Structural properties of Sb₂S₃ under pressure: evidence of an electronic topological transition

Abstract

High-pressure Raman spectroscopy and x-ray diffraction of Sb₂S₃ up to 53 GPa reveals two phase transitions at 5 GPa and 15 GPa. The first transition is evidenced by noticeable compressibility changes in distinct Raman-active modes, in the lattice parameter axial ratios, the unit cell volume, as well as in specific interatomic bond lengths and bond angles. By taking into account relevant results from the literature, we assign these effects to a second-order isostructural transition arising from an electronic topological transition in Sb₂S₃ near 5 GPa. Close comparison between Sb₂S₃ and Sb₂Se₃ up to 10 GPa reveals a slightly diverse structural behavior for these two compounds after the isostructural transition pressure. This structural diversity appears to account for the different pressure-induced electronic behavior of Sb₂S₃ and Sb₂Se₃ up to 10 GPa, i.e. the absence of an insulator-metal transition in Sb₂S₃ up to that pressure. Finally, the second high-pressure modification appearing above 15 GPa appears to trigger a structural disorder at ~20 GPa; full decompression from 53 GPa leads to the recovery of an amorphous state.

Introduction

The Sb₂S₃ material (stibnite) is a well-known binary semiconductor with an optical band gap E_g~ 1.7 eV¹. This material constitutes a promising candidate for solar energy conversion² and optoelectronic applications³. At ambient conditions, Sb₂S₃ crystallizes in a complex orthorhombic structure (SG Pnma, Z = 4, U₂S₃-type)⁴. This Pnma phase can be described as a layered structure, consisting of parallel molecular (Sb₄S₆)_n ribbon-like chains along the short b-axis held together by weak intermolecular forces. The Sb³⁺ ions are located at two different sites in this phase, and their coordination environment can be described as sevenfold for the Sb(1) ion and eightfold (7 + 1) for the Sb(2) ion, respectively (Fig. 1). The same structure is adopted by Sb₂Se₃⁵, whereas Sb₂Te₃ adopts a rhombohedral structure (SG , Z = 3) made up of SbTe₆ octahedral layers piled up along c-axis⁶ due to the absence of the Sb³⁺ lone electron pair stereochemical activity⁷.

Figure 1: Unit cell of Sb₂S₃ at ambient conditions (SG Pnma, Z = 4).

The blue, green, and red spheres correspond to the Sb(1), Sb(2), and S ions, respectively. The blue Sb(1)S₇ and green Sb(2)S₇₊₁ polyhedra are also displayed.

Very recently, Sb₂Se₃ was shown also to undergo an electronic topological transition (ETT) near 3 GPa⁸, with theoretical works corroborating such behavior^9,10. This ETT, which appears to be a common trend for these systems¹¹, was manifested as a second-order isostructural transition via compressibility changes in several structural parameters^11,12. We remind here that an ETT occurs when a band extremum, which is associated to a Van Hove singularity, crosses the Fermi energy (E_F) and leads to a strong redistribution of the electronic density of states (EDOS) near E_F. This EDOS redistribution induces a second-order isostructural transition, i.e. a transition without any volume discontinuity at the transition point or changes in the crystalline symmetry. The elastic constants are affected by the ETT, however, hence leading to distinct compressibility changes of the material under study^13,14. In addition, high-pressure resistivity measurements of Sb₂Se₃ revealed also an insulator-metal transition near 3 GPa, whereas pressure-induced superconductivity was observed above 10 GPa¹². The superconducting state persisted up to 40 GPa, with further compression leading to the transformation of the Pnma structure into a disordered body-centered cubic (bcc) phase above 55 GPa¹⁵.

A similar ETT was recently observed for Sb₂S₃ by means of Raman spectroscopic and resistivity probes near 5 GPa, with a second phase transition following at 20 GPa¹⁶. Even though a x-ray diffraction (XRD) study of Sb₂S₃ up to 10 GPa showed the persistence of the Pnma phase up to that pressure¹⁷, the mechanism of ETT at 5 GPa, the detection of the second transition at 20 GPa, as well as the possibility of additional structural modifications upon further compression^15,18,19,20, calls for an updated structural investigation of Sb₂S₃ in a more extended pressure range.

We present here our combined high-pressure Raman and XRD studies on Sb₂S₃ up to 25 GPa and 53 GPa, respectively. Overall, we have detected two phase transitions at 5 GPa and 15 GPa. The first transition is manifested via compressibility changes in several structural parameters, an observation which correlates strongly with the reported ETT¹⁶. As for the second transition at 15 GPa, this new phase could not be identified due to the onset of structural disorder above 20 GPa. Full decompression of Sb₂S₃ from 53 GPa leads to the recovery of an amorphous state.

