Short range order and topology of Ge$_{x}$Ga$_{x}$Te$_{100-2x}$ glasses

Chemical short range order and topology of Ge$_{x}$Ga$_{x}$Te$_{100-2x}$ glasses was investigated by neutron- and x-ray diffraction as well as Ge and Ga K-edge extended x-ray absorption fine structure (EXAFS) measurements. Large scale structural models were obtained by fitting experimental datasets simultaneously with the reverse Monte Carlo simulation technique. Models, relying only on experimental data and basic physical information without constraining the average coordination numbers, give 3.9 - 4.1 for the number of the atoms in the first coordination sphere of Ge atoms, while the average number of first neighbors of Ga atoms scatters around 3.8. The average coordination number of Te atoms is significantly higher than 2 for $x$ = 12.5 and 14.3. It is found that the vast majority of MTe$_4$ (M=Ge or Ga) tetrahedra have at least one corner sharing MTe$_4$ neighbor.


Introduction
Due to their broad infrared transmission window glassy tellurides are extensively used in various fields of IR optics. The general strategy to find tellurides with excellent glass forming ability is to add a third component to the prototype Ge-Te system. Alloys with Ge-X-Te (X = Ga, As, Se, I, Ag, AgI) composition often possess a broad supercooled liquid region that makes it possible to shape bulk infrared lenses or draw fibers transmitting up to at least 18 μm [1 -3]. It has been shown recently that in binary Ge x Te 100-x (14.5 ≤ x ≤ 23.6) glasses the total average coordination numbers of Ge and Te atoms arewithin the experimental uncertainty -4 and 2, respectively [4]. It has also been revealed that Ge-Te glasses are chemically ordered: Ge-Te bonds are clearly preferred to Ge-Ge ones, even if Ge-Ge bonds can be found in Ge 23.6 Te 76. 4 . Alloying affects the structure of the host Ge-Te network in different ways. Se and I bind predominantly to Ge and do not change the average coordination numbers of Ge and Te [5,6]. In Te-poor compositions As atoms bind to Ge, As and Te atoms but the average coordination numbers of Ge and Te atoms do not change here either [7]. On the other hand, in GeTe 4 -AgI glasses the average coordination number of Te atoms is significantly higher than 2 even if only Ge/Te neighbors are taken into account [8]. Therefore, the topology of the host Ge-Te network changes significantly upon adding AgI.
The first experimental study of Ge-Ga-Te glasses combining diffraction techniques and EXAFS in the framework of reverse Monte Carlo (RMC) simulation technique [5] reported that the total coordination number of Te is 2.36 ± 0.15 while the average number of neighbors of Ga atoms is about 3 in Ge 11.1 Ga 11.1 Te 77.8 (the coordination number of Ge atoms was constrained to be 4). As the average coordination number of Ga was reported to be around 4 in several amorphous systems (e.g. Ga 50 Se 50 [9], Ga-doped Ge:H [10], CsCl-Ga 2 S 3 [11] and CsCl-La 2 S 3 -Ga 2 S 3 [12]) the above study was followed by a further investigation of Ge 11.1 Ga 11.1 Te 77.8 .
In the experimentally constrained density functional (DFT) study of Voleská et al [13] the starting configuration of DFT simulation was obtained by fitting diffraction and EXAFS datasets simultaneously with RMC. The DFT-optimized configuration was then 'experimentally refined' again by RMC by using the DFT bond angle distributions as constraints. This configuration reasonably reproduced the experimental data and had a total energy only 33.8 meV/atom higher than that of the original DFT structure. The average coordination numbers of Ga, Ge and Te atoms were 4.08, 3.77 and 2.59, respectively.
While the coordination number of Ga is rather close to the values found in refs. [9 -12] the average number of neighbors of Te atoms is significantly higher than the experimentally determined coordination number (2.36 ± 0.15). We note here that due to its high concentration in Ge 11.1 Ga 11.1 Te 77.8 the average coordination number of Te can be deduced from experimental data with a relatively low uncertainty.
The discrepancy of experimental (RMC) and DFT values is due the shallow minimum of the Te-Te partial pair correlation function in the DFT-generated model. More recent DFT studies emphasized the importance of the choice of exchange-correlation functionals and the proper treatment of van der Waals interactions [14 -16]. It was demonstrated that by using Becke-Lee-Yang-Parr (BLYP) exchange-correlation functional and van der Waals forces in modelling amorphous tellurides some problems of earlier DFT simulations (e.g. high number of Ge atoms in octahedral environment in a covalent system, too high bond distances) can be avoided. The total coordination number of Te in GeTe 4 is also closer to 2 though the deviation from the experiment-based value is still significant (2.31 vs. 2.00 ± 0.1 in Ge 18.7 Te 81.3 [4]).
In case of Ge-Ga-Te glasses the main difficulty of experimental structure determination is that Ga and Ge possess similar scattering properties both for X-ray and neutron diffraction where Z is the atomic number and b is the coherent neutron scattering length). As Ge and Ga are neighboring elements, Ga K-edge EXAFS signal is limited by the Ge K absorption edge. Another problem is that the mean Ga-Te nearest neighbor distance is between the Ge-Te and Te-Te bond lengths [14], therefore Ga-Te peak parameters (especially the coordination number) are more sensitive to the 'cross talk' between overlapping peaks.
Even if the uncertainty of structural parameters is relatively large for a single composition, reliable information can be obtained from experimental data by measuring a concentration series. For this reason, we studied the structure of Ge x Ga x Te 100-2x glasses by combining X-ray and neutron diffraction data with Ge-and Ga K-edge EXAFS measurements in the framework of the reverse Monte Carlo simulation technique. Short range order parameters of Ge-Ga-Te glasses are compared with those of amorphous Ge-Te, Ge-Ga-S and Ge-Ga-Se alloys as well as with models of Ge-Ga-Te glasses obtained by ab initio molecular dynamics.

