Glassy and liquid Sb₂S₃: insight into the structure and dynamics of a promising functional material

Abstract

Antimony sesquisulfide Sb₂S₃ has become an outstanding advanced functional material in a variety of rapidly growing application fields: smart integrated photonics from the visible to telecom window, cost-efficient photovoltaics, energy storage and transformation. Rational design and tailoring of the required components need a deep insight into the atomic structure and dynamics of liquid and amorphous Sb₂S₃, but detailed information is missing in contrast to crystalline counterparts. Using high-energy X-ray diffraction and Raman spectroscopy over an extended temperature range, supported by first-principles simulations as well as by electrical and thermal studies, we show that the high optical and electric contrast between the SET (crystalline) and RESET (amorphous) logic states is related to the different short and intermediate range order in orthorhombic and vitreous Sb₂S₃. It includes strong asymmetry of the Sb–S nearest neighbor distances and a different coordination of antimony sites in the crystal vs. a distorted trigonal environment of defect octahedral SbS₃ entities in glassy Sb₂S₃. A fast crystallization rate at elevated temperatures in liquid antimony sesquisulfide is related to the enhanced fragility, approaching that of telluride phase-change materials, and to a large fraction of ABAB squares (A: Sb; B: S), combined with a remarkable slowdown of the diffusion processes in the vicinity of the glass transition temperature, ensuring good retention of the amorphous state. Further improvements may be achieved using anionic (Se) or cationic (Bi) substitution that decreases the temperature of a semiconductor–metal transition and allows bandgap engineering, important for both photonics and photovoltaics.

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1. Introduction

Antimony sesquisulfide Sb₂S₃ appears to be an emerging and promising advanced functional material for a variety of rapidly growing application fields:

(1) Wide gap phase-change materials (PCM) for both electrically and light tunable visible photonics or ultralow loss photonics at telecommunication wavelengths. Sb₂S₃ can be used for smart reprogrammable photonic systems with a nanosecond switching time, holographic and nonvolatile ultrathin displays of extremely high resolution, integrated photonic circuits, switchable metasurfaces and varifocal metalenses, nanophotonic and on-chip devices, dielectric nanoantennas, etc.^1–6

(2) High-performance composite anodes for sodium and lithium batteries. Antimony sesquisulfide nanorods, nanoparticles and powders, sometimes combined with other sulfides and encapsulated into a doped carbon matrix or activated carbon, provide superior rate capability, excellent cyclic stability and capacity retention, as well as fast-charging capacity and highly decreased interfacial resistance.^7–10

(3) Alternative absorber materials for thin-film solar cells. Antimony sulfide thin films belong to emerging earth-abundant low-cost photovoltaic materials having a reasonable optical bandgap, tremendous low-light harvesting, and excellent moisture and air stability.^11,12

(4) Thermoelectric materials. The high thermoelectric power of Sb₂S₃ seems to be promising for thermoelectric applications.¹³ However, nanostructured or amorphous antimony sesquisulfide is mostly used as a dopant decreasing the thermal conductivity and increasing the Seebeck coefficient of composite thermoelectrics (lead chalcogenides, (Bi,Sb)₂Te₃, etc.) yielding a significantly enhanced figure of merit zT.^14,15

Rational design and tailoring of optimized functional materials based on Sb₂S₃ need a deep insight into the atomic structure and dynamics of antimony sesquisulfide. The crystal structure of Sb₂S₃ has been extensively studied both under ambient conditions^16–18 and under high pressure.^19–26 Nevertheless, the atomic structure of vitreous and liquid antimony sesquisulfide is largely unknown except for classical X-ray diffraction studies of glassy Sb₂S₃ reported forty years ago and suffering from a limited accessible Q-range and insufficient r-space resolution.^27–29 In the case of PCM applications,^30–32 special attention should be paid to the origin of a high optical and electric contrast between the SET (crystalline) and RESET (amorphous) logic states since antimony sesquisulfide differs considerably from the benchmark telluride PCM (GeTe-Sb₂Te₃, GST, or doped Sb₂Te) in both chemical bonding and local antimony environments. The metavalent bonding³³ seems to be missing in Sb₂S₃; and the four-fold coordinated antimony sites, present in GST and a-Sb₂Te₃,^34,35 were not observed in vitreous Sb₂S₃,^27–29 even though there is a controversy in amorphous tellurides related to the antimony local order.^36,37

Using high-energy X-ray diffraction and Raman spectroscopy supported by first-principles simulations, we will unravel a detailed structural organization of bulk glassy and liquid Sb₂S₃ over an extended temperature range, 298 ≤ T ≤ 1143 K. Thermal properties and electrical conductivity measurements will also be provided showing a remarkable contrast in electronic properties between amorphous, crystalline and liquid states. Finally, the diffusion coefficients and viscosity of liquid Sb₂S₃ will be computed and compared with known experimental data, which reveal a significant fragility of molten antimony sesquisulfide in comparison with canonical dielectric As₂S₃. All these results will explain the promising PCM performance of Sb₂S₃ and an overall trend in functional properties going down the periodic table.

2. Experimental and methods

2.1 Glassy and nanocrystalline Sb₂S₃ preparation

A two-step synthesis was applied for glassy Sb₂S₃. First, a crystalline sample was prepared from high-purity antimony (99.999%, Cerac) and sulfur (99.999%, Alfa Aesar) in an evacuated and sealed silica tube. Then, a small quantity of c-Sb₂S₃ was placed in a thin-walled silica capillary, evacuated to 10⁻⁴ mbar and sealed. The capillary was slowly heated in a furnace to 1050 K and kept at this temperature for one hour with subsequent cooling to 900 K. After an additional equilibration step for at least 30 minutes, the sample was splat-quenched under an argon atmosphere onto a fused silica plate cooled down to ≈80 K. Nanocrystalline nc-Sb₂S₃ was obtained by fast cooling in a silica capillary but without splat-quenching, that is, the estimated cooling rate was ≲1000 K s⁻¹.

2.2 Thermal and electrical measurements

A TA instruments Q200 thermal analyzer was used for differential scanning calorimetry (DSC). The synthesized samples of 3–5 mg were encapsulated in a sealed aluminum pan and heated at a rate of 10 K min⁻¹ under a dry nitrogen atmosphere to determine the glass transition T_g and crystallization temperatures. The ac and dc conductivity measurements were done over the 330 ≤ T ≤ 450 K temperature range. A Hewlett Packard 4339B high resistance meter with applied voltage of 100 volts was used for the dc experiments. The ac conductivity over the 100 Hz to 15 MHz frequency range was measured using a Hewlett Packard 4194A impedance meter.

