Nanostructured Molecular–Network Arsenoselenides from the Border of a Glass-Forming Region: A Disproportionality Analysis Using Complementary Characterization Probes

Binary AsxSe100−x alloys from the border of a glass-forming region (65 < x < 70) subjected to nanomilling in dry and dry–wet modes are characterized by the XRPD, micro-Raman scattering (micro-RS) and revised positron annihilation lifetime (PAL) methods complemented by a disproportionality analysis using the quantum–chemical cluster modeling approach. These alloys are examined with respect to tetra-arsenic biselenide As4Se2 stoichiometry, realized in glassy g-As65Se35, glassy–crystalline g/c-As67Se33 and glassy–crystalline g/c-As70Se30. From the XRPD results, the number of rhombohedral As and cubic arsenolite As2O3 phases in As-Se alloys increases after nanomilling, especially in the wet mode realized in a PVP water solution. Nanomilling-driven amorphization and reamorphization transformations in these alloys are identified by an analysis of diffuse peak halos in their XRPD patterning, showing the interplay between the levels of a medium-range structure (disruption of the intermediate-range ordering at the cost of an extended-range one). From the micro-RS spectroscopy results, these alloys are stabilized by molecular thioarsenides As4Sen (n = 3, 4), regardless of their phase composition, remnants of thioarsenide molecules destructed under nanomilling being reincorporated into a glass network undergoing a polyamorphic transition. From the PAL spectroscopy results, volumetric changes in the wet-milled alloys with respect to the dry-milled ones are identified as resulting from a direct conversion of the bound positron–electron (Ps, positronium) states in the positron traps. Ps-hosting holes in the PVP medium appear instead of positron traps, with ~0.36–0.38 ns lifetimes ascribed to multivacancies in the As-Se matrix. The superposition of PAL spectrum peaks and tails for pelletized PVP, unmilled, dry-milled, and dry–wet-milled As-Se samples shows a spectacular smoothly decaying trend. The microstructure scenarios of the spontaneous (under quenching) and activated (under nanomilling) decomposition of principal network clusters in As4Se2-bearing arsenoselenides are recognized. Over-constrained As6·(2/3) ring-like network clusters acting as pre-cursors of the rhombohedral As phase are the main products of this decomposition. Two spontaneous processes for creating thioarsenides with crystalline counterparts explain the location of the glass-forming border in an As-Se system near the As4Se2 composition, while an activated decomposition process for creating layered As2Se3 structures is responsible for the nanomilling-driven molecular-to-network transition.


Introduction
The binary arsenoselenides of an As x Se 100−x cut-section comprise an important family of substances with saturated covalent bonding [1][2][3][4], where glass-like specimens can easily be obtained via high-entropy melting by quenching (melt-quenching, MQ) within an unprecedentedly wide compositional domain 0 ≤ x < ~70 corresponding to coordination numbers (CN) 2.0 < CN < ~2.70 [1,2].Because of their vitreous state, these materials represent promising candidates for multifunctional applications in electronics, optoelectronics, IR optics, chemical and biochemical sensing, etc. [4][5][6].In the early 2010s, the achieved progress in such implementation spheres was so impressive that a new branch of IR photonics, nominated Chalcogenide Photonics, appeared [7,8].
Nowadays [9][10][11], it is obvious that the most important functionality of arsenoselenides is governed by the specificity of their vitreous state, which can be modified either intrinsically, owing to the optimized technology of MQ, or extrinsically, owing to the post-technological influence on MQ-derived alloys.As for the latter, essential progress has been achieved in the most recent decade on so-called nanostructurization routines like high-energy mechanical milling (MM), also termed nanomilling [12], applied to transfer these substances from the macro-to nanoscopic scales, exploring the unique possibilities of their newly attained nanofunctionality [13][14][15][16][17]. From this point, the As-bearing arsenoselenides beyond stoichiometric arsenic triselenide As 2 Se 3 (x > 40), which possess glass-like structures due to the thioarsenide As 4 Se n molecules stabilized in the network of remaining As-Se bonds, are especially attractive [1][2][3].In this research, the thioarsenide nomenclature As 4 X n recommended for As-rich over-stoichiometric sulphides (X = S) under an analysis of the molecular-packing conformations by Bonazzi and Bindi [18] and the electron density by Gibbs et al. [19] is used for As x Se 100−x alloys.A milling-driven escape towards an optimized nanostructured state occurs in these substances via transitions between the amorphous states, referred to as polyamorphic or reamorphization transitions, similar to the characteristics of chemically stoichiometric arsenic triselenide As 2 Se 3 (corresponding to x = 40 in As x Se 100−x , CN = 2.40) and under-stoichiometric Se-rich glassy alloys (0 < x < 40; 2.0 < CN < 2.40) [20,21].In contrast, in compositional domains where some molecular species can be stabilized in a glass-forming network, transitions between different crystalline and amorphous states (referred to as polymorphic and polyamorphic phase transitions) can be activated by nanomilling in a dry mode, like in Se-rich As x Se 100−x glassy alloys (x < 40), approaching 'pure' Se (0 ≤ x < ~10-12) [22] or As-rich alloys (x > 40) of arsenic monoselenide, g-AsSe (also referred to as tetra-arsenic tetraselenide, g-As 4 Se 4 ) [23].Although such transitions have a higher content of side-oxidized derivatives, they can be activated in alloys subjected to nanomilling in a wet and/or combined dry-wet mode, typically realized in an environment with some surfactants, such as the PVP (polyvinylpyrrolidone) water solution [24][25][26].
