Research Article  Open Access
Investigation of the Atomic Structure of GeSbSe Chalcogenide Glasses
Abstract
Glasses with composition of Se_{60} (x= 40, 35, 32, 27, 20, 15 at. %) have been synthesized. Neutron and Xray diffraction techniques were used to study the atomic glassy structure, and Reverse Monte Carlo (RMC) simulations were applied to model the 3dimensional atomic configurations and thorough mapping of the atomic parameters, such as first and second neighbour distances, coordination numbers, and bondangle distributions. The results are explained with formation of GeSe_{4} and SbSe_{3} structural units, which correlate with the Ge/Sb ratio. For all the studied compositions, the GeSe, SbSe, GeGe, and SeSe bonds are significant. RMC simulations reveal the presence of GeSb and SbSb bonds, being dependent on Ge/Sb ratio. All atomic compositions satisfy formal valence requirements, i.e., Ge is fourfold coordinated, Sb is threefold coordinated, and Se is twofold coordinated. By increasing the Sb content, both the SeGeSe bonds angle of 107±3° and SeSbSe bonds angle of 118±3° decrease, respectively, indicating distortion of the structural units. Far infrared Fourier Transform spectroscopic measurements conducted in the range of 50450 at oblique (75°) incidence radiation have revealed clear dependences of the IR band’s shift and intensity on the glassy composition, showing features around x=27 at.% supporting the topological phase transition to a stable rigid network consisting mainly of SbSe_{3} pyramidal and GeSe_{4} tetrahedral clusters. These results are in agreement with the Reverse Monte Carlo models, which define the Ge and Sb environment.
1. Introduction
In recent years a great deal of interest has been devoted to the optical studies of chalcogenide glasses because of their wide area of applications as electrical and optical components as well as optical fibers in the infrared optical region, which are the basis of many applications [1–4]. Ternary GeSbSe glasses are promising materials for infrared optical fibers application because of their high transparency in the key region and good thermal, mechanical, and chemical properties. The physicochemical, elasticplastic, and optical properties of the ternary GeSbSe chalcogenide system have been intensively studied [5–13], and the influence of Ge/Sb ratio on the optical, electronic, and microstructural properties of GeSbSe system has been considered. A common and useful parameter for the explanation of the compositional dependence on the physical properties is the coordination number Z of covalent bonds per atom, characterizing the structural atomic units [5, 13, 14]. For the compositions under investigation, a value of Z=2.652.67 corresponding to x=2527 at.% has been obtained as critical for a transition from 2D crosslinked chains arrangements to formation of 3D network of tetrahedral GeSe_{4} and pyramidal SbSe_{3} when the x value increases [5, 13].
Still one of the main questions remains how the structure of Ge environment changes, when the Ge atoms are replaced by Sb atoms. A comprehensive answer can be obtained by combining different methods and techniques, such as neutron diffraction (ND), highenergy Xray diffraction (XRD), and far infrared (IR) Fourier Transform spectroscopy, which offers comprehensive information about the atomic structure. In addition, theoretical modeling of such experimental results using Reverse Monte Carlo (RMC) method allows building threedimensional structure models and, thus, obtaining a more detailed description of the atomicscale glassy structure. In connection with this, we have successfully performed experiments combining the ND and XRD techniques and RMC simulation method for the study of ternary AsSeTe [15] and quaternary GeSbS(Se)Te glasses [16–18]. Using the experience gained, we have started to investigate new GeSbSe system. The compositional dependence of the structure and physical and optical properties of ternary GeSbSe system is of interest, especially considering the effects of average coordination number, Z, of covalent bonds per atom.
In this paper, we focused on the atomicscale structure characterization of nonstoichiometric Se_{60} compositions, where x varied between 15 and 40 at. %. For examining the alteration of the glassy structure with changes in composition, we applied an approach in which ND and highenergy XRD techniques with Reverse Monte Carlo (RMC) modeling were combined. The procedure of RMC modeling is considered in details in Section 3.1. By this way, characteristic parameters, such as structure factors, partial atomic pair correlation functions, coordination numbers, and bondangle distribution functions, are established. Recently, the chemical short order in Ge_{20} (x=5, 15, 20) compositions has been studied by the nuclear techniques and extended Xray absorption fine structure measurements [19] as one of the compositions, namely, Ge_{20}Sb_{20}Se_{40}, is among the compositions we study herein. Our results obtained by the combination of different methods would widen the knowledge about these materials and would contribute to a better understanding of the structural changes by composition.
