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Shinya Hosokawa, Yohei Onodera, László Pusztai, Jens Rüdiger Stellhorn, Hiroo Tajiri, Kazutaka Ikeda, Toshiya Otomo
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[Local- and Intermediate-Range Atomic Structures of (Ga 2 S 3 ) 0.25 (GeS 2 ) 0.75 Glass: Complementary Use of X-Rays and Neutrons](https://mdr.nims.go.jp/datasets/11236206-3371-4e07-8e70-b676200e40f6)
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Local- and Intermediate-Range Atomic Structures of (Ga2S3)0.25(GeS2)0.75 Glass: Complementary Use of X-Rays and NeutronsLocal- and Intermediate-Range Atomic Structures of(Ga2S3)0.25(GeS2)0.75 Glass: Complementary Use of X-Raysand NeutronsShinya Hosokawa1,2, Yohei Onodera3, László Pusztai4,5, Jens Rüdiger Stellhorn6, HirooTajiri7, Kazutaka Ikeda8, and Toshiya Otomo91Faculty of Materials for Energy, Shimane University, Matsue 690-8504, Japan2Institute of Industrial Nanomaterials, Kumamoto University, Kumamoto 860-8555, Japan3Center for Basic Research on Materials, National Institute for Materials Science (NIMS), Tsukuba305-0047, Japan4HUN-REN Wigner Centre for Physics, H-1525 Budapest, Hungary5International Research Organization for Advanced Science and Technology (IROAST), KumamotoUniversity, Kumamoto 860-8555, Japan6Co-Creation Institute for Advanced Materials, Shimane University, Matsue, 690-8504, Japan7Japan Synchrotron Radiation Research Institute (JASRI), Sayo 679-5198, Japan8Neutron Industrial Application Promotion Center, Comprehensive Research Organization forScience and Society (CROSS), Tokai 319-1106, Japan9High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, JapanE-mail: s hosokawa@mat.shimane-u.ac.jp(Received December 23, 2024)Local- and intermediate-range atomic arrangements in a (Ga2S3)0.25(GeS2)0.75 glass, having a highinfrared transparent coefficient, were investigated by a combination of anomalous X-ray scattering(AXS), X-ray and neutron diffraction (XRD and ND), and reverse Monte Carlo (RMC) modeling,which are compared with our previous results of a similar (Ga2Se3)0.25(GeSe2)0.75 glass (JPS Conf.Proc. 33, 011069 (2021)). By adding the ND structure factor and pair distribution function to AXSand XRD results, reasonable partial structure factors and partial pair distribution functions were ob-tained, even applying no constraints of shortest interatomic distances during the RMC calculationprocedure. Total coordination numbers around Ga, Ge, and S atoms are 3.55, 3.88, and 2.77, respec-tively, which contradict the 8 − N rule except around Ge. The numbers of Ga-Ga, Ga-Ge, Ge-Ga,Ge-Ge, and S-S wrong bonds were found to be 0.34, 0.54, 0.36, 0.63, and 1.21, respectively. Small butclear differences are found by comparing with the results of selenide glass. In the three-dimensionalatomic configuration, the structure looks inhomogeneous in both density and concentration as in theselenide glass.KEYWORDS: Neutron diffraction, Anomalous X-ray scattering, Reverse Monte Carlomodeling, Glass structure1. IntroductionChalcogenide glasses are characterized by remarkable physical properties [1], such as high in-frared transparency [2] and large photosensitivity [3]. In general, their properties can be fine-tuned byvary- ing the composition of the constituent elements. An excellent example is a Ga-Ge-chalcogenidealloy having a high infrared transparency, which can be used for infrared telecommunications as aglass-fiber material. Although accurate structural characterization of these glasses is very importantto link to the unique properties, experimental works are still heavy tasks. In case of the Ga-Ge-SeJPS Conf. Proc. , 011046 (2026)©2026 The Author(s)https://doi.org/10.7566/JPSCP.45.01104645must maintain attribution to the author(s) and the title of the article, journal citation, and DOI.Proc. 4th J-PARC Symposium 2024011046-1This article is published by the Physical Society of Japan under the terms of the Creative Commons Attribution 4.0 License. Any further distribution of this workProceedings of the 4th J-PARC Symposium 2024Downloaded from journals.jps.jp by （研）物質‧材料研究機構 on 06/16/26http://creativecommons.org/licenses/by/4.0/alloys, the constituent elements of Ga, Ge, and Se in these glasses have similar atomic numbers, cor-responding to similar atomic form factors for X-ray diffraction (XRD), f . For X-ray absorption finestructure (XAFS) spectroscopy, they have similar backscattering amplitudes, and it is very difficultto discriminate the elements of neighboring atoms by the XAFS measurements, Moreover, the scat-tering lengths for neutron diffraction (ND), b, also have only small differences from each other, i.e.,7.288, 8.185, and 7.970 fm for Ga, Ge, and Se atoms [4], respectively, and it is hard to obtain thespectral contrasts between the XRD and ND data.In the case of the Ga-Ge-S alloys, the atomic number of S is much smaller than that of Se;however, it does not help the structural investigation of these alloys. The bS for ND is a small value of2.847 fm [4] as well as the small fS value for XRD. The S K absorption edge is located in the soft X-ray region of 2.472 keV, which makes the XAFS or anomalous X-ray scattering (AXS) experimentsto be very tough works.The existence of metal-metalloid (Ga-Ge) bonds in the Ga-Ge-Se alloys was confirmed by Ramanand NMR data [5], and ND and XAFS measurements combined with reverse Monte Carlo (RMC)modeling [6]. The nature of such ‘wrong’ bonds is, however, still largely disputed, i.e., some studiesclaimed only Ge-Ge homopolar bonds [5] while others found only Ga-Ge bonds [6]. Klee et al. carriedout anomalous X-ray scattering (AXS) [7] and applied that several constraints of dismissing pairs ofGa and Ge in the RMC modeling. However, no specific pairs could be found for the constraints ofthe RMC fits. Recently, Hosokawa et al. reported the results of AXS, XRD, and ND in combinationwith RMC modeling on a (Ga2Se3)0.25(GeSe2)0.75 (GaGeSe) glass [8]. They found the meaningfulexistences of ‘wrong bonds’ in all the pairs of Ga and Ge atoms.Subsequent to this study, we have carried out a similar structural study on a (Ga2S3)0.25(GeS2)0.75(GaGeS) glass by AXS close to the Ga and Ge K absorption edges, XRD, and ND, in combina-tion with the RMC analysis. We will discuss the similarities and differences between these Ga-Ge-chalcogenide glasses.2. Experimental and data analysis procedureA mixture of pure elements with the concentration of GaGeS was sealed in a quartz ampoule,which was heated using a furnace to 1050◦C and kept for 12 h. The temperature was reduced to850◦C by 2◦C/min, and kept for 1 h, followed by a quench in cold water. Then, the sample wasannealed at 350◦C for 3 h, and gradually cooled down to room temperature.The AXS experiments were carried out at the beamline BL13XU of the SPring-8 [9]. The princi-ple and experimental procedure of AXS were given elsewhere [10–12]. Two scattering experimentswere performed to obtain differential structure factors, ∆kS (Q), at 20 and 200 eV below the Ga(10.367 keV) and Ge (11.104 keV) K edges. For the analysis, theoretical values of the real and imag-inary parts of the anomalous terms of the atomic form factor calculated by Sasaki [13] were used.The energy-independent theoretical atomic form factors [14] were also used for obtaining ∆kS (Q).The total XRD structure factors, S X(Q), were obtained at the incident X-ray energy of 10.904 keV.The ND experiments were performed to obtain total ND structure factors, S N(Q), in a wide Qrange from 1.6 to more than 1000 nm−1 using the NOVA spectrometer [15] installed at BL21 of theMaterial and Life Experimental Facility (MLF) of the Japan Proton Accelerator Research Complex(J-PARC), Tokai, Japan. The sample was contained in a V-Ni null scattering sample container withan outer diameter of 6.0 mm and a thickness of 0.1 mm. The incident neutron beam was generatedby the proton accelerator with an output power of 700 MW, and the ND experiment took about 3 h.Measurements were performed in the time-of-flight mode, with neutron energies between 0.0013 and5.7 eV, and a pulse repetition rate of 25 Hz. Details of the neutron detecting procedures are givenelsewhere [16]. The observed scattering intensities from the sample were corrected for instrumentalbackground, absorption of the sample and the cell [17], multiple [18], and incoherent scattering.011046-2JPS Conf. Proc. , 011046 (2026)45Proceedings of the 4th J-PARC Symposium 2024Downloaded from journals.jps.jp by （研）物質‧材料研究機構 on 06/16/26Table I. Wki jfor the i- j correlations by k scattering methods.k\i- j Ga-Ga Ga-Ge Ga-S Ge-Ge Ge-S S-S∆GaS (Q) 0.1737 0.3207 0.4247 0.0362 0.0487 -0.0040∆GeS (Q) -0.0194 0.2143 -0.0449 0.3296 0.5235 -0.0031S X(Q) 0.0475 0.1348 0.2039 0.0973 0.2942 0.2223S