Mikael Kepenekian
email: mikael.kepenekian@univ-rennes1.fr

Yann Molard

Karine Costuas

Pierric Lemoine

Régis Gautier

Soraya Ababou-Girard

Bruno Fabre

Pascal Turban

Stéphane Cordier
email: stephane.cordier@univ-rennes1.fr

Red-NIR luminescence of Mo 6 monolayered assembly directly anchored on Au(001)

Red-NIR luminescence of

] 2-building blocks form a self-assembled monolayer on the Au(001) surface as shown by scanning tunneling microscopy, atomic force microscopy and X-ray photoelectron spectroscopy. Strikingly, the photoluminescence of [Mo 6 Br i 8 (NCS)

a 6

Introduction

Near infrared (NIR) emitting devices are attractive for many applications, including bioimaging, photovoltaics, light conversion or telecommunication. [1][2][3][4][5][6][7][8] While long-lived emission is usually associated with rare-earth based complexes or organic dyes, 2,4 another path involves the use of transition metal atom clusters. The chemical engineering of metal atom clusters enables to prefabricate nanosized building blocks with specific tailored properties starting from solid-state inorganic compounds. Metallic clusters contain metal-metal bonds and can be viewed as 'superatoms', providing an unprecedented ability to design novel materials and functionalized surfaces. [START_REF] Cotton | [END_REF][10][11] M 6 octahedral transition metal atom clusters exhibit unique intrinsic structural and physical properties (photoluminescence, redox properties, generation of singlet oxygen) with an orthogonal disposition of metallic sites that can be selectively functionalized. [12][13][14][15] These make them relevant building blocks for the structuration at the nanometric scale and functionalization of hybrid organic-inorganic materials, supramolecular and hydrogen bonded frameworks, coordination compounds and functional surfaces. In particular, face-capped [Mo 6 X i 8 X a 6 ] 2- clusters, where X is a halogen, can be prepared by solid-state synthesis, 16 and then modified by exchanging the apical halogen X a by specific chemical functions designed to enhance the optical properties or to favor a better integration in organic materials (e.g. polymeers or liquid crystals) or to induce robust anchoring on surfaces. [17][18][19][20] Notably, such a strategy has been developed in order to take advantage of unique electronic and photo-(catalytic) properties of clusters by immobilization onto electronically insulating substrates 21,22 or to design Schottky diodes by A c c e p t e d M a n u s c r i p t the anchoring Mo 6 clusters onto semiconducting surfaces (silicon or carbon). 23 Mo 6 clusters are appealing because, in addition to the flexibility offered by the facile substitution of halogens, they present NIR photoluminescent (PL) properties with multi-component emission. 24 Such properties experience a turbulent partnership with metallic substrates. If an heterogenous environment can lead to the enhancement of the luminescence, 25,26 molecules close to flat metal surface experienced a dramatic quenching. 27,28 As a consequence, studies of luminescence usually require elaborated strategies to decouple the molecule from the surface by using multilayers or long spacers. [29][30][31][32] Herein, we report on the use of [Mo 6 Br i 8 (NCS) a 6 ] 2-building block for the functionalization of monocrystalline Au(001) surfaces. After synthesis and deposition, a self-assembled monolayer is obtained as evidenced by several spectroscopic and computational measurements. Importantly, despite the use of a short anchoring unit, cluster multi-component NIR PL properties are preserved with minor perturbations with respect to the free-standing cluster.

Results and Discussion

Molecular face-capped [Mo 6 X i 8 X a 6 ] 2-cluster anionic units (Figure 1a) are prepared at high temperature by solidstate synthesis (see Electronic Supporting Information, ESI † ). The Mo 6 cluster were then deposited on Au(001) films prepared by molecular beam epitaxy and observed by scanning tunneling microscopy (STM, Figure S3, ESI † ). The procedure used for the deposition of [Mo 6 Br i 8 (NCS) a 6 ] 2-onto gold was similar to that use by Prokopuk and Shriver for the deposition of [Nb 6 X i 12 (NCS) a 6 ] 4-onto gold (see ESI † ). 33 The modified gold surface was characterized by atomic force microscopy (AFM), STM, electrochemistry and X-ray photoelectron spectroscopy (XPS). All these techniques confirmed the formation of one [Mo 6 Br 8 (NCS) 6 ] monolayer with both the expected molecular composition and thickness. First, the AFM analysis shows an almost defect-free smooth surface with a root mean square roughness of about 3.8 Å (Figure S4, ESI † ). The thickness of the deposited film is estimated at 18±3 Å by the scratching method (Figure 2a,b), 34 which is in relatively close agreement with the diameter of the molecular cluster structure determined from X-ray diffraction (ca. 14 Å) to which should be added the typical length of S-Au bonds (ca. 2.4 Å). 35 Electrochemical measurements in CH 2 Cl 2 medium indicate that the metal cluster retains its redox activity after immobilization. Indeed, the cyclic voltammogram of the [Mo 6 Br 8 (NCS) 6 ]modified gold surface shows in reduction an ill-resolved shoulder around 1.70-1.80 V vs. ferrocene/ferrocenium (Fc/Fc + ) reference which can be converted to a well-resolved cathodic peak at 1.73 V on the corresponding semi-derivative voltammogram (Figure 2c). Such a redox process is observed at 1.72 V vs. Fc/Fc + for the dissolved complex and is ascribed to the monoelectronic reduction of the metal cluster (Figure S5, ESI † ). It is worth noting that such a reduction process was either absent or observed at more negative potentials in the case of clusters incorporating other ligands such as halides. 36 This situation originates from the moderate π-acceptor character of (NCS)-ligands.

STM images of the grafted gold surface show a surface morphology preserved after grafting with the characteristic orientation of the Au monoatomic step edges. On the Au atomic terraces, an additional blurry texture is observed. Higher magnification STM image (Figure 2d) further evidences the presence of a dense granular layer on the Au surface with typical grain diameter of 2.6±0.3 nm. These nanometric grains are attributed to individual [Mo 6 Br 8 (NCS) 6 ] 2-grafted cluster as already observed in similar systems prepared on Si(111) surfaces. 23,37 Preliminary scanning tunneling spectroscopy (STS) measurements on the obtained [Mo 6 Br 8 (NCS) 6 ] 2-self-assembled monolayer demonstrate an electronic bandgap of 3.5 eV with a system Fermi level located in the middle of the bandgap (Figure S6,ESI † ).

XPS performed on the grafted surface show characteristics signals of Mo, Br, S and Au (Figure 2e). The thickness of the grafted cluster as deduced from the attenuation of gold signal is 1.9±0.2 nm, in agreement with the estimated thickness from scratching method. A cluster coverage of (2.6±0.8)×10 13 clusters per cm 2 is obtained by comparing the molybdenum XPS intensity to the one-plane silicon intensity measured on a reference sample. 23 The thickness as well as the coverage indicate the formation of one [Mo 6 Br 8 (NCS) 6 ] monolayer on top of the gold layer.