Sample preparation
Four Ge-Ga-Te glasses of nominal compositions Ge 7.5 Ga 7.5 Te 85 , Ge 10 Ga 10 Te 80 , Ge 12.5 Ga 12.5 Te 75 , and Ge 14.3 Ga 14.3 Te 71.4 were used for both neutron and X-ray experiments.
Starting elements from high-purity, germanium pellets (99.999%, Goodfellow), gallium ingots (99.9995%, Sigma-Aldrich), and tellurium ingots (99.9999%, Sigma-Aldrich) were first weighed in stoichiometric quantities (for a total batch of ∼3 g) and introduced in a cylindrical silica tube (11 mm inner diameter, 1 mm thick). The tube was subsequently evacuated under secondary vacuum (10 -5 mbar), sealed and heated up at 1220 K in a furnace with a low heating rate of 10 K/h. The molten batch was held at this temperature for three days and finally quenched in a salt−ice-water after an annealing step of two days at 1073 K.
Neutron diffraction (ND) measurements were carried out at the 7C2 diffractometer of LLB (Saclay, France). The wavelength of incident neutrons was 0.723 Å. Powdered samples were filled into vanadium sample holders of 6 mm diameter and 0.1 mm wall thickness. The wavelength and detector position were determined by measuring a standard Ni powder sample. Raw data were corrected for background scattering and detector efficiency.
High energy X-ray diffraction (XRD) measurement was carried out at the Joint Engineering, Environmental and Processing (I12-JEEP) beamline at Diamond Light Source Ltd (UK). The size of the monochromatic beam was 0.3 × 0.3 mm 2 . A CeO 2 reference sample (NIST Standard Reference Material 674b) was measured at different distances to determine the energy of the incident beam, the sample-to-detector distance, the position of the beam centre and the tilt of the detector. The wavelength of the incident beam and the sample-to detector distance were 0.1255 Å (98.768 eV) and 336 mm, respectively. Collected 2D diffraction data were integrated into reciprocal-space using the DAWN software [17]. X-ray structure factor, S X (Q), were extracted from integrated raw data using the PDFGetX2 software [18].
Ge and Ga K-edge EXAFS spectra were measured in fluorescence mode at beamline P65 of the Petra III source. Samples were finely ground, mixed with cellulose and pressed into tablets. Monochromatic radiation was obtained by a Si(111) double crystal monochromator. χ(k) curves were obtained using the Viper program [19]. Raw χ(k) signals were first forward Fourier-transformed using a Kaiser-Bessel window. The resulting r-space curves were back transformed using a rectangular window over 1.1-2.4 Å.

