Layered CeSO and LiCeSO Oxide Chalcogenides Obtained via Topotactic Oxidative and Reductive Transformations

: The chemical accessibility of the Ce IV oxidation state enables redox chemistry to be performed on the naturally coinage-metal-de ﬁ cient phases CeM 1 − x SO (M = Cu, Ag). A metastable black compound with the PbFCl structure type (space group P 4/ nmm : a = 3.8396(1) Å, c = 6.607(4) Å, V = 97.40(6) Å 3 ) and a composition approaching CeSO is obtained by deintercalation of Ag from CeAg 0.8 SO. High-resolution transmission electron microscopy reveals the presence of large defect-free regions in CeSO, but stacking faults are also evident which can be incorporated into a quantitative model to account for the severe peak anisotropy evident in all the high-resolution X-ray and neutron di ﬀ ractograms of bulk CeSO samples; these suggest that a few percent of residual Ag remains. A straw-colored compound with the ﬁ lled PbFCl (i.e., ZrSiCuAs- or HfCuSi 2 type) structure (space group P 4/ nmm : a = 3.98171(1) Å, c = 8.70913(5) Å, V = 138.075(1) Å 3 ) and a composition close to LiCeSO, but with small amounts of residual Ag, is obtained by direct reductive lithiation of CeAg 0.8 SO or by insertion of Li into CeSO using chemical or electrochemical means. Computation of the band structure of pure, stoichiometric CeSO predicts it to be a Ce 4+ compound with the 4f-states lying approximately 1 eV above the sul ﬁ de-dominated valence band maximum. Accordingly, the e ﬀ ective magnetic moment per Ce ion measured in the CeSO samples is much reduced from the value found for the Ce 3+ -containing LiCeSO, and the residual paramagnetism corresponds to the Ce 3+ ions remaining due to the presence of residual Ag, which presumably re ﬂ ects the di ﬃ culty of stabilizing Ce 4+ in the presence of sul ﬁ de (S 2 − ). Comparison of the behavior of CeCu 0.8 SO with that of CeAg 0.8 SO reveals much slower reaction kinetics associated with the Cu 1 − x S layers, and this enables intermediate CeCu 1 − x Li x SO phases to be isolated. PXRD, PND, and electrochemical measurements. The patterns show evidence for inhomogeneity with some parts of the sample exhibiting streaks along the c * reciprocal lattice direction (seen in the [110] zone shown in part c, but not in part b) which are indicative of stacking disorder. e) HAADF-STEM images showing well- crystallized portions of CeSO (d) as well as regions stacking faults are clearly evident structural model been superimposed in part d to show correspondence of the di ﬀ erent columns to the di ﬀ erent atoms, with the brightest columns being Ce, and less bright columns being S.


■ INTRODUCTION
CeCuSO 1 and CeAg 0.8 SO 2 crystallize in the tetragonal ZrCuSiAs structure (Figure 1), consisting of alternately stacked PbO-type CeO layers and anti-PbO-type CuS layers. Oxide chalcogenides and oxide pnictides with these structures offer diverse properties with potential applications as transparent conductors (e.g., LaCuSO derivatives), 3 high-temperature superconductors (e.g., LaFeAsO derivatives), 4 and fast ion conductors enabled by the high mobility of coinage metal (Cu and Ag) ions in chalcogenide layers (e.g., LaAgSO). 5 The structures and properties of compounds in this class have been reviewed. 6,7 If such oxide chalcogenide compounds contain oxidizable cations, then oxidative deintercalation of the coinage metal may be possible. We have previously shown that some samples reported as "CeCuSO" did not conform to the expectations of the lanthanide contraction because facile oxidation of CeCuSO occurs in moist air to form CeCu 0.87 SO and CuO, with Ce oxidized above the +3 oxidation state, 1 and similar behavior can be exploited in the property tuning of other oxide chalcogenides, notably Sr 2 CoO 2 Cu 2 S 2 which oxidizes readily in moist air, 8 and Sr 2 MnO 2 Cu 1.5 S 2 which may be oxidized to Sr 2 MnO 2 Cu 1.3 S 2 using iodine solution, 9 resulting in significant changes in the details of the crystal structures and the magnetic ordering. Here, we report that the CeAg 1−x SO system is intrinsically Ag-deficient and exploit the high Ag mobility and the Ce 3+/4+ redox chemistry to form the new metastable ternary compound with a composition approaching CeSO which lies close to the limiting composition at which Ce 4+ can be stabilized in a sulfide-rich environment without oxidation of the sulfide anion. We further demonstrate the reversible lithiation of CeAg 0.8 SO and CeSO to form LiCeSO.

■ EXPERIMENTAL SECTION
Synthesis. Due to the air sensitivity of some of the reactants and products, all manipulations were carried out in an argon-filled Glovebox Technology drybox or under nitrogen using Schlenk techniques. The precursor CeAg 0.8 OS was prepared as a single-phase, polycrystalline powder from a mixture of CeS 2 synthesized from the elements (see Supporting Information (SI)), CeO 2 (predried at 900°C ; Alfa, 99.99%), and Ag (Alfa, 99.99%) in a 1:1:1.6 molar ratio. This mixture was ground, pelletized, and heated at 700°C for 6 days in a dried, evacuated silica vessel with an alumina liner. Single-phase polycrystalline powders of the Cu analogue CeCu 0.8 OS were prepared on the scale of a few grams by heating a ground, pelletized mixture of CeCuS 2 , 1,10 CeO 2 (Alfa, 99.99%), and Cu (Alfa, 99.999%) in the mole ratio 1:1:0.6 at 1100°C for 7 days. Reductive lithiation reactions on CeAg 0.8 OS and CeCu 0.8 OS were performed by reacting the compounds with a 5-fold molar excess of n-BuLi (1.6 M in hexane) under nitrogen at ambient temperature with overnight stirring. The products were filtered, washed twice with hexane, dried under vacuum, and unloaded/stored under argon in the glovebox. Oxidative deintercalation reactions on CeAg 0.8 OS were carried out in the following way: the powder was suspended in a dry acetonitrile solution which was 0.1 M in I 2 and 0.13 M in NaI so that the solution contained CeAg 0.8 SO, I 2 , and NaI in the mole ratio 1:1.5:2. The solution was stirred overnight under nitrogen. The product was filtered, washed with dry acetonitrile, dried under vacuum, and stored under argon.