In order to gain a more in-depth understanding of the Mo 6 cluster configuration on the Au(001) surface, we perform periodic DFT calculations using the SIESTA package (see ESI † ). 38,39 On a 5-layer-thick slab consisting of a 5×5 supercell of the Au(001) surface, we deposit the Mo 6 cluster using on various sites of the surface (top, hollow, bridge) and with various numbers of anchoring thiocyanate units in contact with the surface (Figure 3a). The lowest energy is obtained when the cluster interacts through four NCS ligands with the Au(001) surface (Table S4, ESI † ), the four S atoms occupying bridge positions (Figure S7, ESI † ). Concomitantly with energetic stabilization, the raising number of anchors leads, as expected, to an enhanced hybridization between the Mo 6 cluster and the gold surface as marked by the spread of the density of states projected on the cluster states (Figure 3b). In addition, going from 1 to 4 anchors, we observe a monotonous shift of the Fermi energy with respect to the cluster states. In the most stable 4-anchor configuration, the Fermi energy is in the middle of the cluster electronic gap, in agreement with STS results (Figure S6, ESI † ).

Solid-state PL spectra were taken on the bare Au(001) surface, (NH 4 ) 2 [Mo 6 Br 8 (NCS) 6 ] dried powder and the supported monolayer for temperatures ranging from 80 K to room temperature (RT) with a 20 K increment (see ESI † ). The bare gold surface emits from 425 nm to roughly 1000 nm with a maximum be- tween 425 and 510 nm followed by a continuous decrease of the signal that vanished around 1000 nm (Figure 4a). The spectrum exhibits a structured shape with several band maxima (around 510, 545, 575, 600, 640, 695, 745 and 775 nm). The maximum intensity is measured at 545 nm. Let us note that the depletion observed at 945 nm is an artifact due to the absorption of the optical fiber used in the setup and is found in all spectra recorded. The emission spectra of dried (NH 4 ) 2 [Mo 6 Br 8 (NCS) 6 ] powder is characterized at RT by a broad structured band presenting several local maxima at roughly 715 and 770 nm and a shoulder located at 840 nm (Figure 4b). As expected, the emission intensity increases noticeably upon cooling but the shape of the signal also evolves. At 80 K, the emission spectrum shows one band maximum at 770 nm and two pronounced shoulders located at 720 and 835 nm. Similar features have been observed on parent Mobased clusters by PL and cathodoluminescence, 24,40 they are best interpreted as the superposition of several emissions due to different excited states whose population is temperature dependent. For (NH 4 ) 2 [Mo 6 Br 8 (NCS) 6 ] studied herein, the emission intensities of states emitting at 770 and 835-840 nm increase importantly, the latter even more than the former. Interestingly, the in- tensity of the peak at 720 nm increases only till 180 K then diminish upon further cooling to become almost undetectable at 80 K. A similar behavior is observed for the tiny shoulder at 750 nm. Figure 4c shows the PL signal of the grafted surface recorded from 80 K to RT. A direct comparison between this emission spectrum with the one of the bare gold surface on one hand and the one of the dried powder on the other, allows to conclude that the signal ranging from 425 to 600 nm corresponds to the emission of the gold surface and is nearly temperature independent. By contrast, the second part of the spectrum (at higher wavelength) depends strongly on the temperature. While at RT, the emission of the gold surface is predominant, the contribution of the Mo 6 cluster increases and becomes predominant at 80 K. Indeed, at RT, five maxima are spotted: two well defined bands at roughly 695 and 640 nm, two less defined maxima at 750 and 770 nm and one shoulder at 860 nm. These five values fit well with the signal of the bare gold surface (Figure 4a). However, let us note that the emission of the Mo 6 cluster can still be observed at RT (Figure S8, ESI † ). At low temperature, three band maxima become predominant at 710, 750 and 770 nm. Those signals and the second shoulder at 860 nm are attributed to the immobilized clusters.

Importantly, the immobilization of [Mo 6 Br 8 (NCS) 6 ] onto gold surface does not quench its emission. The emission spectra study reveals at least the existence of four emissive states. Their emission wavelengths remain close to the one measured for the powder, with energy shifts ranging from almost zero to 0.04 eV.

We turn again to computational approaches to shed light on the optical properties of the free-standing and supported Mo 6 clusters thanks to molecular calculations using the ADF2016 package (see ESI † ). 41,42 Computational study of the emission properties requires to consider the geometrical relaxations that follow the excitation process. Here, we use the same protocol used for the parent compound [Mo 6 Br 14 ] 2-. 24 In a first step, we consider the free-standing [Mo 6 Br 8 (NCS) 6 ] 2-cluster. Three distinct relaxed triplet excited states, namely T 1 , T 2 and T 3 , are found at +1.882, +1.883 and +2.012 eV above the ground state S 0 , respectively. As for the parent metallic cluster [Mo 6 Br 14 ] 2-, 24 the two lowerlying triplet states correspond to various distortions of the Mo 6 core with the elongation of one apex toward the squared basal plane of the octahedron to which it is coordinated, the opposite S5, ESI † ). The changes in geometry between the third triplet excited state (T 3 ) and the ground state result from the elongation of one Mo-Mo bond from 2.660 to 3.070 Å. The emission wavelengths obtained from these T n optimized geometries are of 707, 720 and 873 nm for T 1 , T 2 , and T 3 , respectively (Table S6). This nicely reproduces the broadness of experimental spectrum (Figure 4a) by recovering the large emission structured band ranging from roughly 650 nm to the NIR part of the emission (950 nm), although the experimental emission peak around 770 nm is missing. It has to be emphasized that the 12 first triplet electronic vertical excitations are found between 2.19 and 2.39 eV. This energy congestion of states leads to unavoidable potential energy surface jumps between excited states during the TD-DFT optimization procedure. However, one can notice that all described excitations implied in the emitting process are centered on the Mo 6 core and involve in far less extent the outer ligand sphere.

In order to assess the anchoring of the cluster on the light emitting properties, we follow the same protocol as before but starting from a constrained geometries taken out of our periodic calculations to mimic the effect of surface grafting. Thus, the singlet ground state const S 0 corresponds to the most stable 4-anchored configuration (Figure 3a). Out of this singlet, two triplet states, const T 1 and const T 2 are obtained. The corresponding optimized geometries result from metal-metal bond elongations very similar to the one observed for the free-standing molecular cluster (Table S5). Those triplet states are characterized by (i) an apex elongation, and (ii) a partial Mo-Mo bond breaking, respectively (Figure 4d). The emission wavelengths calculated from these constrained excited states are 794 and 838 nm for const T 1 and const T 2 , respectively (Table S6). Naturally, our molecular DFT/TD-DFT calculations tend to overestimate the interaction with the surface at the triplet excited states by fixing the position of the interacting thiocyanate ligands. Nevertheless, this demonstrates that even in these strongly constrained geometries the range of emission energies as well as the shape of emitting states are extremely similar to the free-standing system. It appears that the Mo 6 core is extremely robust to the configuration imposed to the outer sphere by the environment. Moreover, the electronic coupling between the metallic core and the gold surface is weak, as indicated by the density of states obtained from surface calculations projected on Mo states on one hand and NCS-ligands on the other (Figure S10, ESI † ). Indeed, the shape of Mo states is essentially preserved, while the ligands states experience a strong broadening pointing to a stronger interaction with the gold surface. As a result, the thiocyanate ligands not only serve as anchors but also as a barrier preserving the optical properties of the cluster by decoupling the Mo 6 core from the metallic surface, thus preventing the quenching expected at the vicinity of a flat metal surface. 27,28 This is in excellent agreement with the small changes observed experimentally between the emission properties of [Mo 6 Br 8 (NCS) 6 ] 2- before and after immobilization on the Au(001) surface. A complete computational treatment of the temperature dependence of the PL properties of the [Mo 6 Br 8 (NCS) 6 ]-modified gold surface would require molecular dynamics performed over the whole system (Mo 6 cluster and Au(001) surface) for each of the many emitting excited triplet states. Unfortunately, such treatment is currently out of reach.

