domain: spi chim

text:
Anatoliy Zavdoveev
email: avzavdoveev@gmail.com

Massimo Rogante

Valeriy Poznyakov

Mark Heaton

Thierry Baudin
email: thierry.baudin@u-psud.fr

Alexandr Gayvoronski

Yuriy Demchenko

Serj Zhdanov

The influence of pulse current arc welding modes on changing the parameters of the weld and HAZ of welded joints made by low alloyed materials

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The influence of pulse current arc welding modes on changing the parameters of the weld and HAZ of welded joints made by low alloyed materials

Introduction

Pulse-current gas metal arc welding (PC-GMAW) is qualitatively different from traditional shielded gas metal arc welding (GMAW), as well as from manual arc welding with modulated current [START_REF] Zavdoveev | Effect of pulsed-arc welding modes on the change of weld metal and haz parameters of welded joints produced with Sv-08kh20N9G7T wire[END_REF][START_REF] Palani | Selection of parameters of pulsed current gas metal arc welding[END_REF][START_REF] Zavdoveev | Development of the PC-GMAW welding technology for TMCP steel in accordance with welding thermal cycle, welding technique, structure, and properties of welded joints[END_REF][START_REF] Tong | Quality and productivity improvement in aluminium alloy thin sheet welding using alternating current pulsed metal inert gas welding system[END_REF][START_REF] Zavdoveev | Features of structure formation and properties of joints of s460m steel made by pulsedarc welding[END_REF][START_REF] Maruo | Effects of Welding Current Waveform on Metal Transfer and Bead Formation in Pulsed MIG Welding[END_REF][START_REF] Rajasekaran | Weld bead characteristics in pulsed GMA welding of Al-Mg alloys[END_REF]. This process is increasingly used in the manufacture of welded structures of aluminum alloys, titanium and structural steels with a strength of up to 500 MPa [START_REF] Berdnikova | Effect of the structure on the mechanical properties and cracking resistance of welded joints of low-alloyed high-strength steels[END_REF][START_REF] Haivorons | Structure and mechanical properties of the heat-affected zone of restored railway wheels[END_REF], as well as wire arc additive manufacturing [START_REF] Cunningham | Cost Modelling and Sensitivity Analysis of Wire and Arc Additive Manufacturing[END_REF], [START_REF] Cunningham | Invited review article: Strategies and processes for high quality wire arc additive manufacturing[END_REF]. This is explained by the fact that PC-GMAW expands the possibilities of controlling the processes of melting and transfer of the electrode metal in different spatial positions, improves the formation of seams, reduces the mixing of the electrode metal with the base metal and the size of the heat affected zone (HAZ) [START_REF] Rajasekaran | Weld bead characteristics in pulsed GMA welding of Al-Mg alloys[END_REF], [START_REF] Murray | Selecting parameters for GMAW using dimensional analysis[END_REF][START_REF] Amin | Pulse current parameters for arc stability and controlled metal transfer in arc welding[END_REF][START_REF] Amin | Synergic control in MIG welding 2-Power-current controllers for steady DC open arc operation[END_REF][START_REF] Lambert | Assessment of the Pulsed MIG technique for tube attachment welding[END_REF][START_REF] Essers | Arc control with pulsed GMA welding[END_REF][START_REF] Dorn | Pulsed current gas metal arc welding under different shielding and pulse parameters; Part 2: Behaviour of metal transfer[END_REF]. This is due to the fact that such well-known companies as Fronius (Austria), Bohler (Germany), ESAB (Sweden) and others, pay considerable attention in their activities to the development and manufacture of equipment for the implementation and expansion of pulse-arc welding process. Much less in the technical literature is the question of the influence of the parameters of PC-GMAW [START_REF] Wu | Effects of single and double pulses on microstructure and mechanical properties of weld joints during high-power double-wire GMAW[END_REF], [START_REF] Sen | Effect of double-pulsed gas metal arc welding (DP-GMAW) process variables on microstructural constituents and hardness of low carbon steel weld deposits[END_REF] on the thermal processes occurring in the HAZ metal of welded joints, and how they affect the structure and mechanical properties of this metal [START_REF] Demarque | Evaluation of the effect of the thermal cycle on the characteristics of welded joints through the variation of the heat input of the austhenitic AISI 316L steels by the GMAW process[END_REF], its resistance to cold cracking and brittle fracture, etc. It is the uncertainty of these issues that constrains the use of pulse-arc welding technologies in the manufacture of metal structures from steels that are sensitive to thermal processes and prone to hardening.

Materials and methodology

To solve this problem, we performed surfacing of the high-alloy welding wire 1.2 mm diameter G3Si1. The surfacing was carried out on 10 mm thick plates made of 9MnSi5 steel (DIN, wt %: C 0.09, Si 0.5-0.8, Mn1.3-1.7). Surfaces were made from the surfacing plates, which measured the parameters of the seams and the HAZ. Pulse current arc welding (f ≥ 25 Hz, PC-GMAW) and pulsed arc welding (f ≤ 25 Hz, PA-GMAW) are distinguished by the frequency of pulses. Using a pulsating arc, the optimal pulsation modes were selected. In this case, the welding mode was as follows: pulse welding current -I p = 140 A, pause current (base current) was 80% of the pulse current I p = 112 A; where I av is the average current of the arc-arc welding, І pulse = 450 А, І pause = 160 А, t pulse and t pause are the pulse duration and pause, respectively. In addition to I av , the effective current of the arc-arc welding also applies:

I ef = 1-d ( ) × I pause 2 + I pulse 2 ( 2
)
where δ = duty cycle. Thus, given the above-mentioned parameters of pulsed-arc welding, I ef results almost 25% higher than I av (Figure 1). Pulse current arc welding (f≥25 Hz, PC-GMAW, Figure 2) and pulsating arc welding (f≤25 Hz, PA-GMAW) are distinguished by the frequency of pulses. Using a pulsating arc, the optimal pulsation modes were selected. In this case, the welding mode was as follows: pulse welding current I p = 140 A, pause current (base current) = 80% of I p = 112 A; arc voltage in the pulse U i = 22 V, arc voltage in the pause U p = 18 V, welding speed = 15 m/h, while the pulse time t i , the pause time t p as well as the current in the pause and duty cycle varied.

Results and discussion

Pulse current gas metal arc welding (PC-GMAW)

When comparing stationery and PC-GMAW modes, it is clear that in PC-GMAW seam roller is more homogeneous and uniform without traces of spraying. Measurements of metal losses on sputtering showed that in pulse-arc welding it decreases by an order of magnitude, from 0.7% in the stationary process to 0.07% in PC-GMAW. Analysis of the cross-section of surfacing performed in different modes showed that the depth of penetration in PC-GMAW increases in comparison with the stationary welding process in the same modes (Table 1). The form of seam penetration in PC-GMAW is significantly different from the process performed by a stationary burning arc. Quantitative analysis showed that with increasing welding current, the width of the seam also increases. The nature of the change in this value is the same for welding with a stationary burning arc, and for PC-GMAW. A similar relationship is observed for the height of the seam. As for the penetration depth, in general, with increasing welding current it increases, but in the case of PC-GMAW, the penetration depth is almost twice as much as in the case of welding with a stationary burning arc (Figure 3). Also, at PC-GMAW, the area of cross section of a seam exceeds the given indicators for welding by a stationary burning arc. The value of HAZ under the root is comparable for both types of welding, and at the root of the HAZ seam during PC-GMAW is less (Figure 3).

Pulsating arc (PA-GMAW)

According to the experiment, it was found that with increasing pause current, the width of the seam increases, with a smaller value of duty cycle corresponds to a larger value of the width of the seam. The height of the seam increases evenly with increasing pause current. The change in the penetration depth has similar patterns, i.e. with increasing pause current increases. Changing the parameters of HAZ under the root is monotonous. The less duty cycle corresponds to large values of HAZ width. It is important to note that the average values of HAZ under the root is lower than when welding stationary burning arc (GMAW).