Results

Given that Raman spectroscopy is a more sensitive probe for isostructural transitions¹¹, we present first our high-pressure Raman spectroscopic investigation on Sb₂S₃. According to group theory, a sum of thirty Raman-active modes are expected for the Pnma phase of Sb₂S₃²¹:

We can resolve ten broad bands in our Raman spectra (Fig. 2), which is consistent with the reported literature^16,22,23. The mode assignment is adopted from the polarization studies of Sereni et al.²³ (Table 1). Upon increasing pressure, most of the Raman modes upshift in frequency; on the contrary, the high-frequency A_g(4), A_g(5), and B_1g(5) modes downshift in energy up to 5 GPa. Beyond that pressure, the A_g(4) and B_1g(5) features display a compressibility change, with the A_g(4) mode exhibiting a completely different pressure-induced behavior after 5 GPa with a positive pressure slope [Fig. 2(b) and Table 1]. In addition, the pressure slope of the B_1g(5) mode reduces substantially beyond 5 GPa. As for the A_g(5) mode, it merges with its neighboring B_1g(5) mode at 7 GPa, and could not be followed above that pressure. Since these modes correspond to the stretching vibrations of the shorter Sb-S distances²², the observed compressibility changes should reflect the pressure-induced behavior of the corresponding bond lengths. Overall, our observations are in excellent agreement with the recent study of Sorb et al.¹⁶.

Figure 2: High-pressure Raman spectroscopic results of Sb₂S₃.

(a) Raman spectra of Sb₂S₃ at selected pressures (λ = 532 nm, T = 300 K). Vertical lines indicate the Sb₂S₃ Raman-active modes. (b) Raman mode frequency evolution of Sb₂S₃ against pressure. Solid and open circles correspond to data collected upon compression and decompression, respectively. Solid lines represent least square fits. The dashed lines mark the onset of phase transitions (see text).

Table 1 Mode assignment²³, Raman mode frequencies, pressure coefficients, and the mode Gruneisen parameters γ of the Raman features of Sb₂S₃ calculated at a reference pressure P_R.

Further compression of Sb₂S₃ results in the appearance of two new low-intensity features beyond 15 GPa [denoted as M1 and M2 in Fig. 2(b), see also supplementary Fig. S1]. Since the strongest Raman features of elemental Sb²⁴ and S^25,26,27 do not reside in these frequencies, we can safely exclude any decomposition and attribute the appearance of the M1 and M2 features to a pressure-induced phase transition. The M2 feature was also detected in the study of Sorb et al. above 20 GPa¹⁶. Beyond 15 GPa, however, the Raman modes exhibit pronounced broadening; consequently, the Raman spectra become rather featureless at 22 GPa [Fig. 2(a)]. Full decompression from 25 GPa leads to the recovery of the original Sb₂S₃ Raman spectrum, indicating the reversibility of the pressure-induced Raman changes.

Having documented the pressure-induced changes from our Raman investigation, we now focus on the structural properties of Sb₂S₃ under pressure. Selected XRD patterns are presented in Fig. 3. As we can observe, the Bragg peaks of the Pnma phase could be detected up to the highest pressure, i.e. 53 GPa. The Bragg peaks, however, exhibit significant broadening beyond 20 GPa, indicating the onset of structural disorder above that pressure. This pressure-induced structural disorder is most likely responsible for the featureless Raman spectra at 22 GPa [Fig. 2(a)]. Further compression leads to the substantial broadening of the Pnma Bragg peaks in our XRD patterns. Upon decompression from 53 GPa we obtain an amorphous-like state, in apparent contradiction with our Raman study where the original phase is recovered upon decompression from 25 GPa [Fig. 2(a)]. It appears that unloading from a significantly larger pressure favors the quenching of an amorphous state instead of the original structure.

Figure 3: Selected XRD patterns of Sb₂S₃ at various pressures pressures (λ = 0.4246 Å, T = 300 K).

The red arrow marks the new Bragg feature. An example of a Rietveld refinement at 4.8 GPa is also provided. The black and red solid lines correspond to the measured and the fitted spectra, whereas their difference is depicted as a blue line. Vertical ticks mark the Bragg peak positions for the Pnma phase.