Specifically, it is expected that both the polymorphic and polyamorphic phase transitions can be activated in the MQ-derived As x Se 100−x alloys at the border of the glassforming region ~(65 < x < 70) enriched in glassy and glassy-crystalline species undergoing nanostructurization by means of MM, with this process being dependent on the MM mode (dry or wet).There are no crystalline counterparts to molecular thioarsenides at the border of the glass-forming region in an As-Se system such as tetra-arsenic biselenide As 4 Se 2 (corresponding to CN = 2.67, which is just at the edge of the glass-forming ability in this system [1,2]), while some thioarsenide molecules in a nearby region (such as tetra-arsenic triselenide As 4 Se 3 with CN = 2.67, or tetra-arsenic monoselenide As 4 Se with CN = 2.80) are still expected under grinding in a high-energy ball mill, serving as a source of possible network-forming derivatives contributing to the final state of these nanostructured substances.
The scope of this work is comprehensive research on the As x Se 100−x alloys from the border of the glass-forming region (2.65 < CN < 2.70) subjected to nanomilling in dry-and combined dry-wet modes, using multi-experimental characterization probes like X-ray powder diffraction (XRPD) analysis in terms of a modified microcrystalline model [20][21][22][23], micro-Raman scattering (micro-RS) spectroscopy [27] and revised positron annihilation lifetime (PAL) analysis within the Positronics approach [28,29], complemented with molecular-network disproportionality analysis in the As-Se system employing ab initio quantum-chemical cluster-modeling algorithm CINCA like in [22,23].In the current research, the compositional domain of interest in the As-Se system, which will be shifted towards the border of the glass-forming region, exemplified by arsenoselenide alloys deviated around tetra-arsenic biselenide As 4 Se 2 thioarsenide stoichiometry, these being under-stoichiometric glassy g-As 65 Se 35 (CN = 2.65), stoichiometric glassy-crystalline g/c-As 67 Se 33 (viz.g/c-As 4 Se 2 , CN = 2.67) and over-stochiometric glassy-crystalline g/c-As 70 Se 30 (CN = 2.70).
In unmilled g/c-As 67 Se 33 (Figure 2a), the elemental As is dominated over its oxide (As 2 O 3 ) due to the sharp 'nanocrystalline' reflexes of this phase superimposed on relatively weak 'amorphous' halos, the FSDP-related diffuse peak halo being equilibrated by intensity with that responsible for the SSDP at ~28-33 • 2θ, which is characteristic of vitreous selenides [39,40].
In dry-milled g/c-As 67 Se 33 treated in a protective argon atmosphere (Figure 2b), the diffuse peak halos prevail over broadened 'nanocrystalline' reflexes from elemental As and its oxide, confirming that strong amorphous-I-to-amorphous-II (reamorphization) transition in this sample is probably accompanied by crystalline-to-amorphous (amorphization) transition, as this occurs in g-AsSe subjected to high-energy MM in a dry mode [23].All three principal diffuse peak halos in dry-milled g/c-As 67 Se 33 fit in a decaying sequence on their intensities like in Sulphur S-bearing glasses [39], meaning that stress generated under grinding does not completely relax over the glass network.Then, in dry-milled g/c-As67Se33 additionally treated in a wet mode (that is, in wet-milled samples, see Figure 2c), 'nanocrystalline' lines of As2O3 phase abnorm grow in intensity and become broader in width over those of elemental As, and th rangement of principal peak halos corresponding to the amorphous phase attains a acteristic irregularity, which dominated the SSDP-related peak halo at ~28-33°2θ as nature of thermodynamically stabilized glassy alloys from the glass-forming region 23].Therefore, it seems quite reasonable that MM in the PVP water solution prom further extraction and oxidation of the As phase.In the g-As65Se35 sample from the of the glass-forming region, which was in the vitreous state before and after dry MM nanomilling in a wet mode results in an arsenolite As2O3 phase without a notable ad ture of the unoxidized elemental As phase (Figure 3).In line with our expectation oxidation process is enhanced under the transition to glassy-crystalline alloys from border of the glass-forming region such as g/c-As70Se30 (see Figure 3).
