Structure reinvestigation of α-, β- and γ-In₂S₃

Semiconducting indium sulfide (In₂S₃) has recently attracted considerable attention as a buffer material in the field of thin film photovoltaics. Compared with this growing interest, however, detailed characterizations of the crystal structure of this material are rather scarce and controversial. In order to close this gap, we have carried out a reinvestigation of the crystal structure of this material with an in situ X-ray diffraction study as a function of temperature using monochromatic synchrotron radiation. For the purpose of this study, high quality polycrystalline In₂S₃ material with nominally stoichiometric composition was synthesized at high temperatures. We found three modifications of In₂S₃ in the temperature range between 300 and 1300 K, with structural phase transitions at temperatures of 717 K and above 1049 K. By Rietveld refinement we extracted the crystal structure data and the temperature coefficients of the lattice constants for all three phases, including a high-temperature trigonal γ-In₂S₃ modification.

1. Introduction

In₂S₃ is a widegap semiconductor with high photoconductive and photoluminescent properties, which makes it a promising material for optoelectronic applications (Shazly et al., 1998). Most prominently, its potential application as a buffer layer in chalcopyrite solar cells has triggered an increased research effort in its fundamental materials properties (e.g. crystal structure, optical properties, electronic bandstructure etc.) as well as in deposition technology. The compatibility with various thin film deposition methods make it a versatile alternative to the commonly applied CdS buffer layer. Among the compatible deposition methods, atomic layer deposition (Naghavi et al., 2003), the ion layer gas reaction (ILGAR) method (Sáez-Araoz et al., 2012), spray pyrolisis (John et al., 2005), sputtering (Hariskos et al., 2005) and evaporation (Strohm et al., 2005) have been successfully applied. The interested reader is referred here to the excellent review by Barreau (2009) on the role of In₂S₃  in the world of photovoltaics. Various reports on In₂S₃ buffer layers correlate deposition process parameters with crystallographic properties (Rao & Kumar, 2012; Larina et al., 2004; Yoosuf & Jayaraj, 2005) and ultimately with final solar cell device parameters (Naghavi et al., 2003; Pistor, Caballero et al., 2009).

For a correct interpretation of the crystallographic data, a comprehensive understanding of the relevant crystal structure modifications of In₂S₃  is mandatory. Data reported on the phase labelling and temperature sequence in the In–S system is contradictory. In view of recent technological and scientific interest in In₂S₃ and the commonly drawn connection to its crystal structure properties, in this contribution we therefore report about a crystal structure reinvestigation of the In₂S₃ system in the temperature range from room temperature up to 1322 K, close to the melting point at 1363 K (Diehl et al., 1976). The present study results in high quality reference powder diffraction data sets and enhanced knowledge on the different structure modifications of In₂S₃, which is expected to have a direct impact on the technological understanding in terms of e.g. material quality or diffusion parameters.

The first to describe the crystal structure of In₂S₃ were Hahn & Klingler (1949). They reported a cubic phase at temperatures below 600 K, which they called α-In₂S₃ and a transition to a tetragonal spinel-like high-temperature modification which they called β-In₂S₃. They already stressed the similarity between both modifications and suggested an ordering of the In atoms to be the main difference between the two phases. Later studies revealed that the cubic phase is in fact the higher-temperature phase and the stoichiometric phase existing at room temperature is tetragonal. However, for sulfur-deficient In₂S₃ the temperature range for the cubic phase extends down to room temperature. So Hahn probably measured a sulfur-deficient cubic α-In₂S₃ at room temperature and called it the lower temperature modification and from here most confusion about the labelling and temperature sequence of phases arises.

While the majority of authors follow Hahn in their nomenclature resulting in an ordering of the phases from low to high temperature as β–α–γ, some have relabeled the cubic and tetragonal phase with a resulting order of α–β–γ. Depending on the author, β-In₂S₃ in recent publications may therefore refer either to the low-temperature tetragonal phase or the cubic high-temperature phase. Although α–β–γ would be the logical order, we will follow the majority in the literature and assign β-In₂S₃ to the low-temperature, tetragonal phase.