In addition, a new Bragg peak could be detected at 2θ ≈ 6.6° near 15 GPa (Fig. 3 and supplementary Fig. S2). This feature could not be assigned either to the Pnma or any “contaminating” phase such as rhenium (gasket material), helium, or ruby. Therefore, the appearance of this extra Bragg peak signals a structural transition of Sb₂S₃ at 15 GPa, in excellent agreement with our Raman study (Fig. 2). Attempts to fit the XRD patterns with any of the reported high-pressure phases of related A₂B₃ compounds^18,19,20,28 proved unsuccessful. A possible elemental decomposition into Sb²⁹ and S³⁰ could also not account for this novel peak. Therefore, we speculate that the Sb₂S₃ XRD patterns consist of a mixture of two phases above 15 GPa, i.e. the Pnma structure and a high-pressure modification. Due to the pronounced Bragg peak broadening and the fact that this high-pressure phase is characterized by a single Bragg feature, however, its identification becomes unattainable at this point.

Given the aforementioned Bragg peak overlap and broadening upon pressure increase, the interatomic and lattice parameters of the Pnma phase could be obtained reliably up to 9 GPa and 20 GPa, respectively. All of these structural data are provided in supplementary Tables S1 and S2, whereas the extracted P-V data are shown in Fig. 4. As we can observe, there is a clear compressibility change in the volume and in the orthorhombic axial ratios near 5 GPa, in excellent agreement with the compressibility changes observed in our Raman spectra (Fig. 2). By taking into account the pressure-induced behavior of isostructural Sb₂Se₃^8,12 and Bi₂S₃³¹ compounds, and in close comparison with the related Bi₂Te₃^32,33, we attribute these compressibility changes to an isostructural transition of Sb₂S₃ near 5 GPa. This isostructural transition is most likely the signature of the reported ETT in Sb₂S₃¹⁶, reflecting a change in the topology of the Fermi surface^8,10,11,13.

Figure 4: Plot of the unit cell volume as a function of pressure for the Pnma phase of Sb₂S₃.

The solid lines represent the fitted Birch-Murnaghan Equation of State. The orthorhombic axial ratios are shown in the inset. The vertical dashed lines mark the onset of phase transitions (see text). The open symbols correspond to data from Lundegaard et al.¹⁷.

The fitting of the P-V data to a Birch-Murnaghan Equation of State (B-M EoS) yielded volumes and bulk moduli values of V₀ = 488.2 (4) ų and B₀ = 27.2(6) GPa, and V = 434.2(7) ų and B = 65(2) GPa (calculated at P = 5 GPa) before and after the isostructural transition, with fixed bulk moduli derivatives of B′₀ = 6 and B’ = 4, respectively. The B₀ value of Sb₂S₃ prior to the transition is consistent with that of Lundegaard et al.¹⁷ and in line with the B₀ value of Sb₂Se₃^12,15.

Except from these compressibility changes in the lattice parameters and the bulk volume, inspection of the interatomic parameters also reveals distinct changes above 4 GPa (Fig. 5). For example, we can observe that the Sb(1)-S(3) short bond distance elongates up to 4 GPa, whereas a reduction is evidenced above that pressure. Actually, this pressure-induced trend is in excellent agreement with the behavior of the stretching A_g(4) Raman-active mode [Fig. 2(b)]. A similar trend applies for the S(3)-Sb(2)-S(3) bond angle (Fig. 5), which reflects the tiltings and distortions of the Sb(1)S₇ polyhedra¹². Overall, the isostructural transition can be readily witnessed from the behavior of the interatomic parameters, a common trend for these systems^12,15,31.

Figure 5: Distinct interatomic Sb₂S₃ parameters as a function of pressure.

(a) Selected Sb-S bond lengths and (b) S-Sb-S bond angles up to 9 GPa. The vertical dashed line marks the onset of the isostructural transition. The nomenclature of the Sb and S ions is provided in supplementary Fig. S3. The open symbols correspond to data from Lundegaard et al.¹⁷.