Conclusions

In summary, we report combined experimental and theoretical investigations on the design of a red-NIR luminescent monolayer of self-assembled Mo 6 inorganic cluster immobilized onto Au(001) surface. To this purpose, our investigations have been driven toward a large scope of methodologies from the synthesis of functional cluster building blocks and their surface deposition, their characterizations by electrochemistry as well as by AFM, STM and XPS measurements to DFT computational study of a Mo 6 molecular cluster immobilized onto a Au(001) surface. The surface modification is straightforward and effective. The resulting device is robust thanks to the ambidentate nature of the NCS linker which leads to strong Mo-N bonds with the cluster metallic core on one hand, and, on the other hand, S-Au covalent bonds anchoring the inorganic luminophor to the surface. Moreover, the intrinsic emission of the [Mo 6 Br i 8 (NCS) a 6 ] cluster-building blocks originating mainly from electronic transfer within the {Mo 6 Br i 8 } cluster core, their luminescence is not significantly altered after immobilization. To the best of our knowledge, this is an unprecedented example of a monolayer of photoluminescent dyes (organic and inorganic) in direct contact to a crystalline gold surface showing unquenched photoluminescence induced by visible irradiation. Thanks to the easy processing, such robust NIR emission of cluster monolayers could be enlarged to cluster-functionalized gold wires or nanoparticles. This work constitutes a breakthrough and a first step to integration in functional devices for applications in bio-imaging, chemical sensors, SERS, photovoltaics or telecommunication.

(NH 4 ) 2 [

 42 Mo 6 Br 8 (NCS) 6 ].4C 3 H 6 O crystallizes in the orthogonal space group Pccn (a=21.726(2) Å, b=13.112(2) Å, c=17.020(2) Å). (NCS)-groups are bonded to the {Mo 6 Br i 8 } 4+ cluster core by nitrogen atom. This arrangement affords peripheral sulfur atoms that are known to exhibit a strong affinity with gold surfaces. It is worth noting that in the structure of (NH 4 ) 2 [Mo 6 Br 8 (NCS) 6 ].4C 3 H 6 O, the [Mo 6 Br i 8 (NCS) a 6 ] units form pseudo hexagonal layers (Figure 1b and Figure S2, ESI † ) where each unit interacts with four other units through van der Waals contacts ((NCS) a • • • Br i =3.424 Å). These layers are stacked according a AA'A-mode along the c-axis of the unit cell. The units interact with adjacent units of layers located above and below trough van der Waals contacts ((NCS) a • • • Br i =3.754 Å and 3.766 Å; Br i • • • Br i =3.680 Å; C• • • Br i =3.405 Å and 3.416 Å).

Fig. 1

 1 Fig. 1 (a) [Mo 6 Br i 8 (NCS) a 6 ] 2-units. Mo, Br, S, N and C atoms are depicted in violet, brown, yellow, blue and gray, respectively. (b) (NH 4 ) 2 [Mo 6 Br 8 (NCS) 6 ].4C 3 H 6 O crystal packing. For clarity, NH 4 and C 3 H 6 O are not depicted.

Fig. 2

 2 Fig. 2 (a) 3×3 µm 2 AFM image of a [Mo 6 Br 8 (NCS) 6 ]-functionalized gold surface after scratching of a ca. 500×500 nm 2 area. (b) Corresponding cross-section profiles along the scratched area. (c) Cyclic voltammograms at 0.1 Vs -1 of (n-Bu 4 N) 2 [Mo 6 Br 8 (NCS) 6 ] at 2 mM on a Pt disk electrode (dotted trace) and [Mo 6 Br 8 (NCS) 6 ]-modified gold disk electrode (black solid trace). The gray trace corresponds to the semi-derivative current of the modified surface. Electrolytic solution: CH 2 Cl 2 + 0.2 M Bu 4 NPF 6 . (d) 150×150 nm 2 STM image of the [Mo 6 Br 8 (NCS) 6 ] 2-selfassembled cluster monolayer with molecular resolution. (e) Wide XPS spectrum recorded on [Mo 6 Br 8 (NCS) 6 ]-functionalized gold surface, at a grazing angle of 45 • to enhance the top surface response.

Fig. 3

 3 Fig. 3 (a) DFT optimized structures of [Mo 6 Br 8 (NCS) 6 ] supported on the Au(001) surface with 1 to 4 anchors. Au, Mo, Br, S, N and C atoms are depicted in gold, violet, brown, yellow, blue and gray, respectively. For clarity, only 1 gold layer is depicted. (b) Density of states projected on [Mo 6 Br 8 (NCS) 6] states for the free-standing Mo cluster and the systems depicted in (a). In the free-standing case, the Fermi energy is taken as the median energy between the highest occupied and lowest unoccupied orbitals.

Fig. 4

 4 Fig. 4 (a) Luminescence spectra taken at T=-190 • C for (NH 4 ) 2 [Mo 6 Br 8 (NCS) 6 ] (dried powder form, dotted line), the Au surface (dashed line) and the grafted surface (plain line). (b) Temperature dependent emission spectra of (NH 4 ) 2 [Mo 6 Br 8 (NCS) 6 ] powder from T=-190 • C up to T=20 • C. (c) Same, for the [Mo 6 Br 8 (NCS) 6 ]-modified gold surface. (d) Schematic representation of the geometry deformations from the const S 0 singlet state to two emissive triplet states const T 1 and const T 2 .

  s c r i p t apex being essentially unaffected upon geometry relaxation (Figure S9 and Table

Mo 6 monolayered assembly directly anchored on Au(001) †

  Mikaël Kepenekian, * a Yann Molard, a Karine Costuas, a Pierric Lemoine, a Régis Gautier, a Soraya Ababou-Girard, b Bruno Fabre, a Pascal Turban, b and Stéphane Cordier, * a A tailored near infrared luminescent Mo 6 octahedral cluster bearing thiocyanate (NCS) terminal ligands, [Mo 6 Br i 8 (NCS)

	a ] 2-, has been synthesized to anchor onto gold substrate. After immo-6 8 (NCS) bilization, [Mo 6 Br i

a 6

Acknowledgements

Computational studies were conducted on the HPC resources of [TGCC/CINES/IDRIS] under the allocation A0020800649 and A0040800649 made by GENCI. M. K. work is supported by Rennes Métropole through the Allocation d'Installation Scientifique program.

