High-Pressure Synthesis of Novel Ternary Transition Metal Chalcogenide Ba₂Re₆Se₁₁

Abstract

A novel ternary transition metal chalcogenide Ba₂Re₆Se₁₁, which crystallizes in the R−3c space group, was synthesized using a high-pressure and high-temperature technique. The lattice is constituted by Re₆Se₈ cube-octahedral clusters connected by additional apical Se anions via the Re-Se-Re pathway, while the Ba atoms reside in the cavities among the Re₆Se₈ units. High-pressure synchrotron X-ray diffraction measurements showed that Ba₂Re₆Se₁₁ maintains a trigonal structure up to a pressure of 60 GPa, with a bulk modulus of 193 GPa. The lattice stability is ascribed to the fully occupied valence bands of the molecular orbital of the Re₆Se₈ cluster with trivalent Re. This fully occupied orbital configuration also gives rise to the diamagnetic state of Ba₂Re₆Se₁₁, which was validated through magnetic measurements. The resistivity of Ba₂Re₆Se₁₁ is as low as several milliohm centimeters, and it follows the thermal activation mechanism at elevated temperatures and the three-dimensional variable-range hopping model at low temperatures, indicating that Ba₂Re₆Se₁₁ is a semiconductor or insulator in close vicinity to a metal–insulator transition.

1. Introduction

Ternary transition metal chalcogenides have attracted intense attention due to their flexibility in forming versatile lattices including zero-dimensional nano particles [1], one-dimensional chains [2], two-dimensional van der Waals stacking layers [3], and three-dimensional (3D) networks [4]. Depending on the transition metals and lattice structures, ternary transition metal chalcogenides exhibit many physical properties and advanced functions such as superconductivity [5,6], semiconductivity [7], photovoltaic capability [8], energy storage [9,10], and electrocatalysis [11].

Among ternary transition metal chalcogenides, 3D ternary transition metal chalcogenides, which are constituted by transition-metal–chalcogen clusters, have important applications [12,13,14]. One of the famous examples is the Chevrel-phase superconductor AM₆X₈ (A = Pb, Ag, Sn, rare earth element, etc.), which has an elevated critical temperature up to 10 K and a remarkable critical magnetic field H_c2 over 40 T at 0 K [15,16]. Furthermore, 3D ternary transition metal chalcogenides also have potential applications in rechargeable batteries and electrocatalysis [17]. However, their disadvantages—including their time/energy-consuming synthesis processes and sensitivity to air—severely impede their further study [1,16].

The high-pressure synthesis technique utilizing a large-volume press (LVP) [18,19] offers a highly effective method for synthesizing ternary transition metal chalcogenides. These high-pressure conditions offer an additional degree of freedom to overcome the potential barrier of chemical reactions [20,21], providing a new pathway for producing novel transition metal chalcogenides [22,23]. Moreover, the LVP guarantees an environment isolated from air and reduces the reaction time, which is beneficial for materials that are sensitive to oxygen and humidity [24,25,26,27].

In this work, we successfully synthesized a novel 3D ternary transition metal chalcogenide, Ba₂Re₆Se₁₁, under high-pressure and high-temperature conditions. It crystallizes into a trigonal structure with the space group R−3c, which is isostructural with its sulfide counterpart Ba₂Re₆Se₁₁ [12,28,29]. The high-pressure synchrotron X-ray diffraction measurements indicate that it maintains the trigonal lattice structure up to a pressure of 60 GPa, with a bulk modulus of 193 GPa. The crystallographic stability can be ascribed to the fully occupied molecular orbital of the Re₆Se₈ cube-octahedra, which also gives rise to the diamagnetic (DM) state of Ba₂Re₆Se₁₁. On the other hand, the resistivity of Ba₂Re₆Se₁₁ is as low as ~10 mΩ cm, and it follows the thermal activation mechanism at elevated temperatures and the 3D variable-range hopping (VRH) model at low temperatures, indicating that Ba₂Re₆Se₁₁ is a semiconductor or insulator fairly near to a metal–insulator transition.