There are some more and sometimes contradictory publications in the literature on the crystal structure of the different In₂S₃ phases, of which the most relevant ones will be shortly introduced in the following. Gödecke & Schubert (1985) suggest a phase diagram in which for the In:S ratio of 2:3 three modifications (β-In₂S₃, α-In₂S₃ and γ-In₂S₃) of indium sulfide exist in three different temperature regimes. King (1962) determined the space group of the tetragonal β-In₂S₃ as I4₁/amd (space group No. 141) and the lattice parameters to a₀ = 7.61 Å and c₀ = 32.24 Å using Weissenberg photographs. The space group was later confirmed by Goodyear & Steigmann (1961) and Steigmann et al. (1965) who reported the lattice parameters as a₀ = 7.623 Å and c₀ = 32.36 Å . Hahn described the space group of the cubic α-In₂S₃ as , with a lattice parameter of 10.72 Å (Hahn & Klingler, 1949). The high-temperature γ-In₂S₃ modification has not been characterized in detail yet since a quenching to room temperature conditions was not successful (Diehl et al., 1976). However, Diehl et al. succeeded in synthesizing a modified γ-In₂S₃ phase with an additional 5 at. % of As or Sb stabilizing it at room temperature. For this modified trigonal γ-In₂S₃ they suggested a space group of with lattice parameters a₀ between 3.806 and 3.831 Å and c₀ between 9.044 and 9.049 Å.

Some recent publications refer to the thin film application of In₂S₃ and cite X-ray diffraction (XRD) database information. An assignment to the tetragonal β-In₂S₃ is often made although the quality of the diffraction data for In₂S₃ is generally poor and does not allow for a definite distinction between the tetragonal β-In₂S₃ and the cubic α-In₂S₃. A correct distinction between the two phases would however allow for a verification of the film stoichiometry, as the β-In₂S₃ only exists in a very small stoichiometry range (Gödecke & Schubert, 1985). It is the scope of this work to reinvestigate the In₂S₃ in view of these aspects and to present a clear and detailed description of its crystal structure over the temperature range from room temperature to above 1300 K.

2. Experimental methods

2.1. Sample preparation

Indium sulfide was synthesized by heating weighted stoichiometric amounts of sulfur and indium in the ratio 3:2 in evacuated quartz ampoules. Source materials were indium granulate (> 99.999% purity) and sulfur flakes (> 99.999% purity). An excess of 4 atomic percent of S was provided for two reasons: (i) to account for sulfur losses during the preparation; (ii) the excess sulfur is not incorporated into the crystal structure according to the phase diagram (Gödecke & Schubert, 1985). The weighted source materials were filled in a graphite boat and placed in a quartz glass ampoule, evacuated (< 10⁻³ mbar) and sealed. The ampoule was placed in a two-zone oven and heated above the melting point to 1373 K for 24 h to enable the complete sulfurization of the indium. To assure that the synthesis was completed, the ampoule was then kept at 1073 K for 2 d, at 873 K for 2 d and at 673 K for 4 d. The synthesized indium sulfide was manually ground in a mortar before XRD measurements and had a brick red appearance.

2.2. Diffraction measurement

For the diffraction measurement, ground indium sulfide powder was sealed in a quartz glass ampoule. The XRD measurements were performed at the ESRF, the European Synchrotron, Grenoble, France, at the beamline ID15B using monochromatic high-energy synchrotron light with a wavelength of 0.14276 Å. XRD patterns were recorded every 5 K, while heating the sample from 304 to 1322 K with a constant heating rate of 300 K h⁻¹. The detector type used was a Pixium 4700, the detector-to-sample distance was 1037.132 mm, and the furnace was a resistively heated tube furnace.

2.3. Details of the Rietveld refinement

The software FullProf Suite (February 2016 version) was used for the Rietveld refinement of the recorded diffractograms (Rodriguez-Carvajal, 2001). Apart from 7 profile parameters, the lattice parameters were fitted, as well as the atomic position coordinate parameters where appropriate, the isotropic temperature factor for all atomic positions, and the occupational factors of the indium positions. In addition we fitted the background by a list of manually inserted points which will add to the list of refined parameters.

3. Results

3.1. Temperature-dependent phase analysis

In₂S₃ powder was prepared from the elements via a high-temperature route as described in §2.1. The mortared In₂S₃ powder was filled into quartz glass ampoules which were instantanously evacuated and sealed. The X-ray diffractograms were recorded in the temperature range from 304 to 1322 K, and details on the diffraction measurements can be found in §2.2. A colorscale map of all diffractograms is depicted in Fig. 1. In this graph, color indicates the counts and the three temperature ranges corresponding to the three different phases with distinct diffraction patterns can be well separated. We find a sharp structural phase transition between the first two phases at a temperature of 717 ± 5 K. This transition is characterized by the disappearance of several minor intensity diffraction peaks, while the main diffraction peak positions and intensities remain appoximately constant for both phases (see Figs. 1 and 2). A second transition was observed in the temperature range between 1049 and 1084 K. Here, all peaks of the α-In₂S₃ disappear and are replaced by the diffraction peaks of γ-In₂S₃ indicating a complete reordering of the atoms in the crystal structure.

