Role of S/Se replacement on the structure of Ge20Se80-xSx glasses

The effect of S-content on the medium-and short-range order structure of Ge20Se80−xSxx=0,15,30at%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left(x=0,15,30 \mathrm {at}\%\right)$$\end{document}, has been investigated by using high-energy X-ray diffraction. Medium-range order changes, as illustrated by the parameters of the first sharp diffraction peak, were discussed in the light of the microcrystalline model. The short-range order parameters have been obtained by the analysis of the first two peaks in the curve of the total radial distribution function. The current results indicate that S-atoms enter the host network of the stiffness composition (Ge20Se80) as compensation of Se-atoms.


Introduction
In contrast to oxide glasses, chalcogenide glasses have semiconductor-type band gap, high refractive index, large third-order nonlinearity, and photosensitivity whilst being free of absorption across the whole of the near-and midinfrared [1][2][3]. Such properties enabled many chalcogenide-based applications to be developed in divers fields including, photonic, medicine, military, and environmental sensing, [4,5]. In addition, chalcogenide glasses seem to be one of most promising materials for catalysts and anticorrosion media [6,7]. Consequently, understanding the short (SRO) and medium-range order (MRO) structure of these chalcogenide glasses is important to build predictive models of structure-property relationships [8].
Owing to its technological applications, the structure of the glassy Ge x Se 1Àx system has been extensively studied during the past decades [8][9][10][11][12][13][14][15][16][17]. Within the glass forming region x\0: 43 ð Þ [18], the structure of these glasses is best described in terms of a chemically ordered network (CON) which depend on heteropolar bonds. The Ge atoms are covalently bonded to four Se atoms constituting GeSe 4 tetrahedra, while Se atoms coordinated with two Ge or Se atoms, depending on the concentration x.
Of all the different compositions of Ge x Se 1Àx , the composition Ge 20 Se 80 acquires a special interest.
According to mean-field constraint-counting theory [19,20], the composition Ge 20 Se 80 is considered as a milestone. The network in the range x\20 is elastic ''floppy'' or underconstrained, and in the range x [ 20 it becomes ''stressed-rigid'' or over-constrained. The network of the composition Ge 20 Se 80 is rigid or isostatic. The number of constraints per atom at this composition equals the degree of freedom. So, this composition constitutes a ''stiffness'' threshold between these excessive situations. Numerous experiments have been performed to show this threshold on the physical properties, various properties have shown extrema at this composition. Thermal expansion, isothermal compressibility, and macroscopic density, these properties show minimization at x = 20 [21,22]. Also, valance band and conduction band photoemission spectral exhibit a special character in this composition [23]. Furthermore, this composition shows a maximum in the pressure transition at which the semiconducting network changes into a metallic crystalline phase [24 and refs. therein].
Considerable effort has been devoted to elucidate the effect of S/Se replacement on the structure of Ge Se 1Àx S x ð Þ 2 [25][26][27][28]. The conclusion is that the structure is a combination of GeSe 4Àn ð Þ=2 S n=2 tetrahedra units n=0-4 ð Þ. Rather less attention has been paid to studying the effect of S/Se replacement on the structure of Ge 20 Se 80Àx S x glasses. Results of Raman studies on bulk and thin films of this system have shown that, first: replacing Se with S leads to formation of both GeSe 4Àn ð Þ=2 S n=2 tetrahedra and Se n chains, and second: The structure of Ge 20 Se 80Àx S x glasses is well described by chemically ordered network model [29,30].
The purpose of the present work is to investigate shortand medium-range order structure of Ge 20 Se 80-x S x (x = 0, 15, 30 at%), by using the method of high energy X-ray diffraction.

Sample preparation
Chemically pure Ge, S and Se (99.999%) are weighted according to the desired composition. Their mixture is immediately sealed in a silica glass ampule of 6 mm in external diameter and of 50 mm in length. Contents of the ampoule were sealed under vacuum of 10 -4 torr. The ampoule is then heated in programmable electric furnace. The temperature is slowly raised up to 1273 K and the melt is kept at this temperature for 24 h. The ampoule was rotated during the melting at regular intervals to achieve homogenous mixing. The glassy samples of Ge 20 Se 80-x S x of x = 0, 15 and 30 at% were produced by quenching the melt-in ice water mixture. The macroscopic densities of the studied system were determined at room temperature by the Archimedes method using distilled water as the immersion fluid.