In the PA-GMAW welding mode -pulse current I pulse = 140 A and a pause current I pause = 112 A (fixed pulse time = 0.5 s) with increasing pause time increases the height of the seam, slightly decreases the width of the seam and decreases the width of the HAZ, and the penetration depth at t p = 0.5 s increases and further practically does not change (Figure 3). In the case of fixing the pause time (0.5 s) and increasing the pulse time, the penetration depth also initially increases and then stabilizes, but confirmation of this fact requires further research. The width of the HAZ changes nonlinearly, and in the case of a fixed pulse time, is less than in the case of GMAW. In the case of fixing the pause time and increasing the pulse time, the width of the HAZ is greater than for PC-GMAW and less than for GMAW.

Welding thermal cycles

The analysis of welding thermal cycles allowed us establishing the following features: in the case of PC-GMAW, the rate of increase of the metal temperature in the coarse-grained HAZ is greater than in the case of GMAW; in the high-temperature region from 1,350 °C to 1,000 °C (stage I), the cooling of the metal when PC-GMAW occurs faster, and in the temperature range less than 1,000 °C (stage II) is slower (Figure 5). The data show that the cooling rate of the metal in the temperature range of the lowest austenite resistance 600-500 °С (stage III) for PC-GMAW is less than in the case of GMAW, and τ 8/1 has close values. The The processes of PC-GMAW and PA-GMAW have greater opportunities to control the weld parameters and the amount of heat input, and could be applied in a wide range of manufacturing problems including wire arc additive manufacturing (WAAM).

  Zavdoveev, Massimo Rogante, Valeriy Poznyakov, Mark Heaton, Thierry Baudin, Alexandr Gayvoronski, Yuriy Demchenko, Serj Zhdanov To cite this version: Anatoliy Zavdoveev, Massimo Rogante, Valeriy Poznyakov, Mark Heaton, Thierry Baudin, et al.. The influence of pulse current arc welding modes on changing the parameters of the weld and HAZ of welded joints made by low alloyed materials. 10th International Conference Mechanical Technologies and Structural Materials, Sep 2021, Split, Croatia. pp.171-176. hal-03049412

  of the arc welding, A Ui, Up -arc voltage in the pulse and in the pause, V Ief -effective current of the arc welding, A arc voltage in the pulse U i = 22 V, arc voltage in the pause U p = 18 V, welding speed equal to 15 m/h, while the pulse time t i and the pause time t p , as well as the current in the pause and duty cycle varied. To detect HAZ, the metallographic samples were macro etched with chlorine iron.Recording of the welding thermal cycles (WTC) of the HAZ overheating section was performed using a 0.5mm Type K thermocouple, installed on the HAZ section, which was heated to a temperature of 1200°C. The following values were selected to assess the effect of pulsed arc welding modes on the weld parameters: I av = 120, 140, 160, 180, 200, 220 A; U = 21, 22, 24, 26, 28, 30 V = 15 m/h; shield gas Ar + 18% CO 2 . The modes for the automated pulsed arc welding were as above mentioned, with: I av = I pulse t pulse + I pause t pause t pulse + t pause[START_REF] Zavdoveev | Effect of pulsed-arc welding modes on the change of weld metal and haz parameters of welded joints produced with Sv-08kh20N9G7T wire[END_REF]

Figure 1 .Figure 2 .

 12 Figure 1. Dependence of the average and effective current from the welding current at PC-GMAW

  that with increasing welding current, the width of the seam also increases. The nature of the change in this value is the same for welding with a stationary burning arc, and for PC-GMAW. A similar relationship is observed for the height of the seam. As for the peculiarities of WTC during PC-GMAW revealed from the graph of the derivative (Figure5b) made it possible to establish that the cooling rate of the metal at the HAZ sections, which are heated to temperatures of 1

Figure 3 .Figure 4 .Figure 5 .

 345 Figure 3. Quantitative characteristics of the parameters of the seams made by GMAW (blue line) and PC-GMAW (red line): aseam width; b -seam hight; c -penetration deeps; d -HAZ in the root (mm)

Table 1 .

 1 Macro samples of surfacing performed in different

modes: PC-GMAW (left), GMAW (right)


Ph.D.; Ildiko Pethes
email: pethes.ildiko@wigner.mta.hu

Andrea Piarristeguy

Annie Pradel

Stefan Michalik

Ruidy Nemausat

Jacques Darpentigny

Pál Jóvári

Ildikó Sincerely

Short range order and topology of Ge x Ga x Te 100-2x glasses

Keywords: chalcogenide glasses, Ge-Ga-Te, structure, diffraction, EXAFS, RMC

Short range order and topology of Ge Ga Te100-2 glasses I. Pethes, A.

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 [START_REF] Jóvári | Local order in binary Ge-Te glasses -An experimental study[END_REF]. 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. [START_REF] Jóvári | Local order in binary Ge-Te glasses -An experimental study[END_REF] . 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 [START_REF] Jóvári | Structure of Te-rich Te-Ge-X (X = I, Se, Ga) glasses[END_REF][START_REF] Rátkai | Microscopic origin of demixing in Ge 20 Se x Te 80-x alloys[END_REF]. 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 [START_REF] Jóvári | Short-Range Order in Ge-As-Te Glasses[END_REF]. 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 [START_REF] Jóvári | Network Rearrangement in AgI-Doped GeTe 4 Glasses[END_REF]. 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 [START_REF] Jóvári | Structure of Te-rich Te-Ge-X (X = I, Se, Ga) glasses[END_REF] 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 [START_REF] Machado | Extended x-ray absorption fine structure, x-ray diffraction and reverse Monte Carlo studies of an amorphous Ga 50 Se 50 alloy produced by mechanical alloying[END_REF], Ga-doped Ge:H [START_REF] Chambouleyron | Internal stress-induced changes of impurity coordination and doping mechanisms in a-Ge:H doped with column III metals[END_REF], CsCl-Ga 2 S 3 [START_REF] Hindle | Structural analysis of xCsCl(1-x)Ga 2 S 3 glasses[END_REF] and CsCl-La 2 S 3 -Ga 2 S 3 [START_REF] Ramos | Structural characterisation of CsCl incorporation in Ga 2 S 3 -La 2 S 3 glasses[END_REF]) the above study was followed by a further investigation of Ge 11.1 Ga 11.1 Te 77. [START_REF] Jóvári | Network Rearrangement in AgI-Doped GeTe 4 Glasses[END_REF] .

In the experimentally constrained density functional (DFT) study of Voleská et al [START_REF] Voleská | Structure, electronic, and vibrational properties of glassy Ga 11 Ge 11 Te 78 : Experimentally constrained density functional study[END_REF] 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 [START_REF] Jóvári | Local order in binary Ge-Te glasses -An experimental study[END_REF]).

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 (Z Ge =32, Z Ga =31, b Ge =8.185 fm, b Ga =7.288 fm, 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 [START_REF] Chaker | First-principles study of the atomic structure of glassy Ga 10 Ge 15 Te 75[END_REF], 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.

Experimental

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 [START_REF] Filik | Processing two-dimensional X-ray diffraction and small-angle scattering data in DAWN 2[END_REF]. X-ray structure factor, S X (Q), were extracted from integrated raw data using the PDFGetX2 software [START_REF] Qiu | PDFgetX2 : a GUI-driven program to obtain the pair distribution function from X-ray powder diffraction data[END_REF].