Then, in dry-milled g/c-As 67 Se 33 additionally treated in a wet mode (that is, in drywet-milled samples, see Figure 2c), 'nanocrystalline' lines of As 2 O 3 phase abnormally grow in intensity and become broader in width over those of elemental As, and the arrangement of principal peak halos corresponding to the amorphous phase attains a characteristic irregularity, which dominated the SSDP-related peak halo at ~28-33 • 2θ as a signature of thermodynamically stabilized glassy alloys from the glass-forming region [20][21][22][23].Therefore, it seems quite reasonable that MM in the PVP water solution promotes further extraction and oxidation of the As phase.In the g-As 65 Se 35 sample from the edge of the glass-forming region, which was in the vitreous state before and after dry MM [26], nanomilling in a wet mode results in an arsenolite As 2 O 3 phase without a notable admixture of the unoxidized elemental As phase (Figure 3).In line with our expectation, this oxidation process is enhanced under the transition to glassy-crystalline alloys from the border of the glass-forming region such as g/c-As 70 Se 30 (see Figure 3).
The MM-driven amorphization and reamorphization processes in the examined arsenoselenides can be adequately identified due to the analysis of the arrangement of diffuse peak halos in their XRPD patterns reproduced in Figures 1-3, the derived FSDP parameters related to intermediate-range ordering in these alloys being summarized in Table 1.[30,31] and cubic arsenolite As 2 O 3 phase (JCPDS No. 36-1490) [38].
distance R can be found to approach ~5.64 Å, instead of ~5.71 Å from solely the Bragg diffraction positioning of this diffuse peak halo (see Table 1).So, another input to the FSDP is expected from the Ehrenfest diffraction contributing through inter-atomic and/or intermolecular correlations, which belong to molecular thioarsenide structures and their network-forming derivatives, with average inter-atomic/molecular distances ds beyond ~7 Å [23].From a detailed inspection of Figure 1, the position of the FSDP-related peak halo in unmilled g/c-As 67 Se 33 at 15.479 • 2θ (equivalent to characteristic distance in the Bragg diffraction R~5.71 Å, or average inter-atomic distance in the Ehrenfest diffraction d s = 7.02 Å) agrees well with the most intensive diffraction line (I = 100%) in orthorhombic As 4 Se 3 which arise from the (111) plane at ~16.90 • 2θ (equivalent to inter-planar distance d = 5.243 Å [32]).One of the strongest (I = 91.3%)lines in other molecular thioarsenide (monoclinic As 4 Se 4 [33,34]) arises from the (120) plane at ~16.07 • 2θ (d = 5.512 Å), which is also close to the FSDP position.The other line (I = 91.2%)ascribed to the (020) plane in monoclinic As 2 Se 3 [35,36] is revealed at higher diffraction angles ~17.9 • 2θ (d = 4.950 Å).Assuming equal contributions from these inter-planar correlations, the FSDP-related characteristic distance R can be found to approach ~5.64 Å, instead of ~5.71 Å from solely the Bragg diffraction positioning of this diffuse peak halo (see Table 1).So, another input to the FSDP is expected from the Ehrenfest diffraction contributing through inter-atomic and/or inter-molecular correlations, which belong to molecular thioarsenide structures and their network-forming derivatives, with average inter-atomic/molecular distances d s beyond ~7 Å [23].
In As-rich g-As x Se 100−x (40 < x < 65) [21], remnants of thioarsenide cage-like As 4 Se n molecules (such as As 4 Se 4 , As 4 Se 3 , As 4 ) are known to be destroyed under MM and reincorporated into a glass network resulting in an increased FSDP position Q 1 and width ∆Q 1 .This amorphization trend corresponding to the crystalline-to-amorphous transition causes a fragmentation impact on the correlation length of the FSDP-responsible entities (L), facilitating changes when distant inter-atomic correlations between some crystalline planes contributing to the FSDP disappear at a cost of others responsible for the SSDP.The disruption of intermediate-range ordering due to weakening of the FSDP-responsible entities accompanied by an enhancement of extended-range ordering due to fragmentation of the SSDP-responsible entities occurs as interplay between different hierarchical levels of the medium-range structure in As-Se alloys from the glass-forming region subjected to MM [21].