High-energy X-ray diffraction
High-energy X-ray diffraction experiments were carried out, using X-rays of energy 86.6 keV (k ¼ 0:1431 A) at room temperature, at the beamline ID-15-B ESRF Grenoble-France. This high energy provides diffraction data over higher values of k k ¼ 4psinh=k ð Þ , leading to high resolution in real space [13].The prepared Samples were gently crushed into fine powder and then sealed in 1.2 mm diameter KaptonÒ capillaries and subjected to X-ray diffraction experiments in transmission geometry. A Perkin-Elmar large area 2D image plate detector was placed centered on and perpendicular to the incident beam 198 mm behind the sample. The sample-detector distance was calibrated using a NIST CeO 2 standard of known lattice parameter. Raw 2D diffraction pattern was corrected for background and then, 1D powder diffraction patterns were obtained by integrating around the Debye-Scherrer rings on the image plate images using the program Fit2D [31]. 1D background-corrected data were corrected for polarization, absorption, fluorescence, and Compton scattering [32,33]. Then, the coherent intensity I coh k ð Þ was normalized to electron units per atom, I coh eu k ð Þ, using Krogh-Moe -Norman method [34].The total structure factor, S k ð Þ, is obtained from I coh eu k ð Þ as follows [35]: where hf i ¼ P m i¼1 x i f i k ð Þ and hf 2 k ð Þi ¼ P m i¼1 x i f 2 i k ð Þ, where x i and f i k ð Þ are, respectively, the atomic concentration and X-ray atomic scattering factor of the atom i. To get real-space structural information, the total radial distribution function, T r ð Þ, has been obtained by Fourier transformation of the reciprocal space S k ð Þ; where r is the radial distance, q r ð Þ is the local atomic number density, and q 0 is the average atomic number density. These stages of data treatments were done with the aid of PDFgetX3 program [36]. The average coordination number, g, around any atom in a spherical shell between radii r 1 and r 2 is given by [37]; 3. Results and discussion 3.1. Reciprocal space properties Figure 1 shows the measured SðkÞ versus k for Ge 20 Se 80- x S x glasses. If all corrections to the experimental data were known accurately and if the coherent and incoherent scattering factors were correct, SðkÞ will oscillate smoothly along the value one at large k-values [25,38]. This condition is satisfied, as shown in Fig. 1. The effect of S/Se substitution on the atomic arrangement of reciprocal kÀ space showed be evident in the characteristics of the first two peaks of SðkÞ. The first peak is called the first sharp diffraction peak (FSDP), observed at low kÀ values (0:8\k\1:6 Å . -1 ) in SðkÞ curves of network-forming glasses and liquids. The second peak is called the Principle Peak (PP). The FSDP is more sharp comparing with the other peaks, and so it was named. Appearance of this peak is frequently considered as a signature for some kind of structure ordering at MRO [39,40]. Origin of this peak-and hence the origin of MRO in non-crystalline materials is still controversy and, to some extent, vague subject. Various models have been proposed to account for the structural origin of the FSDP, [41][42][43][44][45][46]. Till now no theory can comprehensively and uniformly explain the origin of this feature. Sometimes, these comprehensive and unification were considered as a priority for accepting any theory or explanation articulate for MRO in no-crystalline materials [46,47]. Parameters of the FSDP (position k 1 , width Dk 1 and height I 1 ) are normally used as a criteria for the degree of MRO. In this context, MRO is measured by I 1 , characteristic length R ¼ 2p=k 1 and coherence length L ¼ 2p=Dk 1 (where Dk 1 is the full-width at half-maximum of the FSDP) [39,48] The position of FSDP is often associated with oscillations in real space. These oscillations reflect some repetitive characteristic length R between the structural entities [39,48]. Quantitively, it is possible to scale MRO using Debye equation [49]. The scattering intensity curves are deduced from a superposition of few Debye interference functionssins=s, where s ¼ k Á r with r is the period of the interference function. The maxima positions of the function sins=s are given by the conditionsk Á r ¼ const., with const: ¼ 7:728; 14:062; . . . . Now, if the FSDP is characterized by real distance (characteristic length) R corresponding to reciprocal space characteristic lengthk 1 , then R may be estimated as R % 2:5p=k 1 [10,50]. Similar relations were concluded by several author [51,52]. Another estimation of the lengthR, based Bragg's law, leads to R ¼ 2p=k 1 . The first estimation is more probable because, from ono side, it's a direct result of Debye formula, and from the other side Bragg's law is applicable only when interference occurs over a large number of regularly spaced layers, while in the case of non-crystalline materials the number of such layers that may be considered as regularly spaced is not so large [50]. Nevertheless, the difference between the two methods is not so large, and we remarked that some authors used the first, and others used the second method freely. The correlation length,L, over which such quasi-periodic real-space density fluctuations are maintained, can be obtained from the full width at half maximum,Dk 1 ; L ¼ 2p=Dk 1 [53].
