Synthesis and Physical Properties of Iridium-Based Sulfide Ca_1−xIr₄S₆(S₂) [x = 0.23–0.33]

Abstract

We present the synthesis and characterization of the iridium-based sulfide Ca_1−xIr₄S₆(S₂). Quality and phase analysis were conducted by means of energy-dispersive X-ray spectroscopy (EDXS) and powder X-ray diffraction (XRD) techniques. Structure analysis reveals a monoclinic symmetry with the space group C 1 2/m 1 (No. 12), with the lattice constants a = 15.030 (3) Å, b = 3.5747 (5) Å and c = 10.4572 (18) Å. Both X-ray diffraction and EDXS suggest an off-stoichiometry of calcium, leading to the empirical composition Ca_1−xIr_4.0S₆(S₂) [x = 0.23–0.33]. Transport measurements show metallic behavior of the compound in the whole range of measured temperatures. Magnetic measurements down to 1.8 K show no long range order, and Curie–Weiss analysis yields θ_CW = −31.4 K, suggesting that the compound undergoes a magnetic state with short range magnetic correlations. We supplement our study with calculations of the band structure in the framework of the density functional theory.

1. Introduction

The recent materials synthesis and investigation of sulfur-based compounds have shown the presence of exotic insulating ground states, sometimes accompanied by charge density wave and superconducting transitions. For example, BaNiS₂ [1] shows a metal-insulator transition (MIT). This MIT has attracted interest because it is associated with a competition between an insulating antiferromagnetic (AF) phase and a paramagnetic metallic one [2], similar to the case of unconventional superconductors, such as cuprates [3], Fe-based [4], and heavy fermions [5], whereas BaFe₂S₃ is a Mott insulator that shows a stripe-type magnetic order below 119 K [6]. In addition, ternary metal sulfides, such as NiCo₂S₄, have received attention for their catalytic activity in oxygen reduction and evolution reactions [7,8].

Most of these materials are 3d-based sulfur compounds. There are only a few examples of 5d-based, especially Ir-based, compounds, one of which is the spinel structure type CuIr₂S₄ that has a mixed Ir³⁺/Ir⁴⁺ metallic phase and undergoes a first-order transition near 230 K to a low-temperature, charge-ordered, diamagnetic, insulating phase [9,10,11]. In general, 5d-transition metal ions possess a unique combination of spin-orbit coupling, coulomb interactions, and crystal field splitting, which may lead to unique and novel physical properties [12,13]. Iridium in particular has received a lot of attention. For example, it has been used to study the magnetic properties of the geometrically frustrated honeycomb-lattice in Li₂IrO₃ and Na₂IrO₃ [14,15], as well as a variety of compounds of the perovskite [16,17,18,19] and pyrochlore [20,21] families.

However, while numerous iridium oxides are known and investigated [12,20], the combination of iridium ions coordinated by sulfur is so far largely unexplored. In particular, ternary phases containing iridium, sulfur, and an alkaline or alkaline earth metal are unknown. One possible reason for this is that the chemical nature of sulfur is considerably different from oxygen, due to its high tendency to form polysulfides [22,23,24,25]. This often makes the synthesis of new sulfides by simple substitution of oxygen in known oxides difficult or even impossible.

Motivated by this, we performed exploratory chemistry within ternary and quaternary phase diagrams including the elements iridium and sulfur, which lead to the discovery of the previously unknown compound Ca_1−xIr₄S₆(S₂), which is described below. To our best knowledge, this is the first ternary compound in the calcium-iridium-sulfur phase diagram.