Similar peculiarities are found in the examined glassy and glassy-crystalline As-Se alloys from the border of the glass-forming region.Thus, in dry-milled alloys, the FSDP position Q 1 slightly shifts in the high-angular side, while the FSDP width ∆Q 1 obeys a drastic increase, resulting in fragmentation of the correlation length L (see Table 1).These changes prevail in glassy-crystalline substances such as g/c-As 70 Se 30 , confirming that crystalline remainders serve as a possible source for the MM-driven amorphization (crystalline-to-amorphous) transition.As shown in Figure 2, nanomilling in combined dry-wet mode (when the last processing stage is performed in the PVP water solution) increases the breakdown in intermediate-range ordering.Nanomilling in wet mode does not change the principal appearance of diffuse peak halos in the XRPD patterns but leads to drastic broadening in their widths, in favor of enhanced reamorphization in preliminary dry-milled samples.
Thus, remnants of 'crystalline' structures in the examined alloys responsible for inter-molecular correlations with inter-centroid distances between thioarsenide cage-like molecules above ~7 Å (which contribute to the XRPD patterning by the Ehrenfest diffraction) are destroyed under MM, while the inter-planar correlations contribute further to these patterns through Bragg diffraction.Because of molecular-to-network reamorphization transformations in the examined As-Se alloys, the broadened and depressed diffuse peak halos become shifted towards higher scattering vectors.Since remnants of thioarsenide As 4 Se n molecular entities destructed under grinding interact with oxygen, especially under MM in the PVP water solution, the arsenolite (As 2 O 3 ) phase is formed and stabilized in these alloys subjected to nanomilling in combined dry-wet mode.
To shed more light on the microstructure transformations in the examined arsenoselenide alloys, the micro-RS spectra were collected for these samples before and after the respective stages of their processing.For g/c-As 67 Se 33 samples taken as unmilled bulk pieces and pelletized coarse-grained, dry-milled and dry-wet-milled samples, these micro-RS spectra normalized with respect to the amplitude of the dominant band are, respectively, reproduced in Figure 4a-d.
Molecules 2024, 29, x FOR PEER REVIEW 8 of 27 to micro-RS spectroscopy, the appearance of the As phase is expected in MQ-derived g/c-As67Se33 samples due to the RS-active band at ~204 cm −1 ascribed to As4 thioarsenide molecules, while both As4Se4 and As4Se3 molecules are revealed via the strong band at ~236 cm −1 supplemented by a weak shoulder at ~278 cm −1 (see Figure 4a,b).The spectral region between these bands (220-230 cm −1 ) corresponds to the vibration modes of AsSe3 pyramids incorporated in a network via = As-Se-As = bridges.As a result, in g/c-As67Se33, the RS spectrum composed of overlapped high-frequency modes of thioarsenide molecules and network-forming fragments obeys a double-peak-shape characteristic with strong maxima at ~200 and ~240 cm −1 supplemented by a relatively suppressed hump at ~220-230 cm −1 and weak shoulder near ~280 cm −1 (for a comparison, see [3,27,42,45,46]).These features revealed in micro-RS spectra of unmilled g/c-As67Se33 (shown in Figure 4a,b) are essentially broadened in this sample subjected to nanomilling in dry mode (see Figure 4c) or combined dry-wet mode (see Figure 4d).Such behavior speaks in favor of a nanomilling-driven molecular-to-network amorphization transition, which occurs due to the destruction of thioarsenide molecules followed by the incorporation of their remnants into the glass network undergoing a polyamorphic transition (amorphous-I-to-amorphous-II [47,48] or, alternatively, reamorphization transition [23]).These alloys, affected by defects generated under MM, become notably stressed in the nanomilled state, enhancing the calorimetric heat transfer responses, as compared with unmilled bulk samples [27].
Noteworthily, the micro-RS spectroscopic identification of the rhombohedral (grey) As phase, which is expected due to two-fold degenerate Eg and A 1 g modes near ~202 cm −1 and 254 cm −1 [49], is impossible in these alloys because of overlapping with the vibration bands of the arsenoselenide network.The same is true of nanocrystalline inclusions of the These features revealed in micro-RS spectra of unmilled g/c-As 67 Se 33 (shown in Figure 4a,b) are essentially broadened in this sample subjected to nanomilling in dry mode (see Figure 4c) or combined dry-wet mode (see Figure 4d).Such behavior speaks in favor of a nanomilling-driven molecular-to-network amorphization transition, which occurs due to the destruction of thioarsenide molecules followed by the incorporation of their remnants into the glass network undergoing a polyamorphic transition (amorphous-I-to-amorphous-II [47,48] or, alternatively, reamorphization transition [23]).These alloys, affected by defects generated under MM, become notably stressed in the nanomilled state, enhancing the calorimetric heat transfer responses, as compared with unmilled bulk samples [27].