Figure 1 Map of temperature-dependent X-ray diffractograms (XRD) for the In2S3 powder. Each diffractogram is measured at a specific temperature which corresponds to one column in the graph with the y-direction displaying the 2θ diffraction angle. The position of the column in the x-direction corresponds to the temperature at which the diffractogram was recorded, while the colour indicates the XRD intensity in logarhythmic scale (dark blue = low intensity, red = high intensity). Three structural modifications of In2S3 in different temperature regimes can be distinguished according to appearing/disappearing diffraction peaks as indicated in the figure. The wavelength of the incident X-ray photons is 0.14276 Å.

Figure 2 Diffraction data and Rietveld refinement of the three In2S3 modifications fully refined in this study. The displayed residua have been vertically shifted for better comparison. (a) Tetragonal modification measured at 309 K; (b) cubic modification measurement at 749 K; (c) trigonal modification measured at 1099 K.

3.2. Rietveld refinement of the three In₂S₃ modifications

We carried out full Rietveld refinements of the three diffractograms recorded at temperatures of 309, 749 and 1099 K. The refined lattice parameters are listed in Table 1. The three diffractograms, refinements and residues are displayed in Fig. 2. The calculated figures of merit and atomic positions can be found in Tables 2 and 3–5, respectively. For all three phases we obtained a good agreement between measurement and simulation with χ² values below 11 and Bragg R_I-factors below 0.03. More detailed information on the refinement parameters are included in the CIF file in the supporting information.

Table 1
Lattice parameters as extracted from the Rietveld refinement for the three In₂S₃ modifications

		Temperature (K)	Space group	Number	a0 = b0 (Å)	c0 (Å)	(°)	γ (°)
#1	β-In2S3	309	I41/amd	141	7.6231 (4)	32.358 (3)	90	90
#2	α-In2S3	749		227	10.8315 (2)	10.8315 (2)	90	90
#3	γ-In2S3	1099		164	3.8656 (2)	9.1569 (5)	90	120

Table 2
Refinement parameters for the Rietveld refinements performed for the three modifications of In₂S₃

R_B: Bragg R_I factor, : for points with Bragg contribution, R_wp: weighted profile R-factor (not corrected for background), R_exp: expected R-factor (not corrected for background), cR_wp: weighted profile R factor (corrected for background), cR_exp: expected R-factor (corrected for background), Ratio_h/p: ratio between effective number of reflections and intensity parameters.

		Temperature (K)		RB	Rwp	Rexp	cRwp	cRexp	Ratioh/p
#1	β-In2S3	309	10.4	0.014	0.031	0.01	0.049	0.015	5.9
#2	α-In2S3	749	7.9	0.017	0.028	0.01	0.055	0.020	7.3
#3	γ-In2S3	1099	10.8	0.028	0.030	0.01	0.072	0.024	3.8

Table 3
Atomic sites for the tetragonal β-In₂S₃, (space group 141, origin choice No. 2)

Atom	Wickoff	x	y	z	Uiso	Occ.
S1	16h	0	−0.005 (2)	0.2513 (7)	0.013 (4)	1.0
S2	16h	0	0.008 (2)	0.0777 (7)	0.016 (4)	1.0
S3	16h	0	0.020 (2)	0.4133 (7)	0.015 (4)	1.0
In1	8e	0	1/4	0.2046 (2)	0.0097 (8)	0.973 (6)
In2	8c	0	0	0	0.0143 (15)	0.972 (7)
In3	16h	0	−0.0196 (3)	0.3327 (2)	0.0111 (10)	0.974 (6)

Table 4
Atomic sites for the cubic α-In₂S₃ (space group 227, origin choice No. 2)

Atom	Wickoff	x	y	z	Uiso	Occ.
S1	32e	0.2564 (2)	0.2564 (2)	0.2564 (2)	0.0347 (11)	1.0
In1	8a	1/8	1/8	1/8	0.0306 (9)	0.64 (4)
In2	16d	1/2	1/2	1/2	0.0445 (6)	0.978 (6)

Table 5
Atomic sites for the trigonal γ-In₂S₃

Atom	Wickoff	x	y	z	Uiso	Occ.
S1	2d	1/3	2/3	0.3359 (7)	0.054 (4)	1.0
S2	1a	0	0	0	0.091 (5)	1.0
In1	2d	1/3	2/3	0.8085 (3)	0.0510 (9)	0.829 (10)
In2	2d	1/3	2/3	0.6485 (12)	0.064 (6)	0.144 (3)