N(Q) 0.0508 0.1707 0.1784 0.1435 0.2999 0.1567The scattering lengths and absorption cross-sections for the constituent nuclei were taken from theliterature [4]. These corrections were performed by the nvaSq program package coded by the NOVAgroup [19].Table I shows the weighting factors Wki jfor the i- j correlations by k scattering methods (∆GaS (Q),∆GeS (Q), S X(Q), and S N(Q)) for the partial structure factors, S i j(Q). Note that these values are givenat Q = 23 nm−1 near the first peak positions, and the Wki jvalues slightly vary with Q for three X-rayscattering methods. As seen in the table, if i or j corresponds to k, Wki jis enhanced, while if this isnot the case, Wki jis highly suppressed. Another striking feature in this table is that Wki jfor S X(Q)and S N(Q) have very small differences from each other, with which it is difficult to obtain partialstructures from only the contrast between the XRD and ND data.The present RMC calculation was carried out by using the RMC++ program package [20]. Initialconfigurations were generated by hard-sphere Monte Carlo simulation. The simulation box containedtotally 10,000 atoms in a size of 6.377 nm, which was chosen to adjust the number density of thesample, 38.57 nm−3. From the RMC fits, S i j(Q), partial pair distribution functions gi j(r), and thecorresponding 3D atomic configurations were obtained.3. ResultsCircles in Fig. 1(a) show, from top to bottom, experimental data of ∆GaS (Q) and ∆GeS (Q) takenfrom AXS, S X(Q), and S N(Q). The solid curves represent the corresponding RMC fits. Here, weexplain the naming rule for peaks in S (Q) spectra in the glass field. The peaks located usually atabout 10, 22, and 35 nm−1 are called the first sharp diffraction peak (FSDP) or prepeak, first orprimary peak, and second peak, respectively, because FSDP is not observed in usual non-crystallineor liquid materials such as metallic ones. As seen in the figure, the spectral features are very differentfrom each other, owing to different Wki js for S i j(Q)s as shown in Table I. In particular, the heights ofthe FSDPs located at about Q = 10 nm−1 are different from each other. Note that the FSDP heightsare much larger than those of GaGeSe glass given in Fig. 1(a) of Ref. [8]. At the first peak positionof about Q = 21 nm−1, the RMC fit does not reproduce the experimental ∆GeS (Q) result, where aminimum is seen. We speculate that this is due to the lack of ∆SS (Q) data with a large maximumcompensating the minimum in ∆GeS (Q) at the same Q position, as observed in the GaGeSe glass.Another discrepancy is that the spectral features in ∆GaS (Q) are similar to those in ∆GeS (Q) for theGaGeS glass. Thus would be owing to the fact that the atomic arrangements around Ga resemblethose around Ge in the GaGeS glass rather than those in the GaGeSe glass.Figure 1(b) shows the experimental and analytical results for gN(r), which has a sharp and well-defined first peak at about 0.22 nm and a second peak at about 0.34 nm. The coincide between theexperiments and fits are quite good. The above lengths are smaller than those of the GaGeSe glass [8],which may be due to the shorter atomic bond lengths around S than those around Se.Figure 2(a) shows S i j(Q)s obtained from the RMC fits. The features of S i j(Q)s highly depend onthe combinations of partial elements. In the combinations of the Ga and Ge elements, large and sharppeaks with a height of about 3 are observed at the FSDP positions of the total S (Q)s of about Q = 10011046-3JPS Conf. Proc. , 011046 (2026)45Proceedings of the 4th J-PARC Symposium 2024Downloaded from journals.jps.jp by （研）物質‧材料研究機構 on 06/16/26(a)(b)–Fig. 1. (a) From top to bottom, circles show experimental data of ∆GaS (Q) and ∆GeS (Q) taken from AXS,S X(Q), and S N(Q), and the solid curves represent the RMC fits. (b) The same meaning for gN(r).nm−1, which are similar to those of GaGeSe glass. A difference is found in the large FSDP in theGe-S partial with a height of about 2, while a small peak with a height of only 0.3 was detected in theGe-Se partial of the GaGeSe glass [8]. Besides, the other S-related partials have small FSDP signals.At the first peak position of about Q = 21 nm−1, the S-related correlations show small peaks, whilethe others exhibit middle-sized peaks. These results are not similar to those in the GaGeSe glass,where large, middle, and small peaks are