Careful measurements of the FSDP had shown that it can be approximated well by a Lorentzian curve [54,55]. Thus, We used Lorentzian approximation to evaluate the FSDP parameters. Figure (1c) shows the fitting results of Ge 20 Se 80Àx S x samples withx ¼ 0. The characteristic length R and the correlation length L are calculated from the wellresolved FSDP for all samples and are given in Table 1. Table 1, shows that increasing S content leads to slight growth in the intensityI 1 . The same features was observed with S/Se replacement in Ge(Se 1-x S x ) 2 , Ge 3 (Se 1-x S x ) 4 , Ge(S)Se 2 glasses [26,44,56]. On the other side, both k 1 and Dk 1 increase, which means decreasing both R andL, respectively. Conversely, increasing I 1 with increasing Scontent is accompanied by decreasing in the principle peak (PP) position atk PP ¼ 2:0 A À1 . The PP is associated with some extended-range order, which is related to a propagation of short-range ordering [12,57]. Decreasing the intensity of PP would reflect some distortion on SRO with S/Se replacement. This will invstigate later. The opposite behaviors of the FSDP and the PP are frequently observed with S/Se replacement [26,56]. At first glance, the simultaneous increase in I 1 and Dk 1 might be a contradiction. To understand these features, we should have a look at the development of the MRO on Ge(S, Se) glasses. Analysis MRO of the Ge x Se 100-x has been frequently considered [58][59][60]. According to the models which ascribe the FSDP to microcrystalline origin [41,42,62], the composition Ge 20 Se 80 lies in the region of 15\x\0:33 in which GeSe 4/2 units agglomerate into a mixture of corner-sharing ( CS) and edge-sharing (ES) [10,26], resulting in the layerlike structure similar to that of HT-GeSe 2 [62,63]. Prevailing view is that the FSDP originated from correlations containing Ge atoms [26,56,58,59]. The FSDP is also observed in the partial static-structure factor S GeÀSe ðkÞ [64,65]. In the floppy glass region of Ge x Se 1-x glasses (x 20 at%), the FSDP has two contributions of Ge-Ge and Se-Se correlations [66,67]. In connection with MRO of Ge-S system, it was considered that the FSDP of GeS 2 is evoked by 2D-cluster structure due to rings [68] or layerlike outrigger rafts [69] as a remanence of the high temperature layer-like crystalline structure [70]. In GeS 2 the FSDP has a large contribution from Ge-Ge correlations [12]. Furthermore, the results of neutron diffraction show that the height of FSDP shows significant increasing with the transformation from Ge 20 Se 80 to Ge 20 S 80 [71]. In addition, it was shown that in chalcogen-rich system the tendency of Se atoms to form Se-Se chains is higher than that of S atoms, which prefer to bond with cation atoms [25, 73, 74, (ref. 46 in [74])]. Increasing of Dk 1 is accompanied by arising of new correlation characterizing the MRO of Ge-S. Therefore, we have three contributions for MRO, interchains Se-Se [75], interlayer structure of Ge-Se [66], and MRO of Ge-S. The difficulty arises because of the unresolved adjacent three contributions which overlap the positions. Evidence for this comes from the results of inelastic scattering of low energy neutrons [76], where the line associated with either edge-sharing tetrahedra or a vibrational mode of the Se-Se bonds on the edges of ''outriggers rafts'', is not resolved as a separate peak. Consequently, accruing of three types of MRO leads to broadening the FSDP. So, as we think, the results of Dk 1 cannot reflect a distortion on the MRO of our samples. The slight increase in both I 1 and k 1 could be explained according to the differences in the MRO amplitudes of Ge-Se and Ge-S. It is well-known thatf S k ð Þ\f Se k ð Þ, then the growtgh of I 1 implies that MRO of this glasses not arise by correlations include S-S or S-Se atoms but arises by correlations containing Ge (Ge-S, and Ge-Se) [56]. We have explained above that the ability of S atoms to form bonds with Ge is higher than that of Se atoms. Then, we can consider that increasing in Ge-S correlations improve the MRO of our system which in turn increase the height I 1 . This explanation is justified if we take into account the higher value of FSDP position of Ge-S system comparing with that of Ge-Se [42,47], which explains the shift of k 1 of our glasses towards higher values.