3.3. Temperature dependence of the lattice parameters

Finally, the XRD data measured at different temperatures have been processed in batch-mode Rietveld refinements to extract the temperature dependence of the relevant lattice parameters. An example is shown in Fig. 3 for the lattice parameter a₀ of the cubic α-In₂S₃ phase in the temperature range between 749 and 1044 K. The data are well fitted with the linear fit function

From the temperature dependence of the lattice constants, we obtain the linear thermal expansion coeffient α (; Kundra & Ali, 1976) for the cubic phase. In this temperature range, we calculate an average α of 10.3 × 10⁻⁶ K, in relatively good agreement with Kundra & Ali (1976), 10.8 × 10⁻⁶–10.9 × 10⁻⁶ K). The temperature dependence of the remaining lattice parameters of the tetragonal and trigonal phases are obtained accordingly and the fit functions are summarized in Table 6. For the tetragonal β-In₂S₃ we find an average linear expansion coefficient α in the a direction of 11.7 × 10⁻⁶ K and in the c direction of 6.7 × 10⁻⁶ K. For the trigonal phase, an average linear expansion coefficient of 14.1 × 10⁻⁶ K in the a direction and 26.7 × 10⁻⁶ K in the c direction was determined.

Table 6
Linear fit function of the lattice parameters of In₂S₃ from the Rietveld refinements

		Temperature range (K)	Fit function
#1	β-In2S3	309–704	a = 7.5949 (2) Å + 8.967 (31)T × 10^−5 Å K^−1
			c = 32.307 (2) Å + 1.607 (4)T × 10^−4 Å K^−1
#2	α-In2S3	749–1044	a = 10.7480 (2) Å + 1.121 (2)T × 10^−4 Å K^−1
#3	γ-In2S3	1099–1322	a = 3.8044 (2) Å + 5.566 (15)T × 10^−5 Å K^−1
			c = 8.877 (3) Å + 2.52 (2)T × 10^−4 Å K^−1

Figure 3 Temperature dependence of the lattice parameter for the cubic α-In2S3. The resulting fit parameters of a linear fit are listed in the inset.

4. Discussion

In this section we will briefly discuss the crystal structure of the three modifications and how the different modifications may impact the application of In₂S₃ in thin film solar cells.

The low-temperature modification β-In₂S₃ is best described with a defect spinel-type structure. The S atoms form a distorted cubic closed-spaced sublattice, in which the In atoms occupy the tetrahedral and octahedral interstitials the same way cations do in a regular spinel-like MgAl₂O₄ (Kleber et al., 2002). While all the octahedral cation sites are occupied in β-In₂S₃, one third of the tetrahedal sites remain unoccupied. For that reason the In₂S₃ structure is sometimes described in a quasi-ternary compound formula: [In_2/3(Vac)_1/3]^tet[In]^oct₂S₄, where []^tet and []^oct denote tetrahedral and octahedral sites and (Vac) the vacancies. In β-In₂S₃, the vacancies are ordered along the 4₁ screw axis which is by definition parallel to the c-axis. The ordering of the vacancies gives rise to a small distortion of the cubic symmetry of the regular spinel structure. This small distortion is the origin of the tetragonal structure of the β-In₂S₃ with lower symmetry and leads to the additional peaks observed in the X-ray diffraction. Fig. 4 shows a plot of the β-In₂S₃ crystal structure based on the results obtained by the Rietveld refinement.

Figure 4 Structure model of a β-In2S3 unit cell. The tetrahedral bonds are drawn thicker for better identification. The indium vacancies are marked as grey spheres. In the tetragonal β-In2S3 configuration, the vacancies are ordered on a 41 screw axis parallel to the c-axis of the crystal. In the α-In2S3 configuration, the vacancies are randomly distributed over all tetrahedral indium sites. The edges of the unit cell of the tetragonal β-In2S3 structure (cubic α-In2S3) structure are indicated by black (blue) lines.

The transition from β-In₂S₃ to α-In₂S₃ is an order–disorder transition. In α-In₂S₃, the indium vacancies are randomly distributed over all tetrahedral sites, in contrast to the ordered configuration of vacancies in the β-In₂S₃. As a result of the disordering, α-In₂S₃ adopts a cubic crystal structure. The resulting higher crystal symmetry explains the observed disappearance of some of the minor intensity peaks in the diffractograms at the transition from β-In₂S₃ to α-In₂S₃ at 717 K.

Finally, the γ-In₂S₃ can be described as a layered structure as suggested by Diehl et al. and Bartzokas et al. (Diehl et al., 1976; Bartzokas et al., 1978). Here, the S atoms remain in a nearly closed-packed sublattice while the In atoms are exclusively found on octahedral sites forming a layered structure of subsequent S—In—S—In—S slabs.