In addition, we performed Fourier Transform infrared (FTIR) reflectance measurements in the terahertz spectral range in order to get more information about the microstructure and basic chemical bonding of the studied compositions. So far, few far IR spectral measurements have been carried out for studying the longwavelength multiphonon edge of these materials. Raman and FTIR spectra have been reported in [5] and [8, 10, 20, 21], respectively, as in the latter PE pellets are used resulting in a not so good spectrum even when they are converted in absorption units. To avoid this, we carried out the FTIR measurements on thin (~ 1 μm) films deposited on quartz substrates. Using incidence radiation under a large angle of 75° the obtained spectra are more informative about the composition microstructure with variation of x value. The results of this paper correspond to the conclusions presented by other authors and are in agreement with our earlier publications [5] on bulk samples served here as parent materials for thin films preparation.
2. Experimental Section
2.1. Sample Preparation
The binary Ge_{40}Se_{60} and ternary Se_{60} glasses with x=15, 20, 27, 32, and 35 at. % were prepared from elements of 99.999 % purity. Appropriate quantities from Ge, Se, and Sb were sealed into quartz ampoules after evacuation down to a pressure of Pa. The bulk glasses were synthesized by the conventional meltquenching method in a rotary furnace at 950°C. After homogenization for 24 h, the melts were quenched in air.
Part of the bulk samples was powdered. At the ND and XRD studies, powdered material was used as specimen with ~ 3 g/each composition. The powdered glasses served also as parent material at evaporation of thin films for Fourier Transform infrared (FTIR) spectroscopic studies.
The thin films were deposited onto quartz substrates by vacuum thermal evaporation of the powders from the corresponding parent Se_{60} materials at a residual pressure of Pa in the chamber. The thickness of the films (~1 μm) was controlled in situ by MIKI FFV quartz sensor device.
2.2. Neutron and XRay Diffraction Experiments
The neutron diffraction measurements were performed at room temperature in the 2axis ‘PSD’ monochromatic neutron diffractometer (=1.068 Å; Q=0.459.8 ) [22] at the 10 MW Budapest Research Reactor, using thermal neutrons. The powder specimens (~3 g/each) were filled in cylindrical vanadium sample holder of 8 mm diameter. The structure factors, S(Q), were evaluated from the raw experimental data. The overall run of the ND experimental curves is similar for the investigated samples, but characteristic differences especially in the low Qrange can be observed. Figure 1 presents the S(Q) from neutron diffraction experiments, where the results of the Reverse Monte Carlo model calculation are also drawn, but this will be discussed later, in Section 3.
The Xray diffraction experiments were carried out at the beam line BW5 at HASYLAB, DESY [23]. The powdered samples were filled into quartz capillary tubes of 2 mm in diameter (wall thickness of ~0.02 mm) and measured at room temperature. The energy of the radiation was 109.5 keV (λ_{0}=0.113 Å). The highenergy synchrotron Xray radiation makes it possible to reach diffraction data up to highQ values. In this study the XRD structure factors were obtained up to 18 , as for higher Qvalues the experimental data became rather noisy. Because the atomic parameters of the components are similar, the XRD structure factors were similar to ND ones. We consider here the XRD data for four samples which shows well the concentration dependence within the series. The XRD experimental S(Q) data together with the RMC simulation results (details of the RMC modeling will be discussed in Section 3) are presented in Figure 2.
The shape and character of the ND (Figure 1) and XRD (Figure 2) structure factors testify to a fully amorphous glassy structure in nature. However, there are some fine differences between the ND and XRD spectra. The differences in the overall run of these spectra lie in the different values of the weighting factors, , of the partial structure factors, (Q), defined aswhere , are the molar fractions of the components, , are the coherent neutron and , are the Xray scattering amplitudes, and k is the number of elements in the sample. For the binary Ge_{40}Se_{60} sample k is 2, thus k(k+1)/2=3, and for the ternary GeSbSe samples k is 3, thus k(k+1)/2=6, and, therefore, 6 different atom pairs are present in the studied series. The neutron scattering amplitude of an element is constant in the entire Qrange [24], while the Xray scattering amplitude is Qdependent [25] and for each atom it differs in a somewhat different way. To illustrate the differences, the comparison of the corresponding weighting factors, , for the two radiations is shown in Table 1, where and at Q=1.05 are given for the Ge_{15}Sb_{25}Se_{60} sample.

