Sulfur–selenium isomorphous substitution and polymorphism in the Ag2(S,Se) series

Sulfur–selenium isomorphous substitution and polymorphism in the Ag2(S,Se) series

Accepted Manuscript Sulfur–selenium isomorphous substitution and polymorphism in the Ag2(S,Se) series Yurii V. Seryotkin, Galina A. Palyanova, Konstan...

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Accepted Manuscript Sulfur–selenium isomorphous substitution and polymorphism in the Ag2(S,Se) series Yurii V. Seryotkin, Galina A. Palyanova, Konstantin A. Kokh PII: DOI: Reference:

S0925-8388(15)00825-7 http://dx.doi.org/10.1016/j.jallcom.2015.03.112 JALCOM 33723

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Journal of Alloys and Compounds

Received Date: Revised Date: Accepted Date:

9 February 2015 10 March 2015 14 March 2015

Please cite this article as: Y.V. Seryotkin, G.A. Palyanova, K.A. Kokh, Sulfur–selenium isomorphous substitution and polymorphism in the Ag2(S,Se) series, Journal of Alloys and Compounds (2015), doi: http://dx.doi.org/10.1016/ j.jallcom.2015.03.112

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Sulfur–selenium isomorphous substitution and polymorphism in the Ag2(S,Se) series Yurii V. Seryotkin1,2, Galina A. Palyanova1,2, Konstantin A. Kokh1,2* 1

Sobolev Institute of Geology and Mineralogy, SB RAS, Novosibirsk, Russia 2

Novosibirsk State University, Russia

*Corresponding author: IGM SB RAS, Koptyuga ave., 3, Novosibirsk 630090, Russia, Tel/Fax: +7 383 3066392, E-mail: [email protected] Аbstract Ag2S–Ag2Se chalcogenides have been synthesized by heating stoichiometric mixtures of elementary substances in vacuum sealed quartz vessels. Optical microscopy, scanning electron microscopy, X-ray powder diffraction with high-temperature experiments and X-ray single-crystal method were applied to study synthesized silver sulfoselenides. The synthesized silver sulfoselenides are homogeneous under optical and scanning electron microscope. At room temperature, two Ag2S1–xSex polymorphs – monoclinic and orthorhombic – coexist in the interval of 0.6 < x < 0.8. Compositional gap between two solid solutions is absent. At higher temperature, an intermediate monoclinic phase was observed in the range of Ag2S0.25Se0.75 – Ag2S0.175Se0.825. Keywords: isomorphism, sulfur, selenium, solid-solutions Ag2(S,Se), polymorphism, phase transformations, structure features

Introduction In the Ag2S-Ag2Se system, there are three silver chalcogenides occurring naturally as the sulfide acanthite Ag2S, the selenide naumannite Ag2Se, and the sulfoselenide aguilarite Ag4SeS. The Ag2S– Ag2Se chalcogenides are characterized by the presence of phase transitions and structure phase transformations [1-5]. Roy et al. [6] suggested using silver sulfide and selenide transitions as geologic thermometers. The low temperature forms of Ag2 S and Ag2Se are intrinsic semiconductors, the high temperature allotropes are conductors [2,3]. Ag2S, Ag4SSe and Ag2Se have recently attracted considerable attention due to their optical, electrical, and thermoelectric properties [7]. Differential scanning calorimetry demonstrates that the samples of various compositions between Ag2S and Ag2Se synthesized at high temperature in sealed quartz tubing undergo rapid, reversible solid-state phase changes at temperatures between approximately 70 and 178°C [2,3]. These temperatures vary with composition, with maximal values for pure end members Ag2S (178°C) and Ag2Se (134°C), and a minimum in the compositional range between Ag2 S0.4Se0.6 to Ag2S0.3Se0.7 (70°C). Selenium enters into 1