2. Materials and Methods

High-purity polycrystalline Ba₂Re₆Se₁₁ was synthesized using a high-pressure and high-temperature technique. Stoichiometric BaSe, Re (99.9%, Alfa Aesar, Shanghai, China), and Se (99.9%, Alfa Aesar, Shanghai, China) powders were selected as the reactants. The BaSe precursor was prepared by sintering a mixture of Ba (99.9%, Alfa Aesar, Shanghai, China) and Se (99.9%, Alfa Aesar, Shanghai, China) powders at 750 °C for 12 hours in a vacuum-sealed quartz tube (10⁻⁴ Pa). The reactants were finely ground in an agate mortar, pressed into pellets, and subjected to a hinge-type six-anvil LVP. The pressure was slowly increased to 5 GPa over 30 minutes, after which the temperature was increased to 1475 K over 10 minutes and maintained for 30 minutes. Then, the temperature was quenched to room temperature in a few seconds and the pressure was slowly released to ambient pressure over 1 hour. Due to the air sensitivity of Ba, Se, and BaSe, the procedures before and after the high-pressure synthesis were performed in a glove box full of argon gas. It is worth noting that—in contrast to its sulfur counterpart, which can be synthesized in a H₂S gas stream [28]—a highly sealed and high-pressure environment is necessary for synthesizing stoichiometric Ba₂Re₆Se₁₁ in order to prevent the volatilization of Se and decomposition of BaSe.

Powder X-ray diffraction (XRD) was performed using a Rigaku SmartLab diffractometer (Rigaku, Tokyo, Japan) with Cu-Kα radiation. Rietveld refinement [30] was conducted using the GSAS-I software package [31]. The synchrotron XRD (SXRD) measurements were carried out on the BL15U1 beamline of Shanghai Synchrotron Radiation Facility (SSRF) (Shanghai, China) (λ = 0.62 Å). Diamonds with a 300 µm culet and rhenium gaskets were used [32]. No pressure medium was used. The pressures were determined using the ruby fluorescence method.

The magnetic measurements were performed using a superconducting quantum interference device magnetometer (MPMS-3, Quantum Design, San Diego, CA, USA). Both zero-field-cooling (ZFC) and field-cooling (FC) modes were adopted under a magnetic field of 0.1 T. The electrical resistivity was measured using a physical property measurement system (PPMS-DynaCool, Quantum Design, San Diego, CA, USA) with a standard four-probe method. The specific heat was measured using PPMS. The sample (thickness of 0.4 mm) was mounted using Apiezon N grease to ensure good thermal contact. The specific heat data were corrected by subtracting the contributions from the sample puck and the grease.

3. Results and Discussion

3.1. Crystal Structure

Figure 1 displays the XRD pattern of Ba₂Re₆Se₁₁, which is well fitted to that of the R−3c (No. 167) space group with an a = 9.4891(9) Å and c = 33.3975(5) Å. For the Rietveld refinement, the atomic parameters of its sulfide counterpart Ba₂Re₆S₁₁ [28] were adopted as the initial parameters. The refined crystallographic parameters are listed in Table 1. The refined occupancy values of all the atoms are very close to 1, so we fixed them. The variation between the calculated and the experimental XRD derives from the tiny impurities and the background (shifted Chebyshev polynomial, green line in Figure 1). It is worth noting that the thermal factor of Se1 is smaller than those of the other atoms, which is due to Se1 being coordinated with five cations; for comparison, Se2/Se3 is coordinated with four cations. Thus, the bonding of Se1 is relatively rigid, leading to a reduced thermal factor.

Figure 1. XRD pattern and Rietveld refinement of Ba₂Re₆Se₁₁. The black circles, green line, red line, and blue line indicate the observed, background, calculated, and difference, respectively. The magenta ticks indicate the allowed Bragg reflections for space group R−3c. The brown stars indicate minor unidentified impurities. The upper-right inset displays the crystal structure of Ba₂Re₆Se₁₁.

Table 1. Crystallographic parameters of Ba₂Re₆Se₁₁.

Phase Data
Space group: R−3c
a = 9.4891(9) Å, c = 33.3975(5) Å
Rwp = 7.79%, Rp = 5.65%, χ2 = 2.90
Atomic Parameters
Atom	Wyckoff position	x	y	z	Occupancy	Uiso (100 × Å2)
Ba	12c	0	0	0.8120(1)	1	0.99(8)
Re	36f	0.8513(1)	0.8274(1)	0.03344(3)	1	0.34(3)
Se1	36f	0.6704(3)	0.9581(3)	0.03157(9)	1	0.13(7)
Se2	18e	0.7319(4)	0	0.25	1	0.43(11)
Se3	12c	0	0	0.0903(1)	1	0.56(14)

As depicted in the inset of Figure 1, the building block of the structure is the cube-octahedral Re₆Se₈ cluster, which contains a nearly regular Re₆ octahedron (shown in blue) with one Se atom capping each face, forming a Se₈ cubic cage (Se1 and Se3, shown in pink). The Re₆Se₈ clusters are further connected by additional Se (Se2, shown in red) residing at the apical positions of the Re₆ octahedra along the c direction, forming a Re–Se2–Re bond angle of 120.8732(5)°. The Ba atoms occupy the vacancies among the Re₆Se₈ clusters, forming BaSe₁₀ units.