Notes and references


M Shpotyuk
email: yashpotyuk@gmail.com

J Szlęzak

Y Shpotyuk
email: shpotyukmy@yahoo.com

C Boussard-Pledel

B Bureau
email: bruno.bureau@univ-rennes1.fr

V Balitska
email: vbalitska@yahoo.com

V Boyko
email: boykovit@gmail.com

O Shpotyuk
email: olehshpotyuk@yahoo.com

On the glass transition temperature T g against molar volume V m plotting in arsenoselenide glasses

Keywords: chalcogenide glass, arsenoselenides, glass transition temperature, molar volume, glassforming network, Van der Waals interaction

Dependence of glass transition temperature T g (K) on overall mean bonding energy E (kJ/mol) in arsenoselenide glass reexamined under per-atom calculations is shown to obey linearized master equation T g ≅418⋅(E-1.13). Compositional variations in T g against molar volume V m are plotted for g-As x Se 100-x taken within (0≤x≤65) domain assuming preferential cohesive Van der Waals (VDW) bonding between network-constituting entities. The T g values are found to vary as inverse-α-th power of V m , attaining distinct values for different networks, in part, 0D-molecular (α=6/3=2), 1Dchained (α=5/3), 2D-layered (α=4/3), and 3D-spatial (α=3/3=1). These variations originated from macroscopic geometry of VDW interaction are linearized in log-log presentation for networks dominated with chain-like 1D-entities (0≤x<∼8) and cross-linked 3D-entities (∼8<x<30-33), while demonstrate non-linear behavior for cross-linked 3D-and layered 2D-entities (30-33<x<40), and layered 2D-and molecular 0D-entities (40<x<65). Appearance of molecular entities in g-As x Se 100-x (40<x<65) results in self-terminated loop in log-log plotting of T g (1/V m ) dependence.

Introduction

The glass transition phenomenaon defined merely by characteristic temperature where supercooled liquid is frozen in a solid state (known as glass transition temperature T g [START_REF] Angell | Relaxation in glassforming liquids and amorphous solids[END_REF][START_REF] Cangialosi | Dynamics and thermodynamics of polymer glasses[END_REF][START_REF] Zanotto | The glassy state of matter: Its definition and ultimate fate[END_REF]) represents fundamental property of vitreous substances such as chalcogenide glasses (ChG), which play a crucial role in many fields of their applications stretching from phase-change phenomena to multi-cyclic exploitation of externally-induced functionality [START_REF] Feltz | Amorphous Inorganic Materials and Glasses[END_REF][START_REF] Tanaka | Amorphous Chalcogenide Semiconductors and Related Materials[END_REF]. That is why compositional variations in the T g values [START_REF] Rao | Glass transition in As-Se glasses[END_REF][START_REF] Tanaka | Glass transition of covalent glasses[END_REF][START_REF] Saffarini | Glass transition temperature and molar volume versus average coordination number in Ge 100-x S x bulk glasses[END_REF][START_REF] Tichý | Covalent bond approach to the glass-transition temperature of chalcogenide glasses[END_REF][START_REF] Lankhorst | Modelling glass transition temperatures of chalcogenide glasses. Applied to phase-change optical recording materials[END_REF][START_REF] Mazurin | Glass properties: compilation, evaluation, and prediction[END_REF][START_REF] Thiruvikraman | Rings, chains and planes: Variation of Tg with composition in chalcogenide glasses[END_REF], and their interrelation with other materials-specific parameters, which are known to be strongly dependent on cohesive forces and rigidity of covalent-type networks [START_REF] Tichý | Covalent bond approach to the glass-transition temperature of chalcogenide glasses[END_REF][START_REF] Naumis | Variation of the glass transition temperature with rigidity and chemical composition[END_REF][START_REF] Freitas | Some remarks on the glass transition temperature in chalcogenide glasses: a correlation with the microhardness[END_REF], have attracted a widespread attention within a glass-science community.

In general, the glass transition temperature T g serves as indicative of onset in cooperative rearrangement of some structural entities composing glassy network built of atoms, molecules, clusters, segmental chains, layers, etc., where viscosity η overcomes the critical barrier approaching η c ≅10 13 Poise [START_REF] Angell | Relaxation in glassforming liquids and amorphous solids[END_REF][START_REF] Tanaka | Glass transition of covalent glasses[END_REF]. In the Tichy's interpretation [START_REF] Tichý | Covalent bond approach to the glass-transition temperature of chalcogenide glasses[END_REF], to reach the higher mobility of network constituents in ChG, one should supply two energetic contributions, these being firstly to disturb glassy matrix creating such mobile entities, and then to reorient them for moving in a space. The former is evidently relevant to strength of primary covalent bonding, that is number and type of network-composing covalent bonds in ChG [START_REF] Rao | Glass transition in As-Se glasses[END_REF][START_REF] Tanaka | Glass transition of covalent glasses[END_REF]. At a global scale of compositional variation, the T g changes are defined by superposition of these stronger covalent bonds with weaker secondary bonds, mainly of intermolecular or Van der Waals (VDW) type, governing cooperative rearrangement in glass-forming region [START_REF] Rao | Glass transition in As-Se glasses[END_REF][START_REF] Tanaka | Glass transition of covalent glasses[END_REF]. This approach allows prediction of compositional T g variations in ChG in terms of cohesive VDW bonding energy for principal atomic units forming movable segmental entities in their structure. Thus, assuming the Arrhenius relation for viscosity with an effective activation energy of atomic segmental motion of polymer chains or slipping movements of distorted layers (E=E 0 ⋅n Z-1 ) defined as cooperative rearrangement of structural units including n≅5 atoms (E 0 ≅0.15 eV), K.

Tanaka [START_REF] Tanaka | Glass transition of covalent glasses[END_REF] derived simple relationship between T g values and average coordination numbers per atom Z for ChG and molecular materials with hydrogen bonding in the range of 1≤Z≤2.7:

A c c e p t e d M a n u s c r i p t ln(T g ) = 1.6⋅Z + 2.3.

(1)

The above eq. ( 1) describes compositionally driven T g variations in covalent glassy networks possessing zero-(0D), one-(1D) and two-dimensional (2D) glass-forming structural elements.

When strength of VDW bonding approaches dissociation energy of primary network-constituting covalent bonds, as it was expected for A-rich over-stoichiometric ChG of A x B 100-x systems (where A = As, Ge; B = S, Se), the T g values are supposed [START_REF] Tanaka | Glass transition of covalent glasses[END_REF] to be nearly constant due to competitive contribution from weaker homonuclear A-A bonds fractured under glass transition. But this feature is not supported by T g (Z) dependences for g-As-S [START_REF] Feltz | Amorphous Inorganic Materials and Glasses[END_REF], g-As-Se [START_REF] Feltz | Amorphous Inorganic Materials and Glasses[END_REF][START_REF] Feltz | Glass formation and properties of chalcogenide systems XXVI: permittivity and the structure of glasses As x Se l-x and Ge x Se l-x[END_REF][START_REF] Chen | Long term aging of selenide glasses: evidence of sub-T g endotherms and pre-T g exotherms[END_REF][START_REF] Yang | Correlation between structure and physical properties of chalcogenide glasses in the As x Se 1-x system[END_REF], g-Ge-S [START_REF] Feltz | Amorphous Inorganic Materials and Glasses[END_REF][START_REF] Zhu | Correlation between thermo-mechanical properties and network structure in Ge x S 100-x chalcogenide glasses[END_REF], and g-Ge-Se [START_REF] Feltz | Amorphous Inorganic Materials and Glasses[END_REF][START_REF] Feltz | Glass formation and properties of chalcogenide systems XXVI: permittivity and the structure of glasses As x Se l-x and Ge x Se l-x[END_REF][START_REF] Boolchand | Rigidity transitions in binary Ge-Se glasses and the intermediate phase[END_REF], which demonstrate rather decreasing tendency for over-stoichiometric compositions (after reaching more or less pronounced T g maximum at the stoichiometry point) than compositionally-invariant trend.