2.3 Raman spectroscopy measurements

A LabRam HR microRaman spectrometer (Jobin Yvon Horiba Group) was used for the measurements at room temperature. Raman scattering was excited by a 785 nm solid-state laser and recorded in the 50–850 cm⁻¹ spectral range. The laser power was 0.75 mW. Two to three spectra were registered for each sample at different positions to verify the sample homogeneity and the absence of photoinduced phenomena. Raman spectra over the temperature range 293 ≤ T ≤ 873 K were measured using a Senterra Raman spectrometer (Bruker) equipped with a microscope and a Linkam TS1000 hot stage. The spectra were excited by a 785 nm laser diode with a power of 1 mW and recorded in the 75–1500 cm⁻¹ spectral range (reliable data above 100 cm⁻¹). Glassy Sb₂S₃ was placed in a silica tube (2 mm ID/3 mm OD, length 25 mm) and sealed under vacuum.

2.4 High-energy X-ray diffraction

The 6-ID-D beamline at the Advanced Photon Source (Argonne National Laboratory, Chicago) was used for high-energy X-ray diffraction measurements under ambient conditions and as a function of temperature. The photon energy was 99.9593 keV, and the wavelength was 0.124035 Å. A two-dimensional (2D) setup was used for data collection with a Varex area detector, 2880 × 2880 pixels, and a pixel size of 150 × 150 μm². The sample-to-detector distance was 287.7 mm for a room-temperature setup, and 334.9 mm for furnace measurements over the 673 ≤ T ≤ 1143 K temperature range on cooling. Cerium dioxide was used as a calibrant. The exposure time was 0.2 s × 1500 frames, using one dark-field image file followed by five light files. Glass samples were fixed on a Kapton tape for the room temperature measurements. A Sb₂S₃ sample in evacuated silica tube (2 mm ID/3 mm OD) was used for the furnace experiments. The 2D diffraction patterns were reduced using the Fit2D software.³⁸ The measured background intensity (either the Kapton tape or the empty silica at various temperatures) was subtracted, and corrections were made for the different detector geometries and efficiencies, sample self-attenuation, and Compton scattering using standard procedures,³⁹ providing the X-ray structure factor S_X(Q).

S_X(Q) = w_SbSb(Q)S_SbSb(Q) + w_SbS(Q)S_SbS(Q) + w_SS(Q)S_SS(Q), (1)

where w_ij(Q) are Q-dependent X-ray weighting coefficients and S_ij(Q) the Faber–Ziman partial structure factors. Typical raw diffraction data for nanocrystalline and glassy Sb₂S₃ are shown in Fig. S1 (ESI†).

Canonical As₂S₃ glass and liquid were also additionally measured at the BL04B2 beamline of the SPring-8 facility (Hyogo Prefecture, Japan) using a dedicated two-axis diffractometer equipped with four CdTe detectors at low angles and three Ge diodes at high diffraction angles.⁴⁰ The temperature measurements were carried out from 300 to 1223 K in a furnace. The 7-detector setup and incident X-ray energy of 112.6386 keV allows the diffraction pattern to be collected up to Q = 30 Å⁻¹ with a high signal-to-noise ratio and sufficient energy resolution to discriminate both fluorescence from the sample and higher harmonic reflections from the monochromator crystal. The empty silica tube at different temperatures was also measured and used for background intensity subtraction. Further data analysis included absorption, Compton scattering, and polarization corrections using standard procedures⁴¹ giving the total X-ray structure factor of S_X(Q).^42,43

2.5 First-principles simulations

The DFT calculations of vibrational spectra were carried out using Gaussian 16 software.⁴⁴ The structural optimization and harmonic vibrational frequency calculations were performed for size-limited clusters: SbSb₃H₃, SbS₃H₃, Sb₂S₄H₂ (chair and boat conformations), Sb₂S₅H₄, Sb₂S₆H₄, Sb₃S₆H₃, Sb₆S₁₂H₆, Sb₁₂S₁₈H₂, and Sb₁₂S₁₆. The Becke three-parameter hybrid exchange functional⁴⁵ and the Lee–Yang–Parr correlation functional (B3LYP)⁴⁶ were used for these simulations. The small-core relativistic pseudopotential basis set (cc-pVTZ-PP)⁴⁷ and the effective core potentials⁴⁸ were applied for cluster geometry optimization and Raman intensity calculations. Most of the structures were optimized using the tight convergence option ensuring adequate convergence and reliability of computed wavenumbers. An extra quadratically convergent self-consistent field procedure⁴⁹ was used for difficult convergence cases. Further details of the DFT simulations are reported elsewhere.^50–52

Modeling of the diffraction data was carried out using Born–Oppenheimer molecular dynamics implemented within the CP2K package.⁵³ The generalized gradient approximation (GGA) and the PBE0 hybrid^54,55 exchange–correlation functional combining the exact Hartree–Fock and DFT approaches were used, providing better agreement with experiment.^56–59 The Grimme dispersion corrections D3BJ⁶⁰ were also employed, improving first-principles molecular dynamics (FPMD) results for chalcogenide systems.^61,62 The applied FPMD technique was similar to previous reports.^34,63 The initial atomic configurations for vitreous Sb₂S₃ were created and optimized using the RMC_POT++ code⁶⁴ against the experimental S_X(Q). The size of the cubic simulation box, containing 200 atoms (80 Sb and 120 S), was chosen to match the experimental density. Further optimization was carried out using DFT, applying the molecularly optimized correlation consistent polarized triple-zeta valence basis set along with the norm-conserving relativistic Goedecker–Teter–Hutter-type pseudopotentials.⁶⁵ FPMD simulations were performed using a canonical NVT ensemble with a Nosé–Hoover^66,67 thermostat. The simulation boxes were heated from 300 K to 900 K using 100 K steps for 20–25 ps each. At 900 K (above melting), the systems were equilibrated for 70 ps and cooled down to 300 K using the same temperature steps but with a longer simulation time (25–45 ps). Final equilibration and data collection at 300 K were performed for 59 ps. Additional simulations were carried out between 850 and 1150 K (step 100 K for 40–50 ps each) consistent with the experimental data. The connectivity and ring statistics were analyzed using the R. I. N. G. S. package⁶⁸ and a modified connectivity program.⁶⁹ The pyMolDyn code⁷⁰ applying the Dirichlet–Voronoi tessellation was used for the calculation of microscopic voids and cavities.

3. Results and discussion

3.1 Glass-forming, thermal and electric properties

Glassy antimony sesquisulfide was reported to be a difficult material to vitrify.²⁷ Nevertheless, the applied splat-quenching technique⁵⁶ in thin-walled silica capillaries allows fully vitreous small droplets of g-Sb₂S₃ to be obtained. Typical DSC traces for glassy Sb₂S₃ and canonical g-As₂S₃ are shown in Fig. 1. The two end-members are consistent with the reported thermal properties for (Sb₂S₃)_x(As₂S₃)_1−x pseudo-binaries, x ≤ 0.9:^71–73 the glass transition temperature T_g monotonically increases with x from 472 K (x = 0) to 492 K (x = 1), the exothermic crystallization feature emerges above x = 0.5, grows and shifts toward lower T, emphasizing the increasing crystallization ability.

Fig. 1 DSC traces of glassy (a) As₂S₃ and (b) Sb₂S₃. The derived glass transition temperatures are also indicated.