2. Experimental Section

All procedures for the preparation of the reaction mixture were performed in a glove box in an atmosphere of dry argon. For the synthesis of Ca_1−xIr₄S₈, 0.045 g CaS (Alfa Aesar, 99.9%), 0.484 g Ir-metal powder (evochem, 99.9%), and 0.141 g elemental sulfur (Alfa Aesar, 99.5%) were mixed and ground. The powder was filled into an alumina-crucible which was placed in a quartz ampule with a length of 10–15 cm and an inner diameter of 0.8–1.2 cm. The ampule was then evacuated to a pressure of 10⁻⁵ mbar and then sealed under partial argon pressure. Then, the sealed ampule was placed in a box furnace and heated to 900 °C with a heating rate of 150 °C/h. The temperature was kept for 60 h, followed by a cooling to room temperature with a rate of 150 °C/h. After one regrinding step, the annealing was repeated for another 40 h at 900 °C. Following the two steps at 900 °C, the reaction temperature was gradually increased to improve sample quality. The sample was heated to 1000 °C, 1100 °C, and 1150 °C each for 50 h, with similar heating and cooling rates as for the previous steps at 900 °C. The product was obtained as a dark grey, well-sintered powder.

Powder X-ray diffraction (XRD) was performed using the transmission method on a StoeStadi-Powder diffractometer (STOE & Cie GmbH, Damstadt, Germany) with Mo-Kα and Co-Kα radiation, and at DESY High Resolution Powder Diffraction Beamline P02.1. For the Rietveld-refinement, the software package FullProf and JANA2006 was used [26,27,28]. The actual composition of the as-synthesized polycrystalline sample was determined by using an X-ray energy-dispersive spectrometer (INCA X-sight, Oxford Instruments, Abingdon, UK) mounted on a field-emission scanning electron microscope JEOL JSM 6490 LV with a W-cathode. A quantitative analysis of the spectra was performed using the INCA software (Oxford Instruments). Elemental analysis of the Ca content was performed via inductively coupled plasma optical emission spectrometry (ICP-OES) on an iCAP 6500 Duo View spectrometer (Thermo Fisher Scientific, Waltham, MA, USA). Prior to the analysis, the Ca was extracted by alkaline chemical digestion.

Temperature- and field-dependent magnetization studies were performed using a commercial Superconducting Quantum Interference Device (SQUID) magnetometer by Quantum Design (MPMS-XL SQUID-magnetometer, Quantum Design, San Diego, CA, USA). The electrical resistivity measurements were carried out by using a standard four-point technique in a homebuilt dip stick from room temperature down to 4.8 K. Silver wires were electrically connected to the sample surface with silver paint on a pressed pellet with a four-point contact method.

3. Results

3.1. Synthesis

In an attempt to investigate tertiary phases containing calcium, iridium and sulfur, a mixture of CaS, iridium metal and sulfur with the stoichiometry Ca:Ir:S = 1:1:3 reacted at 900 °C. A phase of said composition could not be found. However, amongst residues of the starting materials, the pattern of an unknown structure was found by X-ray diffraction. Via EDX spectroscopy, the composition of this previously unknown phase was determined to be Ca:Ir:S ≈ 1:4:8.

In the following, a phase-pure synthesis of this compound was attempted. The key finding, which made the synthesis of the material possible, was the optimization of the temperature profile. Several sintering temperatures were tested. At 800 °C, no complete reaction occurred. Significant amounts of the educts were still detectable in XRD. Through the reaction at 900 °C, the main phase formed in relatively pure form, but a small peak of unknown origin was visible at 1/d ≈ 0.334 Å⁻¹ (Figure 1) as well as traces of small amounts of leftover iridium metal and CaS. The peak at 0.334 Å⁻¹ disappeared after reannealing the sample at 1000 °C; however, even after two more annealing steps at 1100 °C and 1150 °C, small traces of the starting materials remained in the sample.

SEM and EDXS analysis were also performed on the as-synthesized polycrystalline sample. The chemical composition was measured at 23 points of the sample, yielding the empirical composition Ca_0.75±0.05Ir_4.00±0.20S_8.12±0.98, indicative of substantial Ca-deficiency. The rough sample surface may as well have contributed to the deviations from the nominal composition. We have also analyzed the Ca-content by inductively coupled plasma atomic emission spectroscopy (ICP-OES). The measured calcium content is 2.92 ± 0.15 m%, which corresponds to Ca_0.77±0.04Ir₄S₈. It agrees quite well with the EDX estimation of calcium (Ca_0.75) within the error bars.