Within other approach [START_REF] Thiruvikraman | Rings, chains and planes: Variation of Tg with composition in chalcogenide glasses[END_REF], the VDW interactions are considered as completely responsible for cooperative rearrangement of some atomic units at the glass transition, so that changes in T g values arise from variations in preferential type of these interactions between structural entities composing glass-forming network, which can be defined by molar volume V m . Thus, the T g values were found to vary with glass composition as the inverse-α-th power of molar volume V m :

T g ∼ (1/V m ) α , ( 2
)
where power index α=6/3=2 stands for 0D-dimensional networks characterized by interaction between point-like entities (such as sulphur rings S 8 ), α=5/3≈1.67 is character for preferential 1Ddimensional networks dominated by interaction between chalcogen chains, α=4/3≈1.33 corresponds to 2D-dimensional networks built of atomic sheets, and α=3/3=1 is ascribed to 3D-dimensional networks, where VDW interactions are ascribed to more extended multi-atomic formations. With respect to the structure of over-stoichiometric arsenic sulphides/selenides [START_REF] Feltz | Amorphous Inorganic Materials and Glasses[END_REF], the latter can be imagined as cage-like molecular clusters and their network derivatives. But this suggestion was not clarified in [START_REF] Thiruvikraman | Rings, chains and planes: Variation of Tg with composition in chalcogenide glasses[END_REF] because of limitation to only under-stoichiometric glasses of As-S system (Z<2.40).

A c c e p t e d M a n u s c r i p t

This study is aimed to recognize compositional T g variations in ChG of canonical g-As x Se 100-x system possessing pronounced glass-forming ability in a wide range of compositions ranging from pure g-Se (Z=2.00) to highly As-enriched g-As 65 Se 35 (Z=2.65).

Experimental

The arsenoselenide g-As More details on synthesis procedure can be found elsewhere [START_REF] Ya | Effect of high-energy mechanical milling on the FSDP-related XRPD correlations in Se-rich glassy arsenic selenides[END_REF][START_REF]Chalcogenide Glasses: Preparation, properties and application[END_REF].

The synthesized specimens annealed below glass transition temperature T g were amorphous, as it follows from their powder X-ray diffraction patterns showing only diffuse "amorphous" halos, character conch-like fracture of fresh-ingot cut sections and far IR transparency. Macroscopic densities ρ (±0.005 g⋅cm -3 ) determined at room temperature by Archimedes displacement in ethanol using Mettler Toledo balances, and mid-onset glass transition temperatures T g (±3 o C) determined from DSC scanning under 10 K/min heating rate using TA Instrument Q20 calorimeter, testify in a favor of complete adequacy of the prepared alloys with known counterparts from this binary system [START_REF] Feltz | Amorphous Inorganic Materials and Glasses[END_REF][START_REF] Feltz | Glass formation and properties of chalcogenide systems XXVI: permittivity and the structure of glasses As x Se l-x and Ge x Se l-x[END_REF]. The values of molar volume V m and mean inter-atomic spacing d s m of these glasses derived from their atomic densities ρ are reproduced in

Results and discussion

In the realistic glass-forming structures, the glass transition phenomena are defined by averaged contribution of strong interatomic covalent bonding superimposed by weaker VDW interaction of A c c e p t e d M a n u s c r i p t

super-structural units forming a glassy network [START_REF] Tanaka | Glass transition of covalent glasses[END_REF][START_REF] Tichý | Covalent bond approach to the glass-transition temperature of chalcogenide glasses[END_REF][START_REF] Lankhorst | Modelling glass transition temperatures of chalcogenide glasses. Applied to phase-change optical recording materials[END_REF][START_REF] Thiruvikraman | Rings, chains and planes: Variation of Tg with composition in chalcogenide glasses[END_REF][START_REF] Freitas | Some remarks on the glass transition temperature in chalcogenide glasses: a correlation with the microhardness[END_REF]. Within compositional T g against V m variation, the input of stronger covalent bonding can be assumed as giving continuous power-type dependence with nearly constant power index defined by overall mean bonding energy E dependent on a glass composition. Thus, the dominated variations in T g against V m plotting can be ascribed to changes in the preferential VDW interaction for principal network-forming structures, which can be accepted as prototypes of some macroscopic geometrical configurations analyzed, e.g., in [START_REF] Parsegian | Van der Waals Forces. A handbook for biologists, chemists, engineers, and physicists[END_REF].

Compositional variations in g-As-Se defined by overall mean bonding energy.

Despite illusory simplicity, reliable correlation between glass transition temperature T g and overall mean bonding energy per atom E in ChG like g-As-Se seems not adequately understandable.

Nearly a quarter century ago, Tichý and Tichá [START_REF] Tichý | Covalent bond approach to the glass-transition temperature of chalcogenide glasses[END_REF] suggested the simple master equation for T g dependence on averaged bonding strength E in covalent networks derived for 186 representative ChG:

T g ≅ 311⋅(E -0.9). (3)
However, this equation cannot be accepted as describing realistic T g against E correlations in ChG because of incorrect determination of overall mean bonding energy per atom E. Indeed, the authors [START_REF] Tichý | Covalent bond approach to the glass-transition temperature of chalcogenide glasses[END_REF] defined this energy through two contributions, these being (i) mean energy of average cross-linking originated merely from heteronuclear covalent bonding and (ii) average energy of the 'remaining matrix' originated from homonuclear covalent bonding. To be validated for ChG, both components should be defined per atom of a glassy network (i.e. in respect to atomic fraction of glass ingredients), while the latter (the 'remaining matrix' energy) is introduced in [START_REF] Tichý | Covalent bond approach to the glass-transition temperature of chalcogenide glasses[END_REF] as product of dividing on a half of coordination number Z/2, i.e. respectively to the number of chemical bonds.

As a result, the overall mean bonding energies per atom E for g-As x Se 100-x determined following the procedure described in [START_REF] Tichý | Covalent bond approach to the glass-transition temperature of chalcogenide glasses[END_REF] are systematically under-estimated, i.e. the calculated E values occur to be less than realistic mean bonding energies for glasses in this system.

In application to g-As-Se, this discrepancy is clearly evident with simple structural-statistical assumptions for stoichiometry in this system obeying ideal continuous reticulation model (alternatively known as CO CBN, i.e. chemically-ordered covalent bond network model [START_REF] Feltz | Amorphous Inorganic Materials and Glasses[END_REF][START_REF] Tanaka | Amorphous Chalcogenide Semiconductors and Related Materials[END_REF]) derived by Yang et al. [START_REF] Yang | Correlation between structure and physical properties of chalcogenide glasses in the As x Se 1-x system[END_REF]. These authors [START_REF] Yang | Correlation between structure and physical properties of chalcogenide glasses in the As x Se 1-x system[END_REF] calculated overall mean bonding energies per atom E for these glasses taking into account different types of nearest-neighbor environments possible around Se and As atoms, and using known energies for separate covalent bonds reported by Pauling [START_REF] Pauling | The nature of the chemical bond[END_REF]. Under such approach, these energies should principally coincide with those calculated as suggested in [START_REF] Tichý | Covalent bond approach to the glass-transition temperature of chalcogenide glasses[END_REF], showing close similarity to linear dependence derived from experimental elastic moduli and density measurements for g-As x Se 100-x with distinct maximum at the stoichiometry point (x=40). Linear compositional dependence of E albeit with less pronounced maximum at x=40 is indeed observed [START_REF] Yang | Correlation between structure and physical properties of chalcogenide glasses in the As x Se 1-x system[END_REF], but it differs essentially from that non-linear one calculated in respect to [START_REF] Tichý | Covalent bond approach to the glass-transition temperature of chalcogenide glasses[END_REF] due to systematically under-estimated mean bonding energies E for non-stoichiometric glasses (see Fig. 2). Of course, for stoichiometric g-As 2 Se 3 having no homonuclear bonds in respect to CO CBN model, and g-Se possessing Z=2 with only homonuclear Se-Se bonds, the calculated energies coincide. For convenience reason, we also reproduce data on the overall mean bonding energies E calculated per one bond in g-As x Se 100-x (depicted by black solid line on Fig. 2) known as cohesive energies (CE).