3.2. Crystallographic Stability

To study the structural stability of Ba₂Re₆Se₁₁, we performed SXRD measurements under pressure. As shown in Figure 2a, with increasing pressure, the (1 0 −2), (1 0 4), and (1 1 0) diffraction peaks broaden and their intensities decrease, indicating gradual decrystallization under pressure. Meanwhile, all the diffraction peaks shift to a higher 2θ angle, indicating that the lattice was compressed under pressure. On the other hand, the lattice maintains its symmetry up to a pressure of 60 GPa, without any signs of a structural transition, indicating the robust crystallographic stability of Ba₂Re₆Se₁₁. The non-hydrostaticity is not apparent due to the 3D lattice of Ba₂Re₆Se₁₁ and the specimen being in powder form.

Figure 2. (a) SXRD pattern of Ba₂Re₆Se₁₁ under selected pressures. (b) a and c values as a function of applied pressure. (c) c/c₀, a/a₀ and V/V₀ values as a function of applied pressure.

In order to quantitatively study the lattice parameters under pressure, we extrapolated a, c, and volume V. As depicted in Figure 2b, both a and c monotonously decrease with increasing pressure, without any indication of a phase transition. The c/c₀, a/a₀, and V/V₀ values as a function of applied pressure are shown in Figure 2c, where the subscript “0” indicates the parameters at ambient pressure. One can observe the anisotropy between the in-plane and out-of-plane directions under pressure, with a decreasing by about 14% at a pressure of 60 GPa, whereas c only decreases by 5%, leading to a 30% reduction in V. The bulk modulus was obtained using the formula K = −dP/dV = 193(13) GPa. For comparison, the bulk modulus values for steel and diamond are ~160 GPa and ~600 GPa, respectively.

To determine the mechanism underlying the solid lattice stability of Ba2Re6Se11, we examined the Re₆Se₈ building block, which is reminiscent of M₆X₈ (M: transition metal; X: chalcogen) clusters in similar compounds [33,34,35]. The schematic representation of the molecular orbital of Re in the Re₆Se₈ cluster is depicted in Figure 3. When the M has a d⁴ configuration (e.g., Mo²⁺, Tc³⁺, or Re³⁺), the cluster possess 24 electrons in total and thus the valence bands are fully occupied, leading to the highly symmetrical nature of the Re₆ octahedra as well as the robust lattice stability.

Figure 3. Re₆Se₈ cluster in Ba₂Re₆Se₁₁ and schematic representation of its molecular orbital. Each red arrow indicates one electron with spin-up/down state.

3.3. Magnetic Properties

Figure 4a displays the temperature dependence of the magnetic susceptibility (χ) of Ba₂Re₆Se₁₁. Above 50 K, a negative χ value was observed, indicating a DM nature. Nevertheless, the M(T) curve shows an upturn below 50 K and changes to become positive, indicating the superposition of a paramagnetic or ferromagnetic (FM) contribution of χ = χ_DM + χ_FM. In order to distinguish these contributions, we performed Curie-tail fitting at temperatures above 50 K (χ_FM, green line), and the DM signal was obtained using χ_DM = χ − χ_FM (red line).

Figure 4. (a) Temperature dependence of magnetic susceptibility of Ba₂Re₆Se₁₁ measured under 0.1 T. Experimental ZFC and FC data are shown as hollow circles and solid squares, respectively. Curie-tail fitting and curve are displayed as green and red lines, respectively. (b) Field dependence of magnetization at selected temperatures. (c) DM contribution extracted from field dependence of magnetization curve.

The field dependence of magnetization is displayed in Figure 4b. Above 50 K, the linear M(H) curves with a negative slope agree well with the DM state. However, at lower temperatures, the M(H) curves behave quite differently. For example, at 2 K, as the applied magnetic field increases, the M(H) curve rapidly increases to a maximum and then linearly decreases with a negative slope again. The magnetic moment at its maximum is extremely small (~10⁻⁵ μ_B f.u.⁻¹), excluding the FM configuration of Re³⁺ (5d⁴, S = 1) in Ba₂Re₆Se₁₁. On the other hand, the negative slope of the M(H) curve in a high magnetic field excludes the canted antiferromagnetic configuration [36,37]. Therefore, we conclude that the current Ba₂Re₆Se₁₁ is DM. The upturn of the M(T) curves and the tiny magnetization of the M(H) curves at low temperatures are due to trace amounts of magnetic impurities (tens of ppm). To extract the DM contribution, we performed linear fitting of the M(H) curve in a field above 5 T. The obtained field-dependent magnetization of the DM part is depicted in Figure 4c.

