Theoretical prediction and experimental synthesis of a Ba_0.5Pb_0.5S alloy via the molecular precursor route

Abstract

Semiconductor materials with a wide bandgap hold significant promise in the field of tandem solar cells. Ba–Pb–S ternary alloys have received growing interest due to their robust stability, diverse physicochemical properties and broad application potential based on theoretical predictions, but the experimental synthesis of Ba–Pb–S alloys has not yet been reported. In this article, density functional theory calculations indicate that the Ba_0.5Pb_0.5S alloy possesses desirable optoelectronic properties, including a direct bandgap (1.75 eV), a high optical absorption coefficient, and high defect tolerance. Experimentally, we developed a dibutyldithiocarbamate (DBuDTC) solution process for synthesizing Ba_0.5Pb_0.5S polycrystalline powders and thin films using a discrete molecular precursor strategy. Additionally, atomic-resolution scanning transmission electron microscopy provided invaluable insights into the Ba_0.5Pb_0.5S alloy structure. Moreover, the bandgap of Ba–Pb–S ternary alloys can be adjusted, and they exhibit outstanding storage stability under high-humidity conditions. These favorable optoelectronic properties position Ba–Pb–S alloy materials as excellent candidates for both solar energy conversion and optoelectronic materials.

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Guoxin Wu is an M.S. student majoring in Materials and Chemicals at Shandong University, Jinan, China. His research focuses on lead-based semiconductor materials and devices.

Liang Wang received his PhD degree from Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology, in 2017. Following this, he carried out his postdoctoral research under the guidance of Prof. Jiang Tang at the same institution from 2019 to 2023. His research is primarily concentrated on optoelectronic devices, with particular emphasis on thin-film solar cells, detectors, and light-emitting diodes (LEDs).

Qilin Wei obtained a bachelor's degree from Qufu Normal University in Jining, China, a master's degree from Nanjing Tech University in China, and a doctoral degree from Guangxi University in China. Currently, he is engaged in postdoctoral research at Shandong University in China. His research focuses on first-principles calculations of the electronic properties of semiconductor luminescent materials.

William Yu got his Ph.D. degree from the Institute of Chemistry of the Chinese Academy of Sciences. He is a professor at Shandong University. His research interests include quantum dots, energy conversion, flexible electronics and electrochromism.

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1. Introduction

The multi-junction tandem solar cell (TSC) has attracted significant attention due to its potential to surpass the Shockley–Queisser (SQ) limit, thereby achieving a higher power conversion efficiency (PCE) (>45%).¹ As the top cells in TSCs, wide-bandgap (WBG, >1.60 eV) SCs play a crucial role in harvesting high-energy photons and achieving a high open-circuit voltage (V_oc).² Therefore, exploring high-performance WBG semiconductor materials is of great significance for the development of TSCs. Semiconductor materials containing Pb elements have been intensively studied in recent years.^3–5 The unique properties of the Pb element in semiconductor applications are inextricably linked to the atomic structure. The antibonding hybridization between the Pb 6s and anion p states deeply affects the upper valence bands.⁶ The existence of this antibonding property in the valence bands will increase dispersion and hole mobility, which will lead to good performance in semiconductor applications.^7–10 For instance, lead chalcogenides and lead halide perovskites exhibit high potential as light-absorbing layers for solar cells and photodetectors.^11–13

Lead chalcogenide colloidal nanocrystals (e.g., PbS and PbSe) can be synthesized with size-tunable bandgaps spanning from 0.3 to 2.1 eV.^14–17 In 2011, Wang et al. synthesized PbS quantum dots with a bandgap of 1.6 eV for application in TSCs, showcasing promising prospects in full-spectrum quantum dot SCs.¹⁸ However, challenges such as low reproducibility in the synthesis process, high costs, and diminished conversion efficiency of smaller-sized quantum dots with wider bandgaps (>1.7 eV) often hinder the advancement of related research and industrial applications. Lead halide perovskites can adjust their bandgaps to >1.6 eV by incorporating mixed ions (Br⁻ and I⁻).^19–21 Currently, silicon/perovskite TSCs have achieved efficiencies of 33.9%, while perovskite/perovskite TSCs have reached device performances of 28%, opening up new avenues for developing next-generation high-efficiency solar cell technologies.^4,22 However, the long-term stability of WBG perovskites enriched with I⁻ and Br⁻ ions is constrained by ion migration and phase separation.