In order to reduce the remaining impurities, the synthesis of Ca_1−xIr₄S₈ was also attempted with calcium-deficient starting compositions, specifically with Ca:Ir:S ratios of 0.9:4:8 and 0.8:4:8. For these synthesis attempts, a similar procedure and heating profile was used as described above. However, the phase purity of the target phase could not be improved in this way. Instead, additional secondary phases, such as IrS₂, were detected via XRD.

The Ca_1−xIr₄S₈ sample obtained after reaction at 1150 °C was chosen for further investigations. Air sensitivity was tested by exposure overnight. The X-ray diffraction pattern remained unchanged. Additionally, an XRD measurement at 13 K revealed no temperature dependent structural phase transitions.

Under the same reaction conditions, the synthesis of other similar materials with the stoichiometry CaM₄S₈ with different metals was attempted, namely M = Rh, In, Sb, Ru. These were chosen due to their ability to adopt a M ³⁺ oxidation state and their ionic radii being close to that of iridium. However, the synthesis attempts either only yielded the binary sulfides or no reaction occurred. No ternary phases were observable in X-ray diffraction measurements.

3.2. Structure Description

For an in-depth study of the crystal structure of Ca_1−xIr₄S₈, an XRD measurement with synchrotron radiation (λ = 0.20715 Å) was performed (Figure 2). The refinement was carried out in space group C 1 2/m 1. The resulting data, as obtained by JANA2006, are presented in

Table 1. Crystal structure data for Ca_1−xIr₄S₆(S₂) obtained from JANA2006 refinement. The refined crystal structure model and the powder X-ray diffraction presented here are available in CCDC: Deposition Number 2128279.

Parameters	Temperature (K)	293
	Wavelength λ/Å	0.20715
	2θ range/°	0.0114–22.9118
Crystal Data	Space group	C 1 2/m 1 (12)
	a/Å	15.030 (3)
	b/Å	3.5747 (5)
	c/Å	10.4572 (18)
	α/°	90
	β/°	124.970 (9)
	γ/°	90
	V/Å3	460.39 (15)
Refinement	Goodness-Of-Fit	8.87
	Refined parameters	44
	Profile type	Pseudo-Voigt
	wRp	0.0437
	RF	0.0294

. The iridium-lattice is built up by triangular layers propagating along the b-axis, which are folded to form tunnels (Figure 3). All iridium-ions are six-fold coordinated by regular sulfur S²⁻ and (S₂)²⁻ pairs in distorted octahedra, with the Ir–S distances in the range of 2.316–2.402 Å (Figure 4a). In comparable Ir³⁺-sulfides, distances are similar. For comparison, the S–S distance in IrS₂, which should in fact be written as Ir₂S₂(S₂), is 2.30 Å [29]. It is discussed as being closely related to the observed small band-gap semiconducting properties. Slightly shorter S–S distances are known from other persulfide compounds like pyrite FeS₂ (2.177 Å) [22] and K₂S₂ (2.102 Å) [23]. Hence, Ca_1−xIr₄S₈ has to be written as Ca_1−xIr₄S₆(S₂). The octahedra are edge-sharing along the triangular iridium layers. In contrast, inter-layer connections comprise corner sharing. This intimate connectivity between Ir-S-octahedra is also observed in Ir₂S₂(S₂) [29], suggesting high stability of this arrangement.

The Ca-cations are sitting in the voids formed by the tunnels of the Ir-S lattice and form one-dimensional chains along the b-axis (Figure 4b). From the Rietveld simulation, it is obvious that Ca is site-disordered: two split-positions with different occupancies, set as free parameters during the refinement, are needed to reach a satisfying model. As a result of site disorder and low occupancy, the Ca-S distances are somewhat longer (2.84–3.20 Å; Figure 4b) than those in CaS (2.85 Å). The resulting occupancies suggest a stoichiometry of Ca_1−xIr₄S₆(S₂) (x ≈ 0.33), agreeing approximately with the EDXS data. Furthermore, the high B_iso values suggest delocalization or even mobility of the Ca-cations along the b-axis. For charge neutrality, it is expected that, in part, magnetic Ir⁴⁺ is present. Similar static disorder and split positions are commonly used to describe atomic disorder in tunnel structures, for example in K_1+xMo₁₂S₁₄ (x = 0, 1.1, 1.3, and 1.6) [30] and hollandite K_1.33Mn₈O_16, PbIr₄Se₈ [31,32].

