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

We report on the high-resolution structure analysis of In2S3 powder with monochromatic synchrotron light in the temperature range between 300 and 1300 K. Three modifications could be identified with the two phase transitions taking place at 717 K and above 1049 K. Crystal structure parameters and their temperature dependence for all three phases were extracted from the diffraction data by Rietveld refinement.


Introduction
In 2 S 3 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 (Sá ez-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 In 2 S 3 in the world of photovoltaics. Various reports on In 2 S 3 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;. For a correct interpretation of the crystallographic data, a comprehensive understanding of the relevant crystal structure modifications of In 2 S 3 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 In 2 S 3 and the commonly drawn connection to its crystal structure properties, in this contribution we therefore ISSN 2052-5206 report about a crystal structure reinvestigation of the In 2 S 3 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 In 2 S 3 , 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 In 2 S 3 were Hahn & Klingler (1949). They reported a cubic phase at temperatures below 600 K, which they called -In 2 S 3 and a transition to a tetragonal spinel-like high-temperature modification which they called -In 2 S 3 . 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 In 2 S 3 the temperature range for the cubic phase extends down to room temperature. So Hahn probably measured a sulfur-deficient cubic -In 2 S 3 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 --, some have relabeled the cubic and tetragonal phase with a resulting order of --. Depending on the author, -In 2 S 3 in recent publications may therefore refer either to the low-temperature tetragonal phase or the cubic high-temperature phase. Although -would be the logical order, we will follow the majority in the literature and assign -In 2 S 3 to the low-temperature, tetragonal phase.
There are some more and sometimes contradictory publications in the literature on the crystal structure of the different In 2 S 3 phases, of which the most relevant ones will be shortly introduced in the following. Gö decke & Schubert (1985) suggest a phase diagram in which for the In:S ratio of 2:3 three modifications (-In 2 S 3 , -In 2 S 3 and -In 2 S 3 ) of indium sulfide exist in three different temperature regimes. King (1962) determined the space group of the tetragonal -In 2 S 3 as I4 1 /amd (space group No. 141) and the lattice parameters to a 0 = 7.61 Å and c 0 = 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 a 0 = 7.623 Å and c 0 = 32.36 Å . Hahn described the space group of the cubic -In 2 S 3 as Fd3m, with a lattice parameter of 10.72 Å (Hahn & Klingler, 1949). The high-temperature -In 2 S 3 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 -In 2 S 3 phase with an additional 5 at. % of As or Sb stabilizing it at room temperature. For this modified trigonal -In 2 S 3 they suggested a space group of P3m1 with lattice parameters a 0 between 3.806 and 3.831 Å and c 0 between 9.044 and 9.049 Å .
Some recent publications refer to the thin film application of In 2 S 3 and cite X-ray diffraction (XRD) database information. An assignment to the tetragonal -In 2 S 3 is often made although the quality of the diffraction data for In 2 S 3 is generally poor and does not allow for a definite distinction between the tetragonal -In 2 S 3 and the cubic -In 2 S 3 . A correct distinction between the two phases would however allow for a verification of the film stoichiometry, as the -In 2 S 3 only exists in a very small stoichiometry range (Gö decke & Schubert, 1985). It is the scope of this work to reinvestigate the In 2 S 3 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.

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 (Gö decke & Schubert, 1985). The weighted source materials were filled in a graphite boat and placed in a quartz glass ampoule, evacuated (< 10 À3 mbar) and sealed. The ampoule was placed in a twozone 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.

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 À1 . 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.

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 research papers Acta Cryst. (2016). B72, 410-415 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.

Temperature-dependent phase analysis
In 2 S 3 powder was prepared from the elements via a high-temperature route as described in x2.1. The mortared In 2 S 3 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 x2.2. 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 AE 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 -In 2 S 3 disappear and are replaced by the diffraction peaks of -In 2 S 3 indicating a complete reordering of the atoms in the crystal structure.

Rietveld refinement of the three In 2 S 3 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 Map of temperature-dependent X-ray diffractograms (XRD) for the In 2 S 3 powder. Each diffractogram is measured at a specific temperature which corresponds to one column in the graph with the y-direction displaying the 2 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 In 2 S 3 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 . Table 1 Lattice parameters as extracted from the Rietveld refinement for the three In 2 S 3 modifications.

Temperature (K)
Space group Number  Table 2 Refinement parameters for the Rietveld refinements performed for the three modifications of In 2 S 3 .
R B : Bragg R I factor, 2 : 2 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. detailed information on the refinement parameters are included in the CIF file in the supporting information.