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 [START_REF] Klementev | Extraction of the fine structure from x-ray absorption spectra[END_REF]. 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 [START_REF] Mcgreevy | Reverse Monte Carlo simulation: A new technique for the determination of disordered structures[END_REF] 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 [START_REF] Gereben | A new version of the RMC++ Reverse Monte Carlo programme, aimed at investigating the structure of covalent glasses[END_REF] was used to produce structural models by fitting simultaneously the experimental data sets. The EXAFS backscattering coefficients were calculated by the FEFF8.4 program [START_REF] Ankudinov | Real-space multiple-scattering calculation and interpretation of x-ray-absorption near-edge structure[END_REF].

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 [START_REF] Akola | Binary Alloys of Ge and Te: Order, Voids, and the Eutectic Composition[END_REF][START_REF] Jóvári | Short range order and stability of amorphous Ge x Te 100-x alloys (12 <= x <= 44.6)[END_REF] 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. Ge-Te, Ga-Te and Te-Te bonds were allowed in all simulation runs. In the investigated samples the amount of Te atoms is more than twice of the amount of Ge + Ga atoms, thus besides the formation of MTe 4 (or MTe 3 ) units (M=Ge or Ga) Te-Te pairs must also be present, even if heteronuclear Ge-Te and Ga-Te bonds are preferred. The necessity of M-M type bonds was investigated by test runs for the highest M content Ge 14.3 Ga 14.3 Te 71.4 sample (see below). Allowing them had either no effect on fit quality or resulted in M-M type g(r) functions with an artificially split first peak having maxima around 2.5 Å and 2.8 Å. From these test runs it was concluded that M-M type coordination numbers in glassy Ge 14.3 Ga 14.3 Te 71.4 are around or below the sensitivity of our method (about 0.3-0.4) and even smaller in the other compositions investigated.

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:

mod exp exp (1)
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 (k 3 χ(k)) are shown in Figures 1234. Also shown are the fits of the unconstrained final models, in which only the Ge-Te, Ga-Te and Te-Te bonds were allowed Figs. 1234.

Partial pair correlation functions (g ij (r)) obtained for the unconstrained model are shown in Fig. 5 while bond lengths and average coordination numbers are collected in Tables 3 and4.

Nearest neighbor distances

The Ge-Te bond distances are around 2.60 Å, while the Ga-Te bond length is [START_REF] Chaker | First-principles study of the atomic structure of glassy Ga 10 Ge 15 Te 75[END_REF].

The r GaTe value (2.62-2.63 Å) is the same as it was found experimentally in Ge-Ga-Te glasses by EXAFS [START_REF] Golovchak | Structural evolution of Ga-Ge-Te glasses by combined EXAFS and XPS analysis[END_REF] and by combining experimental (diffraction, EXAFS) data with simulation (RMC and density functional) [START_REF] Voleská | Structure, electronic, and vibrational properties of glassy Ga 11 Ge 11 Te 78 : Experimentally constrained density functional study[END_REF]. Somewhat longer bond length was found in Ref. [START_REF] Chaker | First-principles study of the atomic structure of glassy Ga 10 Ge 15 Te 75[END_REF] (2.67 Å) with first principles molecular dynamics simulation (FPMD).

The Te-Te bond length is around 2.77 Å, except again for the Ge 10 Ga 10

51]).

The average coordination number of Ga atoms is also close to 4, as was found in several Ge-Ga-Ch (Ch=S, Se, Te) glasses: experimentally in Ge-Ga-S glasses [52 -59], in Ge-Ga-Se glasses [54, 60 -65], in amorphous Ge-Ga-Te [START_REF] Voleská | Structure, electronic, and vibrational properties of glassy Ga 11 Ge 11 Te 78 : Experimentally constrained density functional study[END_REF][START_REF] Golovchak | Structural evolution of Ga-Ge-Te glasses by combined EXAFS and XPS analysis[END_REF]. Recent FPMD simulations on 80GeSe 2 -20Ga 2 Se 3 glass [START_REF] Petracovschi | Short and medium range structures of 80GeSe 2 -20Ga 2 Se 3 chalcogenide glasses[END_REF], Ge-Ga-Te liquids [START_REF] Flores-Ruiz | Structural, vibrational, and dynamic properties of Ge-Ga-Te liquids with increasing connectivity: A combined neutron scattering and molecular dynamics study[END_REF] and Ge 15 Ga 10 Te 75 glass [START_REF] Chaker | First-principles study of the atomic structure of glassy Ga 10 Ge 15 Te 75[END_REF] also reported Ga coordination numbers around 4.

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 Ga 12.5 Te 75 and Ge 14.3 Ga 14.3 Te 71.4 (around 2.19 and 2.35, respectively). Test runs were carried out in which the Ge-Te and Ga-Te coordination numbers were constrained to remain 4 and the Te-Te coordination number was forced to decrease so that the total coordination number of Te be equal to 2. The R-factors of the fits for these models were significantly higher (mostly the Rfactors of the ND and XRD data sets, with 20-50%), especially for Ge 12.5 Ga 12.5 Te 75 and Ge 14.3 Ga 14.3 Te 71.4 . Besides the deterioration of the fits, the resulting Te-Te partial pair correlation functions exhibit artificially sharp peaks at around 3.1 Å, next to the upper limit of the coordination constraints.

Te coordination number around 2 was found in Ge x Te 100-x glasses by ND [START_REF] Kameda | Time-of-Flight Neutron Diffraction Study of Amorphous and Liquid Ge-Te Alloys[END_REF] and by EXAFS [START_REF] Sen | Atomic structure and chemical order in binary Ge-Te and As-Te glasses: A Te K-edge X-ray absorption fine structure spectroscopic study[END_REF]. N Te = 2 was obtained by combination of diffraction and EXAFS experiments with RMC simulations in amorphous Ge x Te 100-x [START_REF] Jóvári | Structure of Te-rich Te-Ge-X (X = I, Se, Ga) glasses[END_REF][START_REF] Jóvári | Short range order and stability of amorphous Ge x Te 100-x alloys (12 <= x <= 44.6)[END_REF][START_REF] Jóvári | Short-Range Order in Ge-As-Te Glasses[END_REF][START_REF] Jóvári | Network Rearrangement in AgI-Doped GeTe 4 Glasses[END_REF][START_REF] Jóvári | Local order in binary Ge-Te glasses -An experimental study[END_REF], in Ge-As-Te glasses [START_REF] Jóvári | Short-Range Order in Ge-As-Te Glasses[END_REF] and in amorphous Ge-Sb-Te [START_REF] Jóvári | Wrong bonds" in sputtered amorphous Ge 2 Sb 2 Te 5[END_REF][START_REF] Jóvári | Local order in amorphous Ge 2 Sb 2 Te 5 and GeSb 2 Te 4[END_REF].

