field ground states. Indications of magnetic order above ~1.9 K are not observed for the phases with x < 0.2. Here, the magnetic susceptibilies show a temperature dependence characteristic of a crystal electric field split multiplet of three Kramers doublets. The high temperature susceptibilities of all phases indicate the Ce cations to be in an oxidation state +3

with the effective magnetic moments slightly higher than expected value of 2.54 µB.

Electronic structure properties

DFT calculations were initially carried out on stoichiometric CeSi2 in the three type structures (orthorhombic α-GdSi2 (Imma), tetragonal α-ThSi2 (I41/amd), and hexagonal AlB2 (SG P6/mmm)) in order to gain some insight on its structural and electronic properties. The structural arrangements were optimized (see Table S1 for the pertinent structural optimized parameters)

and their relative energies compared. Interestingly, the three arrangements are almost isoenergetic. Indeed, both α-GdSi2 (SG Imma) and α-ThSi2 (SG I41/amd) arrangements are strictly isoenergetic whereas the AlB2 (SG P6/mmm) is hardly less stable by less than 5 kJ/mol per CeSi2 motif. Given the CeSi2 structural motif, to find equal for the α-GdSi2 (SG Imma) and α-ThSi2 (SG I41/amd) arrangements energies is not too surprising, since they exhibit an alike local atomic environment. Finding similar energies for the AlB2-type (SG P6/mmm) is more unexpected (see Fig. 5). c)

The computed total and atom-projected spin-polarized electronic DOS are sketched in Fig. 7.

They are rather dispersed between from -5 to 5 eV, except the Ce 4f-band localized above the A comparison of the relative energies of these three optimized arrangements (see Table S1 for the pertinent structural optimized parameters) indicates, as for the binary CeSi2, that they are rather close in energy, but this time in favor of the AlB2-derived arrangement (SG P6/mmm) in agreement with experiments (relative energies (kJ/mol) per CeSi1.5B0.5 motif: 4.6, 4.0, and 0 for SG Imm2, Imm2, and P6/mmm arrangements). Additionally, a structure search for CeSi1.5B0.5, combining DFT computations and the evolutionary algorithm USPEX (see above for the computational details), produced also the AlB2-derived arrangement (SG P6/mmm) as the most probable at ambient pressure (see Fig. S1). These results support the experiments showing that incorporation of boron induces a phase transformation of the cerium disilicides.

The computed total and atom-projected spin-polarized electronic DOS of the arrangements are sketched and compared in Fig. 9. Those for the α-ThSi2-derived (SG Imm2), and the most stable AlB2-derived (SG P6/mmm) structure types are hardly polarized and resemble those of the corresponding binaries. On the other hand, the DOS of the α-GdSi2-derived (SG Imm2) structuretype is somewhat spin-polarized, pointing to some exchange interaction and magnetic correlations.

Conclusion

In this work, the effect of boron insertion in the structural and the physical properties of cerium disilicides was investigated. Samples of the alloys CeSi2-хBх with different contents of boron (x = 0, 0.1, 0.2, 0.4, and 0.5) were prepared and their crystal structures, electrical and magnetic properties were determined. The analysis of the data which could be collected, indicated that, depending on the amount of boron the phases CeSi2-хBх crystallize either in the α-ThSi2 structure type (x = 0, 0.1) or in the closely related α-GdSi2 structure type (x = 0.2, 0.4). Interestingly, for x = 0.5, the crystal structure of CeSi1.5B0.5 solved by means of X-ray single crystal diffraction crystallizes in the AlB2 structure type. Measurements of the electrical and magnetic properties indicated that phases CeSi2-xBx (x = 0, 0.1, 0.2, 0.4, 0.5) are metallic and that phases with B substitution x ³ 0.2 exhibit magnetic correlated magnetic behavior, typically below ~15 K. DFT calculations were performed to elucidate the change of electronic and physical properties upon boron substitution.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1 .

 1 Fig. 1. Comparison of observed and calculated X-ray powder profiles for CeSi1.5B0.5 (AlB2 type structure).

Fig. 2 .