It can be seen that the GeSe and SeSe atom pairs have a significant contribution in the neutron experiment, while the SbSb and SbSe atom pairs have a dominant weight in the Xray experiment. On the other hand, the differences appeared for the GeGe and GeSb atom pairs are not more significant than those for the other ones. Taking into consideration all these characteristics, we have concluded that the two radiations give complementary information, and both types of measurements are needed to obtain a real structure for the investigated samples.
2.3. Fourier Transform Infrared Spectrophotometry
In order to detect the basic chemical bonding in the Se_{60} compositions Fourier Transform infrared measurements were performed in the terahertz spectral range of 45050 of the polarized light. FTIR spectra were measured in close to reflectanceabsorbance geometry with an incident radiation angle of 75°, permitting maximal optical path through the sample. A Bruker Vertex 70 instrument and a reflectance accessory Bruker A513/Q were used. The resolution was 2 and the number of scans was 100. A gold standard mirror was used for the spectral normalization.
3. Results and Discussion
3.1. Reverse Monte Carlo Simulation
The experimental diffraction S(Q) data has been simulated by the RMC method [26], which is a widely used effective tool to model disordered structures. The RMC minimizes the squared difference between the experimental S(Q) and the calculated one from a 3D atomic configuration. From the RMC configuration the partial pair correlation functions, (g_{ij}(r)), the coordination numbers, and the bondangle distributions were calculated using the software package RMC^{++} [27].
In order to investigate the possible effect of the starting configuration on the results, the following model was built up. The initial configuration was generated by random distribution of 10 000 atoms in a cubic simulation box. The experimentally measured density was 0.032, 0.030, 0.031, 0.038, 0.039, and 0.038 atoms/Å^{3} [28] corresponding to box edges of 31.90 Å, 34.66 Å, 34.29 Å, 32.05 Å, 31.76 Å, and 32.05 Å for the Ge_{40}Se_{60}, Ge_{35}Sb_{5}Se_{60}, Ge_{32}Sb_{8}Se_{60}, Ge_{27}Sb_{13}Se_{60}, Ge_{20}Sb_{20}Se_{60}, and Ge_{15}Sb_{25}Se_{60} samples, respectively.
The Ge, Sb, and Se elements possess comparable neutron and Xray scattering amplitudes, which makes it rather difficult to identify the atomic positions. In order to avoid unreasonable shortrange orders for all atom pairs, in the RMC simulation procedure constraints were applied to the minimum interatomic distances between atom pairs (cutoff distances). The starting cutoff distances were taken from the previous studies for the similar contents [15, 17] and from the literature based on the results of similar or very close glassy compositions [29, 30]. Several RMC runs have been performed by modifying slightly the cutoff distances for each atom pairs. The final cutoff distances, used further in the RMC modeling, are summarized in Table 2. From our previous study and from literature data, we expect that the main glassy network is built up by the GeSe_{4/2} tetrahedra and the SbSe_{3/2} pyramid units. Therefore, it is suggested that the atomic structure of the ternary glasses is built up by chain connection of GeSe_{4/2} tetrahedra and SbSe_{3/2} pyramid through a 2coordinated Se atoms. Thus, the 4coordinated Ge unit connects through a Se atom to a 3coordinated Sb unit and, therefore, the first neighbour distance of GeSb is less realistic. In the literature, there are studies [29, 31–33], which support this suggestion. Considering the values of the weighting factors in Table 1, one can see that GeSb bond’s weighting factors (=6.24% and =8.49%) are lower than those for GeSe (=21.43% and =13.56%) and SbSe (=24.30% and =36.16%), which bonds have well known first neighbour distances. From these follows that GeSb bonds most probably have the second neighbour distance. Nevertheless, in the RMC modeling, we did not exclude any first neighbour distances and Figure 3 presents all partial pair correlation functions obtained from the RMC calculations.

(a)
(b)
(c)
(d)
(e)
(f)
The experimental structure factors (S(Q)) are compared with those accumulated from the data of the RMC models of the corresponding glass compositions. For each sample, close to 20 RMC configurations were obtained in the intervals of more than 1 500 000 accepted moves of atoms inside of the simulation box. Good agreement between the experimental and calculated diffraction data was achieved. The comparison between the experimental and calculated structure factors are illustrated in Figures 1 and 2. The measured neutron diffraction data in Figure 1 shows significant dependence on the composition, especially at lowQ values. For all compositions, the first and the most intensive peaks were situated at 1.1 and 2.1 , while the next less intensive ones are at 3.55 and at 5.5 . Figure 2 displays the XRD S(Q) spectra, where the first intensive peak is observed at 0.6 , a second intensive peak at 1.8 , and two other broaden and much less intensive peaks at 3.5 and at 5.7 .