FPMD simulations often result in Te coordination number higher than 2 (e.g. in Ge x Te 100-x [START_REF] Akola | Structural phase transitions on the nanoscale: The crucial pattern in the phase-change materials Ge 2 Sb 2 Te 5 and GeTe[END_REF][START_REF] Akola | Binary Alloys of Ge and Te: Order, Voids, and the Eutectic Composition[END_REF][START_REF] Gunasekera | Effect of mixed Ge/Si cross-linking on the physical properties of amorphous Ge-Si-Te networks[END_REF][START_REF] Micoulaut | Quantitative measure of tetrahedral-sp3 geometries in amorphous phase-change alloys[END_REF][START_REF] Bouzid | Role of the van der Waals interactions and impact of the exchange-correlation functional in determining the structure of glassy GeTe 4[END_REF][START_REF] Micoulaut | Towards accurate models for amorphous GeTe: Crucial effect of dispersive van der Waals corrections on the structural properties involved in the phase-change mechanism[END_REF], in Ge-Sb-Te [START_REF] Akola | Structural phase transitions on the nanoscale: The crucial pattern in the phase-change materials Ge 2 Sb 2 Te 5 and GeTe[END_REF][START_REF] Akola | Density functional study of amorphous, liquid and crystalline Ge 2 Sb 2 Te 5 : homopolar bonds and/or AB alternation?[END_REF][START_REF] Akola | Structure of amorphous Ge 8 Sb 2 Te 11 : GeTe-Sb 2 Te 3 alloys and optical storage[END_REF]), the value highly depends on the used exchange correlation functional and on the applying of the VdW forces (see e.g. Ref. [START_REF] Bouzid | Role of the van der Waals interactions and impact of the exchange-correlation functional in determining the structure of glassy GeTe 4[END_REF]:

3.78 PBE, 3.51 PBE+VdW, 2.57 BLYP, 2.31 BLYP+VdW). Recent FPMD simulations proposed Te coordination number 2.9-4.8 in Ge-Ga-Te liquids [START_REF] Flores-Ruiz | Structural, vibrational, and dynamic properties of Ge-Ga-Te liquids with increasing connectivity: A combined neutron scattering and molecular dynamics study[END_REF], and 2.19 in Ge-Ga-Te glass [START_REF] Chaker | First-principles study of the atomic structure of glassy Ga 10 Ge 15 Te 75[END_REF]. 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 [START_REF] Jóvári | Local order in binary Ge-Te glasses -An experimental study[END_REF], 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 Ge 23.6 Te 76.4 [START_REF] Jóvári | Local order in binary Ge-Te glasses -An experimental study[END_REF] no M-M type bonds were found in Ge-Ga-Te glasses. In principle, the investigated Ge-Te and Ge-Ga-Te glasses are all Te-rich therefore M-M bonding could be avoided even if all Te atoms remain twofold coordinated. Still, M-M bonds exist in Ge 23.6 Te 76. [START_REF] Jóvári | Local order in binary Ge-Te glasses -An experimental study[END_REF] and the coordination number of Te is higher than 2 in Ge-Ga-Te glasses. These two tendencies share a common consequence: they increase the Te-Te coordination number.

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 [START_REF] Pethes | Short range order in Ge-Ga-Se glasses[END_REF] or anomalous X-ray scattering and RMC [START_REF] Klee | Distinguishing the local environments of Ga and Ge in amorphous (Ga 2 Se 3 ) 0[END_REF]). Moreover, N S coordination number higher than 2 was proposed in amorphous Ge-Ga-S alloys by Raman [START_REF] Masselin | Spatially resolved Raman analysis of laser induced refractive index variation in chalcogenide glass[END_REF] as well.

Second neighbors

It was found in Ge-Te glasses [START_REF] Jóvári | Local order in binary Ge-Te glasses -An experimental study[END_REF] that GeTe 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.

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 [START_REF] Jóvári | Local order in binary Ge-Te glasses -An experimental study[END_REF], also shown in Fig. 9. The first peaks of Ge-Ga and Ga-Ga partial pair correlation functions are affected in the same way (not shown). These observations strongly suggest that prepeak in Ge x Ga x Te 100-2x and Ge-Te glasses is connected to the well-defined M-M correlations (M = Ge, Ga) manifested in sharp real space M-M peaks. The latter, on the other hand, are the consequence of corner or edge sharing MTe 4 tetrahedra [START_REF] Jóvári | Local order in binary Ge-Te glasses -An experimental study[END_REF].

Conclusions

Short range order and topology of Ge x Ga x Te 100-2x (x = 7.5, 10, 12.5, 14. 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. q max [Å -1 ] q min [Å -1 ] S(q max )-S(q min ) Ge

Tables

  4 units connect to each other by sharing a corner or an edge (two Ge atoms sharing one or two common Te neighbors). The presence of corner (CS) or edge sharing (ES) MTe 4 tetrahedra was investigated in Ge-Ga-Te samples as well. The analyzed configurations were obtained by constrained simulation runs, in which the Ge and Ga atoms were forced to have 4 Te neighbors. (Images of the configurations of Ge 7.5 Ga 7.5 Te 85 and Ge 14.3 Ga 14.3 Te 71.4 glasses are shown in Figs. 6 and 7.) The decomposition of the first peak of the M-M partials to contributions of CS and ES tetrahedra and topologically distant pairs is presented for the Ge-Ge pairs of the Ge 14.3 Ga 14.3 Te 71.4 sample in Fig. 8 (Ga-Ga and Ge-Ga pairs show a similar behavior).

  3) glasses was investigated by diffraction techniques and EXAFS. Structural models were obtained by fitting experimental datasets simultaneously in the framework of the reverse Monte Carlo simulation technique. It was shown that Ga and Ge atoms are mostly fourfold coordinated while N Te , the average coordination number of Te increases with Ga content (N Te = 2.35 ± 0.1 for x = 14.3).

4 NDFigure 2 . 4 XRDFigure 3 .Figure 4 .Figure 5 .

 424345 Figure 1. ND structure factors (symbols) and fits (lines) of the Ge x Ga x Te 100-2x glasses. (The curves are shifted vertically for clarity.)

Figure 6 .

 6 Figure 6. A snapshot about a part of the configuration of the Ge 7.5 Ga 7.5 Te 85 glass obtained by RMC simulation. The Ge, Ga and Te atoms are represented by magenta, blue and grey balls, respectively. Two corner sharing tetrahedra are marked with orange, a chain of Te-Te nearest neighbors is highlighted by red.

Figure 7 .

 7 Figure 7. A snapshot about a part of the configuration of the Ge 14.3 Ga 14.3 Te 71.4 glass obtained by RMC simulation. The Ge, Ga and Te atoms are represented by magenta, blue and grey balls, respectively. Two edge-sharing GaTe 4 tetrahedra are marked by red; chains of cornershared MTe 4 units are highlighted with orange.

Figure 8 .

 8 Figure 8. Decomposition of g GeGe (r) of Ge 14.3 Ga 14.3 Te 71.4 glass to contributions from corner (CS) and edge (ES) sharing tetrahedra and topologically distant Ge-Ge pairs.

Figure 9 .

 9 Figure 9. Comparison of the neutron weighted structure factors (a and c) and the first peak of the Ge-Ge partial pair correlation functions (b and d) of Ge 14.3 Ga 14.3 Te 71.4 and Ge 18.7 Te 81.3 glasses obtained from RMC simulations by (red lines) fitting the experimental neutron diffraction data and (blue line) without fitting ND data. Experimental data (symbols) are also shown for reference.

  2.62-2.63 Å for all glasses except the Ge 10 Ga 10 Te 80 sample for which no EXAFS data were available. For this composition longer Ge-Te and Ga-Te distances are (can be) compensated by a shorter Te-Te distance length showing that diffraction data without EXAFS cannot completely separate Ge-Te, Ga-Te and Te-Te distances. For the other compositions the r GeTe value agrees well with previous results: in amorphous Ge x Te 100-x r GeTe = 2.59 Å was found by ND [31], 2.59-2.62 Å by EXAFS [32 -36], 2.58-2.61 Å by combining diffraction, EXAFS and RMC techniques [4, 8, 24, 37, 38], 2.6 Å by anomalous X-ray scattering and RMC [39]. 2.60-2.64 Å Ge-Te bond Te 100-x [15], 2.63 Å in Ge 2 Sb 2 Te 5 [50] and 2.59 Å in Ge 15 Ga 10 Te 75

distances were found in amorphous Ge-Sb-Te

[40 -42]

, 2.60 Å in Ge-As-Te

[START_REF] Jóvári | Short-Range Order in Ge-As-Te Glasses[END_REF]

and 2.60-2.63 Å in Ge-Ga-Te glasses

[START_REF] Jóvári | Structure of Te-rich Te-Ge-X (X = I, Se, Ga) glasses[END_REF][START_REF] Golovchak | Structural evolution of Ga-Ge-Te glasses by combined EXAFS and XPS analysis[END_REF]

.