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 a 0 of the cubic -In 2 S 3 phase in the temperature range between 749 and 1044 K. The data are well fitted with the linear fit function aðTÞ ¼ 10:7480 Å þ 1:121 ð2ÞT Â 10 À4 Å K À1 : From the temperature dependence of the lattice constants, we obtain the linear thermal expansion coeffient Kundra & Ali, 1976) for the cubic phase. In this temperature range, we calculate an average of 10.3 Â 10 À6 K, in relatively good agreement with Kundra & Ali (1976), 10.8 Â 10 À6 -10.9 Â 10 À6 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 -In 2 S 3 we find an average linear expansion coefficient in the a direction of 11.7 Â 10 À6 K and in the c direction of 6.7 Â 10 À6 K. For the trigonal phase, an average linear expansion coefficient of 14.1 Â 10 À6 K in the a direction and 26.7 Â 10 À6 K in the c direction was determined.

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 In 2 S 3 in thin film solar cells.
The low-temperature modification -In 2 S 3 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 MgAl 2 O 4 (Kleber et al., 2002). While all the octahedral cation sites are occupied in -In 2 S 3 , one third of the tetrahedal sites remain unoccupied. For that reason the In 2 S 3 structure is sometimes described in a quasi-ternary compound formula: [In 2/3 (Vac) 1/3 ] tet [In] oct 2 S 4 , where ½ tet and ½ oct denote tetrahedral and octahedral sites and (Vac) the vacancies. In -In 2 S 3 , the vacancies are ordered  Table 4 Atomic sites for the cubic -In 2 S 3 (space group 227, origin choice No. 2).

Figure 2
Diffraction data and Rietveld refinement of the three In 2 S 3 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. Table 3 Atomic sites for the tetragonal -In 2 S 3 , (space group 141, origin choice No. 2).
Atom Wickoff x y z U iso Occ. S1 16h 0 À0.005 (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) (6) along the 4 1 screw axis which is by definition parallel to the caxis. 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 -In 2 S 3 with lower symmetry and leads to the additional peaks observed in the X-ray diffraction. Fig. 4 shows a plot of the -In 2 S 3 crystal structure based on the results obtained by the Rietveld refinement. The transition from -In 2 S 3 to -In 2 S 3 is an order-disorder transition. In -In 2 S 3 , the indium vacancies are randomly distributed over all tetrahedral sites, in contrast to the ordered configuration of vacancies in the -In 2 S 3 . As a result of the disordering, -In 2 S 3 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 -In 2 S 3 to -In 2 S 3 at 717 K.
Finally, the -In 2 S 3 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 -In 2 S 3 and -In 2 S 3 has a direct phenomenological and technological impact. Because of the large number of natural vacancies in the structure, In 2 S 3 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 In 2 S 3 thin films (Pistor, Allsop et al., 2009;Juma, Kavalakkatt et al., 2012). The diffusion phenomena at interfaces in thin film solar cells containing In 2 S 3 have not yet been fully understood but might benefit from an in-depth knowledge of the crystal (vacancy) structure of In 2 S 3 . Where XRD data of good quality exist, it is an easy task to distinguish between the tetragonal and cubic phase of In 2 S 3 by an examination of the characteristic additional peaks only present for the -In 2 S 3 . The differentiation between -In 2 S 3 and -In 2 S 3 allows testing for stoichiometry, since the tetragonal phase only exists in a very small compositional range. According to Gö decke & Schubert (1985) and Diehl & Nitsche (1975), the compositional range for the -In 2 S 3 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 -In 2 S 3 phase. As a consequence, the crystal structure of off-stoichiometric In 2þx S 3 remains in the cubic -In 2 S 3 modification down to room temperature. This specific feature is used for example to check if In 2 S 3 source material for an evaporation process is still within the described stoichiometry range . Alike the distinction of polycrystalline powder material, this type of analysis tool would be rather desirable for the evalution of In 2 S 3 thin film material as well. Structure model of a -In 2 S 3 unit cell. The tetrahedral bonds are drawn thicker for better identification.
The indium vacancies are marked as grey spheres. In the tetragonal -In 2 S 3 configuration, the vacancies are ordered on a 4 1 screw axis parallel to the c-axis of the crystal. In the -In 2 S 3 configuration, the vacancies are randomly distributed over all tetrahedral indium sites. The edges of the unit cell of the tetragonal -In 2 S 3 structure (cubic -In 2 S 3 ) structure are indicated by black (blue) lines.

Figure 3
Temperature dependence of the lattice parameter for the cubic -In 2 S 3 . The resulting fit parameters of a linear fit are listed in the inset. Table 6 Linear fit function of the lattice parameters of In 2 S 3 from the Rietveld refinements.

Conclusions
We provide a detailed crystal structure analysis of In 2 S 3 over the entire temperature range from room temperature up to close to the melting point covering the three modifications -In 2 S 3 , -In 2 S 3 and -In 2 S 3 . With this, we contribute to the comprehensive understanding of the different phases existent and their interdependence. The high-temperature phase -In 2 S 3 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 In 2 S 3 modifications might have a direct impact on the technological use of In 2 S 3 in applications such as buffer layer deposition in thin film solar cell production.