The structural similarities between the title compound and Ir₂S₂(S₂) are obvious. In Ir₂S₂(S₂), there are extended voids with walls consisting of six octahedra. However, in Ca_1−xIr₄S₈, the presence of Ca causes the tunnels to expand and have eight octahedra in the walls.

3.3. Magnetic Investigation

The temperature dependence of magnetization of Ca_1−xIr₄S₆(S₂) in the range 1.8–300 K is measured and is shown in Figure 5a. It increases with the lowering of the temperature, showing a typical paramagnetic behavior. By measuring in several different fields, the presence of a minor ferromagnetic secondary phase is suggested because higher fields saturate the effect of the extrinsic signal. By Curie–Weiss approximation on the low field data, the magnetic moment per formula unit is estimated to µ_eff = 0.4 µ_B.

Iridium ions in the parent compound Ca²⁺Ir³⁺₄S²⁻₆(S₂)²⁻ have electronic configuration 5d⁶. The crystal field splits the electrons onto duplet e_g and triplet t_2g orbitals as e_g⁰t_2g⁶, which corresponds to a nonmagnetic ion S = 0. However, the doping by the Ca vacancies leads to the mixed valence state Ir³⁺/Ir⁴⁺. Assuming a fully localized picture, the observed value of magnetic moment per formula of 0.4 µ_B is small. This potentially indicates a lower Ca deficiency (x = 0.025). Another common cause for a decreased value of µ_eff is the presence of itinerant electrons that do not contribute to the effective magnetic moment. Given the metallic properties of Ca_1−xIr₄S₆(S₂) (see Section 3.4), this is the most likely explanation.

The Curie–Weiss temperature obtained from the fit is θ_CW = −31.4 K. A negative value is typical for localized spins with antiferromagnetic interactions. However, in Ca_1−xIr₄S₆(S₂), no signs of long-range magnetic order are found.

3.4. Electrical Transport

The temperature dependent electrical transport of Ca_1−xIr₄S₆(S₂) in the range from 4.8 K to 300 K is shown in Figure 6. The electrical resistivity decreases as a function of temperature, clearly showing the metallic nature of the sample. The temperature-dependence is nonlinear. Our analysis yields a power law behavior ρ = (ρ₀ + AT²). In the interval 0–300 K, the resistivity increases by 30% only. It indicates the dirty metal behavior.

3.5. Electronic Band Structure Calculation

To get some insights about the ground state, we have performed calculation of the electronic structure within the DFT theory. For the calculation, we considered the fully stoichiometric parent compound CaIr₄S₆(S₂). We used the crystal structure parameters described in the structure section. The full relativistic generalized gradient approximation (GGA) in the Perdew–Burke–Ernzerhof variant is used for the exchange correlation potential implemented in the full potential local orbital band-structure package (FPLO) [33,34].

The obtained electronic density of states (DOS) is presented in Figure 7. As one can see, the parent compound is a band insulator with an indirect gap of 1 eV. The orbital structure of the valence band is in the energy window from −9 eV to −1 eV and conducting in the energy window from 0 to 3 eV. It consists mainly of 5d Ir orbitals strongly hybridized with 3p S orbitals (see Figure 7).

In Figure 8, we show the orbital projected band structure. For this presentation, we use the local system of coordinates of IrS₄(S₂) octahedra. The orbital structure shows that the origin of the gap is the crystal field split between e_g and t_2g states about 3–4 eV (see Figure 8), and the complete electron configuration of the t_2g states of Ir³⁺. The obtained estimation of the crystal field splitting is comparable with the experimental obtained for Sr₂IrO₄, Sr₃Ir₂O₇ [35]. We would like to note that the origin of the insulating gap is different from one in compounds containing Ir⁴⁺ (e.g., Sr₂IrO_4, Sr₃Ir₂O₇ [12,36]) and Ir⁵⁺ (e.g., Ba₂YIrO₆ [37,38]). In the case of Ir⁴⁺ and Ir⁵⁺, the gap stems from the splitting of t_2g electrons onto two configurations J = 3/2 and J = 1/2. Here, the driving mechanism is the crystal field splitting between e_g and t_2g electrons. Now, we turn to the question of the pairs (S₂). We compare the valence electron numbers within the DFT on a regular sulfur S²⁻ and on a sulfur in the pairs (S₂)²⁻. The former sulfur corresponds to S1–S3 and the latter to S4 in the Table 1. The regular sulfur has 0.36–0.42 electron excess, while the sulfur in a pair (S₂) 0.14, which is consistent with our discussion that the valence of the sulfur in pair (S₂) is half as much as the regular sulfur.