Short-range order of Ge 20 Se 80-x S x glasses
The function T r ð Þ is normally used for extracting information regarding SRO [54]. The parameters describe SRO of glassy Ge 20 Se 80-x S x samples such as the bond length and the coordination number can be extracted from the peak positions and the area under the peaks, respectively. Very high k-range is required to get high real-space resolution [78]. Shortness of the applied wavelength (0.1431 Å ), combined with an appropriate data collection strategy was enabled to record data over a sufficiently high k-range. In these data k max = 24 Å -1 , which permits real space resolution limit of dr ¼ 2p=k max ¼ 0:26 Figure 2 shows TðrÞ curves of our system. The curves show two strong peaks in r-range of 2:2 A\r\4:2 A. In general, TðrÞ of Ge 20 Se 80 glass is in a good agreement with previously published data [14,15,24,80,81]. It is easy to note some general behaviors at the first glance. With increasing S concentration from 0 to 30 at%, the first peak at r % 2:36 A shows slight shift to lower r-values with some decreasing in height and increasing in width. To understand these behaviors, we assigned in Fig. 3 the positions of Ge-Se, Se-Se, and Ge-S bonds, in crystalline GeSe 2 , and GeS 2 , respectively [82][83][84]. The structure of Ge 20 Se 80 is Table 1 The position (k 1 ), the characteristic length R, the full width at half maximum Dk 1 , the correlation length L and the height I 1 of the FSDP of Ge 20 Se 80-x S x glasses frequently studied [14,15,24,58,74,[84][85][86][87][88]. The major attitude is that SRO consists of GeSe 4 tetrahedra connected through Se-Se bonds. This is evidently in Fig. 3. The position r 1 of the first peak at maximum-height coincidences with the length of Ge-Se and Se-Se bonds (2:36 A) [84]. This gives evidence that the first peak of TðrÞ Fig. 2 Full-range plot of the total distribution function T r ð Þ of Ge x Se 80-x S x glasses Fig. 3 The function T r ð Þ of Ge x Se 80-x S x glasses. solid lines represent published bond lengths and interatomic distances. The correlations at 3.47 Å are ascribed to second neighbors of Ge atom as in Ge-Se-Se, or Ge-Se-S curve in Ge 20 Se 80 is basically governed by Ge-Se and Se-Se bonds. These two bonds contribute almost equally to the area of the first peak of TðrÞ curve [84]. Increasing S-content at the expense of Se-content is accompanied by replacement of Se atoms at the corners of GeSe 4 tetrahedra by S atoms. Ge-S bond length (2:22 A) is shorter than both Ge-Se and Se-Se bonds [26,83], which is the reason why the first peak shift to lower r-values with increasing S-content. The slight decrease in height and increase in width of the first peak with increasing S content may due to a small distortion in SRO with the small S percent incorporation within the lattice of Ge-Se glasses [90].