metal sulfides as an isomorphic impurity to form continuous series of solid solutions such as PbSPbSe, FeS2-FeSe2, and HgS-HgSe [8]. The possible solid solution between Ag2S and Ag2Se has been debated for a long time [1-3,9,10]. It is obvious that continuous isomorphic series may exist only for the end members having crystal structures of the same type. However, at room temperature Ag2S and Ag2Se have different crystal lattices. The monoclinic Ag2S (space group P21/n) [11] and orthorhombic Ag2Se (space group P212121) [12,13,14] suggest that the continuous isomorphic series of Ag2(S,Se) solid solution is impossible. Studies of both natural [9] and synthetic silver sulfoselenides [1-3,10] supported the discontinuity of the isomorphic series, however the morphotropic transition range was ambiguously determined by different authors. According to Petruk et al. [9] the miscibility limits for Guanajuato (Mexico) and Silver City (USA) deposits are the following: Ag2S – Ag2S0.85Se0.15 for acanthite, Ag4S0.95Se1.05 – Ag4S1.10Se0.90 for aguilarite, and Ag2S0.12Se0.88 – Ag2Se for naumannite. As for the synthesized samples [2,3], at room temperature there are two solid solutions with different structures, the acanthite-type (monoclinic) and the naumannite-type (orthorhombic), with the miscibility break or the two-phase range between Ag2S0.4Se0.6 and Ag2S0.3Se0.7. According to Bontschewa-Mladenowa and Zaneva [1], the miscibility break occurs at 50 mol. % of Ag2S, i.e., Ag2S0.5Se0.5 or Ag4SSe. However, aguilarite Ag4SSe was recently found to be isostructural to acanthite [10], resulting in an expansion of the stability range of the acanthite structure type to selenium content. The aim of this work was to elucidate structural features of isomorphic S↔Se substitution in the Ag2S–Ag2Se series. By gradual shift of synthesized compositions in the Ag2S0.5Se0.5 – Ag2Se range we tried to define the existence of the morphotropic transition point or the two-phase miscibility region between acanthite and naummanite solid solutions.

Experimental details Experiments were performed with the phases of Ag2S1-xSex (х=0; 0.5; 0.58; 0.61; 0.625; 0.64; 0.67; 0.75; 0.775; 0.8; 0,825; 0,85; 0.875; 1) series by the technique used for the system Ag-Au-S [15,16]. The total charge of silver (99.99%), sulfur, and selenium (99.9%) mixture was 500 mg with ± 0.05 mg accuracy (a Mettler Instrument Ag CH-8606 Greifensee-Zurich balance). Quartz ampoules with the charges were sealed under vacuum and heated for three days with the rate of 0.2-0.5º/min up to 1050ºС, held for 12 h, then cooled to 500ºС with the rate of 0.2º/min, and annealed for three days. After that, the furnace was turned off and the ampoules were cooled to room temperature for about 7 h. Optical microscopy, scanning electron microscopy with energy-dispersive and wavelengthdispersive spectrometers, X-ray powder diffraction with high-temperature experiments and X-ray single-crystal method were applied to study synthesized substances. Studies on the chemical composition of the synthesized substances were carried out using MIRA 3 LMU SEM (TESCAN Ltd.) combined with microanalysis system INCA Energy 450+ on the basis of the high sensitive silicon drift 2

detector XMax-80, and WDS INCA Wave 500 (Oxford Instruments Ltd.). Operation conditions: accelerating voltage, 20 kV; probe current, 1.5 nA; spectrum recording, 15 s. The electron beam was 12 nm in diameter. In all measurements the electron beam was slightly defocused for reducing the effect of a sample microrelief and decreasing the destructive influence of the electron beam on unstable silver sulfoselenides. Pure silver, CuFeS2, and PbSe were used as standards for Ag, S, and Se, respectively. The analysis accuracy was 1-1.5 relative %. X-ray powder diffraction patterns were collected on a Stoe STADI MP diffractometer (CuKα1 radiation, Ge(111) monochromator, 40 kV, 40 mA). Powdered silicon was used as the external standard (a = 5.4309 Å). The diffraction data were collected from 20 to 60° 2θ angular range. The refinement of the unit cell parameters was carried out by Rietveld method using GSAS program [17]. Refined values of unit-cell metrics are presented in Table 1. High-temperature experiments were performed on the same diffractometer with the Eurotherm 2416 device in the temperature range of 30–120°C with the step of 10°C. The powdered sample was loaded into a silica glass capillary 0.3 mm in diameter and was placed in a high-temperature equipment. The temperature was increased by 2°C min–1 to the desired values, and a dwell time of 10 min was used before each measurement. The collected data were processed using the WinXPow (Stoe) program package. All studied crystals of the acanthite-type appeared to be twinned [18], so only naumannite-type compounds were investigated by X-ray single-crystal method on an Oxford Diffraction Xcalibur Gemini diffractometer with a CCD detector (MoKα radiation, graphite monochromator). Data reduction including the corrections for background, Lorentz and polarization effects was performed with the CrysAlis Pro software (Oxford Diffraction). The naumannite-type structures were solved and refined with the Shelx-97 program package [19]. The refinement results are given in Table 2.