In recent years, researchers have begun exploring the synthesis of novel multi-component lead-based chalcogenide compounds.^23–27 Theoretical predictions for Ba–Pb–S ternary alloys indicate adjustable bandgap values, high absorption coefficients, small effective masses, and excellent stability, offering broad prospects for applications in thermoelectric materials and solar cells.^6,28,29 In 2017, Chattopadhyaya et al. utilized density functional theory (DFT) to simulate the physical properties of Ba–Pb–S.²⁹ The calculated band structures, bandgaps, and spectra suggest the potential of this material as an efficient candidate for optoelectronic devices operating in the visible spectral regions. Additionally, in 2020, Li et al. predicted Ba–Pb–S chalcogenide compounds with band gaps of approximately 1.85 eV, strong absorption of visible light, and relatively light effective masses for both holes and electrons (<1 m₀).⁶ Despite extensive theoretical research, the literature on the experimental synthesis of Ba–Pb–S alloys is relatively scarce. Further studies are needed to fill this gap and validate the feasibility of theoretical predictions through experimental verification.

In this work, we first calculated the chemical potential of the Ba_0.5Pb_0.5S alloy using DFT theory, confirming its stability. Subsequently, we delved into the energy band structure and defect formation energy of the alloy phase, revealing a bandgap of 1.75 eV and demonstrating its defect-tolerant behavior. We then utilized the molecular precursor route to synthesize the Ba_0.5Pb_0.5S alloy and investigated its optical properties and photoelectric performance. The experimentally measured bandgap of Ba_0.5Pb_0.5S (1.77 eV) agrees well with the theoretical simulation value (1.75 eV), indicating its suitability for WBG SCs in TSCs. Additionally, we have successfully achieved bandgap adjustability of the alloys with varying Ba–Pb ratios, along with excellent storage stability under high-humidity conditions. We believe that this work not only provides valuable insights into multi-component lead-based chalcogenides but also lays a significant foundation for further exploration of the Ba–Pb–S system in optoelectronic applications.

2. Computational and experimental methods

2.1. Computational methods

All calculations within the density functional theory (DFT) framework are conducted using the Vienna Ab initio Simulation Package (VASP).³⁰ We employed the generalized gradient approximation (GGA) of the Perdew–Burke–Ernzerhof (PBE) parameterization along with the projector-augmented wave (PAW) method to compute exchange and correlation functionals.^31,32 Ultra-soft pseudopotentials were utilized for all elements, including Ba, Pb, and S. A kinetic-energy cutoff of 400 eV was applied, and a 4 × 4 × 4 Monkhorst–Pack k-mesh was employed for the wavefunction basis set. The energy convergence criterion was set to 1.0 × 10⁻⁵ eV for structural relaxations.

2.2. Synthesis of Ba–Pb–S alloys

Barium dibutyldithiocarbamate (BaDBuDTC) was synthesized following a literature method with modifications.³³ 5 mmol of barium hydroxide octahydrate (98%, McLean, China) and 10 mmol of dibutylamine (99%, McLean, China) were placed in a 25 ml round-bottomed flask and stirred at room temperature; then 11 mmol of carbon disulfide (98%, Aladdin, China) was slowly added. After stirring for 4 hours at 65 °C, the residual carbon disulfide and water from the reaction were removed by rotary evaporation under vacuum at 70 °C. The resulting solid was dried under vacuum at 65 °C for 24 hours and could be stored in air without deterioration.

Lead dibutyldithiocarbamate (PbDBuDTC) was synthesized similarly. 5 mmol of lead oxide (99.9%, Aladdin, China) and 10 mmol of dibutylamine were placed in a 25 ml round-bottomed flask and stirred at room temperature; then 11 mmol of carbon disulfide was slowly added. If it solidified, a small amount of toluene could be added. After stirring for 4 hours at 35 °C, the residual carbon disulfide and water from the reaction were removed by rotary evaporation under vacuum at 70 °C. The resulting solid was dried under vacuum at 65 °C for 24 hours and could be stored in air without deterioration.