Discussion

Having resolved the structural evolution of Sb₂S₃ under pressure, a comparison between the pressure-induced behavior of Sb₂S₃ and the isostructural Sb₂Se₃ is in order. Both of these compounds exhibit isostructural transitions at the same pressure, i.e. close to 5 GPa^12,15. In both cases, an electronic topological transition was put forward in order to account for the structural and vibrational changes beyond that pressure^8,12,16. Interestingly, the high-pressure resistivity studies of these compounds reveal diverse behavior^12,16. In particular, the room temperature resistivity of Sb₂S₃ was found to increase up to 5 GPa, where it reached saturation; two anomalies were also detected at 1.4 GPa and 2.4 GPa¹⁶. For Sb₂Se₃ on the other hand, a reduction of resistivity was observed up to 3.5 GPa, where an insulator-metal transition takes place; further compression leads to the induction of superconductivity at 10 GPa (T_c = 2 K)¹². This pressure-induced behavior of Sb₂Se₃ resembles the transport properties of Bi₂Se₃, Bi₂Te₃, and Sb₂Te₃ compounds^{34,35,36,37,38,39}. Given the fact that Sb₂S₃ and Sb₂Se₃ exhibit almost identical electronic band structures^7,40, this diverse behavior in resistivity is puzzling.

A direct comparison between the pressure-induced behavior of the Sb₂S₃ and Sb₂Se₃ structural parameters provides some hints. Generally, the compression mechanism for both compounds is practically identical up to 5 GPa¹⁵. As expected, the b-axis is the least compressible direction, since it contains the Sb₄S(Se)₆ molecular ribbons comprising the Pnma structure (Fig. 1). On the other hand, the a-axis and c-axis reduce much faster compared to b-axis under compression, with a-axis being more compressible than c-axis up to 5 GPa. This is easily evidenced from the increasing rate of the c/a axial ratio up to that pressure [Fig. 6(a)].

Figure 6: Structural comparison between Sb₂S₃ and Sb₂Se₃.

Plot of (a) orthorhombic axial ratios, (b) the X(3)-Sb(2)-X(3) bond angle, (c) Sb(1)X₇ polyhedral volumes, and the Sb(1) cation eccentricity as a function of pressure for both Sb₂S₃ (black) and Sb₂Se₃ (red, data from ref. 15). Dashed lines are guides to the eye. The vertical dashed line marks the isostructural transition.

Beyond 5 GPa, however, Sb₂S₃ and Sb₂Se₃ exhibit slghtly diverse compressibility trends. In particular, the orthorhombic c-axis becomes more compressible and the b-axis less compressible in Sb₂S₃ than Sb₂Se₃ above 5 GPa; the a-axis exhibits similar compressibility for both compounds. As a result, the axial ratios of Sb₂S₃ behave differently than those of Sb₂Se₃ above 5 GPa, e.g. the Sb₂S₃ c/a axial ratio shows a more prominent decreasing trend beyond 5 GPa compared to the Sb₂Se₃ c/a axial ratio [Fig. 6(a)].

A closer look at the microscopic structural behavior reveals additional information. In Fig. 6(b,c) we plot the pressure-induced evolution of the X(3)-Sb(2)-X(3) bond angle, the volume of the Sb(1)X₇ polyhedra (X = S, Se), and the Sb(1) cation eccentricity for both Sb₂S₃ and Sb₂Se₃ compounds. We note that the X(3)-Sb(2)-X(3) bond angle reflects the tiltings of the Sb(1)X₇ polyhedra parallel to the ac plane¹², whereas the cation eccentricity is a quantitative measure of the stereochemical activity of the Sb³⁺ lone electron pair (LEP); the larger the eccentricity value, the more active the LEP^17,41. As we can observe, the X(3)-Sb(2)-X3 bond angles behave similarly for both Sb₂S₃ and Sb₂Se₃ up to 5 GPa, i.e. up to the isostructural transition [Fig. 6(b)]. Further compression, however, leads to the reduction of the S(3)-Sb(2)-S(3) bond angle in Sb₂S₃ in a more pronounced rate compared to the Se(3)-Sb(2)-Se(3) bond angle of Sb₂Se₃. Given that the LEPs are located at the ac plane^42,43, this diverse bond angle changes mirror different Sb³⁺ LEP behaviors in these materials.

Indeed, in Fig. 6(c) we can observe that the Sb(1) cation eccentricities of Sb₂S₃ and Sb₂Se₃ display different behavior beyond 5 GPa. More precisely, the larger Sb(1) eccentricity value for Sb₂S₃ compared to Sb₂Se₃ indicates a larger stereochemical activity for the former after the isostructural transition. In other words, the Sb(1) LEP of Sb₂S₃ does not hybridize strongly with its neighboring S-p orbitals up to 10 GPa, as opposed to Sb₂Se₃ where the Sb(1) cation eccentricity value approaches an almost zero value after 5 GPa (almost complete orbital overlap). We speculate that this lack of LEP hybridization in Sb₂S₃ up to 10 GPa is the reason behind the different pressure-induced behavior in the electronic properties of Sb₂S₃ and Sb₂Se₃, i.e. the reason why an insulator-metal transition is observed for Sb₂Se₃¹² and not in Sb₂S₃ (at least up to 10 GPa)¹⁶. Theoretical calculations are required, however, to verify this scenario.