To understand the origin of the metallic state, we calculated a supercell with one Ca-vacancy per four-unit cells using VASP code. The Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation (GGA) was employed [39]. The resulting DOS is presented in Figure 9. Comparison of the DOS reveals an impurity band at the top of the valence band.

4. Discussion

Ca_1−xIr₄S₆(S₂) adopts a previously not observed structure type. Generally, in many calcium transition metal chalcogenides, the calcium-ion does not form a close-packing with the anions, likely due to its small size. Instead, calcium seems to cause one-dimensional voids through the lattices as in the title phase, Ca_0.75Nb₃O₆ [40] and CaMn₄O₈ [41], where the relative ratio of calcium to transition metal is small. Even in more calcium containing transition metal chalcogenides, calcium performs similarly, for example in CaTi₂O₄ [42] and CaRh₂O₄ [43]. Naturally, exceptions to this trend occur, for example the layered alpha-modification of CaCr₂O₄ [44]. Contrarily, only in the case of the perovskites CaTiO₃, where the metal ratio is 1:1, is a 3D-lattice built from close-packing of calcium and oxygen [45].

From the crystal structure determination and elemental analysis, a Ca-deficiency in the title compound is observed, which explains the presence of Ir⁴⁺. The partial Ir⁴⁺-state contributes to the paramagnetic behavior of Ca_1−xIr₄S₆(S₂). The Curie–Weiss temperature obtained from the fit is θ_CW = −31.4 K. Despite a negative value of θ_CW, which is usually associated with antiferromagnetism, the susceptibility data of Ca_1−xIr₄S₆(S₂) show no signs of a long-range magnetic order.

Resistivity measurements show that the material is metallic. The metallic nature of Ca_1−xIr₄S₆(S₂) stands in strong contrast to many known iridium oxides with octahedrally coordinated iridium. Those iridates are known to have insulating properties [12]. In the case of the title compound, the conducting properties may stem from the Ca-deficiency, since DFT calculations resulted in a band-insulator for the stoichiometric parent compound. To understand the origin of the metallic state, we calculated a supercell with one Ca-vacancy per four-unit cells. Comparison of the DOS reveals impurity states on the top of the valence band.

5. Conclusions

We present the synthesis and characterization of iridium-based sulfide Ca_1−xIr₄S₆(S₂). Through the solid-state synthesis of CaS, iridium metal, and elemental sulfur, it was possible to obtain the compound Ca_1−xIr₄S₆(S₂) (x = 0.23–0.33). The material was characterized by EDXS for compositional analysis and powder X-ray diffraction measurements for the structural analysis. The structural modeling yielded a monoclinic structure within the space group C 1 2/m 1 with the lattice constants a = 15.030 (3) Å, b = 3.5747 (5) Å and c = 10.4572 (18) Å. This previously unknown structure type contains tunnels with walls of IrS₆-octahedra that are sharing edges and vertices and are partially linked by persulfide (S-S) bridges. Within the tunnels, calcium is occupying two different, partly deficient sites. The non-stoichiometry leads to a mixed valence state of iridium, including magnetic Ir⁴⁺-ions. These are responsible for the paramagnetism of the material. No long-range magnetic order is found. Electrical transport measurements on Ca_1−xIr₄S₆(S₂) show metallic behavior despite the strong disorder at the Ca sites. DFT calculations resulted in a band-insulator for the stoichiometric parent compound. Our calculated supercell with one Ca-vacancy per four-unit cell shows impurity states on the top of the valance band.