It worth mentioning the sharper linear decrease in the experimental E values obtained from elastic moduli measurements for g-As x Se 100-x at x>40 was reasonably explained in [START_REF] Yang | Correlation between structure and physical properties of chalcogenide glasses in the As x Se 1-x system[END_REF] as resulting from formation of molecular-like structural fragments in over-stoichiometric glasses of this system.

In general, the overall mean bonding energy per atom E for ChG is simply defined as the weighted total energy of bonds per atom (divided by the total number of bonds) obeying chosen statistics in a glass-forming network [START_REF] Rao | Glass transition in As-Se glasses[END_REF]. Thus, the E values for g-As x Se 100-x can be found accepting bond-dissociation energies (in part, E As-Se =174 kJ/mol, E As-As =134 kJ/mol, and E Se-Se =184 kJ/mol [START_REF] Pauling | The nature of the chemical bond[END_REF]) and preferential type of CBN giving relative concentration of these bonds in a.u. (n As-Se , n As-As and n Se-Se ):

E = Z/2⋅(n As-Se ⋅E As-Se + n As-As ⋅E As-As + n Se-Se ⋅E Se-Se ). ( 4
)
For g-As x Se 100-x obeying CO CBN model, these concentrations can be respectively determined for under-stoichiometric (x≤40, Z≤2.4) and over-stoichiometric (x≥40, Z≥2.4) domains [START_REF] Gaskell | The Structure of non-crystalline mater[END_REF][START_REF]Amorphous Semiconductors[END_REF]: (5)

n As-Se = 0.04⋅x/Z, n As-As = (3 -0.05⋅x)/Z; n Se-Se = 0. (6)
As it was expected, the overall mean bonding energies E for g-As x Se 100-x calculated in respect to the above algorithm (see Fig. 2) occurred to be completely the same as calculated by Yang et al. [START_REF] Yang | Correlation between structure and physical properties of chalcogenide glasses in the As x Se 1-x system[END_REF]. This result can be also achieved in original Tichý and Tichá approach [START_REF] Tichý | Covalent bond approach to the glass-transition temperature of chalcogenide glasses[END_REF] recalculating the average energy of the 'remaining matrix' originated from homonuclear bonding per one atom of a glass (dividing on overall atomic fraction of glass components instead of half of coordination number Z/2). Now, we can respectively reproduce the log-log plotting of the overall mean bonding energy per atom E against inverse molar volume V m in the g-As x Se 100-x (Fig. 3). The lnE against ln(1/V m ) curve can be linearized for under-stoichiometric arsenoselenide glasses (x≤40, Z≤2.4) with the adjusted coefficient of determination R adj 2 =0.996:

lnE = 1.26⋅ln(1/V m ) + 8.89. (7)
Thus, the linear lnE against ln(1/V m ) plotting is expected with compositional variations in g-As x Se 100-x , provided the glass transition temperature T g is defined by the overall mean bonding energy per atom E (which also determines the averaged bond strength in a glassy matrix).

Other remarkable feature in compositionally-variable g-As x Se 100-x emerged from preferential intra-atomic covalent bonding is distinct loop formed in a growing coordination number Z sequence (with increased As content) by over-stoichiometric glasses with x>40. The down-going part of this loop is formed by glasses with increasing molar volumes V m on Fig. 1 (x=40, 45, 50, 55), while those with decreasing V m (x=60, 65) terminate this dependence in the loop as shown in Fig. 3.

With corrected overall mean bonding energies per atom E for g-As x Se 100-x as justified above, it seems interesting to compare realistic T g against E dependence with that predicted by Tichý and Tichá [START_REF] Tichý | Covalent bond approach to the glass-transition temperature of chalcogenide glasses[END_REF] via eq. ( 3), the linearized plotting of such correction being depicted on Fig. 4. Our data for these glasses can be satisfactorily least-square adjusted to the straight line red-coloured on Fig. 4 with more than 30% higher slope (R adj 2 =0.907):

T g ≅ 418⋅(E -1.13). (8)
A c c e p t e d M a n u s c r i p t

Thereby, the linearized T g against E dependence for g-As x Se 100-x occurs indeed to be systematically up-shifted along T g scale (approximately on ∼3% for g-Se and ∼10% for stoichiometric g-As 2 Se 3 ) in respect to the approximation given by Tichý and Tichá via eq. (3).

3.2.

Glass transition temperature T g against molar volume V m plotting in g-As-Se.

Thereby, covalent interactions alone are failure to predict realistic T g vs. V m plotting in ChG like g-As x Se 100-x , testifying in a favour of T g variations essentially governed by VDW interactions.

For 0D-networks built of randomly-packed hard spheres (atoms), simple interatomic interactions obviously prefer, thus giving thermal energy at glass transition k⋅T g proportional to the energy of VDW cohesive interaction between permanent or transient dipoles varying as the inversesixth power of inter-dipole distance 1/d 6 [START_REF] Parsegian | Van der Waals Forces. A handbook for biologists, chemists, engineers, and physicists[END_REF]. Since simple cubic dependence on d is expected for molar volume V m , this case results in inverse-second power of molar volume V m plotting (2).

If inter-chain interactions define glass structure (1D-networks), this T g (1/V m ) plot (2) attains somewhat reduced power index α=5/3, as was shown in [START_REF] Thiruvikraman | Rings, chains and planes: Variation of Tg with composition in chalcogenide glasses[END_REF]. In fact, this is the case of VDW interaction between infinitely long thin cylinders in a parallel configuration far apart d distance with free energy proportional to 1/d 5 [START_REF] Parsegian | Van der Waals Forces. A handbook for biologists, chemists, engineers, and physicists[END_REF].

If 2D-entities like atomic quasi-layers define glass structure, the power index α in plot [START_REF] Cangialosi | Dynamics and thermodynamics of polymer glasses[END_REF] continues further dropping to 4/3. This case can be simulated as preferential VDW interaction geometry involving infinitely long cylinders in perpendicular configuration far apart d distance with free energy proportional to 1/d 4 [START_REF] Parsegian | Van der Waals Forces. A handbook for biologists, chemists, engineers, and physicists[END_REF].

Finally, for most spatially extended 3D-structures, this plot (2) obeys α index tending towards 1.