Noteworthily, the micro-RS spectroscopic identification of the rhombohedral (grey) As phase, which is expected due to two-fold degenerate E g and A 1 g modes near ~202 cm −1 and 254 cm −1 [49], is impossible in these alloys because of overlapping with the vibration bands of the arsenoselenide network.The same is true of nanocrystalline inclusions of the cubic arsenolite (As 2 O 3 ) phase, which is expected in these alloys due to RS-active modes near ~190 cm −1 and ~270 cm −1 [44,49], which are also overlapped with As-Se network modes in this spectral range.Therefore, the absence of the above crystalline inclusions in the examined alloys does not change the principal appearance of their micro-RS spectra, as demonstrated in Figure 5 for purely glassy-like specimens (g-As 65 Se 35 ) studied before and after dry MM.
Molecules 2024, 29, x FOR PEER REVIEW 9 of 27 cubic arsenolite (As2O3) phase, which is expected in these alloys due to RS-active modes near ~190 cm −1 and ~270 cm −1 [44,49], which are also overlapped with As-Se network modes in this spectral range.Therefore, the absence of the above crystalline inclusions in the examined alloys does not change the principal appearance of their micro-RS spectra, as demonstrated in Figure 5 for purely glassy-like specimens (g-As65Se35) studied before and after dry MM.Thus, atomic-specific microstructure transformations in the examined As-Se alloys driven by nanomilling are dominated by the polyamorphic (molecular-to-network) transitions of the existing MQ-derived amorphous phase (forming reamorphization channel), supplemented (especially under MM in a dry mode) by weak polymorphic (crystallineto-amorphous) transitions of crystalline inclusions stabilized in these alloys under MQ (forming amorphization channel).Undoubtedly, because of the principal difference in the atomic packing of amorphous and crystalline phases in arsenoselenide alloys undergoing nanostructurization by MM, such transformations should be accompanied by the notable changes in atomic-deficient (free-volume) microstructure of these alloys.

Atomic-Deficient Microstructure of the Examined Arsenoselenides
The raw PAL spectra reconstructed from unconstrained three-term fitting for g/c-As70Se30 alloys in the unmilled (bulky) state and after the respective stages of nanomilling are depicted in Figure 6, and they are compared with the spectrum of 'pure' PVP pelletized under the same conditions [50].The applicability of this fitting procedure is proved by a scatter of variance (representing minimal statistically weighted least-square deviation between experimental and theoretical curve built of three exponentials) tightly grouped along the time axis in the bottom insets of Figure 6.Similar PAL spectra (not reproduced in Figure 6) were collected for other pelletized arsenoselenides.The best-fit PAL spectra parameters (component lifetimes τi and intensities Ii, I = 1,2,3) for arsenoselenide samples and PVP (pelletized under the same conditions [50]) are gathered in Table 2, and positron-trapping and Ps-decaying modes derived from these PAL spectra within Thus, atomic-specific microstructure transformations in the examined As-Se alloys driven by nanomilling are dominated by the polyamorphic (molecular-to-network) transitions of the existing MQ-derived amorphous phase (forming reamorphization channel), supplemented (especially under MM in a dry mode) by weak polymorphic (crystallineto-amorphous) transitions of crystalline inclusions stabilized in these alloys under MQ (forming amorphization channel).Undoubtedly, because of the principal difference in the atomic packing of amorphous and crystalline phases in arsenoselenide alloys undergoing nanostructurization by MM, such transformations should be accompanied by the notable changes in atomic-deficient (free-volume) microstructure of these alloys.

Atomic-Deficient Microstructure of the Examined Arsenoselenides
The raw PAL spectra reconstructed from unconstrained three-term fitting for g/c-As 70 Se 30 alloys in the unmilled (bulky) state and after the respective stages of nanomilling are depicted in Figure 6, and they are compared with the spectrum of 'pure' PVP pelletized under the same conditions [50].The applicability of this fitting procedure is proved by a scatter of variance (representing minimal statistically weighted least-square deviation between experimental and theoretical curve built of three exponentials) tightly grouped along the time axis in the bottom insets of Figure 6.Similar PAL spectra (not reproduced in Figure 6) were collected for other pelletized arsenoselenides.The best-fit PAL spectra parameters (component lifetimes τ i and intensities I i , I = 1, 2, 3) for arsenoselenide samples and PVP (pelletized under the same conditions [50]) are gathered in Table 2, and positrontrapping and Ps-decaying modes derived from these PAL spectra within two-state simpletrapping model (STM) [28,29] ignoring the Ps-decaying contribution are listed in Table 3.