Early density functional molecular dynamics simulations (DFT) resulted in longer Ge-Te bond lengths: 2.70 -2.78 Å in Ge x Te 100-x and Ge x Sb y Te 100-x-y systems

[23, 43 -45]

. The combination of DFT simulations with RMC refinement gave results closer to the experimental values: 2.65 Å in Ge-Ga-Te

[START_REF] Voleská | Structure, electronic, and vibrational properties of glassy Ga 11 Ge 11 Te 78 : Experimentally constrained density functional study[END_REF]

, 2.58 Å in Ge 15 Te 85

[START_REF] Kalikka | Amorphous Ge 15 Te 85 : density functional, high-energy x-ray and neutron diffraction study[END_REF]

. Recent DFT simulations using the Becke-Lee-Yang-Parr (BLYP) exchange-correlation functional instead of Perdew-Burke-Ernzerhof (PBE), and especially with van der Waals dispersion forces included, have shown improved agreement with experimental values: 2.64-2.66 Å with PBE in Ge x Te 100-x

[15, 47 - 49]

, 2.59-2.62 Å with BLYP in Ge x

  Te 80 sample. Te-Te distances reported in the literature have a broad distribution: in amorphous Ge x Te 100-x 2.76 Å As-Te[START_REF] Jóvári | Short-Range Order in Ge-As-Te Glasses[END_REF], 2.77-2.79 Å in Ge-Te-Ag-I glasses[START_REF] Jóvári | Network Rearrangement in AgI-Doped GeTe 4 Glasses[END_REF] by combination of diffraction, EXAFS and RMC.First principles molecular dynamics simulations result in longer bond lengths: 2.87 Å[START_REF] Akola | Structural phase transitions on the nanoscale: The crucial pattern in the phase-change materials Ge 2 Sb 2 Te 5 and GeTe[END_REF],2.85 Å[START_REF] Akola | Structure of amorphous Ge 8 Sb 2 Te 11 : GeTe-Sb 2 Te 3 alloys and optical storage[END_REF], 2.90 Å[START_REF] Gunasekera | Effect of mixed Ge/Si cross-linking on the physical properties of amorphous Ge-Si-Te networks[END_REF][START_REF] Micoulaut | Quantitative measure of tetrahedral-sp3 geometries in amorphous phase-change alloys[END_REF], 2.89 Å[START_REF] Micoulaut | Towards accurate models for amorphous GeTe: Crucial effect of dispersive van der Waals corrections on the structural properties involved in the phase-change mechanism[END_REF]. Shorter distances were obtained by DFT simulations with RMC refinement: 2.83 Å[START_REF] Voleská | Structure, electronic, and vibrational properties of glassy Ga 11 Ge 11 Te 78 : Experimentally constrained density functional study[END_REF], 2.74 Å[START_REF] Kalikka | Amorphous Ge 15 Te 85 : density functional, high-energy x-ray and neutron diffraction study[END_REF]. Treatment of van der Waals forces (VdW) seems to be important here as well: 2.83 -2.84 Å was obtained with and 2.88-2.89 Å without VdW in GeTe 4[START_REF] Bouzid | Role of the van der Waals interactions and impact of the exchange-correlation functional in determining the structure of glassy GeTe 4[END_REF] and 2.81 Å in Ge 15 Ga 10 Te 75 with BLYP+VdW[START_REF] Chaker | First-principles study of the atomic structure of glassy Ga 10 Ge 15 Te 75[END_REF].

	Average coordination numbers
	The average coordination number of Ge is around 4, as it is expected (and was reported earlier
	by experiments and simulations as well [4, 5, 7, 8, 13-15, 23, 26, 31, 33, 37, 39, 41-43, 45-

was measured by ND

[START_REF] Kameda | Time-of-Flight Neutron Diffraction Study of Amorphous and Liquid Ge-Te Alloys[END_REF]

, 2.77-2.82 Å by EXAFS

[START_REF] Sakurai | Partial structure analysis of amorphous Ge 15 Te 80 M 5 (M=Cu, Ag and In)[END_REF][START_REF] Sen | Atomic structure and chemical order in binary Ge-Te and As-Te glasses: A Te K-edge X-ray absorption fine structure spectroscopic study[END_REF]

, 2.70-2.79 Å by combination of diffraction, EXAFS and RMC

[START_REF] Jóvári | Local order in binary Ge-Te glasses -An experimental study[END_REF][START_REF] Jóvári | Structure of Te-rich Te-Ge-X (X = I, Se, Ga) glasses[END_REF][START_REF] Jóvári | Short-Range Order in Ge-As-Te Glasses[END_REF][START_REF] Jóvári | Network Rearrangement in AgI-Doped GeTe 4 Glasses[END_REF][START_REF] Jóvári | Short range order and stability of amorphous Ge x Te 100-x alloys (12 <= x <= 44.6)[END_REF][START_REF] Kaban | Determination of partial pair distribution functions in amorphous Ge 15 Te 85 by simultaneous RMC simulation of diffraction and EXAFS data[END_REF][START_REF] Piarristeguy | Structural singularities in Ge x Te 100-x films[END_REF]

, 2.73 Å by anomalous X-ray scattering and RMC

[START_REF] Stellhorn | Shortand intermediate-range order in amorphous GeTe[END_REF]

. Te-Te distances around 2.79-2.80 Å were reported in Ge-Ga-Te

[START_REF] Jóvári | Structure of Te-rich Te-Ge-X (X = I, Se, Ga) glasses[END_REF]

, 2.77 Å in Ge-

  The average number of Ge and Ga atoms around Te is less than 1 meaning that formation of CS or ES pairs could be avoided, in principle. With increasing M content the number of the CS or ES sharing tetrahedra also increases. For the Ge 14.3 Ga 14.3 Te 71.4 glass 99.7% of the MTe 4 tetrahedra have at least one CS or ES pair. The number of M atoms participating in ES units is around 12% for Ge 7.5 Ga 7.5 Te 85 and 33% for Ge 14.3 Ga 14.3 Te 71.4 .

Table 1

 1 Estimated densities, number densities, fitted experimental data sets.

		ρ [g/cm 3 ]	Number density [Å -3 ]	Experimental data sets
	Ge 7.5 Ga 7.5 Te 85	5.6	0.0283	ND, XRD, Ge, Ga EXAFS
	Ge 10 Ga 10 Te 80	5.57	0.0288	ND, XRD
	Ge 12.5 Ga 12.5 Te 75 5.53	0.0293	ND, XRD, Ge, Ga EXAFS
	Ge 14.3 Ga 14.3 Te 71.4 5.7	0.0308	ND, XRD, Ge, Ga EXAFS

Table 2

 2 Minimum interatomic distances (in Å) used in the reverse Monte Carlo simulation

	runs
		Ge-Ge	Ge-Ga	Ge-Te	Ga-Ga	Ga-Te	Te-Te
	Bond allowed	2.35	2.35	2.4	2.35	2.4	2.5
	Bond forbidden	3.45	3.45		3.45

Table 3

 3 Nearest neighbor distances (in Å). The uncertainty of distances is about ± 0.02 Å if EXAFS data sets are also fitted, but it can be higher (about 0.05 Å) in case of the Ge 10 Ga 10 Te 80 , where only the two diffraction measurements were available.