Electrochemical lithiation of a CeSO sample which had been synthesized from CeAg 0.8 SO by the reaction with iodine was performed with a positive electrode composed of CeSO mixed with Super P conductive carbon black in a weight ratio of 85:15. Coin-type half cells containing the positive electrode, Li metal as counter elecrode, borosilicate glass fiber separator (Whatman), and electrolyte (1 M LiPF 6 in ethylene carbonate (EC)/dimethyl carbonate (DMC) 1:1 (v/v; Merck)) were assembled in an argon-filled glovebox. Cycling was carried out at rates of C/10 or C/30 (the latter for in situ X-ray diffraction; i.e., 10 or 30 h to reach the theoretical capacity corresponding to 1 mol of Li intercalated into 1 mol of CeSO) using an Arbin battery cycler.
Structural Analysis. Detailed structural information for the CeCu 0.8 OS and CeAg 0.8 OS precursors and for the products obtained from soft chemical reductions or oxidations was obtained by synchrotron powder X-ray diffraction (PXRD) using beamline I11 (Diamond Light Source, Harwell, UK) 11 with a Si-calibrated incident wavelength of approximately 0.823 Å or beamline ID31 (ESRF, Grenoble, France) 12 with a Si-calibrated incident wavelength of aproximately 0.4 Å (see figure captions for precise values for each diffractogram) and with samples sealed in 0.5 mm diameter capillaries. This was followed by time-of-flight powder neutron diffraction (PND), using either the high-resolution instrument HRPD or the medium-resolution, high-flux instrument POLARIS 13 at the ISIS pulsed neutron facility on separate large samples of the products; samples were contained in 6 mm diameter vanadium cans sealed with indium gaskets. The samples synthesized electrochemically were examined ex situ and in situ using a PANalytical Empyrean powder diffractometer using Cu Kα 1 /Kα 2 radiation. Rietveld analysis was performed using the Topas Academic software 14 with the capability of Version 6 of the software 15 enabling the quantitative treatment of stacking faults in some of the samples.
Transmission Electron Microscopy Measurements. Selected area electron diffraction patterns were taken using a Philips CM20 transmission electron microscope (200 kV, equipped with CCD camera). High-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) images were obtained using a FEI Titan 80-300 "cubed" microscope equipped with a Super-X detector and operated at 300 kV. Samples for transmission electron microscopy were prepared by crushing the powder in ethanol and depositing the solution on a copper grid covered with holey carbon.
Magnetometry. All measurements used a Quantum Design MPMS-XL SQUID magnetometer with samples of approximately 30 mg in mass contained in gelatin capsules. Measurements of the magnetic moment of the sample were made in fields of 3 and 4 T in the temperature range 5−300 K, and the magnetic susceptibility was determined from the difference in the measurements in the two fields; this was to ensure the measurements were not compromised by lowfield nonlinearity in the sample moment with field as a consequence of minuscule amounts of ferromagnetic impurity.
Computation. All calculations were performed using the periodic density functional theory (DFT) code VASP, 16,17 which employs a plane-wave basis set to describe the valence electronic states. The Perdew−Burke−Ernzerhof (PBE) 18  ) and the valence electrons were described using the projector-augmented wave 19 (PAW) method. The screened hybrid-DFT methodology of Heyd, Scuseria, and Ernzerhof (HSE06) 20−22 was used, replacing 25% of the PBE exchange with exact Fock exchange, as described in detail elsewhere. 23 The HSE06 approach has previously been shown to give improved results for semiconducting systems over GGA and meta-GGA approaches, including accurate calculation of structures and band gaps, 24−27 and simulation of defective 28−31 and magnetic 32−34 systems.
In the calculations, structural optimizations of the bulk materials were performed at a series of volumes in order to calculate the equilibrium lattice parameters. In each case, the atomic positions, lattice vectors, and cell angles were allowed to relax, while the total volume was held constant. The resulting energy−volume curves were fitted to the Murnaghan equation of state 35 to obtain the equilibrium bulk cell volume. This approach avoids the isotropic problems of Pulay stress and changes in basis set which can accompany volume changes in plane wave calculations. 36 Convergence with respect to kpoint sampling and plane-wave energy cutoff were checked, with a cutoff of 500 eV and a k-point sampling of 5 × 5 × 3 with a Γcentered mesh found to be sufficient for both LiCeSO and CeSO. Structural optimizations were deemed to have converged when the force on every ion was less than 0.01 eV Å −1 . Bader charges were calculated using Henkelman's code 37 in which the distribution of the valence charge density is calculated using electron basins defined from the total charge density. This ensures that basins can be properly defined for atoms with very few valence electrons such as Li. The Bader charges given for CeO 2 are taken from a unit cell minimized using an identical HSE06 methodology and a 6 × 6 × 6 Monkhorst− Pack k-point mesh.