The defect spinel-type structure of the β-In₂S₃ and α-In₂S₃ has a direct phenomenological and technological impact. Because of the large number of natural vacancies in the structure, In₂S₃ can host various other atoms such as Na or Cu within its original lattice configuration (Barreau et al., 2006). Both have been found to diffuse efficiently through In₂S₃ thin films (Pistor, Allsop et al., 2009; Juma, Pistor et al., 2012; Juma, Kavalakkatt et al., 2012). The diffusion phenomena at interfaces in thin film solar cells containing In₂S₃ have not yet been fully understood but might benefit from an in-depth knowledge of the crystal (vacancy) structure of In₂S₃. Where XRD data of good quality exist, it is an easy task to distinguish between the tetragonal and cubic phase of In₂S₃ by an examination of the characteristic additional peaks only present for the β-In₂S₃. The differentiation between α-In₂S₃ and β-In₂S₃ allows testing for stoichiometry, since the tetragonal phase only exists in a very small compositional range. According to Gödecke & Schubert (1985) and Diehl & Nitsche (1975), the compositional range for the β-In₂S₃ is less than 1 at %. The addition of a very small amount of surplus indium effectively surpresses the ordering of the In vacancies and therefore the formation of the tetragonal β-In₂S₃ phase. As a consequence, the crystal structure of off-stoichiometric In_2+xS₃ remains in the cubic α-In₂S₃ modification down to room temperature. This specific feature is used for example to check if In₂S₃ source material for an evaporation process is still within the described stoichiometry range (Pistor, Caballero et al., 2009). Alike the distinction of polycrystalline powder material, this type of analysis tool would be rather desirable for the evalution of In₂S₃ thin film material as well. However, reasonable X-ray diffraction data are necessary to distinguish between the two very similar spectra in order to resolve the fine additional peaks, a criterion often not met for XRD patterns available on In₂S₃ thin films.

5. Conclusions

We provide a detailed crystal structure analysis of In₂S₃ over the entire temperature range from room temperature up to close to the melting point covering the three modifications β-In₂S₃, α-In₂S₃ and γ-In₂S₃. With this, we contribute to the comprehensive understanding of the different phases existent and their interdependence. The high-temperature phase γ-In₂S₃ has been analysed and refined for the first time in the pure phase. Finally we show how the detailed knowledge of the phase diagram and the different In₂S₃ modifications might have a direct impact on the technological use of In₂S₃ in applications such as buffer layer deposition in thin film solar cell production.

Supporting information

Computing details

For all compounds, program(s) used to refine structure: FULLPROF.

(TetragonalIn2S3)

Crystal data

In2S3	V = 1880.4 (2) Å^3
Mr = 5115.31	Z = 1
Tetragonal, I41/amd	Melting point: 1323 K
Hall symbol: -I 4bd 2	Synchrotron radiation
a = 7.6231 (4) Å	T = 309 K
c = 32.358 (3) Å	Specimen preparation: Prepared at 1373 K

Data collection

Beamline ID 15B at ESRF diffractometer	2θmin = 0.060°, 2θmax = 13.598°, 2θstep = 0.008°
Radiation source: synchrotron radiation

Refinement

Rp = 0.022	Excluded region(s): 2
Rwp = 0.031	50 parameters
Rexp = 0.010	1 restraint
RBragg = 0.014	(Δ/σ)max = 0.002
1624 data points

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
S1	0.00000	−0.005 (2)	0.2513 (7)	0.013 (4)
S2	0.00000	0.008 (2)	0.0777 (7)	0.016 (4)
S3	0.00000	0.020 (2)	0.4133 (7)	0.015 (3)
In1	0.00000	0.25000	0.20459 (11)	0.0097 (8)	0.973 (6)
In2	0.00000	0.00000	0.00000	0.0143 (15)	0.972 (7)
In3	0.00000	−0.0196 (3)	0.33273 (12)	0.0111 (10)	0.974 (6)

Geometric parameters (Å, º)