Results The synthesized silver sulfoselenides seem to be homogeneous under optical and scanning electron microscope and their compositions show no variation outside the specified analytical precision. Isolated native selenium (black) or sulfur (yellow) hemispheres were present on the walls of some ampoules. Filamentous or skeletal silver microcrystals were observed on the top of the ingots in some experiments. Microcrystals of silver sulfoselenides were observed on top or side parts of sinters. Figure 1 shows the morphology of the silver sulfoselenide crystals from the experiments with Ag2S0.625Se0.375, Ag2S0.33Se0.67 and Ag2S0.175Se0.825 bulk compositions.

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According to X-ray diffraction data, the samples of Ag2S1–xSex with 0 ≤ x ≤ 0.6 have the structure of acanthite, while the compositions with 0.8 ≤ x ≤ 1 correspond to naumannite (Table 1). Lattice constants are linearly increasing to selenium end member. These results agree well with those of [3]. The interval 0.6 < x < 0.8 is the most interesting since a miscibility break was found there in previous studies. Our X-ray powder diffraction study indicates that the sample from Ag2S0.375Se0.625 has the acanthite-type structure (see Table 1). Its unit cell parameters fit the linear relation between the unit-cell volume and the selenium concentration for acanthite-like compounds (Figure 2). However, Xray structure analysis of a single crystal selected from this experiment has shown the naumannite structure, space group P212121, with slightly smaller volume because of the sulfur presence (Table 2). From the structure refinement (Table 3), the Se/S molar ratio is in agreement with that specified in the experiment within the error limits. Thus, the Ag 2S0.375Se0.625 silver sulfoselenide represents a mixture of two phases – prevailing acanthite- and naumannite-like that occurring in small amounts. X-ray powder pattern of Ag2S0.33Se0.67 collected right after grinding of the sample showed the peaks of monoclinic phase only (Fig. 3, XRD pattern 1). After keeping the sample for three months at room conditions we obtained a mixture of monoclinic and orthorhombic phases with the ratio ≈ 90:10 (Fig. 3, XRD pattern 2). A “fresh” sample of Ag2S0.25Se0.75 contains both phases relating as 75:25, respectively. However, an increase in orthorhombic phase to 90% was observed after 3 months (Fig.3, XRD pattern 3,4). X-ray study of Ag2S0.25Se0.75 at different temperatures has shown that cubic phase Im3m [20] is stable at temperature ≥ 90°С (Fig. 4). Below 90°С, a first-order phase transition to monoclinic P21/n acanthite-type structure was observed. Further cooling of the sample results in the appearance of peaks corresponding to naumannite-like structure (P212121). The intensity of these peaks increases with cooling, however the monoclinic phase still exists at room temperature (Fig. 4). Ag2S0.225Se0.775 has the same behavior during cooling. It demonstrates cubic → monoclinic at ≈80°C and monoclinic → orthorhombic transition below 60°С. The sample Ag2S0.175Se0.825 is orthorhombic at room temperature. It has the same sequence of phase transitions but the temperature range of monoclinic structure is smaller. At 100°С the sample is cubic, while the majority of peaks at 80°С correspond already to orthorhombic phase. Last traces of monoclinic peaks disappear at 60°С. The sample Ag2S0.15Se0.85 has no intermediate monoclinic transition, so the cubic phase directly transforms to orthorhombic one. Linear dependencies of cell volume versus Se/(Se+S) remain unchanged for both series. This confirms the fact revealed by SEM that the compositions of monoclinic and orthorhombic phases are equal to the bulk compositions.