Synthesis of Ba_0.5Pb_0.5S: 1 mmol of BaDBuDTC and 1 mmol of PbDBuDTC were dispersed evenly in 2 ml of carbon disulfide in a glass sample bottle. The dispersion was then transferred to a crucible and placed in a tube furnace. After three slow nitrogen replacements, the temperature was raised from room temperature for 120 minutes to 700 °C under nitrogen. After being maintained at 700 °C for 4 hours, the alloy powder sample was naturally cooled to room temperature. If the solution was applied dropwise to quartz glass and reacted in a tube furnace, a thin film of the alloy loaded on the quartz glass was obtained. It was worth noting that in order to prevent oxygen from oxidizing barium sulfide to barium sulfate, the purity of the nitrogen used should be higher than 99.99%.

2.3. Characterization

The crystal structures of the obtained powders were detected using an X-ray powder diffractometer (Rigaku SmartLab 9KW) with monochromatized Cu Kα radiation (λ = 0.1540593 nm). UV-Vis diffuse reflection absorption spectra of the samples were detected using a Shimadzu UV-2550 equipped with an integration sphere and BaSO₄ was used as the substrate background. HAADF-STEM images and EDS mappings were collected at 300 kV on a ThermoFisher Scientific Spectra 300 scanning transmission electron microscope equipped with a Super-X EDS detector system. Thermogravimetric analysis measurements of the precursors were performed using a TA-SDT Q600 under a heating rate of 10 °C min⁻¹ under nitrogen. The elemental contents of barium and lead were analyzed using a NEXION350X inductively coupled plasma mass spectrometer (ICP-MS). The Ba_0.5Pb_0.5S thin film surface morphology was characterized using a field-emission scanning electron microscope (SEM, GeminiSEM 300). X-ray photoelectron spectroscopy (XPS) was performed on Thermo Fisher ESCALAB XI+. At the data-processing stage, we normalized the indeterminate carbon peak at 284.8 eV to calibrate all the spectra.

3. Results and discussion

3.1. Computational section

We first discussed the structure and optical properties of the Ba_0.5Pb_0.5S alloy from our first-principles simulation. In Fig. 1a, we plotted the crystal structure of Ba_0.5Pb_0.5S, where the alloy remained in the same cubic lattice structure as PbS and BaS. In this structure, Pb and Ba are situated in the cationic sublattice, while S occupies the anionic sublattice. We performed first-principles calculations for the energy band structure of the Ba_0.5Pb_0.5S alloy (Fig. 1b), which has a direct energy band gap of 1.75 eV, with the maximum valence band point and the minimum conduction band point occurring at point A in the Brillouin zone, exhibiting an energy band structure similar to that of PbS. As shown in Fig. S1,† the Ba_0.5Pb_0.5S alloy exhibits strong absorption in the visible range, which predicts that the alloy may exhibit a significant photovoltaic response. Fig. 1c shows the total density of states (TDOS) and the partial density of states (PDOS) for Ba_0.5Pb_0.5S. The valence band predominantly originates from the 3p states of S, which are influenced by Pb's 6p orbitals, alongside significant Ba 4d orbitals, and a minor presence of S 3p orbitals. The conduction band is composed of the p-orbitals of Pb with a slight overlap with the p-orbitals of S. This distribution of states predicts that the electronic properties of the Ba–Pb–S alloy can be tuned by adjusting the Pb : Ba molar ratios.

Fig. 1 (a) Crystal structure model of the Ba_0.5Pb_0.5S alloy. (b) Band structure of the Ba_0.5Pb_0.5S alloy. (c) Density of states (DOS) of the Ba_0.5Pb_0.5S alloy.