In order to get comprehensive structural information about the studied series, we have investigated all homopolar and heteropolar atomic distances. The partial atomic pair correlation functions, (r), were revealed from the RMC simulation with a good reproducibility and acceptable statistics. The obtained partial pair distribution functions are presented in Figure 3. The first peaks are well defined and, thus, we could perform an unambiguous evaluation of distances.
It was found that GeSe, SbSe, GeGe, and SeSe bonds are significant in the studied samples. The peaks related to the first interatomic distances appear at 2.35±0.01 Å, 2.54±0.01 Å, 2.47±0.03 Å, and 2.32±0.02 Å, respectively, as these peaks appear at the same position within the error for all the studied compositions. Because of the allowed cutoff distances (Table 2), first interatomic distances between GeSb and SbSb atoms were found at 2.55±0.05 Å and 2.57±0.03 Å, but the corresponding first peak’s intensity was very low (Figures 3(c) and 3(e)). This suggests that second neighbour distance between Ge and Sb is more realistic. Second characteristic peaks were obtained for GeSb, GeGe, SbSb, and SeSe atom pairs, which are displayed at 3.80±0.05 Å, 3.85±0.05 Å, 3.80±0.05 Å, and 3.80±0.05 Å, respectively.
The partial atomic pair correlation functions are summarized in Table 3. These values, with exceptions of GeSb and GeGe, are close to the data given in [19], but the differences could be due to the annealing of samples in that work, which altered their glassy structure.

The great advance of the RMC method is that the coordination number, , can be obtained from the final particle configurations. From the partial pair distribution functions we calculated the number of nearest neighbours for Ge, Sb, and Se atoms using the corresponding bond cutoff distances. It is necessary to specify the range of r within which atoms are counted as neighbours and which determine the coordination shells. We introduced the quantities r_{1} and r_{2}, where r_{1} and r_{2} are the positions of minimum values on the lower and upper side of the corresponding peaks, respectively. From the literature, we know some details related to the coordination numbers of the present atoms: concerning the Ge atoms, they are 4coordinated, the Sb atoms are 3coordinated, and Se atoms expected to be close to 2coordinated sites. To obtain more information about the atomic structure, we carried out constrained simulations, in which Ge and Sb atoms were forced to have four and three neighbours, respectively. The corresponding average coordination numbers, , obtained from the RMC simulations, are tabulated in Table 4. The coordination numbers show a clear dependence with the Ge/Sb ratio. The results suggest the presence of two basic structural units, namely, the GeSe_{4} tetrahedral units with fourfold coordinated Ge atom and SbSe_{3} pyramids with threefold coordinated Sb atom.

In Figure 4 the average coordination number distributions of the possible chemical bonds, calculated from the RMC modeling, are presented. It can be seen that the average coordination number around Ge atoms is close to four atoms, as is expected by the formation of tetrahedral units in the network.
(a)
(b)
However, with increasing Sb content the GeSe coordination number, , slightly increases from 3.10 to 3.84 atoms, which indicates a small degree of angle distortion affecting the tetrahedral surrounding. This may be caused by the formation of SeGe bonds, as the coordination of Se atoms increases from 2.02 to 2.16. The average coordination number increases from 3.69 to 3.96 with increasing Sb content. This suggests that the chalcogenide network consists of stable tetrahedral Ge units. The coordination number continuously decreases from 2.97 to 2.50 with increasing Sb concentration. The SbX average coordination number slightly varied from 3.00 to 2.85. The SeGe coordination number continuously decreases from 1.98 to 0.96 with increasing Sb concentration, while the SeSb coordination number increases from 0.21 to 1.08; nevertheless, the concentration of Se atoms is kept constant.
Figure 5 shows the bondangle distributions for the Ge and Sb atoms with SeGeSe and SeSbSe threeparticle bond angles. We calculated the threeparticle bondangle distributions using the final atomic configuration of the RMC algorithm, plotted both as the function of (scale below) and Θ (upper scale), where Θ represents the actual bond angle.