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Discussion Table 4 lists the unit cell parameters of Ag2S, Ag2Se, and Ag4SeS from literature. The structure data reported for these phases are contradictory. Three different sets with two space groups have been proposed for the acanthite. Variations in data by [11] and [18] reduce to the selection of two alternative        sets of the unit cell metrics related by aF  aS , bF  bS , cF  aS  cS , resulting in different space groups (Table 4). In other aspects the structures are similar. The structure data reported by Blanton et al. [21] are not clear, as the unit cell parameters (see Table 4) differ from those obtained by Frueh [11] or Sadanaga et al. [18]. Generally, the anion lattice in the structure is in agreement with that of [11], although it is noticeably distorted. The distributions of the Ag atoms differ essentially as well as their coordination by S atoms. The unusually short Ag–S distances are observed along with a total decrease in the number of contacts. In our opinion, data of [21] need to be recalculated. The phase diagram of Ag2S-Ag2Se (Fig. 5) and Ag2S1-xSex solid solutions existing over the lowtemperature range of 25 - 300°С were studied in a few experimental works [1-3]. There are certain discrepancies between the results obtained. Bontschewa-Mladenowa and Zaneva [1] have investigated the system (within the composition interval from 0 to 100 % with a step of 5 mol. % Ag2Se) by DTA, X-ray diffraction, and microstructure analysis with an additional study of the density and microhardness. They recognized that at temperatures below the transition temperature there are two continuous solid solutions with the miscibility break at 50 mol. % Ag2S (i.e., Ag2S0.5Se0.5 or Ag4SSe). Pingitore et al. [2] have studied the compositions in the system with a step of 10 mol. % by optical microscopy, electron-probe microanalysis and X-ray diffraction. They concluded that under normal conditions there are two solid solutions. One series with monoclinic symmetry covers the range from Ag2S to Ag2S0.4Se0.6, whereas the other, from Ag2S0.3Se0.7 to Ag2Se, belongs to the orthorhombic system. Calorimetric research by [3] has confirmed the continuous character of each solid solution and revealed the smooth variation of the transition temperature with the composition. As to the Ag2S0.4Se0.6 – Ag2S0.3Se0.7 range, the authors failed to recognize whether or not the two-phase region takes place and the miscibility range exists or there is a single-phase region and the third solid solution is stable. According to our data, there is no miscibility break in the Ag2S–Ag2Se solid solutions. However there is a range of compositions represented by coexisting monoclinic and orthorhombic phases. Noteworthy is the difference in the unit cell parameters for two-phase region between our data and those of [2]. Our results evidence that the acanthite – naumannite phase transition is accompanied by a noticeable decrease in the volume, whereas [2] show this transition to be rather smooth (Figure 2). It should be emphasized that the space groups of acanthite and naumannite cannot be changed from one to other by decreasing or increasing symmetry of the system, since one is not the subgroup of the other. Therefore, the smooth transformation of one structure into other is not probable. 5

Our results confirm the conclusions of Pingitore et al. [2,3] that there exist two solid solutions of different structure types. Our data slightly extend the existence range for the acanthite Ag2S1–xSex series lying from x=0 to ≈ 0.8 and the naumannite series, from x ≈ 0.6 to 1. The data on the chemical composition of acanthite and naumannite cover the whole range between Ag2S and Ag2Se [9,23-29]. According to our results the compositions Ag2S1−xSex with х < 0.6 and х> 0.8 should be attributed to acanthite and naumannite series, correspondingly. The compositions with 0.6 <х < 0.8 should be additionally analyzed by diffraction techniques since they may contain either or both structures. The recent study of Bindi and Pingitore (2013) proved that aguilarite is isostructural with acanthite. Our data also show that Ag 4SSe composition has monoclinic (acanthite type) structure. This fact argues against Ag4SSe as a distinct mineral species. In turn the silver sulfoselenides with small deviations from Ag4SSe stoichiometry are also acanthite series, even if they are often referred to aguilarite solid solution [9,25,27,28].

Acknowledgements X-ray diffraction experiments were carried out at the Centre on Molecular Design and Ecologically Safe Technologies at Novosibirsk State University. The authors thank Karmanov N.S. (IGM SB RAS) for X-ray microspectral determination of the composition of synthetic phases. Also sincere thanks to Dr. Nigel J.

Cook for the constructive suggestions. The work was financially supported by the SB RAS and FEB RAS (integration project No. 12 and 48).