The phase stability and defect physics of the Ba_0.5Pb_0.5S alloy were discussed from our first-principles simulation. Fig. S2† shows a phase stability diagram with two independent variables, revealing a stabilizing region (pink region) of the Ba_0.5Pb_0.5S alloy. The synthesized samples within this stable range should ideally manifest as single-phase Ba_0.5Pb_0.5S crystals. Nevertheless, the potential for intrinsic point defects persists, contingent upon their formation energies. The preparation of chalcogenide compounds involves controlling sulfur partial pressure to reduce defect formation such as CZTS, Sb₂S₃, etc., facilitating high-quality thin films.^34–37 We further calculated charge-state transition levels and formation energies of intrinsic point defects in Ba_0.5Pb_0.5S under S-rich and S-poor conditions (Fig. 2a and b). Among these defects, 5 kinds of point defects (S interstitial (I_S), Pb vacancy (V_Pb), Ba replacing S (Ba_S), Ba replacing Pb (Ba_Pb) and S replacing Pb (S_Pb)) have relatively low ΔH_f values (<1 eV) and are the dominant defects, while the other defects including those with deep states (e.g., I_Pb, Pb_S, S_Ba, etc.) have high ΔH_f values (>1 eV). Interestingly, all the dominant defects are shallow defects (e.g., Ba_S acts as shallow acceptors, while V_Pb serves as shallow donors), without deep states in the bandgap. These results indicate that Ba_0.5Pb_0.5S should be defect-tolerant, which is desired for optoelectronic devices.

Fig. 2 (a) Calculated charge-state transition levels of intrinsic defects in the Ba_0.5Pb_0.5S alloy. (b). Defect formation energy of the Ba_0.5Pb_0.5S alloy under S-rich and S-poor conditions.

3.2. Experimental section

Building upon the theoretical investigations into the suitable band gap and favorable defect properties mentioned above, we now turn to the experimental studies on Ba_0.5Pb_0.5S powder and thin films (Fig. 3a). Initially, we synthesized the molecular precursors BaDBuDTC and PbDBuDTC according to the preparation method outlined in the synthesis section. Because of the high sensitivity of barium to the element oxygen, an oxygen-free solvent should be chosen to disperse the two precursors to avoid the formation of BaSO₄ at high temperatures. We found that PbDBuDTC had good solubility in some oxygen-free solvents (e.g., toluene, butylamine, and carbon disulfide), whereas BaDBuDTC can only be well dispersed in carbon disulfide. Therefore, carbon disulfide was chosen as the dispersing solvent for both precursors.

Fig. 3 (a) Schematic illustration of the preparation scheme of the Ba_0.5Pb_0.5S alloy. (b) TGA profiles of PbDBuDTC and BaDBuDTC. (c) XRD patterns of the Ba_0.5Pb_0.5S alloy at different reaction temperatures.

We employed thermogravimetric analysis (TGA) to ascertain the decomposition temperatures of the metal precursors, enabling us to determine the preparation temperatures for both powders and thin films. As illustrated in Fig. 3b, it was observed that both precursors decomposed at 400 °C. The structure of the decomposition product was further determined by powder XRD. After reacting BaDBuDTC : PbDBuDTC at a 1 : 1 molar ratio at 400 °C for 4 h, the obtained powder exhibited a cubic phase mixture of BaS and PbS (Fig. 3c). It was evident that both precursors together at 400 °C or 500 °C, yielded PbS and BaS, but without further alloying. However, upon increasing the reaction temperature to 600 °C, the intensities of the PbS and BaS peaks decreased, with a new set of peaks emerging between them. Ultimately, at a reaction temperature of 700 °C, the peaks corresponding to PbS and BaS disappeared completely, and the peaks on the same crystal plane merged into one, indicating the formation of the Ba_0.5Pb_0.5S alloy. Dense thin films are a prerequisite for most semiconductor device applications, prompting us to conduct a preliminary exploration of the film-forming method for the Ba_0.5Pb_0.5S alloy. We examined the microscopic morphology of the film by drop-coating the precursor solution, revealing its good compactness in a scanning electron microscope (SEM) image (Fig. S3†). This exploration provides a reference program for future thin film preparation in this system.

According to the changes in the peak positions and intensities of BaS and PbS in Fig. 3c, we hypothesize that the alloy formation process entails the gradual filling of PbS into the lattice of BaS. During alloying, Pb tends to infiltrate the BaS lattice more readily because of its smaller ionic radius. This infiltration leads to a decrease in the lattice constant of BaS and a corresponding shift of its XRD peak towards higher angles. Conversely, the peak position of PbS gradually shifts towards lower angles. Ultimately, this process culminates in the formation of the Ba_xPb_1−xS alloy. Inductively coupled plasma mass spectrometry (ICP-MS) was utilized to quantify the elemental composition of the resultant alloy. As shown in Table S1,† the calculated molar ratio of Ba to Pb is 1.09. Two possible reasons contributed to the deviation of the measured result from 1. First, the purity of the metal precursors may not be 100%, potentially altering the actual molar feed ratio. Second, there might slight volatilization of PbS during the process.