S1—In1	2.462 (19)	In1—S3^iv	2.454 (12)
S1—In2^i	2.669 (11)	In2—S1^iii	2.669 (11)
S1—In2^ii	2.669 (11)	In2—S1^iv	2.669 (11)
S1—In3	2.64 (2)	In2—S1^viii	2.669 (11)
S2—In2	2.51 (2)	In2—S1^ix	2.669 (11)
S2—In3^iii	2.552 (11)	In2—S2	2.51 (2)
S2—In3^iv	2.552 (11)	In2—S2^x	2.51 (2)
S3—In1^i	2.454 (18)	In3—S1	2.64 (2)
S3—In3	2.62 (2)	In3—S2^i	2.552 (11)
S3—In3^v	2.705 (10)	In3—S2^ii	2.552 (11)
S3—In3^vi	2.705 (10)	In3—S3	2.62 (2)
In1—S1	2.462 (19)	In3—S3^v	2.705 (12)
In1—S1^vii	2.462 (19)	In3—S3^vi	2.705 (12)
In1—S3^iii	2.454 (12)
In1—S1—In2^i	122.9 (5)	S1^iv—In2—S1^viii	91.2 (7)
In1—S1—In2^ii	122.9 (5)	S1^iv—In2—S1^ix	180.0 (7)
In1—S1—In3	130.3 (7)	S1^iv—In2—S2	88.1 (9)
In2^i—S1—In2^ii	91.1 (3)	S1^iv—In2—S2^x	91.9 (10)
In2^i—S1—In3	89.2 (6)	S1^viii—In2—S1^ix	88.8 (3)
In2^ii—S1—In3	89.2 (6)	S1^viii—In2—S2	91.9 (10)
In2—S2—In3^iii	94.7 (6)	S1^viii—In2—S2^x	88.1 (9)
In2—S2—In3^iv	94.7 (6)	S1^ix—In2—S2	91.9 (10)
In3^iii—S2—In3^iv	87.0 (4)	S1^ix—In2—S2^x	88.1 (9)
In1^i—S3—In3	116.4 (7)	S2—In2—S2^x	180.0 (16)
In1^i—S3—In3^v	121.2 (5)	S1—In3—S2^i	88.0 (9)
In1^i—S3—In3^vi	121.2 (5)	S1—In3—S2^ii	88.0 (9)
In3—S3—In3^v	97.0 (6)	S1—In3—S3	171.0 (16)
In3—S3—In3^vi	97.0 (6)	S1—In3—S3^v	90.9 (10)
In3^v—S3—In3^vi	98.9 (3)	S1—In3—S3^vi	90.9 (10)
S1—In1—S1^vii	104.3 (10)	S2^i—In3—S2^ii	92.6 (3)
S1—In1—S3^iii	109.5 (11)	S2^i—In3—S3	98.2 (10)
S1—In1—S3^iv	109.5 (11)	S2^i—In3—S3^v	174.0 (8)
S1^vii—In1—S3^iii	109.5 (11)	S2^i—In3—S3^vi	93.3 (8)
S1^vii—In1—S3^iv	109.5 (11)	S2^ii—In3—S3	98.2 (10)
S3^iii—In1—S3^iv	114.0 (4)	S2^ii—In3—S3^v	93.3 (8)
S1^iii—In2—S1^iv	88.8 (3)	S2^ii—In3—S3^vi	174.0 (8)
S1^iii—In2—S1^viii	180.0 (7)	S3—In3—S3^v	82.3 (9)
S1^iii—In2—S1^ix	91.2 (7)	S3—In3—S3^vi	82.3 (9)
S1^iii—In2—S2	88.1 (9)	S3^v—In3—S3^vi	80.8 (4)
S1^iii—In2—S2^x	91.9 (10)

Symmetry codes: (i) −y+1/4, x−1/4, z+1/4; (ii) y−1/4, x−1/4, z+1/4; (iii) y+1/4, −x+1/4, z−1/4; (iv) −y−1/4, −x+1/4, z−1/4; (v) y−1/4, −x+1/4, −z+3/4; (vi) −y+1/4, −x+1/4, −z+3/4; (vii) −x, −y+1/2, z; (viii) −y−1/4, x−1/4, −z+1/4; (ix) y+1/4, x−1/4, −z+1/4; (x) −x, −y, −z.

(CubicIn2S3)

Crystal data

In2S3	V = 1270.76 (4) Å^3
Mr = 3408.76	Z = 1
Cubic, Fd3m	Melting point: 1323 K
Hall symbol: -F 4vw 2vw 3	Synchrotron radiation
a = 10.8315 (2) Å	T = 749 K

Data collection

Beamline ID 15B at ESRF diffractometer	2θmin = 0.060°, 2θmax = 13.606°, 2θstep = 0.008°
Radiation source: synchrotron radiation

Refinement

Rp = 0.019	Excluded region(s): 2
Rwp = 0.028	68 parameters
Rexp = 0.010	0 restraints
RBragg = 0.017	(Δ/σ)max = 0.002
1625 data points