		Ge-Te	Ga-Te	Te-Te
	Ge 7.5 Ga 7.5 Te 85	2.60	2.62	2.78
	Ge 10 Ga 10 Te 80	2.64	2.64	2.74
	Ge 12.5 Ga 12.5 Te 75	2.60	2.63	2.77
	Ge 14.3 Ga 14.3 Te 71.4	2.61	2.62	2.77

Table 4

 4 Coordination numbers of the investigated glasses obtained by unconstrained

	simulations.
	Pair (upper limit)	Ge 7.5 Ga 7.5 Te 85	Ge 10 Ga 10 Te 80	Ge 12.5 Ga 12.5 Te 75 Ge 14.3 Ga 14.3 Te 71.4
	N Ge-Te (3.1 Å)	4.0 (-0.4+0.6)	4.1 (-0.4+0.7)	3.9 (-0.4+0.5)	3.95 (±0.3)
	N Te-Ge (3.1 Å)	0.35 (-0.03+0.06) 0.51(-0.05+0.1) 0.65 (±0.08)	0.79 (±0.06)

Table 5

 5 Percentage of Ge and Ga atoms participating in corner or/and edge sharing units. Ga 7.5 Te 85 Ge 10 Ga 10 Te 80 Ge 12.5 Ga 12.5 Te 75 Ge 14.3 Ga 14.3 Te 71.4

	Uncertainties were determined from 10 simulation runs started from different initial
	configurations.
	Ge 7.5 Neither CS nor ES Ge 16.5 (±1)	6.8	1.5	0.3 (±0.1)
	Neither CS nor ES Ga 16.5 (±2)	5.6	1.1	0.25 (±0.15)
	Only CS Ge	71.5 (±1.5)	75	71	65 (±1.5)
	Only CS Ga	71.5 (±2)	75	71	67 (±1)
	Only ES Ge	3.2 (±0.5)	2.9	1.6	0.8 (±0.2)
	Only ES Ga	3.2 (±0.5)	2.3	1.5	0.5 (±0.2)
	CS and ES Ge	9 (±1)	15	26	34 (±2)
	CS and ES Ga	9 (±1)	17	26	32 (±1)

Table 6

 6 Position of the FSDP (q max ) and amplitude of the FSDP (see text for definition)

Acknowledgment I. P. and P. J. were supported by NKFIH (National Research, Development and Innovation Office) Grant No. KH 130425. The neutron diffraction experiment was carried out at the ORPHÉE reactor, Laboratoire Léon Brillouin, CEA-Saclay, France. EXAFS measurements

were carried out at PETRA III at DESY, a member of the Helmholtz Association (HGF). We thank Diamond Light Source Ltd. for access to beamline I12-JEEP (cm19662-1) that contributed to the results presented here.


Moussa Kafal

Jaume Benoit

Geoffrey Beck

Antoine Dupret

Constructing the Topology of Complex Wire Networks Using Reflectometry Response and Newton-Based Optimization Algorithms

Keywords: Wiring networks, topology reconstruction, time domain reflectometry, newton-based optimization algorithms

Based on Time-Domain Reflectometry (TDR) technique, a new method which could reconstruct the topology of an unknown or partially unknown network is proposed in this paper. This approach, the TDR-NEW approach, allows the network to be retrieved by drawing its interconnections and estimating the lengths of branches. Two complementary steps are addressed. In the first step the direct problem is modeled using RLCG circuit parameters. Then the Finite Difference Time Domain (FDTD) method conjugated with the ABCD matrix method is used to model the signal propagation in a branched network. This model, the FDTD-ABCD, provides a simple and accurate method to simulate Time Domain Reflectometry responses. In the second step the newton-based optimization method is combined with the wire propagation model to solve the inverse problem and to deduce physical informations about the network from the reflectometry response. Numerical and experimental results pointing out the performance of the TDR-NEW method in reconstructing the topology of branched networks are reported.

I. INTRODUCTION

Fundamental changes are taking place in the monitoring, control and protection of almost all modern systems where an increasing amount of electrical cables are progressively and massively hosted [START_REF] Dupret | Imaging Techniques for soft fault detection and location in wiring networks[END_REF]. On the other hand, it is also generally acknowledged that electrical systems are evolving and becoming more complex accompanied by the enormous increase of electrical employments, which require new transmission and distribution lines [START_REF] Auzanneau | Wire troubleshooting and diagnosis: Review and perspectives[END_REF]. Due to their ubiquitous use in any small, medium or large infrastructure (e.g., smart grids, buildings, transport systems, vehicles, and power plants) and their primary role in energy and signal distribution, wire networks became fundamental subsystems whose proper functioning and good performance is of critical importance.

It is noteworthy that a great number of electrical wires are dedicated to safety and control operations, thus any shortening in their performance due to the appearance of a defect might be highly expensive in terms of lives and from an economical aspect. One estimate is that highly trained technicians spend between 1 million to 2 million man-hours each year at the operational level to troubleshoot and repair wiring system problems in the U.S navy alone [START_REF] Science | Review of federal programs for wire system safety: final report[END_REF]. Accordingly, ensuring the reliable use of wire networks requires the availability of techniques capable of detecting the presence of faults that could potentially put in jeopardy the infrastructures relying on these networks. Fault location problems have been extensively studied in the literature for many years and numerous methods have been proposed for this purpose. Nevertheless, despite the vast amount of literature, the problem of fault location still represents a serious challenge. Although several electric and non-electric wire diagnosis methods have been studied and developed throughout the last few decades, reflectometry-based techniques are still in the center stage of research and industrial applications in this domain [START_REF] Smith | Analysis of spread spectrum time domain reflectometry for wire fault location[END_REF]- [START_REF] Cabanillas | Automated Phase Offset Correction using Reflectometry in Fault Detection Systems[END_REF].

Reflectometry are high frequency methods adopted from the concept of radar that allow relatively simple test setups for the analysis of a network under test (NUT). Typically, a test signal is injected into the NUT which propagates until it encounters an impedance discontinuity, e.g., a branch junction, a load, or a local unwanted modification of the line, i.e., a fault. Hard faults (open or short circuits) prevent the test signal from ongoing throughout the NUT while soft faults e.g., a partial wearing of the insulation or a chafing, partially reflect it back to the injection point. The analysis of the reflectometry response provides valuable information about the fault (presence, position, and nature).

In general, the accuracy of reflectometry methods are mainly affected by several factors including: pre-fault system condition, network's topology, fault impedance, and presence of noise. In particular, the problem of soft faults is more critical and requires in-depth studies as their corresponding reflected weak echoes might be easily masked from reflectometry detection by pseudo echoes generated by higher reflectivity impedance discontinuities like junctions [START_REF] Cozza | Echo response of faults in transmission lines: Models and limitations to fault detection[END_REF]. Although these methods have promising capabilities to locate faults on single cables, their applicability is declined on branched NUTs. In practice, cables are always used in distribution networks where a set of cables, usually of the same type, interconnect according to well defined topology standards (bus, star, mesh, ring, tree, etc.). As a matter of fact, testing such kinds of networks has proven to be challenging. This is because branches in a network add a further level of complexity to the reflectometry response due to the superposition of multiple reflections from different branches and branch ends [START_REF] Abboud | A matched-pulse approach for soft-fault detection in complex wire networks[END_REF]. The number of reflections also tend to grow exponentially with the number of branches in the network; hence, complex network topologies produce extremely complex reflectometry responses leading to ambiguous results.