All optical absorption spectra, as well as the optical transition matrices, were calculated within the transversal approximation. 38 This approach sums all direct valence band (VB) to conduction band (CB) transitions on the k-point grids to determine the optical absorption  and does not include indirect and intraband transitions. 39 As only single-particle transitions are included, any electron−hole correlations would require higher-order electronic structure methods. 40,41 However, this approach has been shown to provide reasonable optical absorption spectra in comparison with experiment. 42−45 ■ RESULTS Soft Chemical Transformations of CeAg 0.8 SO. CeAg 1−x SO has previously been characterized as being intrinsically Ag-deficient by Chan et al., 2 from single crystal X-ray diffraction studies of a sample with refined composition CeAg 0.77 SO. The same authors used evidence from powder diffraction measurements to suggest that stoichiometric CeAgSO with significantly larger unit cell parameters than those of their well-characterized crystal was attainable. We attempted to synthesize stoichiometric CeAgSO, but all these attempts were unsuccessful with excess elemental Ag evident in the powder diffraction patterns of samples of composition CeAgSO. Comparison of the unit cell volumes of LnAgSO and LnCuSO (which are stoichiometric for less oxidizable lanthanides than Ce) with our reported results for stoichiometric CeCuSO 1 and the reported cell volume for the proposed stoichiometric "CeAgSO" 2 is consistent with the results of our syntheses that the maximum Ag content obtainable using the high-temperature synthesis is close to CeAg 0.9 SO. Further description and analysis on this point is supplied in the SI (Table S1, Figure S1). For the chemical transformations, we synthesized phase pure samples of composition CeAg 0.8 SO (i.e., close to the single crystal results already reported by Chan et al. 2 ). See Figure S2 and Table S2.
Ambient temperature lithiation using n-BuLi of black CeAg 0.8 SO resulted in the formation of a dark-green product and a decrease in the unit cell volume by 2.1% but with apparent retention of the crystal structure. The laboratory PXRD data showed enormous changes in the intensities of the reflections compared with CeAg 0.8 SO, and quantitative Rietveld analysis showed that nearly all the Ag had been extruded as the element and replaced with Li with the formation of a product of approximate composition LiCeSO. This complete, or almost complete, extrusion of the coinage metal on lithiation is similar to that observed in the structurally related Sr 2 MnO 2 Cu 2m−0.5 S m+1 series, 46−48 and in other chalcogenides such as the thiospinel CuZr 2 S 4 . 49 Further reaction with iodine in acetonitrile of this product "LiCeSO + 0.8Ag" obtained from the lithiation of CeAg 0.8 SO or, alternatively, direct reaction of CeAg 0.8 SO with I 2 /NaI in acetonitrile resulted in the formation of a new product that could still be indexed on a primitive tetragonal unit cell, but with a unit cell volume that was 32% smaller than that of CeAg 0.8 SO and with the contraction dominated by a 27% shortening of the c lattice parameter. The products of iodination reactions with either "LiCeSO + 0.8Ag" or CeAg 0.8 SO had similar lattice parameters suggesting that a common product had been produced. Addition of NaI to the solution of I 2 in acetonitrile as described in the Experimental Section resulted in solubilization of the AgI 50 enabling it to be washed away, thus yielding uncontaminated products. Quantitative analysis of the PXRD data was consistent with the topotactic formation of the product with a composition very close to stoichiometric CeSO with the PbFCl structure type, making the compound analogous to ThSO 51 and the high-pressure tetragonal polymorph of ZrSO, 52,53 by extraction of the Ag or Li from the sulfide layer. Subsequently, the synthesis of a sample approaching the CeSO composition by the direct iodination of CeAg 0.8 SO enabled lithiation using n-BuLi to be used to produce a sample of pale-yellow LiCeSO free from contamination by elemental Ag, and such a sample of CeSO was also used in investigations of the electrochemical intercalation of Li. We also verified that CeSO is metastable and requires these low-temperature synthetic methods. Heating to 700°C resulted in the formation of mixed-valent Ce 4 O 4 S 3 , which is known to decompose further to the fully reduced Ce 2 O 2 S at higher temperatures. 54 Figure 1 summarizes the chemical transformations applied to CeAg 0.8 SO and its derivatives. Analyses of the compositions, crystal structures, magnetic properties, and electrochemistry of these experimental samples approaching the compositions LiCeSO and CeSO, together with discussion of the electronic structures of stoichiometric LiCeSO and CeSO, are presented below.
Structural Characterization of LiCeSO. Figure 2 shows the results of Rietveld refinement against synchrotron PXRD data obtained on a sample of LiCeSO free of elemental Ag produced by lithiation of a sample of CeSO obtained by direct Ag deintercalation from CeAg 0.8 SO. Figure 3 shows a refinement against PND data on an elemental-Ag-containing sample obtained by direct lithiation of CeAg 0.8 SO. The crystal structure was refined in space group P4/nmm using the structure of CeAg 0.8 SO as the starting model. The key refinement parameters are listed in Table 1, and further structural details are supplied in Table 3.  The contraction in unit cell volume on transforming CeAg 0.8 SO to LiCeSO is dominated by a contraction along the stacking direction (c parameter), consistent with the decrease of ionic radius of the ion in the tetrahedral sites in the sulfide layer (tetrahedral Ag + = 114 pm vs Li + = 73 pm). 55 Analysis of the diffraction data on different samples suggested that there was a small amount of residual Ag that was not extruded in the reactions. A sample obtained by intercalation of Li into CeSO had a refined composition of Li 0.9455(5) -Ag 0.0545(5) CeSO (Table 1 and Figure 2), and this has implications for the precise composition of CeSO as discussed below. Analysis of PND data on a sample obtained from direct lithiation of CeAg 0.8 SO (Table 1 and Figure 3) yielded a refined composition of Li 0.987(3) Ag 0.013(3) CeSO (with the refinement constrained such that the site must be fully occupied). This analysis is complicated slightly by the negative neutron scattering length of Li, and an alternative model with no Ag on the 2b site and free refinement of the Li occupancy yielded a refined composition with a significant Li-deficiency of Li 0.95(1) CeSO. The two models are not distinguishable by PND alone, but consideration of both the XRD refinements which suggest that the scattering in the sulfide layer corresponds to slightly more than one Li ion, and the fact that the lithiations were carried out with excess n-BuLi, suggests that the compound we describe as LiCeSO contains a sulfide layer fully occupied by Li ions apart from a small number (∼1−5%) of residual Ag ions. Hence, the experimentally prepared samples reproducibly do not quite reach the LiCeSO stoichiometry. Similar behavior is found in the lithiation of the thiospinel CuZr 2 S 4 . 49 Structural Characterization of CeSO. Rietveld refinement against PXRD ( Figure S4) and PND data ( Figure 4) was consistent with the topotactic formation of the product CeSO with the PbFCl structure type by complete oxidative deintercalation of either Ag or Li from the sulfide layers of CeAg 0.8 SO or LiCeSO, respectively, making the compound analogous to oxide chalcogenides of metals that can readily attain the +4 oxidation state: ZrSO, 52,53 ThSO, USO, and NpSO. 51 Full analysis of the crystal structure (using powder diffraction and TEM, Figures 4−7), properties, and electrochemistry was carried out on a single sample of CeSO prepared by direct oxidative deintercalation of Ag from CeAg 0.8 SO.