The conductivity temperature dependences σ(T) for glassy and crystalline (this work), and molten⁷⁴ Sb₂S₃ are shown in Fig. 2 using an Arrhenius plot:

σ(T) = σ₀ exp(−E_a/k_BT), (2)

where σ₀ is the pre-exponential factor, E_a is the conductivity activation energy, and k_B and T have their usual meaning. We note a significant electrical contrast between glassy and crystalline samples, ≈4.5 orders of magnitude at room temperature with the corresponding difference in activation energy, E^cryst_a = 0.733 eV but E^glass_a = 1.009 eV. The conductivity increases on melting by three orders of magnitude compared to the extrapolated glass value, while the activation energy drops nearly by a factor of 2. The pre-exponential factor appears to be very similar for all three Sb₂S₃ phases, 400 ≤ σ₀ ≤ 800 S cm⁻¹, and indicates a conductivity mechanism over extended (delocalized) electron states.⁷⁵ The obtained results are consistent with the reported values of conductivity parameters and optical bandgap E_g for bulk crystalline samples and amorphous or crystalline thin films, 1.5 ≤ E_g (c-Sb₂S₃) ≤ 1.8 eV and 2.0 ≤ E_g (a-Sb₂S₃) ≤ 2.4 eV.^1,76–79 In addition, the conductivity seems to be intrinsic since 2E_a ≅ E_g.

Fig. 2 Conductivity σ(T) of glassy (g), crystalline (c) samples (this work), and liquid L-Sb₂S₃.⁷⁴ The inserts show g-Sb₂S₃ and c-Sb₂S₃.

3.2 Nanocrystalline Sb₂S₃

An insufficiently rapid quenching rate or wrong starting temperature for splat-cooling yields a nanocrystalline alloy, which is slightly different from the stable orthorhombic polymorph, space group Pnma.¹⁶ The observed Bragg peaks mostly correspond to orthorhombic antimony sesquisulfide, but we should note slight deviations of the peak positions and their different amplitudes compared to the reference compound (Fig. 3(a)). Besides, a non-negligible amorphous fraction is also present and possibly some traces of monoclinic high-T Sb₂S₃ polymorph, which is metastable at room temperature.¹⁸

Fig. 3 Nanocrystalline (nc) and orthorhombic Sb₂S₃. (a) Bragg peaks of the nanocrystalline sample in comparison with the orthorhombic polymorph,¹⁶ space group Pnma; (b) X-ray structure factor S_X(Q) over the entire Q-range; (c) (Sb₄S₆)_∞ ribbons in orthorhombic Sb₂S₃: left, atomic arrangements using projection on the (a,c) plane, right, a single ribbon oriented parallel to the b axis; (d) X-ray total correlation function T_X(r) of nc-Sb₂S₃; (e) Sb–S (magenta), Sb–Sb (light brown) and S–S (yellow) T_ij(r) partials for orthorhombic Sb₂S₃. The dashed red lines in (c), left panel, show the shortest inter-ribbon Sb–S distances (3.167–3.642 Å). The black dashed lines in (d and e) separate intra- (2.455–2.854 Å) and inter-ribbon Sb–S nearest contacts.

The X-ray total correlation function T_X(r) of nanocrystalline Sb₂S₃, Fig. 3(d), obtained by the usual Fourier transform of the structure factor S_X(Q), Fig. 3(b),

where M(Q) is a modification function and ρ₀ is the experimental number density, confirms characteristic differences between nanocrystalline and orthorhombic antimony sesquisulfides. The latter is formed by infinite quasi one-dimensional (1D) (Sb₄S₆)_∞ ribbons oriented parallel to the b axis, Fig. 3(c). The inner Sb(II) atoms have 5 sulfur neighbors forming a distorted square pyramid with Sb(II) species located 0.17 Å below the basal plan of the pyramid. The outer Sb(I) counterparts reside at the apex of trigonal SbS₃ units connected by two-fold sulfur at the ribbon periphery and three-fold sulfur toward Sb(II) and the ribbon interior. The average intra-ribbon antimony coordination appears to be 〈N^intra_Sb–S〉 = 4 while their sulfur neighbors have 〈N^intra_S–Sb〉 = 2.67. The Sb(II)–S nearest neighbor (NN) distances reveal a strong Peierls distortion, r^5F_Sb(II)–S = 2.70 ± 0.16 Å, while the intra-ribbon contacts for trigonal Sb(I) are uniform, r^3F_Sb(I)–S = 2.53 ± 0.01 Å. The 1D-(Sb₄S₆)_∞ entities are held together by rather strong inter-ribbon forces forming puckered sheets within the (a,c) plane. The shortest Sb–S inter-ribbon distances, 3.167 ≤ r^inter_Sb–S ≤ 3.642 Å, are smaller than the sum of the van der Waals radii, r^vdW_S = 1.8 Å and r^vdW_Sb = 2.2 Å,⁸⁰ but larger than the Sb–S intra-ribbon NN contacts, 2.455 ≤ r^intra_Sb–S ≤ 2.854 Å. The intra- and inter-ribbon separations are well distinguished using the T_SbS(r) partials for both orthorhombic and nanocrystalline Sb₂S₃, Fig. 3(d and e). The main difference between the two forms resides in the inter-ribbon connectivity. On average, each antimony in orthorhombic Sb₂S₃ has three short Sb–S inter-ribbon contacts, 〈N^inter_Sb–S〉 = 3, while the connectivity in nc-Sb₂S₃ is reduced, 〈N^inter_Sb–S〉 ≈ 1.5. In other words, the 1D-(Sb₄S₆)_∞ ribbons are becoming more isolated in the nanocrystalline lattice.

3.3 Raman spectroscopy and DFT modeling

Typical Raman spectra of glassy Sb₂S₃ as a function of temperature are shown in Fig. 4(b). The temperatures between 293 ≤ T ≤ 423 K correspond to the solid glass, Fig. 4(a). Above T_g = 492 K, the supercooled liquid rapidly crystallizes at 523 K, Fig. 4(c), just in the vicinity of the DSC crystallization onset. Cooling down the crystallized sample, one obtains a typical spectrum of orthorhombic Sb₂S₃, characterized by multiple Raman-active modes Γ = 10A_g + 5B_1g+ 10B_2g + 5B_3g, expected for the Pnma polymorph.⁸¹ Usually, about ten modes are clearly distinguishable.^20,21,26

Fig. 4 Raman spectra of antimony sesquisulfide: (a) DSC trace of g-Sb₂S₃, the arrows show the Raman measurement temperatures; (b) spectra of a solid glass as a function of temperature, the insert shows S–S stretching at ≈490 cm⁻¹; (c) spectra of the orthorhombic polymorph at 523 K and after cooling to room temperature; (d) Raman spectrum of molten Sb₂S₃ at 873 K. The dashed red line in (b) also shows the As–S stretching envelope in g-As2S3. See the text for further details.