Molecules 2024, 29, x FOR PEER REVIEW 10 of 27 two-state simple-trapping model (STM) [28,29] ignoring the Ps-decaying contribution are listed in Table 3. Table 2.The best-fit PAL spectra parameterization in the pelletized arsenoselenide samples in unmilled state and after nanomilling in dry-and dry-wet modes compared with these parameters in the PVP samples pelletized under the same conditions [50].Just from a visual inspection of Figure 6, it is clear that occupation of the 'tail' states related to bound positron-electron (positronium, Ps) states grows notably in bulk and  Just from a visual inspection of Figure 6, it is clear that occupation of the 'tail' states related to bound positron-electron (positronium, Ps) states grows notably in bulk and dry-milled As-Se alloys under the transition to dry-wet-milled samples, approaching that in 'pure' PVP.This means that the transition from preferential annihilation via positron trapping to Ps decays.The PAL spectra of both unmilled and dry-milled arsenoselenides reveal a defect-specific lifetime of τ 2 ~0.36-0.39ns (Table 2), the value characteristic for multiatomic (bi-, tri-, quadruple) vacancies in amorphous As-Se [29,[51][52][53][54][55].The third component in the collected PAL spectra of these samples with τ 3 ~2.1 ns and small fractional free volume below f v ~0.3 can be ascribed to holes with a radius of R 3 ~0.30nm (Table 3).Because of the small input from the Ps-decay channel, the derived defect-free bulk lifetime τ b approaches ~0.27 ns for the unmilled g-As 65 Se 35 sample and somewhat lower, ~0.25 ns, for the g/c-As 70 Se 30 sample.Noteworthily, the τ b lifetime in crystalline arsenic triselenide is ~0.24 ns [51], which increased to ~0.28-0.29 ns in the amorphous matrix [29,[52][53][54][55]. Therefore, positron trapping in unmilled and dry-milled arsenoselenides is expected to occur preferentially in the disordered As-Se network.
With the transition to samples pelletized from dry-wet-milled arsenoselenides (representing, in fact, PVP-capped nanocomposites [24][25][26]), the location of the preferential annihilation channel is changed.As follows from Table 2, the τ 2 lifetime is notably increased in dry-wet-milled samples approaching ~0.43 ns (the value characteristic for positron trapping in large vacancies in As-Se matrix [51,52]), while the τ 3 lifetime is decreased to ~1.9 ns (closer to Ps-related lifetime in PVP, τ 3 = 1.867 ns [50]), resulting in an evidently increased average lifetime, τ av.~0.38 ns.It means that additional free volume contributes to positron trapping sites in wet-milled samples while disappearing in Ps-hosting holes.Nevertheless, the more than three-times increased third component intensity (I 3 ) speaks in favor of the fragmentation of Ps-decay sites, leading to fractional free volume f v ~0.8 (Table 3).These changes are counterbalanced by decreased I 2 , preferring (under criterion [56]) an increased Ps-formation probability in the transition from dry-milled to dry-wet-milled arsenoselenide samples.
Therefore, the Ps decay in the PVP-capped nanocomposites occurs rather in 'pure' PVP environment than in the amorphous As-Se matrix.A comparative presentation of the respective PAL spectra for these arsenoselenide alloys and PVP shows a spectacular trend in their superposition, specifically the compositionally tuned behavior in the overlapped PAL spectra highlighted in Figure 7. Smooth monotonic changes are observed in both PAL spectra peaks and tails in these samples undergoing nanostructurization in the transition between states characteristic for unmilled (or dry-milled) and wet-milled samples.Similar behavior was also observed in other As-Se alloys from the glass-forming region [24][25][26].In contrast, in the examined glassy and glassy-crystalline alloys from the border of the glass-forming region, an almost invariant tendency is observed in the PAL spectra peaks depressed on the right wing after wet milling due to the moderated Ps formation probability in PVP water solution and slightly changed average positron lifetime (τ av ).These changes in the PAL spectra tails for unmilled, dry-milled and dry-wet-milled samples are due to the increased density of Ps-hosting holes, defined merely by the I 3 intensity.There is no evident empty gap between these spectra tails for dry-milled and dry-wet-milled g-As 65 Se 35 samples (Figure 7a), as compared with glassy-crystalline g/c-As 67 Se 33 or g/c-As 70 Se 30 samples (see Figure 7b,c) caused by changes in the Ps-decaying channel under the transition from amorphous As-Se to the PVP-bearing environment.The richer variety of positron traps in glassy-crystalline alloys with τ 2 ~0.43 ns (see Table 2) facilitates the formation of such an empty gap, as follows from the comparison between respective PAL spectra in Figure 7.