The refinements showed that the deintercalation of Ag is topotactic and simply involves the removal of the tetrahedral coinage metal cation with collapse of the structure along the c axis, so that compared with CeAg 0.8 SO the c lattice parameter decreases by 27% and the Ce coordination number increases from 4 × S + 4 × O to 5 × S + 4 × O as shown in Figure 1 and Table 1

Inorganic Chemistry
Article described further below. The P4/nmm symmetry is retained. The structural parameters are compared below with those of LiCeSO and CeAg 0.8 SO in Table 3. Despite the removal of almost all the Ag + from the tetrahedral sites in the sulfide layers, there is no evidence for the formation of S−S bonds following this oxidative deintercalation. This contrasts with the case for compounds with trivalent lanthanides in which compounds of formula LnSO contain [S 2 ] 2− ions. 56 The preliminary analyses of diffraction patterns of CeSO samples measured using high-resolution synchrotron X-ray diffraction using peak shapes with only Gaussian and Lorentzian terms to account for particle size and strain broadening (as used in the refinement of the LiCeSO model) were inadequate ( Figure  S4). Such a refinement gave a numerical goodness of fit parameter χ 2 of 3.03 but generally accounted poorly for the shapes of the peaks: the hk0 reflections were relatively narrow compared with the widths of hkl reflections. For the refinement against POLARIS neutron data of medium resolution shown in Figure 4, this was modeled using a Stephens-type anisotropic peak broadening. 57 In the analysis of the higher-resolution Xray data from I11, the fit to the integrated intensities using this commonly used treatment ( Figure S5) gave an improved χ 2 of 2.32, but there remained a considerable mismatch to the profile, particularly to the best-resolved peaks at low angles with strong asymmetry: the 00l reflections were overbroadened, and some reflections were found to be slightly out of position. Using the Stephens-type anisotropic peak broadening terms appropriate to an orthorhombic crystal structure gave some further improvement to the fit through the introduction of further parameters, but there was no evidence that the structure was lower in symmetry than tetragonal. We concluded that the Stephens-type anisotropic peak broadening is inadequate in accounting for high-resolution data on CeSO, and the interpretation of this is discussed below.
Transmission electron microscopy measurements were performed on the same CeSO sample as was used in the PXRD and PND measurements in order to probe the crystal structure on a shorter length scale in an effort to account for the anomalies in the high-resolution synchrotron powder data. Electron diffraction patterns (Figure 5a,b) confirmed the cell deduced from PXRD and PND data, but the majority of [110] zones showed streaking along the c* direction, suggestive of stacking disorder (Figure 5c). In addition to the streaks, some additional, very weak reflections were also evident (see Figure  S11), suggestive of a possible structural modulation on the length scale probed by electron diffraction. HAADF-STEM images revealed large well-ordered regions of the structure (Figure 5d and larger overview in Figure S12) but also revealed the presence of stacking faults (Figure 5e) which are consistent with the observation of the streaking evident in the electron diffractograms ( Figure 5c) and with the broadening of the lcontaining reflections in the PXRD patterns. On HAADF-STEM images, the brightness of the projected atom columns is approximately proportional to Z 2 , where Z is the atomic number; therefore, in Figure 5d the brightest columns correspond to the Ce columns and the weaker ones to the S columns. The sample was found to be somewhat unstable in the electron beam, so energy dispersive X-ray analysis with high spatial resolution was not able to test the possible scenarios such as the faulted regions containing some residual Ag atoms which had not been removed in the synthesis (as suggested by the analysis of the average structure of LiCeSO described above) or a more significant reconstruction of the structure, such as the formation of a fluorite-type region, or the formation of some disulfide units ([S 2 ] 2− ) by sulfide oxidation rather than pure oxidation of Ce 3+ to Ce 4+ . Moreover, the

Inorganic Chemistry
Article image in Figure 5e shows a complex set of features differing over the faulted region, most probably because of the projected character of HAADF-STEM images, which prevents deducing the precise nature of the stacking faults from the images.