(a)
(b)
For the SeGeSe bonds, the peak positions are at 107±3° (for the ternary samples) [in agreement with [34]] and at 109.6±2° (for the binary sample) [35] which are very close to the tetrahedral angle of 109.47°. The peak distribution is very similar for all the studied samples. The broad distribution is quite asymmetric, but with the increase of Sb concentration, a shift down can be observed suggesting that the tetrahedral environment has become distorted. The distribution of SeSbSe bonding angles is broad and asymmetric, the average angles being 118±3° and 111±5°. The broad distribution suggests that 3fold Sb atoms are present. The SeSbSe bond angles distribution also shows similar characteristics for all samples, as with the increase of Sb concentration a shift down to the 111±5° can be observed implying considerable distortion in Sb_{3} planar geometry. In most of the cases, a weak peak around 60±3° appears, strongly dependent on glassy composition, which is due to the occasional presence of threefold rings [35].
The present RMC simulation of the ND and XRD data points out that the Sb atoms incorporated in Ge_{40}Se_{60} glass bind covalently to Se and form SbSe_{3}  trigonal units. On the other hand, Se atoms, which are also connected to Ge, form GeSe_{4} tetrahedral structural units. These findings are in agreement with several spectroscopic studies [5, 8, 36].
The atomic parameters support the formation of Getetrahedral and Sbtrigonal units in Ge_{40}Se_{60} glass structure. When the Sb content gradually increases, strong Sb units are formed with light influence of the tetrahedral Ge network, which causes only negligible changing of the partial pair distribution functions, coordination numbers, and bondangle distributions. The GeSb bonds show a broad distribution at 3.8 Å, which suggests the existence of connection between Getetrahedral and Sbpyramidal units through Se atoms. Nevertheless, the GeGe bonds indicate connections between the Getetrahedral, even if in the literature only theoretical bonding is reported. Based on these findings we suppose that a few numbers of Geclusters exist, which are connected to the Sbpyramids. From the values of bond lengths and coordination numbers, we can conclude that the network structure is constructed through connection of tetrahedral GeSe_{4} and trigonal SbSe_{3} structural units. The average coordination numbers vary with glassy composition, as it follows from Figure 4. In all the studied samples, the concentration of the Se atoms is constant. With increasing of Sb concentration, coordination of Ge atoms becomes close to 4, while the coordination of Sb atoms becomes close to 3, both coordination sites being close to theoretical ones. These results are in agreement with the literature and support formation of tetrahedral Ge and pyramidal Sb units [19, 29, 37]. For the Se atoms, the coordination distribution changes in opposite direction, and with increasing of Sb concentration the SeGe coordination numbers decrease and the SeSb coordination numbers increase. This indicates that Se atom prefers to bind to Sb atom rather than Ge atom.
From the above considerations we can conclude that the changes in the distribution of the chemical bonds from the Se_{60} compositions with average coordination numbers Z < 2.67 to the compositions with Z > 2.67 are responsible for the structural rearrangement of the glassy network [5, 6, 13]
3.2. FTIR Spectra Analysis
The FTIR reflectance spectra in dependence on the index x (Ge content) are presented in Figure 6. They show considerably rich set of bands because unlike the crystal structure, the lack of symmetry in amorphous material changes the selection rules and, thus, some forbidden IR modes become active. The spectra present well pronounced reflectanceabsorbance bands of collective lowfrequency vibrations. Although the spectral change with the Ge content is very small, there are bands which can be assigned to the vibrations affected by the x variation.
The band at 250 is characteristic for binary materials [12, 38]. With increasing Ge and with introducing Sb in our Se_{60} samples the band becomes larger and more intensive. As we have already established that in Se_{60} glasses structural transformation occurs at x= 2527 at.% [6], we assume that GeSe_{2} and GeSe_{4} units coexist [5, 10, 13] together with SeSe bond vibration (shoulder at 288 ) [8]. With increasing the Ge content and, respectively, decreasing the content of heavier Sb atoms, these bands move to shorter wavelengths, as seen in Figure 7, where a peculiarity appears at x=27 at.%, corresponding to an average coordination number of Z=2.67.
(a)
(b)
The broad and structured band at 160210 is also sensitive to the x variation. Its components at 168, 187, and 203 are reduced in intensity by increasing the Ge content. In [5, 39] the authors have discussed Raman spectra in this spectral region assigning the measured frequencies to the dynamics of the tetrahedral GeSe_{4} vibrations with addition of Sb atoms and to the appearance of pyramidal SbSe_{3} vibrations. Moreover, the heteropolar SbSe and GeSe bonds vibrational modes have close position at 190 and 200 , respectively [5, 38]. The distinct peak around 168 can be connected with formation of GeGe bonds by crosslinked Ge atoms in the Ge_{2}Se_{6/2} chains (Se_{3}GeGeSe_{3} units) [5, 40, 41]. We are convinced that these modes are responsible for forming the complex band as IR active due to the lack of symmetry in our amorphous samples, as it was obtained by FTIR transmission measurements in [10, 21].