The Raman spectrum of L-Sb₂S₃ at 873 K appears to be reminiscent of its glassy counterpart, Fig. 4(d), except for a strong S–S stretching at 490 cm⁻¹. Assuming a dissociation reaction 2Sb−S ⇄ Sb–Sb + S–S, we also should expect a broad Sb–Sb stretching at ≈145 cm⁻¹ as in amorphous antimony,^82,83 also confirmed by DFT modeling (Fig. S2, ESI†). A low-frequency vibration feature below 180 cm⁻¹ may contain both Sb–S bending and Sb–Sb stretching. We should however note that the appearance of intense S–S stretching in liquid Sb₂S₃ can be a transient phenomenon. Previously, both sulfur and antimony were detected on heating or laser-induced processing of amorphous Sb₂S₃ thin films, partly as intermediate species.^84–87 A limited accessible temperature range for our in situ Raman measurements does not enable further experiments at higher T. Nevertheless, temperature-dependent dynamics on melting was observed over a limited T-range, Fig. S3 (ESI†).

Basically, a broad asymmetric unresolved feature centered at in glassy Sb₂S₃ is similar to that in g-As₂S₃ but shifted to lower frequencies, Fig. 4(b), roughly scaling with the molecular mass ratio, . Amorphous a-Sb₂S₃ thin films and antimony-containing bulk sulfide glasses reveal similar vibrational features.^2,88–92 Assuming trigonal antimony local coordination²⁷ and the above resemblance in Raman spectra, various DFT simulations have been carried out. Isolated pyramidal units SbS₃H₃, corner- CS-Sb₂S₅H₄ and edge-sharing ES-Sb₂S₄H₂ dimers of different conformation, and small rings, Sb₃S₆H₃ or Sb₆S₁₂H₆, systematically reveal overestimated Sb–S stretching frequencies, centered at 320 ≤ 〈ν^Sb–S_max〉 350 ≤ cm⁻¹, Fig. S4 (ESI†). Reasonable results yield complicated clusters Sb₁₂S₁₈H₂ and Sb₁₂S₁₆, originating from the modified ribbons in orthorhombic Sb₂S₃ but with exclusively trigonal antimony coordination, Fig. 5. Both symmetric and asymmetric stretching frequencies, as well as low-frequency bending and deformation modes below 190 cm⁻¹ are well reproduced by these clusters. As expected, the Sb–Sb stretching in Sb₁₂S₁₆ is overlapping with the Sb–S bending and deformation making it impossible to distinguish these vibrations experimentally. In contrast, the S–S stretching at 490 cm⁻¹ is clearly visible in Raman scattering, Fig. 4(b and d), and confirmed by DFT simulations, Fig. S4 (ESI†), cluster Sb₂S₆H₄. The geometry of DFT-optimized size-limited clusters is consistent with crystalline references and glassy Sb₂S₃, Fig. S5 and S6 (ESI†), specifically that of Sb₁₂S₁₈H₂ and Sb₁₂S₁₆.

Fig. 5 DFT Raman spectra of (a) Sb₁₂S₁₈H₂ and (b) Sb₁₂S₁₆ size-limited clusters in comparison with the experimental Raman spectrum of g-Sb₂S₃, highlighted in yellow for the two panels. The terminal hydrogen species in (a) are omitted, and the H-related vibrations are removed from the spectrum. The inserts show DFT-optimized clusters. Weak Sb–Sb stretching in (b) is emphasized by the red circle.

Raman spectroscopy measurements show that the glass structure hardly evolves at T ≲ T_g; a negligible red shift of the Sb–S stretching envelope can only be observed, Fig. 4(b). The rapid crystallization above T_g seems to be related to the presence of modified structural motifs originating from the (Sb₄S₆)_∞ entities, although the Sb(II) species lose their 5-fold coordination in the glass. Further insight into the atomic glass structure yields high-energy X-ray diffraction supported by first-principles molecular dynamics (FPMD).

3.4 High-energy X-ray diffraction over the extended temperature range

Typical X-ray structure factors S_X(Q) for g-Sb₂S₃, supercooled (673–773 K) and normal (T ≥ 843 K) liquids are shown in Fig. 6(a and b). The S_X(Q)s exhibit well-defined oscillations up to 30 Å⁻¹, ensuring high-resolution in the r-space. The oscillations amplitude decreases with increasing temperature but more significant changes are observed at low Q ≲ 5 Å⁻¹.

Fig. 6 High-energy X-ray diffraction data in Q-space for glassy and liquid Sb₂S₃: (a) X-ray structure factor S_X(Q) over a limited Q-range and (b) interference function Q[S_X(Q) − 1] as a function of temperature; (c) isolated first sharp diffraction peak (FSDP) and Sb–Sb diffraction feature PP_Sb as a function of temperature; (d) the FSDP position Q₀(T) and (e) amplitude A₀(Q₀,T). The dash-dotted line in (d) shows the expected Q₀(T) trend taking into account the thermal expansion. The arrows show the glass transition temperature T_g and melting point T_m for Sb₂S₃. The solid and dashed lines in (e) are a guide to the eye.

Except for the distinct first sharp diffraction peak (FSDP) at Q₀ = 1.22 Å⁻¹, which is typical for a large majority of chalcogenide glasses (see, for example, Fig. S7 (ESI†) for glassy and liquid As₂S₃), vitreous Sb₂S₃ reveals an additional low-Q feature at Q_Sb = 1.75 Å⁻¹, specific for antimony, which emerges and increases in glassy (Sb₂S₃)_x(As₂S₃)_1−x pseudo-binaries with increasing x.⁷¹ Later, we will see that the 1.75 Å⁻¹ feature corresponds to the principle peak PP_Sb in the Sb–Sb partial structure factor S_SbSb(Q), diverging from that in the S_SS(Q) partial at Q_S = 2.24 Å⁻¹ because of a large difference in atomic size of antimony and sulfur, whose covalent radii are r_Sb = 1.45 Å and r_S = 1.03 Å.^93,94 The FSDP and PP_Sb are more visible after removing the background underneath the low-Q features using the subtraction procedure,^95,96Fig. 6(c).

The FSDP amplitude A₀(Q₀) slightly decreases in intensity with increasing T and shifts to lower Q, Fig. 6(c). In contrast, changes in the PP_Sb amplitude are more significant (especially between the solid glass and liquids) and similar to other peaks and distant oscillations, Fig. 6(a and b). In addition, these temperature changes are characteristic for chalcogenide glasses and liquids, while the FSDP behaves differently. In particular, the FSDP position Q₀(T) for Sb₂S₃ follows the thermal expansion, Q₀(T) ∝ ρ(T)^1/3,⁹⁷ where ρ(T) is the macroscopic number density.