In order to account for the asymmetry, anisotropic peak broadening, and positional mismatches evident in the standard Rietveld refinement against the synchrotron PXRD data, and to account for the evidence of stacking faults in regions of the sample obtained from the TEM measurements, we used the Topas Academic Version 6 software to perform Rietveld refinements that included stacking faults. 15 Supercells were constructed using the stacking units shown in Figure 6 of either Ce 2 O 2 , S 2, Ag 2 S 2 , Ce 4 O 4 , or Ce 2 O 2 Ag 2 S 2 in a method similar to that adopted by Ainsworth et al. 58 Supercells of 3000 layers were constructed by assigning a probability for each type of layer stacking on top of each other type of layer. For example, a model equivalent to the unit cell of perfect, stoichiometric CeSO is described by assigning the probability of a Ce 2 O 2 layer following a S 2 layer to be 1, assigning the probability of a S 2 layer following a Ce 2 O 2 layer also to be 1, and assigning all other possibilities to 0. Using this methodology we considered the following: (model A) 0.5−10% of the sulfide layers containing silver, randomly distributed in the supercell; (model B) 0.5−10% of the cerium oxide layers being fluorite-type Ce 4 O 4 layers, randomly distributed in the supercell; and (model C) 1−10% of sulfide layers containing silver, with a 5−70% probability of the next sulfide layer also containing silver. Also considered was model D, a stack of 200 Ce 2 O 2 and S 2 layers only, with turbostratic disorder introduced by refining a shift of each layer in the xy plane with respect to its neighbors, as is sometimes responsible for asymmetrically broadened line profiles in diffraction peaks of layered materials (e.g., in layered double hydroxides 59 or kaolinite). 60 Full details of how the models were implemented are given in the Supporting Information. Minimum χ 2 values achieved for models A, B, C, and D were 1.80, 2.26, 1.82, and 2.53, respectively. The best fit of model C was one almost equivalent to model A, with poorer agreement achieved when a high probability of silver-containing layers clustering together was assigned. A plot of the agreement factor for the refinement, χ 2 , against concentration of Ag 2 S 2 layers gives the minimum value with 5.5% of such layers included (Figure 7, inset). Since HAADF-STEM images (Figure 5d, Figure S12) show that some large regions of the sample contain no stacking faults, a "faultless" stoichiometric CeSO phase was added to the refinement, with its lattice parameters, atomic coordinates, and thermal displacements made equivalent to a summation of one Ce 2 O 2 and one S 2 layer. Inclusion of the faultless phase improved further to χ 2 to 1.31 and accounted for 20% of the total scattering intensity which is consistent with the observation above that "the majority of [110] zones showed streaking [in the electron diffraction patterns]." The total percentage of sulfide layers containing silver is therefore estimated at 4.4% (0.8 × 5.5%) by this refinement, shown in Figure 7, with refined structural parameters listed in Tables 2  and 3. Thus, the stacking fault model that best accounted for the profile contained a small proportion of sulfide layers from which Ag had not been removed. This is quantitatively consistent with the analysis of LiCeSO samples (which have much more well-behaved peak shapes) in which the average electron count of the species in the tetrahedral sites in the sulfide layers cannot be accounted for by full Li occupancy alone. It is proposed that these regions lead to some of the weak reflections evident in the electron diffractograms ( Figure  S11) as well as the streaks evident along the c* direction (Figure 5c). This behavior in which lithiation or direct deintercalation fails to fully extrude or deintercalate a few remaining percent of the coinage metal has precedent in the behavior of the thiospinel system CuZr 2 S 4 in which Cu extrusion by Li from n-BuLi to form LiCuZr 2 S 4 followed by oxidative deintercalation by I 2 in MeCN produces Cu 0.05 Zr 2 S 4 . 53 Magnetometry. The magnetic susceptibility of Ce 3+containing binary oxides has been described by Engelhardt and Figgis. 61 They describe that crystal field effects generally reduce the effective moment from the free-ion value of 2.54 μ B , and that these effects result in very significant deviations from the Curie−Weiss law. In the case of LiCeSO, measurement of the magnetic susceptibility at 300 K yielded an effective magnetic moment of 2.28(1) μ B which is very similar to the value found for Ce 2 O 3 and Ce 3+ ions in a La 2 O 3 matrix by Engelhardt and Figgis. 61 There was no evidence for magnetic ordering of the Ce 3+ moments down to 5 K. CeAg 0.8 SO had a susceptibility which could be accounted for by 79(1)% of the Ce ions being Ce 3+ with an effective moment of 2.28 μ B , consistent with the assumption that the Ag-deficiency results in Ce oxidation. The oxidized product CeSO had a much lower magnetic susceptibility than that of LiCeSO or CeAg 0.8 SO (Figure 8). Measurement at 300 K produced a value of the susceptibility that could be accounted for by 8(1)% of the Ce ions with an effective moment of 2.28 μ B . These measurements show that the oxidation proceeds via the oxidation of Ce 3+ and not S 2− which is consistent with the computational results shown below, and consistent with the relatively facile oxidation of Ce 3+ . The magnetometry is also in reasonable quantitative agreement with the interpretation of the stacking faults in the high-resolution powder X-ray diffraction data as arising from   the presence of remanent Ag + ions, each of which will yield one Ce 3+ ion through considerations of charge balance. We cannot rule out that Ce 3+ moments are also present in surface states.
Comparison of the Crystal Structures of LiCeSO and CeSO. The HSE06-calculated lattice parameters and bond lengths for idealized stoichiometric LiCeSO and CeSO are given in Table 3 where they are compared with the parameters obtained experimentally from Rietveld refinements against data from the samples with very similar composition (experimental data for CeAg 0.8 SO are also included for comparison). Overall, the calculated parameters are in good agreement with those determined experimentally.
Both LiCeSO and CeSO contain CeO layers which are fragments of the fluorite structure. They are also commonly described as PbO-type layers. In LiCeSO (Figure 9b), these CeO layers alternate with anti-PbO-type LiS layers. The Li and O ions are thus four-coordinate, in distorted tetrahedral environments, while the Ce and S atoms are both in eightcoordinate sites which can be described as distorted square antiprisms (with the parallel square faces having areas in the ratio 2:1).