The diamagnetism of Ba₂Re₆Se₁₁ can be explained by the molecular orbital of the Re₆Se₈ cluster (Figure 3). The molecular orbital of the Re₆ octahedral cluster, with a Re³⁺ (5d⁴) state, has 24 electrons at its highest occupied molecular orbital level that fully occupy the shell, giving rise to a diamagnetic state. Similar diamagnetic behavior has been observed in other compounds constituted by Re₆ octahedral clusters, such as Ba₂Re₆S₁₁ [28] and Tl₄Re₆X₁₂ (X = S, Se) [38].

3.4. Transport Properties

Figure 5a depicts the temperature dependence of the resistivity (ρ) of Ba₂Re₆Se₁₁. The ρ value is smaller than 12 mΩ cm for the whole temperature range of 2–300 K, whereas it gradually increases with cooling. In order to quantitatively study the electrical conductivity, we fitted the ρ(T) plot using the thermal activation model at an elevated temperature range of 150–300 K and the formula lnρ = E_a/k_BT + lnρ₀, where k_B is the Boltzmann constant (Figure 5b). The activation energy was calculated to be E_a = 3.4(1) meV and the residual resistivity is ρ₀ = 4.19(1) mΩ cm. At low temperatures below 20 K, the ρ(T) plot is well fitted to the 3D VRH model with the equation lnρ = (T₀/T)^1/4 + lnρ₀ (Figure 5c). The obtained ρ₀ = 4.59(2) mΩ cm is in agreement with the values obtained from the activation model. Thus, Ba₂Re₆Se₁₁ can be regarded as a semiconductor or insulator in close vicinity to a metal–insulator transition. It is worth noting that extrinsic effects, such as defect/impurity activation, grain-boundary barriers, and hopping conduction, can also contribute to the measured resistivity.

Figure 5. (a) Temperature dependence of resistivity of Ba₂Re₆Se₁₁. (b) lnρ–T⁻¹ plot of experimental data (black circles) and fitting result (red line) of thermal activation model. (c) lnρ–T^−1/4 plot of experimental data (black circles) and fitting result (red line) of 3D VRH model.

The semiconductivity of Ba₂Re₆Se₁₁ can also be explained by the molecular orbital of the Re₆ cluster depicted in Figure 3. The valence bands are fully occupied and the conducting bands are empty, with the Fermi level located at the top of the valence state. The close vicinity to a metal–insulator transition can be ascribed to the delocalization of the molecular orbital due to Re-Se covalency [23,24].

3.5. Heat Capacity

Figure 6 displays the temperature dependence of the heat capacity of Ba₂Re₆Se₁₁. In order to determine the components of the heat capacity, we plotted the C_P/T–T² plot at 2–15 K (inset of Figure 6). It forms a linear curve with a zero intercept at the vertical axis, indicating that only the phonons contribute to the heat capacity. This behavior is consistent with Ba₂Re₆Se₁₁ being diamagnetic and semiconductive. The C_P/T–T² curve is well fitted to the formula C_P/T = βT², where β = 4.72 mJ mol⁻¹ K⁻⁴ (inset of Figure 6). The Debye temperature was found to be Θ_D = (12nπ⁴R/5β)^1/3 = 199 K, where n = 19 is the number of atoms per chemical formula and R = 8.314 J mol⁻¹ K⁻¹ is the ideal gas constant.

Figure 6. Temperature dependence of heat capacity of Ba₂Re₆Se₁₁. Inset displays C_P/T–T² plot at 2–15 K. Experimental data and fitting result are displayed as black circles and a red line, respectively.

4. Conclusions

Using a high-pressure synthesis technique, a novel ternary transition metal chalcogenide, Ba₂Re₆Se₁₁, was synthesized. It crystallizes in the R−3c space group with an a = 9.4891(9) Å and c = 33.3975(5) Å. The structure is constituted by Re₆Se₈ cube-octahedral clusters connected by additional apical Se anions via the Re-Se-Re pathway, and the Ba atoms reside in the cavities between the Re₆Se₈ units. The Re has a valence state of +3, with four electrons occupying the 5d orbital for each Re atom. Consequently, the Re₆ octahedron possesses 24 electrons at its molecular orbital level and forms a full-shell electron occupation configuration, giving rise to the robust lattice stability with a bulk modulus of 193 GPa. The fully occupied molecular orbital also gives rise to a diamagnetic state for Ba₂Re₆Se₁₁, which was validated through magnetic measurements. The resistivity of Ba₂Re₆Se₁₁ is as low as several milliohm centimeters, and it follows the thermal activation mechanism at elevated temperatures and the three-dimensional variable-range hopping model at low temperatures, indicating that Ba₂Re₆Se₁₁ is a semiconductor or insulator in close vicinity to a metal–insulator transition.