The band picked at 150 with a shoulder at 157 does not shift with x but its intensity varies (see Figure 8). It could be related to the SbSe (at small x) and to the GeSe (at higher x) nonsymmetric vibrations, respectively, [8, 21]. At the highest value of x=35 at.%, the band is slightly enlarged thus showing the coexistence of these vibrations.
The main bands in the terahertz range, 106 and 74 , belong to the vibrations of GeSe_{4} tetrahedral and respectively to SbSe_{3} pyramidal units [8, 21]. Because of these complex structures, they are surrounded with many weak peaks and shoulders. In Figure 8, it can be seen that the band intensities as function of x evolve in opposite directions, following the variation of the Ge and Sb content, respectively.
Bands in the FTIR spectra, located in the 250320 region (Figure 6) have very low intensity and a tendency to vanish by increasing the Ge at.% and decreasing the Sb at.%, respectively. They may be attributed to several vibrations of SeSe, GeGe, and GeSb bonds in modified GeSe_{4}  structural units [21, 38, 41].
In the 450350 spectral range, a very broad band, centred at 420 and with a weak shoulder around 340 , is observed. It is independent on the glassy composition and is related to vibration of oxygen impurity atoms in GeO bonding [42, 43]. The presence of oxygenrelated impurity bonds in these GeSbSe films has been detected by infrared ellipsometric measurements performed in the 400 4000 spectral range [44].
From the study of the basic chemical bonds vibrational modes in chalcogenide Se_{60} films considering the FTIR reflection spectra at oblique (75°) incidence radiation, we obtained specific dependences of the band’s shift and intensity on the film composition. Figures 7 and 8 show features around x=27 at.%, thus confirming the earlier published model of the topological phase transition to a stable rigid network consisting mainly of SbSe_{3} pyramidal and GeSe_{4} tetrahedral clusters. These results support the RMC modeling, which reveals that through connection of these GeSe_{4} and SbSe_{3} structural units, it is constructed a GeSbSe network structure.
4. Conclusions
Binary Ge_{40}Se_{60} and ternary Se_{60} glasses with x=35, 32, 27, 20, and 15 at.% compositions have been synthesized. Their structural properties have been investigated by neutron and Xray diffraction measurements and RMC simulation procedures, in which all the possible chemical bonds in the glasses are taken into consideration. All specimens are fully amorphous in nature as confirmed by the ND and XRD patterns. It is revealed that addition of Sb atom to the binary GeSe glass does not change significantly the basic Getetrahedral structural units but leads to their distortion. With increasing of Sb concentration, welldefined Sbpyramidal units are formed in the ternary glass structure. The Se_{60} glassy network builds up from GeSe_{4/2} tetrahedra and the SbSe_{3/2} pyramid units, connected through 2coordinated Se atoms. Therefore, we may conclude that the “structural unit”based description of the RMC results is one possible way of interpreting the measured diffraction data.
The FTIR reflection spectra of chalcogenide Se_{60} films studied in the terahertz spectral range at oblique (75°) incidence radiation showed characteristic bands related to SbSe and GeSe chemical bonds vibration in SbSe_{3} pyramidal and GeSe_{4} tetrahedral units, respectively. The peculiarities in the compositional dependences of the band positions and intensities confirm the existence of a topological phase transition in the Se_{60} glasses around a critical Ge content of x=27 at.%., corresponding to an average coordination number Z=2.67.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
The authors would like to thank Dr. Martin von Zimmermann for assistance in using BW5 beamline, under Hasylab Project No. I20100116EC. The authors also acknowledge thanks to V. Pamukchieva for synthesizing the studied materials. The support from the Hungarian, Bulgarian, and Romanian Academies under the 20142017 Collaboration Agreements is highly appreciated. K. Antonova and A. Szekeres thank the European Regional Development Fund, Ministry of Economy of Bulgaria, Operational Programme “Development of the Competitiveness of the Bulgarian Economy” 2007–2013, Contract No. BG161PO0031.2.040027С0001, for purchasing the BRUKER spectrophotometer Vertex 70. N. Dulgheru and M. Gartner gratefully acknowledge the support of the research infrastructure under POSCCEO 2.2.1 INFRANANOCHEM  project, No. 19/01.03.2009.
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