References [1] Z. Bontschewa-Mladenowa, K. Zaneva, Untersuchung des Systems Ag2Se-Ag2S, Zeitschrift für anorganische und allgemeine Chemie 437 (1977) 253-262. [2] N.E. Pingitore, B.F. Ponce, M.P. Eastman, F. Moreno, C. Podpora, Solid solutions in the system Ag2S–Ag2Se, Journal of Materials Research 7 (1992) 2219–2224. [3] N.E. Pingitore, B.F. Ponce, L. Estrada, M.P. Eastman, H.L. Yuan, L.C. Porter, G. Estrada, Calorimetric analysis of the system Ag2S–Ag2Se between 25 and 250°C, Journal of Materials Research 8 (1993) 3126–3130. [4] S.M. Alekperova, I.A. Akhmedov, G.S. Hajiyev, H.J. Dzhalilova, Giant magnetoresistance and transport phenomena in n-Ag4SSe in the vicinity of the phase transition, Physics of the Solid State 49 (2007) 512–515. [5] G.A. Pal’yanova, K.V. Chudnenko, T.V. Zhuravkova, Thermodynamic properties of solid solutions in the Ag2S-Ag2Se system, Thermochimica Acta 575 (2014) 90-96. [6] R. Roy, A.J. Majumdar, C.W. Hulbe, The Ag2S and Ag2Se transitions as geologic thermometers, Economic Geology 54 (1959) 1278–1280. [7] C. Xiao, J. Xu, K. Li, J. Feng, J. Yang, Y. Xie, Superionic phase transition in silver chalcogenide nanocrystals realizing optimized thermoelectric performance, Journal of the American Chemical Society 134 (2012) 4287–4293. [8] J.W. Earley, Description and synthesis of the selenide minerals, American Mineralogist 35 (1950) 337-364. [9] W. Petruk, D.R. Owens, J.M. Stewart, E.J. Murray, Observations on acanthite, aguilarite and naumannite, Canadian Mineralogist 12 (1974) 365–369. 6

[10] L. Bindi, N.E. Pingitore, On the symmetry and crystal structure of aguilarite, Ag 4SeS, Mineralogical Magazine 77 (2013) 21–31. [11] A.J. Frueh, The crystallography of silver sulfide, Ag2S, Zeitschrift für Kristallographie 110 (1958) 136–144. [12] G.A. Wiegers, The crystal structure of the low-temperature form of silver selenide, American Mineralogist 56 (1971) 1882–1888. [13] J. Yu, H. Yun, Reinvestigation of the low-temperature form of Ag2Se (naumannite) based on single-crystal data, Acta Crystallographica E67 (2011) i45. [14] A. Vymazalova, D. Chareev, A. Kristavchuk, F. Laufek, M. Drabek, The system Ag-Pd-Se: Phase relations involving minerals and potential new minerals, Canadian Mineralogist 52 (2014) 77-89. [15] G.A. Pal’yanova, K.A. Kokh, Y.V. Seryotkin, Formation of gold and silver sulfides in the system Ag-Au-S, Russian Geology and Geophysics 52 (2011) 443-449. [16] Y.V. Seryotkin, G.A. Pal’yanova, V.V. Bakakin, K.A. Kokh, Synthesis and crystal structure of gold-silver sulfoselenides: morphotropy in the Ag3 Au(Se,S)2 series, Physics and Chemistry of Minerals 40 (2013) 229–237. [17] A.C.Larson, R.B. von Dreele, General structure analysis system, Los Alamos national laboratory report (2000) 86-748. [18] R. Sadanaga, S.Sueno, X-ray study of α–β transition of Ag2S, Mineralogical Journal 5 (1967) 124–148. [19] G.M. Sheldrick, A short history of SHELX, Acta Crystallographica A64 (2008) 112–122. [20] R.J. Cava, F. Reidinger, B.J. Wuensch, Single-crystal neutron diffraction study of the fast-ion conductor -Ag2S between 186 and 325°C, Journal of Solid State Chemistry 31 (1980) 69–80. [21] T. Blanton, S. Misture, N. Dontula, S. Zdzieszynski, In situ high-temperature X-ray diffraction characterization of silver sulfide, Ag2S, Powder Diffraction 26 (2011) 114–114. [22] V.S. Vassilev, Z.G. Ivanova, Reversible α–β phase transition in the narrow-gap semiconducting Ag4SSe compound, Bulletin of the Chemists and Technologists of Macedonia 22 (2003) 21–24. [23] N. Shikazono, Selenium content of acanthite and the chemical environments of Japanese veintype deposits, Econ. Geol. 73 (1978) 524-533. [24] L.F.V. Morales, Y.S. Borodayev, New data on mineral series acanthite-aguilarite-naumannite, Dokl. Akad. Nauk 264 (1982) 685-688. [25] I.Y. Nekrasov, Gold-silver deposit Alpha in Ulahan-Sis ridge (Yana river basin), Dokl. RAN 353 (1997) 97-99. [26] N.E. Savva, G.A. Pal’yanova, M.A. Byankin, The problem of genesis of gold and silver sulfides and selenides in the Kupol deposit (Chukot Peninsula, Russia), Russian Geology and Geophysics 53 (2012) 457-466. [27] M.S. Saharova, I.A. Bryzgalov, S.K. Ryahovskaya, Mineralogy of selenides in volcanogene ridges, Zapiski VMO 222 (1993) 1-9. [28] I.W. Warmada, B. Lehmann, M. Simandjuntak, Polymetallic sulfides and sulfosalts of the Pongkor epithermal gold-silver deposit, West Java, Indonesia, Canad. Miner. 41 (2003) 185-200. [29] H.A. Cocker, J.L. Mauk, S.D.C. Rabone, The origin of Ag-Au-S-Se minerals in adulariasericite epithermal deposits: constraints from the Broken Hills deposit, Hauraki Goldfield, New Zealand, Mineralium Deposita 48 (2013) 249-266.