observed in the Se-Se, Ga-Se, and Ga-Ga correlations,respectively, whereas the Ga-Ge, Ge-Ge, and Ge-Se partials have ‘negative’ pits at this Q [8].Figure 2(b) shows gi j(r)s obtained from the RMC fits. The first peaks of most partials showsimilar features with the height of more than 6, while that of S-S represents a small peak with theheight of about 3. These spectral features are very different from those of GaGeSe glass showinga variety of heights [8]. It is interesting that the present GaGeS glass has small numbers of cationhomopolar ‘wrong’ bonds although they were also found with large magnitudes in the GaGeSe glass.The second peaks at about 0.36 nm exhibit interesting features; 1) the cation-S correlations showsmall peaks at the longer positions indicating that the cation-(S)-S correlations are small, 2) thecation-cation correlations show large peaks with relatively shorter positions corresponding to thecation-S-cation correlations, and 3) the S-S partial exhibits small and broad peak being composed ofthe mixture of S-Ga-S and S-Ge-S connections.4. DiscussionTo analyze the local atomic structures of this GaGeS glass in detail, partial interatomic distancesbetween the i- j pairs, ri j are listed in Table II. All of the ri j values are mostly the same values of0.218-0.225 nm for either heteropolar or homopolar bonds, although the Ga-related ones are slightlylonger. Pethes et al. reported the partial structures of the same GaGeS glass by measuring total XRD011046-4JPS Conf. Proc. , 011046 (2026)45Proceedings of the 4th J-PARC Symposium 2024Downloaded from journals.jps.jp by （研）物質‧材料研究機構 on 06/16/26(a) (b)–Fig. 2. (a) S i j(Q)s and (b) gi j(r)s obtained from the RMC fits.and XAFS close to the Ga and Ge K edges and analyzing with the RMC modeling [21]. Owingprobably to the above structural information limited to mainly in the first neighboring region, theRMC analysis was performed with large constraints for the first nearest neighbors, i.e., only the Ga-Ga correlations were allowed for the wrong bonds, and their results [21] are also presented in Table II.Nevertheless, the cation-S bond lengths are in good agreement with each other, and the discrepancyis only seen in the Ga-Ga length. As a reference, the results of GaGeSe glass are also given in thetable, where the measurements and analyses are performed in the same way except for the lack of theAXS experiment near the S edge. The obtained ri j values are systematically larger due to the largeratomic radius of Se than that of S.Table II also shows the partial coordination numbers of the first neighbor jth element along the ithelement, Ni j. The values were calculated from gi j(r)s by integrating up to r = 0.26 nm, and the totalcoordination numbers, Ni, were obtained as the sum around the ith element. Remarkable differencesfrom the previous RMC results by Pethes et al. [21] are found in Nis. Namely, NGa = 3.55 largelyexceeds the 8 − N value of three, although NGe = 3.88 is near that of four, both of which are smallerthan the previous RMC results of 3.85 and 4.07, respectively [21]. It should be noted that NS = 2.76is much larger than the 8 − N value of two and the previous RMC result of 2.13 [21]. Since the gN(r)result was included in the present RMC calculation, we believe that the obtained Ni results are muchmore reliable than the previous report [21].Figure 3 shows three-dimensional (3D) atomic configurations obtained from the present RMCfits, where the small blue, small red, and large yellow balls indicate the Ga, Ge, and S atoms, re-spectively. In (a) and (b), atomic configurations around the Ga and Ge atoms are marked by drawingpolyhedra around them, respectively. At a glance, the polyhedra around the Ga and Ge atoms exhibitindividual clusters at the different regions. In (c), the S-S homopolar bonds are represented by or-ange lines, where the Ga and Ge atoms are made invisible. The S-S bonds also form inhomogeneousconfigurations. It should be noted that the S-S bond-rich regions are located at the tetrahedra-rich011046-5JPS Conf. Proc. , 011046 (2026)45Proceedings of the 4th J-PARC Symposium 2024Downloaded from journals.jps.jp by （研）物質‧材料研究機構 on 06/16/26Table II. ri j and Ni j of the GaGeS glass as well as those of the GaGeSe glass. In the case of GaGeSe glass,S in the left column should be replaced with Se.ri j Ni jPresent RMC [21] RMC [8] Present Present