 2 Fig. 2. Crystal structure of CeSi1.5B0.5 (AlB2-type). Large grey and small black balls are Ce and B/Si atoms, respectively.

  (a) and (b)) do not show indication of long-range order at low temperatures. Their inverse susceptibilities at high temperatures (T > 200 K) follow Curie-Weiss laws given by

Fig. 3 .

 3 Fig. 3. Molar magnetic susceptibilities for the samples CeSi2-xBx (x = 0, 0.1, 0.2, 0.4, 0.5) (from top to bottom). The main frames display the zero-field cooled (zfc, red dots) and the field-cooled susceptibilities (fc, blue dots) collected in an external magnetic field of 100 Oe. The insets show the inverse susceptibilities taken in an external field of 10 kOe (for (b), (c), (d), and (e)). The solid red lines are fits to a Curie-Weis law with parameters compiled in Table4. For (a) the susceptibilities reveal a slight magnetic field dependence, possibly due to minute traces of a ferromagnetic impurity. The Curie-Weiss fit was performed using the data collected at 7 T. The left inset in (c) displays the low-temperature specific heat capacity of CeSi1.6B0.4.

Fig. 4

 4 Fig. 4 Electrical resistivities (r) of the phases CeSi2-xBx (x = 0, 0.1, 0.2, 0.4, 0.5) (from top to bottom).

Fig. 5 .

 5 Fig. 5. DFT-optimized structural arrangements of CeSi2 with (a) the α-GdSi2 (Imma), (b) α-ThSi2 (I41/amd), and (c) AlB2 (P6/mmm) structure-types. Large grey and small black balls are Ce and Si atoms, respectively.

Fig. 6 .

 6 Fig. 6. Total and atom-projected phonon density of states (DOS in states/THz/cell) (left) and phonon band dispersion (right) for CeSi2 with (a) the α-GdSi2 (Imma), (b) α-ThSi2 (I41/amd), and (c) AlB2 (P6/mmm) structural arrangements.

FermiFig. 7 .Fig. 8 .

 78 Fig. 7. Total and atom-projected spin-polarized PBE0+SO electronic DOS of CeSi2 with (a) the α-GdSi2 (Imma), (b) α-ThSi2 (I41/amd), and (c) AlB2 (P6/mmm) structural arrangements. Fermi level (εF) set at 0 eV.

Fig. 9 .

 9 Total and atom-projected spin-polarized PBE0+SO electronic DOS of CeSi1.5B0.5 with (a) the α-GdSi2-derived (Imm2), (b) the α-ThSi2-derived (Imm2), and (c) the AlB2-derived (P6/mmm) structure-types. Fermi level (εF) set at 0 eV.

Table 2

 2 Single crystal crystallographic data for CeSi1.5B0.5.

	Empirical formula Crystal system Space group Pearson symbol Lattice parameters a, Å c, Å Unit cell volume V, Å CeSi1.5B0.5 Hexagonal P6/mmm (No. 191) hP3 3.9922(2) 4.3053(4) 59.424(8)
	5.292
	19.519
	0.12 x 0.09 x 0.02
	Mo Kα, 0.71069
	Bruker D8 Venture
	7, F 2
	72.13, 0.828
	-6 < h < 6, -6 < k < 6, -7 < l < 7
	973
	191 (Rint = 0.049)
	191 (Rσ = 0.035)
	0.019 (0.019)
	0.041 (0.041)
	1.16
	-1.43/1.43
	a

3

Calculated density, g cm

-3

Absorption coefficient, cm -1 Crystal size, mm 3 Radiation and wavelength, Å Diffractometer Refined parameters, refinement 2Θmax and (sinΘ/λ)max h, k, l Collected reflections Independent reflections Reflections with Io > 2σ(Io) Final R1 indices (R1 all data) a Weighted wR2 factor (wR2 all data) b Goodness-of-fit on F 2 Largest diff. peak and hole / (e -/Å -3 )

Acknowledgments

The authors gratefully thank Dr. V. Smetana (Stockholm University, Sweden) for X-ray intensity data collection and E. Brücher (Max-Planck-Institut für Festkörperforschung) for the magnetization and resistance measurements.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi. org/10.1016/j.solidstatesciences…