According to X-rays and neutrons diffraction data, T(r) of the glassy system Ge x Se 100-x x ! 20at% ð Þshows small features (a weak peak or shoulder) at r % 3:0À 3.3 A. Anomalous x-ray scattering results show that the height of these features at r ¼ 3:3 A increases with decreasing x from x = 0.23 to x = 0.195 at% [30], while results of neutron diffraction show increasing the area of this peak on TðrÞ curve with increasing x [14,15]. These structures may be assigned to the correlation between a Ge atom at a tetrahedral center and a Se atom additionally attached to a tetrahedron corner, i.e., the Ge-(Se)-Se correlation [30]. Another viewpoint ascribes these features to Ge-Ge of edge-sharing GeSe 4 tetrahedra, like those in Ge 33 Se 67 [14,15,24,82,92]. In fact, weakness of these features in addition to the spurious ripples, produced by the truncation the limited k-value, prevent a detailed discussion of the  [91]. Molecular dynamic modeling of liquid Ge 20 Se 80 , however, had shown that Ge-Ge correlation of corner-and edgesharing spread out on a broad peak between 3 and 4 A [24]. It is noteworthy that neutron diffraction study performed the absence of these features in S-enriched Ge-S system, with assertion to the existence of corner-sharing tetrahedra [93]. This may explains vanishing this shoulder with increasing S-content, look Fig. 3. At the same time, this vanishing is accompanied by strengthen a new one atr % 3:47 A. The position of this structure is near the position r ¼ 3:47 A previously observed in Ge-S and Ge(Se 1-x S x ) 2 [26,83]. The origin of this structure is attributed to second neighbors of Ge atom as Ge-Se-Se, or Ge-Se-S in which highly crimped CS tetrahedra are connected through Se-Se or Se-S chains (look Fig. 3 in ref. [85] and Fig. 5 (d) in ref. [84]). The possibility of rocking Se-S(Se) bridging atoms causes changing the position between nearby GeSe 4 tetrahedra. This behavior was used to explain the abrupt increase in the mole polarization around the composition Ge 20 Se 80 [94]. This effect in our case is accomplished by replacing some Se atoms with S atoms as shown, schematically, in Fig. 4.
The maximum height of the second peak is located at r 2 max % 3: 83 A, which is in a good agreement with the previously published data in case of Ge 20 Se 80 [14,15,95]. This location corresponding to the Se-Se intratetrahedra distances. The bond angle h h ¼ 2sin À1 r 2 max =2r 1 ð Þ¼ À 108:47 o Þ are in a good agreement with the tetrahedral angle [17,24,64,90]. With increasing S-content, this peak exhibits some shift towards lower r-values. This behavior is expected if we consider replacement Ge-Se bonds by Ge-S of shorter bond length, as we allowed before, see Fig. 4.
To examine SRO parameters, the first peak of TðrÞwas fitted using Gaussian function, [77]: where r 1 and u 1 represent, respectively, the position and the half-width at half-height of the first peak. The amplitude a i is related to the area (the weighted average coordination number g i ) by: Figure 5 shows the results of Gaussian fitting and SRO parameters. With S/Se replacement, the weighted coordination number g 1 vary slightly around an average value of 2.7. This refers to that S-atoms enter as compensations of Se atoms. It is well known that the SRO structure of Ge 20 Se 80 can be well explained using chemical order network model CONM [24,84]. Therefore, the comparable values of g 1 give us a semi-consensus that Ge 20 Se 80-x S x glasses are governed by CONM [26,30]. Investigation of this statement needs more assertion through calculating partial-structure factors and paircorrelation functions by using reverse Monte Carlo simulation and /or molecular dynamic simulation.
It is worth noting that, according to these results, replacing Se atoms with S-atoms transfers the structure of Ge 20 Se 80-x S x from Ge 20 Se 80 like-structure to Ge 20 S 80 likestructure, and this is accompanied by increasing the ionic character of the compound [88]. This gradually transfers the applications of these materials to more ionic characterdependent properties.

Conclusions
High energy X-ray diffraction was applied to study the effect of S-atoms addition on both short-and medium-range order of Ge 20 Se 80-x S x (where x = 0, 15 and 30 at%) chalcogenide glasses.. The origin of the first sharp diffraction peak on the structure factor was discussed according to the microcrystalline model. The results refer to increasing S-content leads to enhancement of the medium range order. Short-range order parameters indicate that S-atoms inter the host network of the stiffness composition Ge 20 Se 80 as compensation of Se-atoms.
Author contribution AFE Data analysis and processing, Writing manuscript, discussion, preparing revised manuscript. MD supervision and discussion. MSE sample preparation, Data analysis and processing. SM Sample preparation.
Funding Openaccess funding provided by The Science, Technology & Innovation Funding Authority (STDF) incooperation with The Egyptian Knowledge Bank (EKB). This research work was funded by Science UP Faculty of Science grants, project number 6601. Therefore, authors gratefully acknowledge technical and financial support from the Academy of Science Research & Technology (ASRT).
Data availability The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

Declarations
Conflict of interest Authors declare that they have no conflict of interest.
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