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
s1	0.25638 (14)	0.25638 (14)	0.25638 (14)	0.0347 (12)
in1	0.12500	0.12500	0.12500	0.0306 (9)	0.640 (4)
in2	0.50000	0.50000	0.50000	0.0444 (6)	0.978 (6)

Geometric parameters (Å, º)

s1—in1	2.4648 (15)	in1—s1^vi	2.4648 (15)
s1—in2^i	2.6406 (15)	in2—s1^vii	2.6406 (15)
s1—in2^ii	2.6406 (15)	in2—s1^viii	2.6406 (15)
s1—in2^iii	2.6406 (15)	in2—s1^ix	2.6406 (15)
in1—s1	2.4648 (15)	in2—s1^x	2.6406 (15)
in1—s1^iv	2.4648 (15)	in2—s1^xi	2.6406 (15)
in1—s1^v	2.4648 (15)	in2—s1^xii	2.6406 (15)
in1—s1—in2^i	123.14 (5)	s1^vii—in2—s1^x	93.04 (8)
in1—s1—in2^ii	123.14 (5)	s1^vii—in2—s1^xi	86.96 (8)
in1—s1—in2^iii	123.14 (5)	s1^vii—in2—s1^xii	93.04 (8)
in2^i—s1—in2^ii	92.96 (5)	s1^viii—in2—s1^ix	93.04 (8)
in2^i—s1—in2^iii	92.96 (5)	s1^viii—in2—s1^x	86.96 (8)
in2^ii—s1—in2^iii	92.96 (5)	s1^viii—in2—s1^xi	93.04 (8)
s1—in1—s1^iv	109.47 (10)	s1^viii—in2—s1^xii	86.96 (8)
s1—in1—s1^v	109.47 (10)	s1^ix—in2—s1^x	180.00 (10)
s1—in1—s1^vi	109.47 (10)	s1^ix—in2—s1^xi	86.96 (8)
s1^iv—in1—s1^v	109.47 (10)	s1^ix—in2—s1^xii	93.04 (8)
s1^iv—in1—s1^vi	109.47 (10)	s1^x—in2—s1^xi	93.04 (8)
s1^v—in1—s1^vi	109.47 (10)	s1^x—in2—s1^xii	86.96 (8)
s1^vii—in2—s1^viii	180.00 (10)	s1^xi—in2—s1^xii	180.00 (10)
s1^vii—in2—s1^ix	86.96 (8)

Symmetry codes: (i) −x+1, y−1/4, z−1/4; (ii) x−1/4, −y+1, z−1/4; (iii) x−1/4, y−1/4, −z+1; (iv) x, −y+1/4, −z+1/4; (v) −x+1/4, y, −z+1/4; (vi) −x+1/4, −y+1/4, z; (vii) −x+3/4, −y+3/4, z; (viii) x+1/4, y+1/4, −z+1; (ix) −x+3/4, y, −z+3/4; (x) x+1/4, −y+1, z+1/4; (xi) x, −y+3/4, −z+3/4; (xii) −x+1, y+1/4, z+1/4.

(TrigonalIn2S3)

Crystal data

In2S3	V = 118.50 (1) Å^3
Mr = 319.85	Z = 1
Trigonal, P3m1	Melting point: 1323 K
Hall symbol: -P 3 2"	Synchrotron radiation
a = 3.86564 (14) Å	T = 1099 K
c = 9.1569 (5) Å

Data collection

Beamline ID 15B at ESRF diffractometer	2θmin = 0.058°, 2θmax = 13.598°, 2θstep = 0.008°
Radiation source: synchrotron radiation

Refinement

Rp = 0.020	Excluded region(s): 2
Rwp = 0.030	60 parameters
Rexp = 0.010	0 restraints
RBragg = 0.028	(Δ/σ)max = 0.002
1624 data points

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
S1	0.33333	0.66666	0.3359 (7)	0.054 (3)
S2	0.00000	0.00000	0.00000	0.091 (5)
In1	0.33333	0.66666	0.8085 (3)	0.0510 (9)	0.829 (10)
In2	0.33333	0.66666	0.6485 (12)	0.064 (6)	0.144 (3)

Geometric parameters (Å, º)