The X-ray total correlation functions T_X(r) for glassy and liquid Sb₂S₃, obtained by the usual Fourier transform of S_X(Q), are shown in Fig. 7. The first peak at 2.484 ± 0.004 Å corresponds to Sb–S nearest neighbors followed by a strongly asymmetric second neighbor (2nd N) peak at 3.83 ± 0.02 Å with additional unresolved correlations between 2.8 and 3.4 Å. The third distinct feature at 5.7 Å seems to be related to a center-center distance between the Sb–S entities. All peaks become less intense and broader with increasing temperature, also leading to a stronger overlapping between NN and second neighbor correlations. More distant broad peaks at 7.3 and 9 Å appear to be hardly visible in L-Sb₂S₃. Gaussian fitting of the NN and 2nd N correlations is inappropriate because of the peak asymmetry. Typical fitting with asymmetric functions is shown in Fig. 7(a) and yields reasonable results. The average antimony coordination N_Sb–X, where X = S and/or Sb, was found to be trigonal and consisting of two contributions, N_Sb–X = N_Sb–S + N_Sb–Sb = 2.90(5) + 0.10(5) (Fig. 7(c), and see also Table 1). The Sb–S and Sb–Sb NN distances slightly increase with temperature; both interatomic separations, r_Sb–S = 2.484 ± 0.004 Å and r_Sb–Sb = 2.92 ± 0.02 Å, are consistent with crystalline and amorphous references for trigonal antimony sulfides and elemental Sb.^{16–18,93,98} Typical broadening of the Sb–S NN feature as a function of temperature is shown in Fig. 7(f). Both supercooled and normal liquids Sb₂S₃ exhibit a monotonic increase of w_Sb–S(T).

Fig. 7 High-energy X-ray diffraction data in r-space for glassy and liquid Sb₂S₃: (a) typical T_X(r) fitting with asymmetric functions; Sb–S and Sb–Sb nearest neighbor (NN) correlations are highlighted in cyan and light red, respectively; (b) total correlation functions T_X(r) over the temperature range 298 ≤ T ≤ 1143 K; (c) antimony local coordination number as a function of temperature; (purple squares) N_Sb–S + N_Sb–Sb, (dark blue circles) N_Sb–S; interatomic NN distances (d) Sb–Sb and (e) Sb–S as a function of T; (f) temperature dependence of asymmetric peak width for Sb–S NN correlations w_Sb–S; the solid glass and supercooled or normal liquid temperature domains are highlighted in blue and red, respectively. The dashed line in (f) is a guide to the eye. The other solid lines are a least-square fit of the experimental data.

Table 1 Interatomic distances r_ij and partial coordination numbers N_ij in glassy and liquid Sb₂S₃

Temperature (K)	S–S		Sb–S		Sb–Sb
	r S–S (Å)	N S–S	r Sb–S (Å)	NSb–S	r Sb–Sb (Å)	NSb–Sb
High-energy X-ray diffraction
298	—	—	2.480(6)	2.95(4)	2.93(2)	0.10(5)
673	—	—	2.486(6)	2.85(4)	2.91(2)	0.13(5)
773	—	—	2.486(6)	2.85(4)	2.90(2)	0.13(5)
843	—	—	2.485(6)	2.93(4)	2.92(2)	0.08(5)
943	—	—	2.486(6)	2.94(4)	2.93(2)	0.08(5)
1043	—	—	2.488(6)	2.90(4)	2.93(2)	0.10(5)
1143	—	—	2.487(6)	2.87(4)	2.93(2)	0.12(5)
First-principles molecular dynamics
300	2.07	0.07	2.471	2.93	2.90	0.10
700	2.07	0.08	2.474	2.88	2.90	0.12
800	2.07	0.08	2.478	2.89	2.90	0.12
850	2.07	0.08	2.478	2.92	2.91	0.12
950	2.07	0.08	2.482	2.91	2.91	0.13
1050	2.08	0.08	2.480	2.95	2.90	0.13
1150	2.07	0.08	2.478	2.94	2.90	0.13

---

3.5 First-principles molecular dynamics modeling of glassy and liquid Sb₂S₃

The derived FPMD interference functions Q[S_X(Q) − 1] and pair-distribution functions g_X(r) for the two extremes in experimental series at 300 and 1150 K are shown in Fig. 8. As reported earlier,^56–59 the FPMD with hybrid functional PBE0 yields good agreement with experimental data for chalcogenide systems. The FPMD replicas in Q-space reproduce well both the positions and amplitudes of oscillations for Q[S_X(Q) − 1], Fig. 8(a,b). As a result, the derived interatomic distances in r-space are also consistent with the diffraction results, Fig. 8(c,d). In contrast, FPMD modeling with the standard functional PBE suffers from over- or underestimated correlations in Q- and r-space as shown in Fig. S8 (ESI†).

Fig. 8 FPMD modeling results using the hybrid functional GGA/PBE0 in comparison with experimental high-energy X-ray diffraction data for Sb₂S₃; interference function Q[S_X(Q) − 1] at (a) 1150 K and (b) 300 K; pair-distribution function g_X(r) at (c) 1150 K and (d) 300 K. The solid circles correspond to experimental data; the solid lines are the FPMD results.

The partial structure factors S_ij(Q) and pair-distribution functions g_ij(r) are revealed in Fig. 9(a and b). We note divergent positions of PP_Sb and PP_S for the S_SbSb(Q) and S_SS(Q) partials, as well as a negative amplitude of S_SbS(Q) in this range, explaining the appearance of an additional low-Q feature at Q_Sb = 1.75 Å⁻¹ in the X-ray structure factor discussed above, Fig. 6(a–c). Astonishingly, the FSDP origin appears to be related to Sb–S correlations instead of the expected Sb–Sb counterparts. We note, however, that in glassy As₂S₃, the FSDP origin changes from As–As (major contribution) and As–S (minor component) at ambient pressure to mostly As–S correlations above 4 GPa, Fig. S9 (ESI†).

Fig. 9 Derived FPMD partial functions for glassy Sb₂S₃ at 300 K in (a) Q-space, S_ij(Q), and (b) r-space, g_ij(r); and local coordination numbers for (c) sulfur, N_S–X, and (d) antimony, N_Sb–X, where X = S or Sb.

The partial pair-distributions g_ij(r) are consistent with experimental findings. The Sb–S NN peak at 2.477 ± 0.004 Å exhibits an asymmetric shape, increasing with temperature, Fig. S10 (ESI†). The fitting with asymmetric functions yields very similar results to the experimental data, 〈N_Sb–S〉 = 2.91 ± 0.03, and the antimony local trigonal coordination is completed by the Sb–Sb nearest neighbors at 2.903 ± 0.002 Å, 〈N_Sb–Sb〉 = 0.12 ± 0.01, Table 1. The Sb–S second neighbors are located rather close to the Sb–S NN correlations and overlap significantly with increasing temperature despite the shift of r^2nd_Sb–S to higher distances from 3.36 Å (300 K) to 3.51 Å (1150 K), mostly because of a strong broadening of the NN and 2nd N correlations, Fig. S10 (ESI†).

The g_SS(r) partial also shows S–S homopolar bonds at 2.07 Å, Fig. 9(b), 〈N_S–S〉 = 0.08 ± 0.01, Table 1. The Raman spectroscopy confirms this result, Fig. 4(b). Nevertheless, their concentration is too low to be observed by high-energy X-ray diffraction. In particular, Fig. 8(c and d) reveals that the S–S FPMD diffraction features are less intense compared to the experimental noise of g_X(r).