The CeSO structure (Figure 9a) is related to that of LiCeSO by removal of the layer of Li + ions and collapse of the structure along the c direction. The results of magnetometry measurements show that this results in oxidation of Ce 3+ to Ce 4+ rather than the oxidation of sulfide, and this is confirmed by the calculations of the electronic structure described below. In the transformation from LiCeSO to CeSO, the coordination number of Ce increases from 8 to 9 with the formation of a further Ce−S bond (2.858(3) Å) parallel to the c axis so that the Ce coordination environment describes an irregular square antiprism with the larger square face capped by sulfide. With the loss of the Li ions, the sulfide ion becomes five-coordinate by Ce ions which describe a square-based pyramid. The four Ce−S bonds present in LiCeSO also contract significantly in CeSO partly as a consequence of the oxidation of Ce 3+ to Ce 4+ , but presumably mainly in response to the decrease in the coordination number of sulfide. The loss of the short Li−S bonds with the deintercalation of Li results in a small expansion in the basal lattice vectors, presumably to optimize the Ce−S and Ce−O bonding.
Electronic Structure and Bonding. The presence of an unpaired f-electron on the Ce 3+ ions in LiCeSO results in the possibility of different magnetic structures for this compound. In the simulation of the structure of LiCeSO, two different magnetic structures were attempted: a ferromagnetic structure, with all spins aligned in the same direction, and an "A-type" antiferromagnetic solution, where ferromagnetic ab sheets of Ce 3+ moment ions alternate between up and down spin along the c vector. Although the ferromagnetic configuration was found to have the lowest absolute energy, the difference was very small (0.30 × 10 −3 eV). For ease of analysis, all results and discussion on LiCeSO are therefore made from the  Figure  S2 and Table S2). c Values from refinements against PND data (Figures 3 and 4).   antiferromagnetic phase. We note that our experimental analysis shows no magnetic ordering transition in LiCeSO down to 5 K. The HSE06-calculated total and partial (ion and l-and mquantum number decomposed) electronic densities of states (EDOS/PEDOS) for the two materials are given in Figure 10.
For LiCeSO, the top of the valence band is composed of Ce 4f-states resulting from the unpaired f-electron. Below this peak is a separation of ∼0.9 eV to the top of the next band. This contains contributions from both O and S, with the S states higher in energy, and hence closer to the valence band maximum (VBM), than O. Li states also appear within this region; however, due to the high electropositivity of Li, the electron density is extremely small, so they make a minor contribution to the DOS. The bottom of the conduction band which is separated by about 3 eV from the occupied Ce 4fstates is primarily composed of a combination of Ce 4f-states and O/S p-states. These unoccupied 4f-states are higher in energy due to shielding by the occupied 4f-electron which results in them appearing in the band structure with the rest of the unoccupied states.
The PEDOS of CeSO are similar to those for LiCeSO, with the exception of the Ce 4f-states. The calculations suggest the Ce(IV) oxidation state in CeSO with all the 4f-states unoccupied, and therefore resident in the conduction band (CB). This is consistent with the experimental observation that the magnetic moment of the sample of composition close to CeSO is only about 8% of the value expected for a Ce 3+ compound with evidence that it arises from an inhomogeneous slight nonstoichiometry as discussed above. The top of the valence band in CeSO is made up of O and S p-states, with the latter forming the VBM. In comparison to the equivalent region in LiCeSO, there is a little more peak definition in CeSO and the region itself is much wider in energy. The unoccupied Ce 4f-states in CeSO appear as a single broad peak and lie at a slightly lower energy compared with the LiCeSO case since there are no occupied 4f-states to shield them from the Ce nuclear charge. Some mixing with unoccupied O/S pstates is also observed.
Bader charges were calculated for the different species and are listed in Table 4. Comparison between calculated values for LiCeSO and for stoichiometric CeCuSO 1 shows that the Ce and O species have similar charges in the two compounds. However, the Bader charges calculated for the S ions in the two compounds, −1.57 and −1.13 for LiCeSO and CuCeSO, respectively, differ substantially, consistent with the difference in the charges calculated for the M(I) species: Li in LiCeSO has a Bader charge of 0.84, close to the fully ionic charge of 1.00, while Cu in CeCuSO has a Bader charge of 0.40. This shows that the replacement of the coinage metal by Li results in a much more ionic sulfide layer.
The presence of Ce 4+ ions in CeSO gives rise to different charges from those calculated for LiCeSO. The Ce atoms themselves have a higher charge, as expected. The charges of O and S are calculated to be smaller than those in LiCeSO, suggesting that the Ce−O and Ce−S bonds have more covalent character in CeSO. Comparison between CeSO and CeO 2 shows that although the O atoms have similar Bader charges in the two materials, the Ce ions in CeSO have a lower Bader charge than those in CeO 2 , consistent with greater covalency in the Ce−S bonds than in the Ce−O bonds.
Band Structures. The HSE06-calculated band structures along the high-symmetry points 62 for both CeSO and LiCeSO are shown in Figure 11. LiCeSO is calculated to have an indirect band gap of 2.51 eV, with the VBM observed at the A point (1/2, 1/2, 1/2) and the conduction band minimum (CBM) at Γ (0, 0,0). The smallest direct fundamental band gap is located at (0.398, 0.398, 0.000) which is offset from M  in the Γ direction with an energy of 3.01 eV. Conversely, CeSO is calculated to be a direct band gap material, with a fundamental gap of 0.92 eV at the Γ point. The band structures reflect the differences in the PEDOS, with the movement of the occupied 4f-band in LiCeSO into the conduction band in CeSO, and the increase in bandwidth of the occupied O/S p-states. For LiCeSO, the occupied Ce 4fband is seen to be split off from the O/S p-band, as observed in the PEDOS. On oxidation to CeSO, when the 4f-states become unoccupied, these states all lie in the range 1−2 eV above the VBM.