Under those circumstances, developing new techniques that can be integrated with reflectometry methods to improve and enhance the analysis of the reflectometry responses became essential. Significantly, inverse problems showed to be suitable for this purpose, where baselining an approach relying on comparing the response of the faulty network with either the pre-measured or simulated response of its (known) healthy condition improved the performance of reflectometry [START_REF] Furse | A critical comparison of reflectometry methods for location of wiring faults[END_REF]. The rationale for this method is based on the following observation: while echoes from soft faults are often dwarfed by those generated by, e.g., junctions, a baseline measurement contains exactly the same echoes from the same junctions; taking the difference of the two results is intended to cancel out the contribution from the NUT itself (i.e., the junctions in this example), making the fault response detectable. Baselining is indeed widely used in reflectometry as a contrast-enhancing technique, especially with complex branched NUTs and weak reflectivity soft faults [START_REF] Kafal | Baselining: A critical approach used for soft fault detection in wire networks[END_REF]. Additionally, it formed an important basis for the application of the new trend of time reversal techniques that have shown to be efficient in locating soft faults in different complexity NUTS [START_REF] Abboud | A noniterative method for locating soft faults in complex wire networks[END_REF]- [START_REF] Kafal | Locating faults with high resolution using single-frequency tr-music processing[END_REF].

Consequently, it can be claimed that analyzing networks of unknown topology can therefore be particularly very difficult. In fact, wire networks have been deployed in many applications decades ago, as a result many of their datasheets might have been lost with time. Furthermore, there exists a wide range of networks that can be hardly accessed especially those that are either embedded or present in critical situations as nuclear power plants. Accordingly, testing such networks can sometimes be impossible.

In this paper we propose an efficient method for the reconstruction of wiring networks using the reflectometry response, particularly the time domain reflectometry (TDR), and newtonbased optimization algorithms. We are going to introduce and develop a technique for constructing an unknown network topology where the studied network will be considered as a black box having a definite number of ports. A direct model describes the propagation of the wave along the lines of a network using a numerical method. Then a newton-based algorithm is used to solve the inverse problem reducing the differences between the measured reflectometry response of the unknown NUT and the response given by the direct model. The result will be revealing the most compelling network topology while constructing all branches and junctions with the right cable lengths.

II. THE WIRE NETWORK NUMERICAL MODEL

To better understand the tenets of the proposed approach in reconstructing the topology of an unknown network, it is necessary to understand how an electromagnetic wave propagates in a transmission line. The aim of this section is first to position our work within the framework of the transmission line theory and in the context of wiring modeling techniques and then present a method for modeling a wire network. For our case study we considered two-conductor transmission lines under the assumption that the electric and magnetic fields are transverse to the axis of propagation (TEM wave).

A. The Transmission Line propagation Model

In literature, the methods used to simulate and study the transmission line behavior are different. Most of them are obtained from the time dependent telegraphers equations ( 1) &(2) modeled by RLCG circuit parameters for an infinitesimal length of the line. Notably, these equations describe the evolution of voltage and current along the transmission line as functions of the per unit length parameters of the line demonstrated by the quantities R (resistance), L (inductance), C (capacitance) and G (conductance).

In our work, we opted to use the finite difference time domain (FDTD) method in order solve telegraphers equations and model the signal propagation in a transmission line. The FDTD method is a simple and intuitive electromagnetic modeling technique which converts the differential equations into finite difference equations leading to the computation of the voltage and current propagation along a line.

∂v(x, t) ∂x = -Ri(x, t) -L ∂i(x, t) ∂t (1) ∂i(x, t) ∂x = -Gv(x, t) -C ∂v(x, t) ∂t (2)

B. Branched network analysis

In real-life environments such as aerospace and automotive, wired networking interconnect dozens or even hundreds of electrical systems together. These wired networks consist of a set of wires, usually of the same type, interconnected according to well defined topology standards. Numerous transmission line techniques have been used for modeling wired networks, where we adopted a joint FDTD-ABCD method which formed a suitable solution for such analysis of branched NUTs. It is worthy to note that this model has been developed at CEA as an inhouse solver offering excellent fidelity and computational efficiency.

To model networks, transmission conditions have to be implemented at the junctions. Accordingly, for a uniform transmission line of characteristic impedance Z c ending by a load impedance Z l , the reflection coefficient Γ i at any discontinuity Z i can be defined as the ratio between the reflected V ref lected and incident V incident voltages as given in eq. 3. Certainly, hard faults whether open or short circuits result in an absolute reflection coefficient equal to 1 (|Γ i | = 1), whereas any other kind of defect will result in a |Γ i | < 1. For instance, a junction branching into three wires having the same Z c as that shown in Fig. 1 results in a Z i = Z c /3. It is important to note here that we are going to deal with networks composed of branches having the same characteristic impedance Z c . In effect, the corresponding reflection coefficient of this junction will be Γ i = -1/2. In general, for a junction of n branches Z i = Z c /n, the reflection coefficient can be defined as shown in eq. 4.

Γ f = V ref lected V incident = Z i -Z c Z i + Zc (3)
Γ i = Z c -Zc n Z c + Zc n = 1 -n 1 + n (4)

C. Reflectometry for a branched network topology

In order to validate the propagation model in complex branched networks, we will consider the FDTD-ABCD model to simulate the time domain reflectometry (TDR) response of the four junction NUT of Fig. 1. The network is composed from 10 ideal non-dispersive branches with a characteristic impedance Z c = 50Ω interconnected by four junctions.

One of the network's extremities will then be selected to serve as a reference testing port and will be denoted as P test . A normalized amplitude Gaussian pulse with a total bandwidth of 2 GHz will be injected into P test of the NUT. Notably, all NUT extremities are matched to the characteristic impedance of the network. The corresponding TDR response is shown in the reflectogram of Fig. 2. The same pulse will be re-injected into the same network but this time while having open circuited extremities. The corresponding reflectogram is also presented in Fig. 2.

Several points need to be commented here. First of all, it shall be noted that for the case of matched end networks, the first two reflections of the TDR response are strictly attached to those of the first two consecutive junctions. Therefore, the first peak value is the first junction's reflection coefficient while its position corresponds to the distance at which it is located. On the other hand, the second peak value hints at the second junction's reflection coefficient according to the relation given by equation 5 where Γ 2 and Γ ′ 2 are the actual junction's reflection coefficient and its peak value respectively. Accordingly, once Γ 2 is computed, the number of branches n 2 originating from it can be inferred from eq. 4 while its distance from P test is the location of its peak value.

Γ 2 = Γ ′ 2 (1 + Γ 1 ) 2 (5)
As an illustration, if we reconsider the reflectogram of Fig. 2 Γ 1 = -1/2. Thus according to eq. 4 n 1 = 3 while l 1 = 1.5 m is the first junction location from P test . On the other hand, the second junction seems to be located at l 2 = 4 m from the reference testing ports and interconnecting n 2 = 2 branches.

With this in mind, if we consider an unknown network embedded in a black box while having access to all its extremities, the TDR response computed from a single testing port while matching all other ends permits building a preliminary network configuration. In fact, we can infer according to what has been detailed before the location of the first two junctions along with the number of branches connected to each. Due to the characteristics of wiring networks, the presence of multiple junctions and different load terminations provides multiple and intermediate reflections in the reflectometry response as shown in Fig. 2. These reflections occur because the primary reflections from the junctions and terminations intercept other junctions during their return path to the source. In these conditions, if the network topology is not known in advance, it is very difficult to deduce the length of the different branches from the reflectometry response. Thus the reflectometry response of an open circuited network alone is not sufficient to reconstruct a wiring network. The coming section introduces a novel method for the reconstruction of an unknown wiring network from reflectometry data based on the conclusions built from the matched end observations.

III. THE PROPOSED TDR-NEW ALGORITHM

The TDR-NEW approach consists of two main parts. The first part comprises a numerical model for constructing possible NUTs based on the matched end TDR methodology illustrated in section II-C. The second part is the newtonbased optimization which is used to minimize the differences between the measured open-ended reflectometry response of the unknown NUT and the responses given by the direct numerical model. The network's topology and its corresponding branch lengths would be retrieved once convergence is reached between the measured response and the one corresponding to the right NUT configuration generated by the numerical model.