Sulfur and antimony coordination distributions are plotted in Fig. 9(c and d). As expected, the overwhelming majority of the two species have a two-fold (91%) and trigonal (95%) local coordination, respectively. With increasing temperature, the population of two-fold sulfur and three-fold antimony decreases, while the fractions of under- and over-coordinated species grow, Fig. S11 (ESI†). The number of sulfur or antimony local configurations with homopolar bonds, that is, S(Sb₁S₁) instead of S(Sb₂) or Sb(S₂Sb₁) vs. Sb(S₃) remains low at all temperatures.

The bond angle distributions B(θ) for S–Sb–S and Sb–S–Sb triplets in glassy Sb₂S₃ are plotted in Fig. 10 in comparison with two crystalline counterparts: orthorhombic and monoclinic Sb₂S₃. The geometry of SbS₃ trigonal pyramids is different from that in canonical g-As₂S₃; the maximum of a broad asymmetric distribution B_SSbS(θ) is located at 87° opposite to 98° in arsenic sesquisulfide,⁹⁹ ensuring a more compact local structure of g-Sb₂S₃. Roughly speaking, SbS₃ pyramids can be considered as distorted defect octahedral entities, whose three missing Sb–S bonds became excessively long, and the corresponding sulfur species were transformed into the second neighbors. The above-mentioned fitting of T_SbS(r) partials, Fig. S10 (ESI†), is consistent with this hypothesis, revealing three 2nd N correlations at ≈3.4 Å. The remnants of octahedral geometry are also evidenced by a weak contribution at θ ≈ 160°. The B_SSbS(θ) distributions in orthorhombic and monoclinic polymorphs are rather similar to that in the glass, especially in the high-temperature C2/c form, including a low-intensity component at 168 ± 4° of four-fold coordinated Sb(5)/Sb(6) species.¹⁸ The 5-fold coordinated Sb(II) atoms in orthorhombic Sb₂S₃ yield an intense contribution at θ ≈ 171°.¹⁶

Fig. 10 Bond angle distributions B(θ) for glassy Sb₂S₃: (a) S–Sb–S and (b) Sb–S–Sb angles in comparison with orthorhombic Sb₂S₃, space group Pnma;¹⁶ and (c) S–Sb–S and (d) Sb–S–Sb in comparison with monoclinic Sb₂S₃, space group C2/c.¹⁸

The connectivity of trigonal pyramids, reflected by B_SbSSb(θ) peaked at 97°, also appeared to be in favor of a more compact structure of glassy Sb₂S₃ compared to canonical g-As₂S₃. The B_AsSAs(θ) distribution in the latter has a maximum at 105°.⁹⁹ Crystalline Sb₂S₃ counterparts exhibit similar connectivities to glassy antimony sesquisulfide, slightly less evident for the orthorhombic polymorph.

As expected, the supercooled and normal Sb₂S₃ liquids are characterized by even more distorted Sb–S polyhedra and polyhedral connectivities. Both B_SSbS(θ) and B_SbSSb(θ) distributions become broader and less symmetric with increasing temperature, Fig. S12 (ESI†).

The connectivity analysis shows that 96% of Sb and S are forming a single connected fragment. The homopolar bonds in the glass network are mostly related to few Sb–Sb and S–S dimers. Typical structural fragments in g-Sb₂S₃ are shown in Fig. 11(a). We note a certain similarity in the intermediate range order and ring statistics with orthorhombic and monoclinic polymorphs, Fig. 11, expected from the bond angle distributions. The orthorhombic crystal has ABAB squares (A: Sb; B: S) and six-membered rings Sb₃S₃; the monoclinic form, in addition to 6-fold entities, exhibits also big Sb₁₁S₁₁ rings, Fig. 11(g). Glassy and liquid Sb₂S₃ reveal a large variety of even- and odd-membered rings Sb_pS_q, 3 ≤ p + q ≤ 30, related to chemical and topological disorder. Nevertheless, the most populated entities have size p + q = 4 and 6. The big rings, showing a broad distribution peaked at p + q = 22, become progressively unstable with increasing temperature. Their derived population R_c(p + q)⁶⁸ appears to be comparable with temporal fluctuations, reflected by the R_c(p + q) uncertainty. At the highest temperature (1150 K), the population of ABAB squares exceeds any other R_c(p + q), at least by a factor of 4, Fig. 11(b).

Fig. 11 Structural motifs and ring statistics; (a) typical fragments in g-Sb₂S₃; ring statistics in glassy, and liquid Sb₂S₃ as a function of temperature: (b) 1150 K (normal liquid), (c) 700 K (supercooled liquid), and (d) 300 K (solid glass); (e) structural motifs in monoclinic Sb₂S₃, space group C2/c,¹⁸ and orthorhombic Sb₂S₃, space group Pnma;¹⁶ ring statistics in (f) orthorhombic Sb₂S₃, (g) monoclinic Sb₂S₃, and (h) glassy As₂S₃.

The ring statistics in g-As₂S₃ is rather similar to that in glassy antimony sesquisulfide. As it was reported previously,⁹⁹ the 12-membered rings As₆S₆, the only rings in monoclinic orpiment¹⁰⁰ and triclinic anorpiment¹⁰¹ As₂S₃ are absent in glassy arsenic sulfide, Fig. 11(h).

More dense packing of glassy antimony sesquisulfide, evidenced by bond angle distributions B_SSbS(θ) and B_SbSSb(θ), suggests less microscopic voids and cavities in the glass network compared to g-As₂S₃. The Dirichlet–Voronoi tessellation⁷⁰ allows the cavity fraction V_c, normalized to the volume of the FPMD simulation box, 0 ≤ V_c ≤ 1, to be computed. The results are given in Fig. 12 for the two sesquisulfides. As expected, the V_c in g-Sb₂S₃ is by a factor of two smaller than that of its arsenic counterpart, 21 ± 1% vs. 44 ± 4%, respectively. The average size distribution of microscopic voids is rather similar in the two cases, 0.5 ≤ r_c ≤ 4 Å, where r_c is the cavity radius, Fig. 12(a,b), although the average 〈r_c〉 is slightly smaller in glassy As₂S₃.

Fig. 12 Void statistics: characteristic cavity radii in glassy (a) As₂S₃ and (b) Sb₂S₃; microscopic voids in (c) g-As₂S₃ and (d) g-Sb₂S₃.