To shed more light on the examined As-Se alloys undergoing nanomilling-driven volumetric changes, the PAL spectra of dry-milled samples are considered with respect to these spectra in wet-milled samples employing revised positron lifetime analysis within the Positronics approach [28,29].The trapping conversion parameters derived from such comparisons are presented in Table 4. Positive values of the first and second component intensities (I n and I int ) in the reconstructed PAL spectrum of the heterogeneous medium undergoing volumetric nanostructurization, along with the well-defined component inputs, testify that Ps-hosting holes in these nanocomposites (g-As 65 Se 35 /PVP, g/c-As 67 Se 33 /PVP and g/c-As 70 Se 30 /PVP) are transformed in positron traps typical for dry-milled samples.The defect-specific lifetimes τ int ~0.36-0.38 ns (Table 4) show that positron traps are large interfacial free-volume voids close to the multiatomic vacancies in the amorphous As-Se matrix [51][52][53][54][55].This finding agrees with (τ int -τ b NP ) ~0.09-0.11ns and τ int /τ b NP ~1.4,indicative of large vacancies in chalcogenide compounds [57].The overall conversion process, i.e., appearance of positron traps with τ int ~0.36-0.38 ns instead of Ps-hosting holes with τ 3 ~2.1 ns, occurs in an environment with an effective bulk lifetime of τ b NP ~0.29 ns, which is above τ b in crystalline arsenic selenide (~0.240 ns [51]) approaching the value characteristic for glassy As-Se (~0.28-0.29 ns) [52][53][54][55].Therefore, we can reasonably speculate that a heterogeneous medium accommodates the products of direct Ps-to-positron conversion, i.e., unoccupied free-volume spaces where positron traps (typical for dry-milled As-Se alloys) appear instead of Ps-decaying holes (typical for PVP-stabilized nanocomposites) is the amorphous As-Se matrix, slightly enriched in some impurity products such as arsenic oxide.
As65Se35 samples (Figure 7a), as compared with glassy-crystalline g/c-As67Se33 or g/c-As70Se30 samples (see Figure 7b,c) caused by changes in the Ps-decaying channel under the transition from amorphous As-Se to the PVP-bearing environment.The richer variety of positron traps in glassy-crystalline alloys with τ2~0.43 ns (see Table 2) facilitates the formation of such an empty gap, as follows from the comparison between respective PAL spectra in Figure 7.The changes in the PAL spectra tails of unmilled, dry-and dry-wet-milled samples are due to increase in density of o-Ps hosting holes.There is no evident empty gap between the PAL spectra tails for dry-milled and dry-wet-milled glassy samples as compared with glassy-crystalline samples caused by changes in Ps decaying states under transition to annihilation in PVP-bearing medium.
To shed more light on the examined As-Se alloys undergoing nanomilling-driven volumetric changes, the PAL spectra of dry-milled samples are considered with respect to  In substances like thioarsenide As 4 Se n -bearing compounds in the As x Se 100−x system, effects from the selective localization of positron-trapping and Ps-hosting sites are strongly enhanced due to the glassy-crystalline environment around intrinsic free-volumes elements (such as voids, atomic vacancies, vacancy-like clusters, pores, cracks, etc.) acting as potential setting places for trapped positrons and bound positron-electron (positronium, Ps) states [28,29].Following the famous prediction of Blachnik and Wickel in 1984 on the thermal decomposition of A 4 B 3 cage-like molecules into A 4 B 4 ones and unidentified amorphous products [58], it has been proved recently [59] that nanomilling facilitates the decomposition of As 4 Se 3 molecules in arsenoselenides within the glass-forming region in the vicinity of x = 57 (dimorphite-type composition), resulting in a reamorphized glass structure enriched in realgar-type As 4 Se 4 molecules (prevailing near x = 50) and network remainders close to tetra-arsenic biselenide As 4 Se 2 (dominated at x = 67).Since there are no molecular thioarsenides among products of devitrification in arsenoselenides from the border of the glass-forming region in the As x Se 100−x system (65 < x < 70), it seems reasonable to assume that crystallization processes are a result of the spontaneous (under MQ) or activated (under thermal or mechanical energy) decomposition of some network derivatives near As 4 Se 2 composition (x = 67).