The change in VBM and CBM character will have consequences for the conduction properties of the two materials. LiCeSO has a relatively flat VBM composed of Ce 4f-states, and a more dispersive CBM indicating that mobility for n-type conductivity will be higher; however, with Ce 3+ already present, the formation of such charge carriers will be difficult. In CeSO where the dispersion of the VBM makes ptype conductivity more favorable, the formation of hole charge carriers by partial oxidation of sulfide might be plausible. The conductivities of these compounds prepared by soft chemical approaches are difficult to measure experimentally because the compounds are not stable to sintering attempts.
The calculated optical absorption spectra are shown in Figure S14. The analysis gives calculated optical band gaps 63 of 1.5 and 3.6 eV for CeSO and LiCeSO, respectively.
Electrochemistry of LiCeSO and CeSO. Figure 12a shows the discharge profile for a cell composed of a positive electrode containing the sample close in composition to CeSO (obtained by direct deintercalation of Ag from CeAg 0.8 SO) and a Li metal negative electrode recorded during an in situ PXRD measurement carried out at a rate of C/30 (i.e., full discharge over a period of 30 h). Cycling results obtained at a C/10 rate are shown in Figure S15. Discharge of the cells shows a plateau at about 2 V (vs the Li + /Li couple), suggestive of a two-phase region which is confirmed by the in situ PXRD measurements (Figure 12b); the specific capacity on discharging the cell to 0.7 V corresponds closely to the 142 mAhr g −1 expected for the intercalation of Li into CeSO to produce LiCeSO. The X-ray diffractogram (Figure 13b) of the sample extracted from a fully discharged cell (discharged to 0 V vs Li + /Li) corresponds quantitatively to LiCeSO, and the diffractograms of the electrode material before (Figure 13a) and after discharge ( Figure 13b) emphasize the improvement in crystallinity on intercalation to produce LiCeSO, consistent with the presence of stacking faults in CeSO. Rietveld analysis of the diffractograms obtained during the in situ PXRD measurement show that two phases are present and that a phase with lattice parameters similar to those of LiCeSO increases in phase fraction at the expense of the CeSO phase. The lattice parameters of the LiCeSO-like phase were found to evolve during the conversion (Figure 12c), in particular the basal lattice parameter a increases significantly during the plateau in the voltage profile, suggesting the formation of a range of

Inorganic Chemistry
Article Li 1−x CeSO phases during the reduction process, with full lithiation coinciding with the voltage drop at the end of the plateau in the voltage profile. By comparing the variation in unit cell volume with that found for CeCu 1−x SO phases 1 we estimate that Li 1−x CeSO phases with 0 < x < 0.2 are formed during the intercalation of Li into CeSO. This observation of a change in composition is consistent with the 6 Li NMR data collected during the first discharge of the cell (Figure 14) which show not only an increase in the intensity of the 6 Li resonance as Li is inserted, but also an increasing paramagnetic shift of the resonance in the two-phase region which continues beyond the plateau in the voltage profile. The shift, which is presumably due to the presence of the paramagnetic Ce 3+ centers, reaches a maximum when the cell has been discharged to 0.7 V, i.e., just below the sharp step in the voltage profile and consistent with the expected capacity for intercalation of 1 mol of Li per mole of CeSO, and discharging to 0 V does not result in a further shift in the resonance suggesting that Ce is fully reduced to Ce 3+ at 0.7 V. The paramagnetic shift of −95 ppm in fully reduced LiCeSO is ascribed to the Fermi contact interaction of the Li nuclear spins with unpaired spin density of the Ce 3+ ions. Each Li ion is involved with 12 neighboring Ce 3+ ions via 16 Ce−S−Li interactions. For contrast, in the series Sr 2 MnO 2 Li 2m S m+1 (m = 1, 2, 3), the paramagnetic shift of the 6 Li resonance in lithium sulfide layers was determined to be approximately 100 ppm for each Mn 2+ ion engaged in a rather weak covalent interaction Mn−S−Li via long Mn−S bonds. 47 The order-of-magnitude-smaller shift per neighboring Ce 3+ ion in LiCeSO presumably reflects the weak covalency of the interactions between not only the Li 2s-and S 3p-states, but also between the Ce 4f-and S 3p-states. This is consistent with the computational results and chemical expectations.
Comparison of the Soft Chemistry of CeAg 0.8 SO and CeCu 0.8 SO. CeCu 0.8 SO was also synthesized and used as a precursor for soft chemical transformations in order to make a comparison with the Ag analogue of similar coinage metal composition. The lithiations of both CeCu 0.8 SO and CeAg 0.8 SO at ambient temperature using n-BuLi both produced clear color changes. The black Ag-containing precursor CeAg 0.8 SO yielded a highly air-sensitive powder of a dark-green color (a mixture of elemental Ag and LiCeSO as described above). The black Cu-containing precursor CeCu 0.8 SO yielded an extremely air-sensitive light-brown/ yellow powder which turned black within seconds on air exposure. In contrast to the Ag case, laboratory PXRD showed the product of lithiation of the Cu precursor to be single-phase, retaining the ZrCuSiAs structure with a unit cell volume of 135.870(4) Å 3 that was 5.0% larger than that of CeCu 0.8 SO (129.448(4) Å 3 ), and which exceeded the cell volume of 132.405 Å 3 found for the fully stoichiometric CeCuSO, 1 although it was significantly smaller than the volume of 138.075(1)Å 3 found for LiCeSO obtained by the analogous reaction with CeAg 0.8 SO and described above.