The partial pair-distribution functions g_AsS(r) and g_SbS(r) for g-As₂S₃/g-Sb₂S₃ yield additional evidence for a more compact or densified network in vitreous sulfides with increasing atomic number. Plotted on the normalized r/r₀ scale, where r₀ is the As–S or Sb–S NN distance, the g_SbS(r) shows a remarkable shift of the Sb–S second neighbors to shorter distances, approaching the NN shell, Fig. S13(a) in the ESI.† A similar more compact network compared to g-As₂S₃ under ambient conditions can be reproduced for glassy As₂S₃ under high pressure, e.g. in a diamond anvil cell at 6.3 GPa, Fig. S13(b), ESI.†

In summary, glassy and liquid antimony sesquisulfide has distinctly different structural features compared to orthorhombic Sb₂S₃. First, the antimony short range order in the crystal has a bimodal site distribution: 5-fold coordinated Sb(II) species with a strong Peierls distortion and regular trigonal Sb(I) entities. The Sb–S bonding asymmetry is absent in glassy and liquid polymorphs, characterized by a distorted antimony trigonal environment and shorter average 〈r^NN_Sb–S〉 distances, 2.64 ± 0.15 Å (c-Sb₂S₃, Pnma) vs. 2.48 ± 0.01 Å (g- and L-Sb₂S₃). This difference is clearly seen by ¹²¹Sb-Mössbauer spectroscopy,^102,103 which is very sensitive to the local antimony environment.

Second, the intermediate range order in orthorhombic and glassy Sb₂S₃ is also different. The crystal structure is composed of infinite 1D-(Sb₄S₆)_∞ ribbons with rather strong inter-ribbon interactions, while the glass network has a 2D layered structure, roughly reminiscent of that in canonical As₂S₃ but with remarkable differences. We should note comparable glass transition temperatures for the two vitreous alloys, Fig. 1, similar shape of the Raman spectra, Fig. 4, identical pnictide and sulfur local coordination and resembling ring statistics. However, the topology of antimony defect octahedral sites SbS₃, evidenced by bond angle distributions, is closer to crystalline Sb₂S₃ forms than to vitreous As₂S₃.

3.6 Electronic structure and atomic dynamics in glassy and liquid Sb₂S₃

The total electronic density of states (eDOS), calculated from the Kohn–Sham eigenvalue spectra, is shown in Fig. 13. The valence band (VB) consists of three sub-bands between the Fermi energy E_F and −20 eV, as in a large majority of crystalline and glassy chalcogenides.^{35,58,75,104–106} The upper asymmetric part, mostly involving sulfur and antimony p-electron populations, shows a predominant contribution at −2.8 eV (g-Sb₂S₃ at 300 K) or −2.3 eV (L-Sb₂S₃ at 1050 K), related to S 3p lone pairs. The bonding states at lower energies consist of Sb 5p, 5d and 5s together with S 3p orbitals. The middle sub-band centered at −10.7 eV (g-Sb₂S₃) or −10.0 eV (L-Sb₂S₃) has predominantly the s-character as well as the low-energy part at approximately −15 eV. The bandgap for glassy (E_g = 2.28 eV) and liquid (E_g = 1.06 eV) antimony sesquisulfide are consistent with the reported optical data^1,76–79 and electrical measurements (Fig. 2).

Fig. 13 Electronic properties of glassy and liquid Sb₂S₃; solid glass at 300 K: (a) the electronic density of states (eDOS) and the inverse participation ratio (IPR, red spikes), the projected eDOS (pDOS) on (b) antimony s (blue), p (violet), and d (magenta), and (c) sulfur s (green) and p (yellow) pseudo-wave functions; normal liquid at 1050 K: (d) eDOS and IPR, (e) antimony pDOS, and (f) sulfur pDOS. The valence band (VB) is highlighted in dark blue, the conduction band (CB) in light blue. See the text for further details.

The derived eDOS is in good agreement with experimental data¹⁰⁷ and previously reported simulation results.^{22,106,108–110} We should however note that simulations with the standard functionals yield a strongly underestimated bandgap (roughly by a factor of 2) in addition to insufficient agreement with the nearest and second neighbor correlations (see also Fig. S8, ESI†).

The inverse participation ratio (IPR),^35,111Fig. 13(a and d), characterizes the degree of localization of a single-particle Kohn–Sham eigenfunction ψ(r)

A small IPR value (∝N⁻¹, where N is the number of atoms in the simulation box) corresponds to an extended (delocalized) wave function, while a large IPR (limIPR → 1) indicates a strong localization around a specific covalent bond. Similar to previously reported results^35,58,111 and theoretical predictions,⁷⁵ the electron states in glassy and liquid Sb₂S₃ are mostly localized at the band tails (that is, the top of the valence and the bottom of the conduction bands) and in lower-lying bonding states. The remaining electron states in the vicinity of the bandgap are delocalized.

Benchmark telluride PCMs are characterized by low viscosity and high fragility of the melt^112–116 ensuring fast atomic mobility at elevated temperature, which enables rapid crystallization within the nanosecond range, and a good retention of the amorphous phase in the vicinity of T_g and at lower T. The simulated dynamics in Sb₂S₃ reveals fast diffusion at high temperatures and a sudden decrease of diffusivity approaching the glass transition.

Typical Sb and S mean square displacements 〈r²(t)〉 are shown in Fig. 14(a and b)

where r_i(0) and r_i(t) are the positions of particle i for the initial time and time t, respectively, N_i is the total number of particles i in the simulation box, and the angle brackets represent the average over the initial times. Below 30 fs, a ballistic regime is observed, mostly depending on temperature T and atomic mass m_i¹¹⁷

〈r²(t)〉 ∝ (k_BT/m_i)t², (6)

where k_B is the Boltzmann constant. On a log–log scale, the slope s = 2 is indicative of this regime, Fig. 14(b).

Fig. 14 Mean-square displacements 〈r²(t)〉 and viscosity of Sb₂S₃. Antimony (dark purple) and sulfur (yellow) 〈r²(t)〉 on (a) linear and (b) log–log scales. The dashed lines in (a) represent least-square fits of the 〈r²(t)〉 data. The ballistic (s = 2) and diffusion (s = 1) regimes in (b) are shown by the dash-dotted and dashed lines, respectively. (c) Angell plot for the temperature dependence of viscosity η(T) for As₂S₃ (blue) and Sb₂S₃ (magenta). The experimental viscosity data^118–123 are shown by the solid squares of different shades of blue for As₂S₃, and by the magenta squares for Sb₂S₃. The FPMD viscosity calculated using the Stokes–Einstein relation, eqn (9), is shown by the purple circles (this work). The dashed-dotted and solid lines represent the MYEGA¹²⁴ viscosity, eqn (10), for the two sesquisulfides. The derived fragility indices m are also shown. See the text for further details.

Above 5 ps, a diffusive motion is visible

〈r²(t)〉 ∝ D_it, (7)

where D_i is the average diffusion coefficient of particles i, approaching the slope s = 1. The diffusion coefficients D_Sb and D_S were calculated using the Einstein equationThe derived D_Sb(T) and D_S(T) are shown in Fig. S14 (ESI†), plotted on the Arrhenius scale and following thermally activated motion with temperature-dependent activation energy, 0.37 ≤ E_d ≤ 1.02 eV in the vicinity of 1150 and 850 K, respectively.

The Stokes–Einstein relationship was used to calculate the FPMD viscosity

where the effective atomic diffusion coefficient is D_eff(T) = 0.4D_Sb(T) + 0.6D_S(T), and the effective temperature-dependent hydrodynamic radius r_H was determined using a Wigner–Seitz approach , where V_m(T) is the melt molar volume and N_A is the Avogadro constant.