S1—In1^i	2.594 (4)	In1—S1^i	2.594 (4)
S1—In1^ii	2.594 (4)	In1—S1^ii	2.594 (4)
S1—In1^iii	2.594 (4)	In1—S1^iii	2.594 (4)
S1—In2	2.862 (13)	In1—S2^viii	2.8383 (17)
S1—In2^i	2.2364 (8)	In1—S2^ix	2.8383 (17)
S1—In2^ii	2.2364 (8)	In1—S2^x	2.8383 (17)
S1—In2^iii	2.2364 (8)	In1—In2	1.465 (11)
S2—In1^iv	2.8383 (17)	In2—S1	2.862 (13)
S2—In1^v	2.8383 (17)	In2—S1^i	2.2364 (8)
S2—In1^vi	2.8383 (17)	In2—S1^ii	2.2364 (8)
S2—In1^vii	2.8383 (17)	In2—S1^iii	2.2364 (8)
S2—In1^i	2.8383 (17)	In2—In1	1.465 (11)
S2—In1^ii	2.8383 (17)
In1^i—S1—In1^ii	96.33 (11)	In1^i—S2—In1^ii	85.84 (5)
In1^i—S1—In1^iii	96.33 (11)	S1^i—In1—S1^ii	96.33 (11)
In1^i—S1—In2	120.6 (5)	S1^i—In1—S1^iii	96.33 (11)
In1^i—S1—In2^ii	117.51 (18)	S1^i—In1—S2^viii	88.66 (18)
In1^i—S1—In2^iii	117.51 (18)	S1^i—In1—S2^ix	88.66 (18)
In1^ii—S1—In1^iii	96.33 (11)	S1^i—In1—S2^x	172.49 (18)
In1^ii—S1—In2	120.6 (5)	S1^i—In1—In2	59.4 (5)
In1^ii—S1—In2^i	117.51 (18)	S1^ii—In1—S1^iii	96.33 (11)
In1^ii—S1—In2^iii	117.51 (18)	S1^ii—In1—S2^viii	88.66 (18)
In1^iii—S1—In2	120.6 (5)	S1^ii—In1—S2^ix	172.49 (18)
In1^iii—S1—In2^i	117.51 (18)	S1^ii—In1—S2^x	88.66 (18)
In1^iii—S1—In2^ii	117.51 (18)	S1^ii—In1—In2	59.4 (5)
In2—S1—In2^i	86.3 (5)	S1^iii—In1—S2^viii	172.49 (18)
In2—S1—In2^ii	86.3 (5)	S1^iii—In1—S2^ix	88.66 (18)
In2—S1—In2^iii	86.3 (5)	S1^iii—In1—S2^x	88.66 (18)
In2^i—S1—In2^ii	119.60 (3)	S1^iii—In1—In2	59.4 (5)
In2^i—S1—In2^iii	119.59 (3)	S2^viii—In1—S2^ix	85.84 (5)
In2^ii—S1—In2^iii	119.59 (3)	S2^viii—In1—S2^x	85.84 (5)
In1^iv—S2—In1^v	85.84 (5)	S2^viii—In1—In2	128.2 (7)
In1^iv—S2—In1^vi	85.84 (5)	S2^ix—In1—S2^x	85.84 (5)
In1^iv—S2—In1^vii	94.16 (11)	S2^ix—In1—In2	128.2 (7)
In1^iv—S2—In1^i	94.16 (11)	S2^x—In1—In2	128.2 (7)
In1^iv—S2—In1^ii	179.97 (11)	S1—In2—S1^i	93.7 (4)
In1^v—S2—In1^vi	85.84 (5)	S1—In2—S1^ii	93.7 (4)
In1^v—S2—In1^vii	94.16 (11)	S1—In2—S1^iii	93.7 (4)
In1^v—S2—In1^i	179.97 (11)	S1—In2—In1	180.0 (7)
In1^v—S2—In1^ii	94.16 (11)	S1^i—In2—S1^ii	119.60 (3)
In1^vi—S2—In1^vii	179.97 (11)	S1^i—In2—S1^iii	119.59 (3)
In1^vi—S2—In1^i	94.16 (11)	S1^i—In2—In1	86.3 (5)
In1^vi—S2—In1^ii	94.16 (11)	S1^ii—In2—S1^iii	119.59 (3)
In1^vii—S2—In1^i	85.84 (5)	S1^ii—In2—In1	86.3 (5)
In1^vii—S2—In1^ii	85.84 (5)	S1^iii—In2—In1	86.3 (5)

Symmetry codes: (i) −x, −y+1, −z+1; (ii) −x+1, −y+1, −z+1; (iii) −x+1, −y+2, −z+1; (iv) x−1, y−1, z−1; (v) x, y−1, z−1; (vi) x, y, z−1; (vii) −x, −y, −z+1; (viii) x, y, z+1; (ix) x, y+1, z+1; (x) x+1, y+1, z+1.

 

Footnotes

‡Current address: IREC – Catalonia Institute for Energy Research, Sant Adriá de Besós, Spain.