This case represents geometry of VDW interaction between small spheres of defined radius far from other sphere of radius much greater than distance d between them, which results finally in free energy of VDW interaction proportional to 1/d 3 [START_REF] Parsegian | Van der Waals Forces. A handbook for biologists, chemists, engineers, and physicists[END_REF].

Therefore, the above deviations in the preferential geometry of VDW interaction varying T g against (1/V m ) plot ( 2) can be linearized in log-log presentation:

ln(T g ) = a + b⋅ln(1/V m ) = a -b⋅ln(V m ), (9)
A c c e p t e d M a n u s c r i p t

where a is the materials-related constant, and slope of this linearized dependence b represents some value directly related to α index in the inverse-α-th power plot (2).

The lnT g against ln(1/V m ) plotting reconstructed from experimentally measured glass transition temperatures T g and atomic densities ρ for g-As x Se 100-x is depicted in Fig. 5. A few characteristic regions can be distinguished on this graph with increase in the average coordination number Z from g-Se (Z=2.00) to g-As 40 Se 60 (Z=2.40), where these glasses obey known chain crossing model [START_REF] Tanaka | Amorphous Chalcogenide Semiconductors and Related Materials[END_REF][START_REF] Yang | Correlation between structure and physical properties of chalcogenide glasses in the As x Se 1-x system[END_REF][START_REF] Bureau | Medium range order studied in selenide glasses by 77 Se NMR[END_REF][START_REF] Bureau | Solid State 77 Se NMR investigations on arsenic-selenium glasses and crystals[END_REF][START_REF] Shpotyuk | Reversibility windows in selenide-based chalcogenide glasses[END_REF][START_REF] Shpotyuk | Physical aging of chalcogenide glasses[END_REF][START_REF] Golovchak | Structure of Se-rich As-Se glasses by high-resolution X-ray photoelectron spectroscopy[END_REF][START_REF] Golovchak | Experimental verification of the reversibility window concept in binary As-Se glasses subjected to a long-term physical aging[END_REF][START_REF] Shpotyuk | Compositionally-dependent structural variations in glassy chalcogenides: The case of binary As-Se system[END_REF], these being as follows 0≤Z<∼2.08; ∼2.08<Z<∼(2.29-2.33) and ∼(2.29-2.33)<Z<2.40.

Firstly, within 2.0≤Z<∼2.08 range (0≤x<∼8), the linearized log-log plotting (2) demonstrates steep dependence with slope b approaching 4.5 (linearization with adjusted coefficient of determination R adj 2 =0.998). In respect to Raman scattering [START_REF] Yang | Correlation between structure and physical properties of chalcogenide glasses in the As x Se 1-x system[END_REF] and XPS [START_REF] Shpotyuk | Reversibility windows in selenide-based chalcogenide glasses[END_REF][START_REF] Golovchak | Structure of Se-rich As-Se glasses by high-resolution X-ray photoelectron spectroscopy[END_REF] studies, the As-Se glasses in this compositional range possess 1D-structures built of Se chains stretching between some branchy points formed by trigonal AsSe 3/2 pyramids (thus forming network of AsSe 3/2branched Se-chains in preferential parallel configuration).

At further increase in As content in g-As x Se 100-x within ∼2.08<Z<∼(2.30-2.33) domain (∼8<x<∼29-33), chain-like entities occur in orthogonal configuration due to frequent cross-linking.

The studied glasses became, in fact, 3D-structured [START_REF] Yang | Correlation between structure and physical properties of chalcogenide glasses in the As x Se 1-x system[END_REF][START_REF] Shpotyuk | Physical aging of chalcogenide glasses[END_REF]. The slope b of the linearized log-log plot (3) drops to 2.5 (linearization with R adj 2 =0.982), which is in good respect with expected ∼70% dropping in the power index α when going from 1D-structures (α=5/3) to 3D-ones (α=1).

Within ∼(2.29-2.33)<Z<2.40 domain (corresponding to ∼29-33<x<40), the log-log plot [START_REF] Cangialosi | Dynamics and thermodynamics of polymer glasses[END_REF] losses its linearity tending to ever steeper dependence (the slope b estimated for glasses with x=40 and x=37 reaches 11.3, Fig. 5). In respect to characterization due to Raman scattering [START_REF] Yang | Correlation between structure and physical properties of chalcogenide glasses in the As x Se 1-x system[END_REF] and XPS studies [START_REF] Shpotyuk | Physical aging of chalcogenide glasses[END_REF][START_REF] Golovchak | Structure of Se-rich As-Se glasses by high-resolution X-ray photoelectron spectroscopy[END_REF], this region in g-As-Se is distinguished by transition to layer-type 2D-entities, which dominate in stoichiometric g-As 2 Se 3 , i.e. non-linearity in this compositional domain results from superposition of cross-linked 3D-and layered 2D-structures in g-As x Se 100-x with ∼30-33<x<40.

The character S-shaped T g (x) curve for g-As x Se 100-x around x=20 (representing the eutectic point on the phase diagram of As-Se system [START_REF] Golovchak | Experimental verification of the reversibility window concept in binary As-Se glasses subjected to a long-term physical aging[END_REF]) was pointed out by Phillips in his famous paper [START_REF] Phillips | Topology of covalent non-crystalline solids I: Short-range order in chalcogenide alloys[END_REF].

Contrary to g-As-S, where phase separation is merely dominated in a whole chalcogen-rich region,

A c c e p t e d M a n u s c r i p t such behavior was accepted as an evidence of incipient immiscibility in this glass-forming system. After Feltz's et al. opinion [START_REF] Feltz | Glass formation and properties of chalcogenide systems XXVI: permittivity and the structure of glasses As x Se l-x and Ge x Se l-x[END_REF], the composition of AsSe 3 (viz. g-As 25 Se 75 ) in this system, where AsSe 3/2 pyramids are interconnected by -Se-Se-bridging dimers (forming -Se 2 =As-Se-Se-As=Se 2network) can be accepted as chemically ordered glass-forming compound in non-crystalline state.

Changes in the slope of dielectric constant curve at this composition also suggest that =As-Se-As= bridges character for stoichiometric g-As 40 Se 60 are absent or exists only in negligible concentration in g-As x Se 100-x at x<25.

With further increase in the As-content (that is in over-stoichiometric g-As x Se 100-x with 40<x<65), the glass transition temperature T g decreases in unison with decrease in atomic density ρ (Table 1). The recalculated values of molar volume V m for these glasses demonstrate slight stretched maximum near x≅55 (see Fig. 1). Such changes result in a reverse trend in log-log plot [START_REF] Cangialosi | Dynamics and thermodynamics of polymer glasses[END_REF] with evidently increasing tendency in the slope b with ever growing x parameter. As a result, the T g values are completely renewed in over-stoichiometric g-As x Se 100-x samples at the end of this region (x=60, 65), creating in such a way the self-closed T g (1/V m ) loop as it clearly demonstrated in Fig. 5.