We further analyzed the lattice spacing and element distribution by high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) (Fig. 4). As shown in Table S2,† we compared the crystal spacing and cell parameter data for BaS, PbS and Ba_0.5Pb_0.5S from XRD with the crystal spacing data for Ba_0.5Pb_0.5S from HAADF-STEM. The lattice spacings of the cubic phase alloy measured by HAADF-STEM are 0.309 nm and 0.219 nm, which correspond exactly to the experimentally measured XRD peaks of the alloy in the (200) and (220) directions. These values fall between the corresponding lattice spacings of the (200) and (220) crystal planes of PbS (0.297 nm and 0.210 nm) and BaS (0.319 nm and 0.226 nm), providing further evidence of the alloy formation. The cell parameter of the alloy was also calculated from the XRD data as a = b = c = 6.180, which is a decrease compared to the cell parameter of BaS and an increase compared to PbS, which further corroborates the formation of the alloy. Energy dispersive X-ray spectroscopy (EDS) was performed on the area captured in Fig. 4a, revealing a uniform distribution of Ba, Pb and S within the region (Fig. 4b and d), further confirming the formation of the Ba_0.5Pb_0.5S alloy.

Fig. 4 HAADF-STEM image and EDS elemental mappings of the Ba_0.5Pb_0.5S alloy.

X-ray photoelectron spectroscopy was employed to investigate the ionic valence states of the Ba_0.5Pb_0.5S alloy. Fig. S5† provides the complete spectral information of the alloy exposed to ambient conditions. The high-resolution spectra and corresponding peak fittings for the S 2p, Ba 3d, and Pb 4f regions are given in Fig. S4–S7,† respectively, with fitted peak positions and peak splitting values detailed in Table S3.† The deconvolution of the Ba(3d) spectra for the sample provides Ba 3d_5/2 and 3d_3/2 peaks with binding energies of 780.8 and 796.2 eV, respectively. Notably, the Ba 3d doublets exhibit a singular chemical environment with a characteristic spin–orbit splitting of 15.4 eV. In the Pb 4f region, two sets of doublets can be observed, each with a splitting of 4.9 eV. The higher binding energy doublet (centered at 138.8 and 143.7 eV) is attributed to oxidized lead species (PbO_x) on the surface. Conversely, the lower binding energy doublet (centered at 137.2 and 142.1 eV) is associated with Pb²⁺ in a sulfide environment. This observation of two different lead environments parallels previous reports.²³ In the S 2p region, a doublet and an unresolved singlet can be deconvoluted from the high-resolution spectrum. The doublet, with a splitting of 1.2 eV, is attributed to the 2p_1/2 and 2p_3/2 of S²⁻, while a broad singlet centered at 162.3 eV is indicative of surface oxidation (i.e., SO_x).²³ Thus, XPS analysis verified the valence states of +2, +2, and −2 for Ba, Pb, and S, respectively, in the material, as well as the oxidation of the surface.

The absorption coefficient (α) and optical band gap of the resulting Ba_0.5Pb_0.5S were measured by UV–Vis–NIR spectroscopy. The absorption spectrum and the optical band gap are provided in Fig. 5a and b, respectively.³⁸ The absorption coefficient in the visible region reaches 10⁴ cm⁻¹, which is consistent with the theoretical calculation (Fig. S8†). The Fig. 5b shows the (αhυ)² − hυ Tauc plot for the direct transition. The alloy powder with a 1 : 1 molar feed ratio of Ba : Pb exhibits a direct bandgap width of 1.77 eV, slightly higher than the theoretical simulation of the bandgap width (1.75 eV) of the Ba_0.5Pb_0.5S alloy. In addition, the stability of Ba_0.5Pb_0.5S against moisture is also investigated. After being exposed to a relative humidity of 60% for 30 days in ambient air, the alloy retained its original structure, demonstrating remarkable stability compared to organic–inorganic metal halide perovskite materials (Fig. S9†).^39,40

Fig. 5 (a) Absorption spectrum of the Ba_0.5Pb_0.5S alloy. (b) Band gap estimation of the Ba_0.5Pb_0.5S alloy. (c) Photodetector based on the Ba_0.5Pb_0.5S alloy. (d) Dynamic response of the device upon on–off switching of a 365 nm LED.