Finally, we would like to briefly address the structural disorder in Sb₂S₃ initiating beyond 20 GPa (Fig. 3). Interestingly, the onset of this structural disorder lies at much lower pressures compared to Sb₂Se₃¹⁵ and Bi₂S₃³¹, but close with that of α-Sb₂O₃⁴⁴. Such disorder can generally be accounted for by two mechanisms⁴⁵: (a) the disordered phase may be a precursor of a structural transformation into another crystalline phase, which cannot be formed due to kinetic barriers, or (b) the tendency of the material to decompose into its constituents. Given the pressure-induced trends of Bi₂Te₃^19,35,46, Sb₂Te₃^18,28, Bi₂Se₃^{20,37,47,48,49}, and Sb₂Se₃¹⁵ towards high-pressure disordered phases instead of elemental decomposition, however, the scenario of a kinetically-hindered structural transition in Sb₂S₃ appears more plausible. Actually, the appearance of the high-pressure modification above 15 GPa might be exactly that, i.e. the onset of a structural transformation of the Pnma phase towards another crystalline state, which is obstructed due to kinetic effects; a combined high-pressure and high-temperature structural study will be needed in order to resolve this matter. Considering nevertheless the structural trends of the A₂B₃ series under pressure, we can expect that this new structure will exhibit higher cationic coordinations.

In conclusion, our combined high-pressure Raman and XRD investigations revealed two phase transitions in Sb₂S₃ at 5 GPa and 15 GPa. The first transition is manifested via noticeable compressibility changes in several structural parameters. By taking into account an earlier report¹⁶, we assign these changes to a second-order isostructural transition arising from changes in the electronic structure of Sb₂S₃. Close comparison between the Sb₂S₃ and Sb₂Se₃ compounds up to 10 GPa reveals a slightly diverse pressure-induced behavior in the Sb³⁺ LEP activity after the isostructural transition, a plausible reason behind their different high-pressure electronic behavior above 5 GPa^12,16. As for the second transition of Sb₂S₃ at 15 GPa, the new phase could not be identified due to the onset of structural disorder above 20 GPa. We speculate that the structural disorder is a transient state of this new high-pressure phase, which cannot be completed due to kinetic effects. Finally, an amorphous state is recovered upon full decompression from 53 GPa.

Materials and Methods

Sample and high-pressure technique details

Polycrystalline Sb₂S₃ powder was purchased commercially (Alfa-Aesar, 99.999% purity). The XRD measurements at ambient conditions did not detect any impurity phases. Pressure was generated with a gasketed symmetric diamond anvil cell, equipped with a set of diamonds with 300 μm culet diameter. The ruby luminescence method was employed for pressure calibration⁵⁰.

High-pressure Raman spectroscopy

The high-pressure Raman measurements were conducted with a solid-state laser (λ = 532 nm) coupled to a single-stage spectrometer and a charge-coupled device. The spectral resolution was 2 cm⁻¹ and the lowest resolvable frequency was ~90 cm⁻¹. Given the photo-sensitivity of the material⁵¹, the incident laser power was kept below 2 mW outside the DAC, whereas the size of the laser spot on the sample was approximately 30 μm. Mixtures of methanol-ethanol 4:1 and methanol-ethanol-water 16:3:1 served as pressure transmitiing media (PTM) in separate experimental runs.

High-pressure angle-dispersive powder x-ray diffraction

The monochromatic angle-dispersive powder x-ray diffraction (XRD) measurements under pressure were performed at the 16BM-D beamline of the High Pressure Collaborative Access Team’s facility, at the Advanced Photon Source of Argonne National Laboratory (APS-ANL). The x-ray beam wavelength was λ = 0.4246 Å and the sample-detector distance about 320 mm. The XRD patterns were collected with a MAR345 Image Plate detector. The geometrical parameters were calibrated with a CeO₂ standard from NIST. The intensity versus 2θ spectra were processed with the FIT2D software⁵². Refinements were performed with the GSAS + EXPGUI software packages⁵³, whereas crystal-chemical calculations with the IVTON software⁵⁴. The P-V data were fitted with a Birch-Murnaghan equation of state (B-M EoS)⁵⁵. Helium was employed as PTM; the compressed gas loading took place at the gas-loading system of GeoSoilEnviroCARS⁵⁶ (Sector 13, APS-ANL).