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Figure captions Fig. 1. The morphology of the silver sulfoselenide crystals from the experiments with Ag2S0.51Se0.49, Ag2S0.33Se0.67 and Ag2S0.175Se0.825 bulk compositions. Fig. 2. Unit-cell volume of Ag2(S,Se) vs. Se/(Se+S) ratio: X-ray single-crystal (●) and powder (■) diffraction data. For comparison, data by [2] are shown as open triangles. Fig. 3. X-ray powder diffraction patterns of Ag2S0.33Se0.67 (1,2) and Ag2S0.25Se0.75 (3,4) compounds. 1, 3 – immediately after crushing, 2, 4 – three months later. On 2 and 3, the weak peaks of orthorhombic phase are marked by asterisks. Fig. 4. X-ray diffraction pattern changes of Ag2S0.25Se0.75 compound under cooling. Fig.5. Phase diagram of Ag2S-Ag2Se system constructed using data from: 1 – [1], 2 – [3], 3 – [22], 4 – [4], 5 – [7], 6 – this paper.

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9

10

11

Table 1. Unit-cell parameters for synthesized phases of Ag2S1-xSex compounds.

Ag2S Ag2S0.5Se0.5 Ag2S0.42Se0.58 Ag2S0.39Se0.61 Ag2S0.375Se0.625 Ag2S0.33Se0.67 Ag2S0.25Se0.75 Ag2S0.33Se0.67 Ag2S0.25Se0.75 Ag2S0.225Se0.775 Ag2S0.20Se0.80 Ag2S0.175Se0.825 Ag2S0.15Se0.85 Ag2S0.125Se0.875 Ag2Se

Space group

a (Ǻ)

b (Ǻ)

c (Ǻ)

 (deg.)

V (Ǻ3)

P21/n P21/n P21/n P21/n P21/n P21/n P21/n P212121 P212121 P212121 P212121 P212121 P212121 P212121 P212121

4.22918(26) 4.25308(16) 4.25743(21) 4.25912(18) 4.26102(22) 4.26518(19) 4.27159(20) 4.2845(17) 4.2997(3) 4.3043(3) 4.3083(3) 4.3124(4) 4.3155(3) 4.31543(23) 4.33590(19)

6.9302(4) 6.94753(25) 6.9529(3) 6.95375(29) 6.9566(3) 6.9617(3) 6.9707(3) 7.001(3) 7.0239(4) 7.0297(4) 7.0352(4) 7.0403(5) 7.0435(5) 7.0443(3) 7.06674(28)