The derived viscosity is shown using an Angell plot, log η vs. T_g/T, Fig. 14(c), together with experimental viscosity data of different research groups for canonical As₂S₃ and Sb₂S₃.^118–123 The antimony sesquisulfide viscosity was obtained by extrapolation of the (GeS₂)_x(Sb₂S₃)_1−x data, 0.1 ≤ x ≤ 0.9.¹²³ At low x ≤ 0.5, the log η(T,x) composition dependence is changing smoothly, enabling a reliable extrapolation of log η(T,x) to x = 0.

Both viscosities, η(As₂S₃) and η(Sb₂S₃), follow the Mauro–Yue–Ellison–Gupta–Allan (MYEGA) relationship¹²⁴ but with different fragilities

where the fragility index m = [∂log η/∂(T_g/T)]_T=Tg, η₀ and η(T_g) = 10¹² Pa s are the viscosity values at T = ∞ and T_g, respectively. The m(As₂S₃) = 26 is typical for canonical chalcogenide glasses with a network structure.^{113–116,125,126} Antimony sesquisulfide exhibits a higher fragility, m (Sb₂S₃) = 59, approaching that of telluride PCMs.^113–116 We should also note good agreement between the experimental η(T) and calculated η^FPMD(T) viscosity.

We do not expect for Sb₂S₃ either a fragile-to-strong transition^112–115 or mesoscopic immiscibility accompanied by a viscosity anomaly^116,127 since both the experimental conductivity (Fig. 2) and FPMD simulations (Fig. 13) reveal a semiconducting behavior over the studied temperature range.

Nevertheless, we estimate that a semiconductor–metal (SC–M) transition is taking place between 1250 and 1550 K in comparison with T_SC–M = 1600 ± 150 K for L-As₂S₃^114,128 (Fig. S15 and related details in the ESI†). We also note a lower SC-M transition temperature, 900 K ≲ T_SC–M ≲ 1100 K, for liquid antimony selenides.^114,129 In addition, anionic (Se) or cationic (Bi) substitution can be used for bandgap engineering, since E_g (Sb₂Se₃) = 1.0–1.3 eV^12,130 and E_g (Bi₂S₃) = 1.2–1.4 eV,^131,132 remaining within the wider gap materials compared to tellurides, E_g (Sb₂Te₃) = 0.5 eV.¹³³ Isomorphic mixed crystalline Sb₂(S,Se)₃ thin films were already studied for solar photovoltaics and exhibit the highest power conversion efficiency between Sb₂X₃-based tandem solar cells.^134,135 The anionic substitution is expected to be equally beneficial in smart reprogrammable photonics for both SET and RESET logic states by tuning the bandgap within telecommunication wavelengths and improving the optical contrast, switching rate and energy efficiency. The cationic (Bi) doping is also started to be used in photovoltaics and seems to yield promising results.¹³⁶

4. Concluding remarks

Summarizing the above observations, we can emphasize favorable features in the atomic structure and dynamics of vitreous and liquid Sb₂S₃ as a promising next-generation PCM for integrated smart photonics from the visible to telecom window. A high optical and electric contrast between the SET and RESET logic states in antimony sesquisulfide is based on a different short and intermediate range order in orthorhombic and amorphous Sb₂S₃. The orthorhombic polymorph is composed of quasi 1D-(Sb₄S₆)_∞ ribbons with a strong asymmetry of the Sb–S nearest neighbor distances for three-fold and 5-fold antimony species (2.46 ≤ r^NN_Sb–S ≤ 2.85 Å) and significant inter-ribbon interactions. Glassy Sb₂S₃ reveals a 2D-disordered network built from defect octahedral entities SbS₃ (r^NN_Sb–S = 2.48 ± 0.01 Å), whose three missing Sb–S bonds became excessively long, and the respective sulfur atoms were transformed into the second neighbors at ≈3.4 Å. A more compact network structure of g-Sb₂S₃ compared to canonical As₂S₃, evidenced by the bond angle distributions, shorter Sb–S second neighbor distances and a lower population of microscopic voids and cavities, appears to be a good compromise between the stability of the amorphous state and the ability of fast crystallization. An additional positive feature is related to the intermediate range structure of liquid Sb₂S₃, predominantly composed of ABAB squares, which are speeding up the crystallization phenomena. Another favorable aspect for the rapid SET-RESET transition is an enhanced fragility of liquid Sb₂S₃. The fragility index m = 59 is approaching those of the benchmark telluride PCMs and enables fast crystallization processes at elevated temperatures and simultaneously a remarkable slowdown in the vicinity of T_g, ensuring good retention of the amorphous phase. Furthermore, anionic (Se) and/or cationic (Bi) substitution may be used to decrease the temperature of a SC-M transition, thus improving the dynamics of the SET-RESET change, and allowing bandgap engineering equally important for photonics and photovoltaics.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the Région Hauts de France and the Ministère de l’Enseignement Supérieur et de la Recherche (CPER Climibio), as well as by the European Fund for Regional Economic Development. Work at the Advanced Photon Source, Argonne National Laboratory, was supported in part by the Office of Basic Energy Sciences, US Department of Energy, under Contract No. DE-AC02-06CH1135. The experiments at SPring-8 were approved by the Japan Synchrotron Radiation Research Institute (proposal No. 2017B1771 and 2022B1471) and supported by the Centre for Advanced Science and Technology (Japan) as well as by JSPS KAKENHI, Japan (Grant Number 20H02430). MKh work at ILIT RAS was supported by state assignment FSRC “Crystallography and Photonics”, Russian Academy of Sciences. This work was granted access to the HPC resources of IDRIS (France) under the allocation 2022-A0130910639 made by Grand Equipement National de Calcul Intensif (GENCI) and to use the CALCULCO computing platform, supported by Service COmmun du Système d’Information de l’Université du Littoral Côte d’Opale (SCoSI/ULCO). The FPMD simulations were also carried out using the equipment of the shared research facilities of HPC computing resources at Lomonosov Moscow State University.

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Footnote

† Electronic supplementary information (ESI) available: Raw diffraction patterns of Sb₂S₃, Raman spectrum of amorphous antimony, evolution of Raman spectra for Sb₂S₃ as a function of temperature, DFT Raman spectra of size-limited clusters, S–Sb–S bond angle distributions for DFT-optimized clusters, distributions of Sb–S interatomic distances in DFT-optimized clusters, diffraction data for glassy and liquid As₂S₃, comparison of FPMD modeling with standard PBE and hybrid PBE0 functionals, FPMD modeling of glassy As₂S₃ under high-pressure, fitting Sb–S partials with asymmetric functions, coordination distributions of sulfur and antimony, bond angle distributions in glassy and liquid Sb₂S₃, FPMD partial pair-distribution functions in g-Sb₂S₃ and g-As₂S₃, derived Sb and S diffusion coefficients plotted on the Arrhenius scale, and FPMD estimation of the semiconductor–metal (SC–M) transition temperature T_SC–M for liquid Sb₂S₃. See DOI: https://doi.org/10.1039/d3tc00081h

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