These changes find reasonable explanation within known models on structural evolution in Asrich g-As x Se 100-x composed of molecular-type entities [START_REF] Yang | Correlation between structure and physical properties of chalcogenide glasses in the As x Se 1-x system[END_REF][START_REF] Shpotyuk | Physical aging of chalcogenide glasses[END_REF][START_REF] Shpotyuk | Compositionally-dependent structural variations in glassy chalcogenides: The case of binary As-Se system[END_REF][START_REF] Yang | Fragile-strong behavior in the As x Se 1-x glass forming system in relation to structural dimensionality[END_REF]. With first As additions to g-As 2 Se 3 , the layered 2D-network is essentially destroyed, giving rise to mixed structures built of 0Dentities (partially and/or completely-polymerized realgar-type As 4 Se 4 , dimorphite-type As 4 Se 3 or As 4 cage-like molecules and their network derivatives), accommodated in a preferential 3D-network of As-Se remainder [START_REF] Yang | Correlation between structure and physical properties of chalcogenide glasses in the As x Se 1-x system[END_REF][START_REF] Yang | Fragile-strong behavior in the As x Se 1-x glass forming system in relation to structural dimensionality[END_REF]. Thus, from a viewpoint of VDW interactions, the governing role in such glasses belongs to admixture of destroyed 2D-structural entities possessing power index α in eq. ( 2) approaching 4/3 and 3D-entities having α close to 1 with 0D-structures of molecular-type As 4 Se n clusters giving steeper slope (α=2), the latter being evidently dominated with As content.

Noteworthy, the dimorphite-type As 4 Se 3 ring-like molecular cages (and their network derivatives) possessing close-to-spherical symmetry [START_REF] Aitken | GeAs sulfide glasses with unusually low network connectivity[END_REF][START_REF] Wright | Neutron studies of an inorganic plastic glass[END_REF] evidently dominate in g-As x Se 100-x at higher As content (x>55) [START_REF] Yang | Correlation between structure and physical properties of chalcogenide glasses in the As x Se 1-x system[END_REF][START_REF] Yang | Fragile-strong behavior in the As x Se 1-x glass forming system in relation to structural dimensionality[END_REF], thus ensuring extra-rapid dropping in the glass transition temperature T g owing to rotational diffusion appropriate to extremely low network connectivity (enhanced plasticity of glass-forming network) [START_REF] Aitken | GeAs sulfide glasses with unusually low network connectivity[END_REF]. In fact, these structural species ensure terminated loop-forming trend in a log-log plotting (2) as shown in Fig. 5 for last three compositions in this row (x=55, 60, 65). Therefore, it should be emphasized that loop-forming trend in T g (1/V m ) dependence is produced in g-As x Se 100-x by domination of molecular 0D-structural entities (such as dimorphite-type As 4 Se 3 ring-like cages) over layered 2D-and spatially cross-linked 3D-structures of As-Se remainder.

By finalizing, the above consideration discloses speculative character of some attempts to ascribe local maximum in the observed compositional T g (x) dependence near mean coordination number Z approaching 2.06-2.08 in physically-aged g-As x Se 100-x [START_REF] Chen | Long term aging of selenide glasses: evidence of sub-T g endotherms and pre-T g exotherms[END_REF] and g-Ge x Se 100-x [START_REF] Dash | Molecular origin of aging of pure Se glass: Growth of interchain structural correlations, network compaction, and partial ordering[END_REF] to topological threshold into super-flexible state. Realistically, in this domain, structure of g-As x Se 100-x changes from 1D-chain network with only some branchy points to spatially-extended cross-linked 3D-network, the respective T g (1/V m ) dependences being depicted on Fig. 5 by straight lines with slopes b approaching 4.5 and 2.5, respectively. Under physical ageing at ambient temperature T a , both lines are up-shifted due to increased T g . However, in ChG with compositions closer to pure Se, this effect is merely suppressed due to short distance from T g . Thus, the resulting changes produce local maximum in ∆T g for g-As x Se 100-x near x≅8, as it is clearly evidenced from Fig. 5.

Conclusions

It is shown that dependence of glass transition temperature T g (K) on overall mean covalent bonding energy E (kJ/mol) for g-As x Se 100-x critically examined under energy calculations performed per one atom of a glass network obeys the linearized master equation defined as T g ≅418⋅(E-1.13).

Compositional variations in T g against molar volume V m are plotted for g-As x Se 100-x taken from whole glass-forming region (0≤x≤65) assuming preferential cohesive Van der Waals (VDW) bonding between network-constituting entities. The T g values are found to vary as the inverse-α-th power of molar volume V m in arsenoselenide glasses, attaining several distinct values for different networks, in part, 0D-molecular (α=6/3=2), 1D-chained (α=5/3), 2D-layered (α=4/3), 3D-spatial (α=3/3=1). These variations originated from preferential geometry of VDW interaction between derived from estimation in respect to Tichý and Tichá algorithm [START_REF] Tichý | Covalent bond approach to the glass-transition temperature of chalcogenide glasses[END_REF] (red curve), as compared with statistical estimation of Yang et al. [START_REF] Yang | Correlation between structure and physical properties of chalcogenide glasses in the As x Se 1-x system[END_REF] and current calculations for CO CBN model (blue curve).

The cohesive energies CE determined per one covalent bond are plotted by black line.

Fig. 1 .

 1 They show an obvious global minimum-type tendency near stoichiometry Z=2.40 (x=40) superimposed on more stretched local maximum positioned at Z≅2.55 (x≅55).

A c c e p t e d M a n u s c r i p t

A c c e

  p t e d M a n u s c r i p t n As-Se = 0.06⋅x/Z, n As-As = 0, n Se-Se = (2 -0.05⋅x)/ Z;

A c c e p t e d M a n u s c r i p t

A c c e

  p t e d M a n u s c r i p t network-constituting elements are linearized in log-log presentation for specific network-forming domains, composed of chain-like 1D-entities 0≤x<∼8) and cross-linked 3D-entities (∼8<x<30-33), while they demonstrate complicated non-linear behavior for networks composed of mixed crosslinked 3D-and layered 2D-entities (30-33<x<40), as well as layered 2D-and molecular 0D-entities (40<x<65). Appearance of partially and/or completely-polymerized As 4 Se 4 , As 4 Se 3 and As 4 molecular-type entities in over-stoichiometric g-As x Se 100-x (40<x<65) results in terminated loopforming trend in log-log plotting of T g (1/V m ) dependence.

Figure captions:Fig. 1 .Fig. 2 .

 12 Figure captions:

Fig. 3 .

 3 Fig. 3. Linearized log-log presentation showing overall mean bonding energy per atom E against

Fig. 4 .

 4 Fig. 4. Glass transition temperature T g variation with the overall mean bond energy in g-As x Se 100-x .

Fig. 5 .

 5 Fig. 5. Linearized log-log plot showing glass transition temperature T g against inverse molar

Fig. 1 .

 1 Fig. 1. Compositional variations of the macroscopic atomic densities ρ, mean inter-atomic spacing d s m and molar volume V m in g-As x Se 100-x .

Fig. 3 .

 3 Fig. 3. Linearized log-log presentation showing overall mean bonding energy per atom E against

Fig. 4 .

 4 Fig. 4. Glass transition temperature T g variation with the overall mean bond energy in g-As x Se 100-x .

Fig. 5 .

 5 Fig. 5. Linearized log-log plot showing glass transition temperature T g against inverse molar

A c c e

  p t e d M a n u s c r i p t

Acknowledgement

The paper is a part of research done within the projects No 0119U100357 and 0117U007189 funded by Ministry of Education and Science of Ukraine. This research is supported by POLONIUM common action program (2018-2019) in respect to bilateral Agreement on scientifictechnical cooperation between Polish and French governments.