7.8863(5) 8.0294(4) 8.0535(4) 8.0635(4) 8.0689(4) 8.0845(4) 8.1113(4) 7.739(3) 7.7281(4) 7.7339(4) 7.7382(5) 7.7416(6) 7.7440(5) 7.7496(4) 7.7666(3)

99.648(6) 100.267(3) 100.449(5) 100.527(4) 100.545(4) 100.629(4) 100.802(4)

227.292(18) 233.457(13) 234.443(15) 234.796(12) 235.142(13) 235.934(13) 237.245(14) 232.15(9) 233.395(14) 234.010(14) 234.541(15) 235.04(2) 235.392(18) 235.581(13) 237.975(11)

Table 2. Crystallographic and experimental data for naumannite-type Ag2S1–xSex compounds.

a (Å) b (Å) c (Å) V (Å3) Space group Z d (g/cm3)  (MoK) (mm–1) Number of Ihkl measured Number of unique F2hkl Rint Number of observed reflections [I>2 Number of variables Flack x parameter R1, wR2 for observed reflections [I>2 R1, wR2 for all data Residual electron density (e/ Å3)

Ag2S0.375Se0.625

Ag2S0.125Se0.875

4.28262(13) 7.0083(2) 7.7071(4) 231.321(16) P212121 4 7.957 26.653 4272 774 0.0293 730 29 0.00 0.0311, 0.0673 0.0348, 0.0688 –1.130, 1.425

4.32079(16) 7.0463(3) 7.7485(3) 235.908(16) P212121 4 8.132 29.770 5764 959 0.0364 911 29 0.00 0.0353, 0.0791 0.0387, 0.0805 –1.455, 1.727

Table 3. Positional and thermal parameters for naumannite-type Ag2S1–xSex compounds. Occupancy

x

y

z

Ueq

Ag2Se0.625S0.375 Ag1 1 0.13859(16) 0.11259(9) Ag2 1 0.47579(17) 0.27550(9) X Se0.627(6)S0.373(6) 0.1105(2) 0.49862(11)

0.45040(10) 0.03995(18) 0.14274(11) 0.0428(2) 0.34890(12) 0.0219(2)

Ag2Se0.875S0.125 Ag1 1 0.14414(17) 0.11430(10) Ag2 1 0.47462(18) 0.27483(10) X Se0.887(6)S0.113(6) 0.11151(17) 0.49805(10) U11

U22

U33

0.45089(10) 0.03628(18) 0.13956(11) 0.0402(2) 0.34769(10) 0.01998(19)

U12

U13

U23

0.0011(3) 0.0105(3) 0.0007(3)

–0.0048(3) 0.0099(3) 0.0005(3)

0.0076(3) 0.0038(3) 0.0003(3)

–0.0075(3) 0.0102(3) 0.0007(3)

0.0065(3) 0.0050(3) 0.0004(3)

Ag2Se0.625S0.375 Ag1 Ag2 X

0.0348(3) 0.0443(4) 0.0219(4)

0.0382(3) 0.0319(3) 0.0167(3)

0.0468(4) 0.0520(4) 0.0271(4)

Ag2Se0.875S0.125 Ag1 Ag2 X

0.0305(3) 0.0390(4) 0.0179(3)

0.0372(3) 0.0330(3) 0.0177(3)

0.0411(4) 0.0486(4) 0.0243(3)

0.0014(3) 0.0122(3) 0.0007(3)

Table 4. Crystallographic data for phases of β–Ag2S, β–Ag2Se и β–Ag4SeS from literature. Formula unit

Space group

a (Ǻ)

b (Ǻ)

c (Ǻ)

β (deg.)

V (Ǻ3)

References

Ag2S

P21/n

4.23

6.91

7.87

99.58

226.82

[11]

Ag2S

P21/c

4.231

6.930

9.526

125.48

227.45

[17]

Ag2S

P21/n

4.2275

6.9303

8.2855

110.564

227.28

[20]

Ag4SSe

P21/n

4.2478

6.9432

8.0042

100.103

232.41

[10]

Ag2Se

P212121

4.3359

7.070

7.774

238.34

[13]

Graphical abstract

Highlights Ag2S-Ag2Se samples were synthesized Compositional gap between acanthite and naumannite is absent The existence ranges of solid solutions were specified

12