To further evaluate the potential for optoelectronic applications, we conducted experiments on the transient photoelectric response of a Ba_0.5Pb_0.5S device. Fig. 5c depicts the schematic structure of the photodetector with a channel width and length of 0.6 mm and 4 mm, respectively. We examined the photoelectric response of the device using an LED emitting light at 365 nm, with an optical power density of 0.94 mW cm⁻². Fig. 5d demonstrates the photocurrent responsivity of the Ba_0.5Pb_0.5S alloy. Under a bias voltage of 1 V, our detector exhibits a very low dark current (1.11 nA) and a high photocurrent on/off repeatability. Additionally, our detector also showed a fast response speed with a rise and decay time of less than 50 ms. We further calculated the responsivity (R = 1.77 × 10⁻⁶ A W⁻¹) and specific detectivity (D* = 1.45 × 10⁷ Jones) of the photodetector.⁴¹ Furthermore, the adjustable bandgap characteristic of Ba–Pb–S alloys can be realized by tuning the Ba : Pb molar ratios (Fig. S10–S12†). As the proportion of Ba in the alloy increases, the band gap widens. Conversely, increasing the proportion of Pb narrows the band gap. By adjusting the Ba molar ratio from 2 : 1 to 1 : 2, the band gap can be reduced from 2.10 eV to 1.50 eV. This suggests that precise control over the Ba and Pb ratios in the alloy could allow for customized synthesis of a certain band gap value. In addition, we used ultraviolet photoelectron spectroscopy (UPS) combined with the forbidden bandwidth to determine the energy level position of the Ba0.5Pb0.5S alloy (Fig. S13†). The results show that the conduction band minimum is located at −3.33 eV, the valence band maximum at −5.10 eV, and the Fermi energy level at −4.23 eV, confirming that the alloy behaves as a p-type semiconductor. These findings open up the possibility of potential applications for the alloy in optoelectronic devices.

4. Summary

Our first-principles calculations revealed that the Ba_0.5Pb_0.5S alloy boasts a direct bandgap of 1.77 eV, coupled with a high absorption coefficient and defect-tolerant properties, showcasing its promising potential for applications in solar energy conversion and optoelectronic materials. Subsequently, we successfully synthesized Ba–Pb–S powders and films via a molecular precursor route, effectively filling the experimental gap in this area. Moreover, we demonstrated the tunability of the alloy's bandgap width by adjusting the molar ratios of Ba to Pb. Notably, the alloy exhibited exceptional stability under ambient conditions. In addition, our attempts to construct a photodetector utilizing the Ba_0.5Pb_0.5S alloy yielded encouraging results, with exceptionally low dark current and excellent photoelectric response capability. We believe that this work will serve as an important reference for advancing the development of Ba–Pb–S alloys in the optoelectronic application domain.

Author contributions

Liang Wang and William W. Yu designed and led the project, revised the manuscript, and acquired funding. Qilin Wei was responsible for the theoretical calculations of the materials. Guoxin Wu performed materials synthesis and characterization and wrote the original draft. Kepeng Song was responsible for the acquisition of HAADF-STEM images and EDS elemental mappings. Jiashuo Xu and Xinzhuo Fang helped in the synthesis and characterization of the material. Jinghai Li helped in the preparation of photodetectors. Dan Huang was responsible for the acquisition of simulation software. Liqiang Zheng provided a student to complete the experiment.

Date availability

All relevant data are within the manuscript and its ESI.†

Conflicts of interest

The authors declare no conflict of interest.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (62374103 and 62374104) and Taishan Scholar Foundation of Shandong Province (No. tsqn2023120051105) of Shandong Province.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4qi02090a

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