Reverse Monte Carlo simulations
The reverse Monte Carlo (RMC) method [20] is robust tool to obtain large three-dimensional structural models consistent with the supplied (experimental and/or theoretical) data sets. It can be used with any quantity that can be obtained from the atomic coordinates, such as total structure factors from ND or XRD experiments or EXAFS curves. A strength of the method is that the data sets can be fitted simultaneously. During the simulation particles are moved around randomly to minimize the differences between experimental and model curves. Finally particle configurations compatible with all fitted data sets (within the experimental error) are obtained. From these configurations short range order parameters (partial pair correlation functions, average coordination numbers etc.) can be calculated.
The RMC++ code [21] was used to produce structural models by fitting simultaneously the experimental data sets. The EXAFS backscattering coefficients were calculated by the FEFF8.4 program [22].
The investigated samples, their estimated densities and the fitted data sets are collected in Table 1. Densities were estimated using literature values of amorphous Ge x Te 100-x [23,24] and Ga x Ge y Te 100-x-y glasses [25 -29]. The simulation boxes contained 10000 atoms for the test runs and 40000 atoms for the final results. Initial configurations were obtained by placing the atoms randomly in the boxes and moving them around to satisfy the minimum interatomic distance (cutoff) requirements. Starting values of the cutoff distances were usually around 85-90% of the sum of the corresponding atomic radii (r Ge  1.25 Å, r Ga  1.3 Å , r Te  1.4 Å) [30], the final values are collected in Table 2 In the final models all M-M type bonds were forbidden by using cutoff values higher than the expected bond lengths. In all simulation runs some low coordination numbers of the atoms (0 for Te, 0 and 1 for Ga, and 0, 1 and 2 for Ge) were eliminated. In the so called 'unconstrained' models only the above coordination constraints were used. The quality of the fits of different models were compared via their 'goodness-of-fit' (R-factor) values: Here Q i are the experimental points while 'mod' and 'exp' refer to model and experiment, respectively. Similar expression is valid for the EXAFS curves.

Results and discussion
The experimental total structure factors (S(Q)) and filtered, k 3 -weighted EXAFS curves  Tables 3 and 4.

Nearest neighbor distances
The Test simulation runs were made in which coordination constraints were used to force Ge and Ga atoms to have exactly 4 neighbors (about 95% of the atoms satisfied this requirement). It was found that the quality of the fits of these models was as good as that of the unconstrained model.
The total coordination number of Te increases with increasing Ge/Ga content (see Table 4). It is around 2 for the Ge 7.5 Ga 7.5 Te 85 glass and significantly higher than 2 for Ge 12. 5  . The first minimum of g TeTe (r) obtained by these simulations is far from zero, thus the second coordination sphere may also contribute to the coordination number of Te.
As in Ge-Te glasses the Te coordination number follows from fitting simultaneously diffraction and EXAFS datasets with RMC simulation [4], the higher coordination of Te in Ge-Ga-Te glasses is due the presence of Ga atoms. It is to be noted that chemical ordering is also different in the two systems. While Ge-Ge bonds can be observed in melt quenched Further experimental and theoretical studies are needed to see whether this is just a coincidence or a certain number of Te-Te bonds is required by the glassy state due to energetic or kinetic reasons. It is to be noted that N Se higher than 2 was found in Ge-Ga-Se glasses also by using various techniques (e.g. ND, EXAFS and RMC [64] or anomalous X-ray scattering and RMC [65]). Moreover, N S coordination number higher than 2 was proposed in amorphous Ge-Ga-S alloys by Raman [57] as well.

Second neighbors
It was found in Ge-Te glasses [4] that It was found that even for the Ge 7.5 Ga 7.5 Te 85 sample about 84% of GeTe 4 and GaTe 4 tetrahedra have at least one corner sharing MTe 4 neighbor (see Table 5). This value seems to be rather high in view of the low Ge/Ga-content of this glass. The average number of Ge and

Prepeak in the ND total structure factor
The neutron diffraction structure factor of Ge x Ga x Te 100-2x glasses has a first sharp diffraction peak (FSDP) or prepeak at q max ≈ 1 Å -1 . (A less pronounced peak can be observed in X-ray diffraction structure factor as well.) Peak positions and heights are given in Table 6. The height of the prepeak is defined as S(q max ) -S(q min ) where q min is the first minimum after the prepeak. For Ge 7.5 Ga 7.5 Te 85 there is only a shoulder therefore we used the q min value of Ge 10 Ga 10 Te 80 . It can be observed that in case of Ge x Ga x Te 100-x glasses the height of the prepeak increases with increasing Ge/Ga content.
The connection of medium range order and prepeak intensity is confirmed by comparing the models of Ge 14.3 Ga 14.3 Te 71.4 obtained with and without fitting neutron diffraction data. Some results of these runs are shown in Fig. 9. It can be observed that models obtained without fitting neutron diffraction data fail to reproduce the prepeak of neutron diffraction structure factors. The other effect of omitting neutron diffraction data from the models is the rather flat first peak of the Ge-Ge partial pair correlation function. A similar behavior can be observed in Ge 18.7 Te 81.3 [4], also shown in Fig. 9. The majority of Ge/Ga atoms are linked to other Ge/Ga atoms via one or two common Te neighbors forming corner and edge sharing tetrahedra.