RMC [21] RMC [8]1st GaGeSe 2nd GaGeSeGa-Ga 0.224(1) 0.261 0.280 0.361(2) 0.34 0.29 0.71Ga-Ge 0.223(1) – 0.246 0.351(1) 0.54 – 1.32Ga-S 0.225(1) 0.2275 0.243 0.368(1) 2.67 3.56 1.77Ga total 3.55 3.85 3.80Ge-Ga 0.223(1) – 0.246 0.351(1) 0.36 – 0.76Ge-Ge 0.222(1) – 0.236 0.365(2) 0.63 – 1.12Ge-S 0.222(1) 0.2215 0.236 0.358(2) 2.89 4.07 2.80Ge total 3.88 4.07 4.68S-Ga 0.225(1) 0.2275 0.243 0.368(1) 0.59 0.79 0.31S-Ge 0.222(1) 0.2215 0.236 0.358(2) 0.96 1.36 0.93S-S 0.218(2) – 0.236 0.365(1) 1.21 – 1.01S total 2.76 2.15 2.25regions around the Ge atoms, i.e., the locations of the Ge tetrahedra and the Se-Se bonds are highlysynchronized. These atomic configurations clearly indicate the formation of both the density- andconcentration fluctuations in this glass. Note that the same configurations were also observed in theGaGeSe glass [8].(a) (b) (c)Ga Ge SFig. 3. 3D atomic configurations of Ga, Ge, and S atoms indicated by small blue, small red, and large yellowballs, respectively, obtained from the RMC fits, with polyhedra around the (a) Ga and (b) Ge atoms, and (c)S-S bonds (orange lines).To be honest, the present analyses are somewhat less than perfect when compared with the previ-ous GaGeSe results [8]. Particularly, the RMC fits to ∆GeS (Q) shown in Fig. 1(a) are insufficientin the first minimum region of about Q = 20 nm−1, where the fitting quality highly affects theintermediate-range atomic structures around the Ge atoms. As mentioned above, the direct reasonfor this inconvenience may originate from the lack of ∆SS (Q) data in the GaGeS results, which helpsthe fit quality of the large negative dip in ∆GeS (Q) as seen in Fig. 1 of Ref. [8]. An XAFS experimentclose to the S K edge can improve the quality of local atomic arrangements around the S atoms,while it is doubtful for that of the intermediate-range atomic structure because this technique is help-011046-6JPS Conf. Proc. , 011046 (2026)45Proceedings of the 4th J-PARC Symposium 2024Downloaded from journals.jps.jp by （研）物質‧材料研究機構 on 06/16/26ful to determine only the nearest-neighbor information. Another method to improve the fits may beto operate the constraints in the RMC modeling procedures. There were no constraints in the cur-rent calculation, whereas it would be better to include constraints of coordination numbers if there isadditional structural information such as NMR data. Another malfunction is seen again in ∆GeS (Q),where the magnitude of oscillations in the experimental data is much larger than that of the RMC fits.It would come from the overestimate of the theoretical f ′ value of Ge [12], which may be solved byusing experimental data through a detailed measurement of X-ray absorption close to the Ge K edgeas was done in Ref. [22].5. SummaryLocal- and intermediate-range atomic structures of (Ga2S3)0.25(GeS2)0.75 glass were investigatedin detail by the measurements of XRD, AXS close to the Ga and Ge K edges, and ND in combinationwith RMC modeling. The inclusion of real space gN(r) data may highly improve the reliability of thecoordination number results. The total coordination numbers around the Ga, Ge, and S atoms weredetermined to be 3.55, 3.88, and 2.76, respectively, which contradict the 8−N rule except NGe and theprevious RMC results. Large numbers of wrong bonds of Ga-Ga, Ga-Ge, Ge-Ge, and S-S pairs wereobserved. Inhomogeneous atomic arrangements were found in both the density and concentrationfrom the obtained 3D atomic configurations, similar to those in the (Ga2Se3)0.25(GeSe2)0.75 glass [8].AcknowledgmentsND measurements were performed at BL21 of the J-PARC MLF (Nos. 2021B0051 and 2017B-0047). AXS experiments were carried out at BL13XU of the SPring-8 (Nos. 2021B1110, 2021A1181,2019A1556 and 2018B1208). SH acknowledges financial supports by JSPS Grant-in-Aid for Trans-formative Research Areas (A) ‘Hyper-Ordered Structures Science’ (Nos. 23H04117 and 21H05569)and for Scientific Research (C) (No. 22K12662), and by the Japan Science and Technology Agency(JST) with Core Research for Evolutional Science and Technology (CREST) (No. JPMJCR1861).References[1] B. Bureau, X. H. Zhang, F. Smektala, J.-L. Adam, J. Troles, H.-L. Ma, C. Boussard-Plèdel, J. Lucas, P.Lucas, D. Le Coq, M. R. Riley, and J. H. Simmons, J. Non-Cryst Solids 345&346, 276 (2004).[2] J.-L. Adam, L. Calvez, J. Trolès, and V. 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