A. Newton's Method

Newton's method is a basic tool in numerical analysis and numerous applications, including operations in data mining, management science, industrial and financial research, optimization and control. Its role in optimization cannot be underestimated as it is the basis for the most effective procedures in linear and nonlinear programming. For instance, the polynomial time interior point algorithms in convex optimization are based on Newton's method.

The basic idea of Newtons method is very simple: it is linearization. Suppose F : R 1 → R 1 is a differentiable function, and we are solving the equation F (x) = 0. Starting from an initial point x 0 we can construct the linear approximation of F (x) in the neighborhood of x 0 : F (x 0 + h) ≈ F (x 0 ) + F ′ (x 0 )h and solve the arising linear equation F (x 0 )+F ′ (x 0 )h = 0. Thus, we obtain by the recurrent method

x k+1 = x k -F ′ (x k ) -1 F (x k ), k = 0, 1, 2.... (6)
In optimization, Newton's method is applied to the derivative F ′ of a twice-differentiable function F to find the roots of the derivative (solutions to F ′ (x) = 0), also known as the stationary points of F [START_REF] Fletcher | Practical methods of optimization[END_REF].

B. The TDR-NEW approach

In order to illustrate the steps followed by the TDR-NEW algorithm in reconstructing the topology of an unknown network, we are going to consider a random NUT built inside a black-box. We assume having no information about any of its connections except the knowledge of the number of extremities M . The following step is to assign a reference testing port P test where two TDR measurements will be done. The first will be accomplished while matching all the NUT's extremities whose corresponding reflectometry response will be denoted as V mes match . On the other hand, V mes open will be the TDR response resulting from an open-ended network extremities measurement.

After having measured the matched end reflectometry response V mes match , the first part of the TDR-NEW approach begins by numerically constructing all N possible NUT configurations N U T i sim (i = 1, 2, ..., N ) based on the knowledge of the NUT's M extremities. In fact, V mes match permits extracting position and the number of branches of the first two junctions in the network (l 1 , n 1 , l 2 , and n 2 ) as previously detailed in II-C. Therefore, the number of possible NUTs would decrease as the number of free extremities M diminishes. The TDR response V i sim of each N U T i sim is determined by the numerical model described section II.

The problem now is to select the N U T i sim that best resembles the unknown studied network. Notably, V mes open allows retrieving different branch interconnections due to the multiple reflections present in its TDR response. To accomplish that, both the measured V mes open and the direct model of all remaining N U T i sim are used to reconstruct the wiring network. The design variables are the lengths of different branches L i composing N U T i sim excluding the first two junction positions l 1 and l 2 previously determined.

From the reflectometry data V mes open of the NUT, the methodology of reconstruction leads to the resolution of an inverse problem: the newton-based algorithm is used minimize the objective function given by equation 7 between V mes and each V i sim . Accordingly, we will start with an initial population of the n branch lengths L = [L 1 , L 2 , , L n -2] composing the N U T i sim . These solutions then undergo the newton-based optimization process described in sec. III-A. After each optimization process the fitness values F i val will be sorted and the N U T i sim with the highest F i val will be dropped. This process will be iterated till we reach a stopping criterion demonstrated by the lowest F i val corresponding to N U T i sim whose solution L best fits the branch lengths of the tested network.

F i val = V i sim -V mes 2 (7)
For clarification purposes, the diagram of Fig. 3 summarizes all the steps we followed in the proposed TDR-GA algorithm.

IV. RESULTS AND DISCUSSIONS

In order to better illustrate the benefits introduced by the TDR-NEW method in retrieving the topology of an unknown network we opted to test it numerically and experimentally on different NUTs.

A. Numerical Verification

Numerical results have been deducted using the network configuration already considered in Fig. 1. The same network characteristics and simulation parameters considered in section II-C were followed. The very first step of the TDR-NEW algorithm is to numerically construct all possible hypothesized network topologies based on the diagnosed NUT's number of extremities. To accomplish this task, the analysis of the matched-end reflectometry response V mes match of the corresponding NUT as detailed in section II-C shows that the first junction is located at l 1 = 1.5 m from the reference testing port P test and interconnecting n 1 = 3 branches. On the other hand, the second consecutive junction appears to be located at l 2 = 4 m from P test while interconnecting n 2 = 2 branches. Consequently, based on the presence of M = 6 extremities and the knowledge of n 1 and n 2 , we are left by 4 free ports as demonstrated in Fig. 4. Therefore, we can claim that we To clear up all doubts we will apply the newton-based optimization algorithm to solve the inverse problem between the open-circuited reflectometry response V open match and V i sim of each of the three hypothesized N U T i sim . The number of design length variables of each optimization process depends on the number of branches composing each N U T i sim excluding the retrieved lengths l 1 and l 2 . Therefore, continuing the TDR-NEW algorithm detailed in section III-B qualifies the NUT configuration that best resembles the tested NUT as demonstrated in Fig. 5 in a total duration of 123 seconds using a standard state-of-the art computer. The comparison between the obtained NUT with the original tested network shows that the TDR-NEW approach efficiently reconstructed the unknown tested wire network with accurate and precise values of the branch lengths.

B. Experimental Validation

Experimental tests were also conducted in an effort to validate the proposed TDR-NEW approach on practical reallife networks. We considered a double Y-junction NUT composed of 50Ω coaxial cables connected as shown in Fig. The same methodology followed in the numerical verification in section IV-A demonstrating the advantages of the TDR-NEW approach detailed in sec. III-B will be repeated. The resulting reconstructed network is shown in Fig. 8 after a total processing period of 200 seconds; notably it appears to perfectly resemble the tested NUT of Fig. 6. Significantly, a clear close agreement can be noticed from the obtained results.

V. CONCLUSION

In this paper we addressed the network reconstruction problem of estimating the topology and the branch lengths of a wire network. The TDR-NEW approach, a non-destructive testing method, was proposed which is based on reflectometry response and newton-based optimization algorithms. The numerical and experimental result has proven the effectiveness and feasibility of the proposed approach in precisely reconstructing unknown branched networks. We showed that the proposed approach is computationally efficient (short processing time), consistent (return correct topology), and robust (can tolerate a maximum level of measurement errors). The framework provides a powerful tool for future implementation on structure and dynamics of large-scale networks. Future work will need to deal with advanced global optimization tools, namely the genetic algorithms, for more computational efficiency and shorter processing periods. Besides, it could be interesting to reconstruct the network's topology without having to disconnect the network and force specific measurement frameworks.

Fig. 1 .

 1 Fig.1. Layout of the four Y-junction NUT considered for the numerical validation of the TDR-NEW approach including the branch lengths.

Fig. 2 .

 2 Fig. 2. The TDR reflectometry responses corresponding to the network of Fig. 1 in the cases of matched and open-ended extremities.

Fig. 3 .

 3 Fig.3. A diagram illustrating the differebt steps followed by the TDR-GA algorithm.

Fig. 4 .

 4 Fig. 4. The hypothesized numerical NUTs constructed based on the 6 extrimities of the tested NUT and the results obtained from the matched-end TDR response analysis.

Fig. 5 .

 5 Fig. 5. The constructed NUT after applying the TDR-NEW approach on the numerically simulated TDR response of the NUT of Fig. 1.

Fig. 6 .

 6 Fig. 6. Layout of the double Y-junction NUT considered for the experimental validation of the TDR-NEW approach including the branch lengths.

Fig. 7 .

 7 Fig. 7. The TDR reflectometry responses corresponding to the experimental validation of the network of Fig. 6 in the cases of matched and open-ended extremities.

Fig. 8 .

 8 Fig.8. The constructed NUT after applying the TDR-NEW approach on the measured TDR response of the NUT of Fig.6.

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