Analysis of the diffraction data for the lithiated product ( Figure 15 and Figure S16; Table S3) showed that lithium had been inserted to fill the vacant sites in the sulfide layers. However, there was no evidence for the measurable extrusion of elemental Cu from the powder patterns of the lithiated products. This is in stark contrast to the coinage metal extrusion that occurs with the CeAg 0.8 SO precursor and with Figure 13. X-ray diffractograms of the positive electrode composite containing CeSO (a) before discharge (the Rietveld fit is to the structural model for CeSO) and (b) after discharge of the cell to 0 V vs Li + /Li (the Rietveld fit is to the structural model for LiCeSO). Note the increase of crystallinity that occurs on intercalation. Lowangle regions containing background contributions from the other components of the electrode material were excluded from the refinements. Data (blue), fit (red), and difference (gray) are shown. Tick marks for the relevant phases in each case are also shown. Figure 14. Shift of the 6 Li NMR measurements made during cell discharge. The shift of the resonance is consistent with the changing composition of the intercalation product evident from the in situ PXRD measurements ( Figure 12). The electrochemical profile corresponding to this experiment is also shown.  46,47 Refinement against PND data from HRPD ( Figure 15 and Figure S16) confirmed that in the lithiation product of CeCu 0.8 SO the Cu occupancy was unchanged from that in the precursor and that within the experimental uncertainty the remaining sites in the sulfide layer were completely filled by Li ions producing Li 0.2 CeCu 0.8 SO. A full description of the structure of this compound is included in Table S3.

Inorganic Chemistry
We propose that the difference in behavior between CeCu 0.8 SO and CeAg 0.8 SO, where only the coinage metal cation changes, arises in part from the larger separation of adjacent sulfide layers in the Ag case: in order to accommodate the larger Ag + ion the S−S separations between adjacent slabs of composition CeSO must increase, but in the basal direction they are constrained to change very little as the basal lattice parameters are constrained by the geometry of the CeO layers. Thus, Ag in CeAg 0.8 SO is in a AgS 4 tetrahedron that is highly distorted (two S−Ag−S angles of 94.9°and four of 117.2°) 2 and which is relatively extended in the direction parallel to the c lattice vector compared with the almost regular CuS 4 tetrahedron in CeCu 0.8 SO (two S−Cu−S angles of 108.8°a nd four of 109.8°) 2 as also discussed elsewhere. 64 This likely enhances the mobility of Ag + ions compared with the Cu + ions in CeCu 0.8 SO, in line with the observations that the activation barrier for Ag + motion in LaAgSO which is reported as 0.195 eV 65 or 0.22 eV 5 is significantly smaller than that reported for Cu + (0.32 eV) in the analogue LaCuSO. 66

■ CONCLUSIONS
We have shown that the high mobility of coinage metal ions, particularly Ag + , in layered oxide sulfides enables soft chemical transformations to be performed. Oxidative topotactic deintercalation of Ag from CeAg 0.8 SO produces a metastable compound with a composition approaching CeSO with oxidation of Ce to the +4 oxidation state, which in turn acts as an intercalation host for Li, leading reversibly to LiCeSO using chemical or electrochemical methods. While the results of computational analysis on stoichiometric CeSO show that the Ce 4f-states lie completely above the Fermi level, magnetometry measurements show a significant remaining Curie paramagnetism which we ascribe to a few percent of residual Ce 3+ moments consistent with the structural analysis of CeSO using high-resolution PXRD and PND and TEM which reveal stacking faults which are best modeled as arising from incomplete removal of Ag ions at the level of about 5% with the result that some paramagnetic Ce 3+ ions remain.
CeSO with the PbFCl-type structure is isostructural with the compounds ThSO, USO, and NpSO reported from powder data collected in the 1940s, 51 and with the recently reported polymorph of ZrSO obtained pure by high-pressure synthesis. 53 The early reports do not describe any anomalies in the appearance of the powder patterns such as anisotropic peak broadening, although, if present, these might not have been evident in the data collected. The tetragonal ZrSO phase 53 shows no evidence for such broadening. The clear presence of faulting in the structure of CeSO may reflect the difficulty of stabilizing this high oxidation state of +4 for Ce in the presence of sulfide, and it may also be a consequence of the synthetic method, but the failure to completely remove all the coinage metal from the original CeAg 0.8 SO precursor has precedent (e.g., in the chemistry of CuZr 2 S 4 ). 49 While the calculations of the band structure presented here show that in the idealized CeSO composition a bona f ide Ce 4+ species is attainable in the presence of a mixture of oxide and sulfide ions, reliable crystallographic investigations of pure sulfides of Ce which are more sulfide-rich than Ce 2 S 3 show that these invariably contain oxidized anions [S 2 ] 2− . These include CeS 1.9 and two polymorphs of CeS 2 in which S−S distances in the [S 2 ] 2− anions are similar, within the uncertainties, to those found for the analogous compounds with the less oxidizable light lanthanides at 2.154(8) Å for α-CeS 2 and 2.115(3) for β-CeS 2 , 67 distances characteristic of [S 2 ] 2− anions (cf., 2.103(3) Å in the [S 2 ] 2− ions of LaSO). 56 Thus, Ce 4+ readily oxidizes sulfide, and this may reflect the difficulty in completely deintercalating all the Ag from CeAg 0.8 SO to obtain pure CeSO. In contrast, CeSO, with no S−S contacts shorter than 3.23 Å, resembles other systems with only monosulfide ions, e.g., ZrS 2 with no S−S contacts shorter than 3.59 Å (a Zr 4+ compound with six-coordinate Zr in the CdCl 2 structure type), 68 and ThS 2 with no S−S contacts shorter than 3.19 Å (a Th 4+ compound with nine-coordinate Th in the PbCl 2 structure type). 69 However, the evident difficulty in stabilizing Ce 4+ in the presence of S 2− anions may be the origin of the defective structure of CeSO.  Figure 15. Rietveld refinements against PND data (HRPD 90°bank shown) for Li 0.2 CeCu 0.8 SO. Data (blue), fit (red), and difference (gray) are shown. Tick marks for the main phase (upper), V sample holder (middle), and a small CeO 2 impurity (1.8% by mass) (lower) are shown. Further fits and refinement parameters are provided as Supporting Information ( Figure S16 and Table S3).

Inorganic Chemistry
Article