Thus, in a group of tetra-arsenic tetraselenide thioarsenides, the strong molecularforming tendency becomes dominated with under-constrained (n c = 2.875) realgar-type As 4 Se 4 cage molecules of D 2d symmetry, with E f ~−72.713kcal/mol, which is 0.40 kcal/mol better than E f in the AsSe 3/2 unit [23].Among network derivatives from this As 4 Se 4 molecule, the most plausible is an optimally constrained cluster (n c = 3.0) that appeared due to a single break in one of four Se atom positions (E f ~0.25 kcal/mol), which can be labelled as x1-As 4 Se 4 following the accepted CINCA nomenclature [60,61].
Among tetra-arsenic triselenide thioarsenides (corresponding to x = 57), the dimorphitetype As 4 Se 3 cage molecule (under-constrained in view of n c = 2.71) composed of a triangularpyramidal (As 3 )-As conformation is most plausible, possessing E f ~0.33 kcal/mol (with respect to AsSe 3/2 pyramid) [59].All seven atoms in this molecule of C 3v symmetry (isostructural with the molecule refined in αand β-modifications of mineral dimorphite As 4 S 3 by Whitfield [68,69]) are located in the same sphere, resulting in a specific 0D structure with low heat transfer and strong thermal expansion responses, which are accepted as characteristic features of the plastically crystalline As 4 Se 3 modification [58,70].Other molecular clusters of this type and their network-forming derivatives reconstructed by the break in Se atom positions are unfavorable, as compared with this dimorphite-type As 4 Se 3 molecule [59], and, therefore, cannot be taken into consideration under compre-hensive analysis of molecular-network disproportionality in arsenoselenides of similar chemical compositions.
In a group of tetra-arsenic biselenide (As 4 Se 2 ) thioarsenides (x = 67), both molecular entities, the As 4 Se 2 -I cluster with n c = 2.67 composed of four (As-As) bonds in a zig-zag sequence (see Figure 8a) and the As 4 Se 2 -II cluster with n c = 2.50 composed of a (As-As) bond attached to the As 3 triangle (Figure 8b), are unfavorable in view of E f energy, approaching −4.42 kcal/mol and −3.59 kcal/mol, respectively.The same concerns network-forming clusters derived from these molecules by breaking in one of the Se atom positions, with both As 4 Se 3 H 2 molecular prototypes reproduced in Figure 8c,d   Thus, in a group of tetra-arsenic As4 clusters (corresponding to x = 100 in AsxSe100−x system), the situation is non-trivial and complicated.The most stable amorphous and crystalline structures related to As polymorphs can be reconstructed from two principal building blocks typical for gaseous and condensed As states, these being, respectively, (i) the thioarsenide molecular cluster in the form of a regular four-atom pyramid-shaped As4 tetrahedron and (ii) the thioarsenide-type network-forming cluster in the form of a flattened pyramid-shaped unit derived through distortion from this regular As4-tetrahedrallike molecule by breaking in one of three As-As bonds at each As atom composed of a two-dimensional double-layer network of chair-configurated six-fold rings (As6⋅(2/3) = As4).These blocks within the arrangement of the three nearest neighbors can be differentiated by the Ef energies derived from the CINCA modelling, while distortion pathways beyond the three nearest neighbors explain the emergence of As allotropes in orthorhombic and rhombohedral structures [30], but this specificity cannot be accounted for within this cluster modelling routine.The under-constrained configuration of the tetrahedral As4 molecule (nc = 2.25) in Figure 10a is found to be very unfavorable in realistic structures in view of Ef ~ −4.31 kcal/mol.This finding is in line with the fact that yellow As (also named insulator, γ-As) consisting of As4 tetrahedra exists only in the gaseous state [71,72].In contrast, the Ef energy of over-constrained network clusters (nc = 4.5) composed of a double-layer honeycomb structure of chair-configurated (As6⋅(2/3) = As4) rings (see Figure 10b) typical of both rhombohedral (grey or metallic, α-As) and orthorhombic (black or semiconducting, β-As) allotropes [30,31,71,72] seems very promising in view of Ef ~ −2.46 kcal/mol.This finding explains the appearance of the rhombohedral As phase as the most stable allotrope under crystallization in MQ-derived As-Se alloys.Thus, in a group of tetra-arsenic As 4 clusters (corresponding to x = 100 in As x Se 100−x system), the situation is non-trivial and complicated.The most stable amorphous and crystalline structures related to As polymorphs can be reconstructed from two principal building blocks typical for gaseous and condensed As states, these being, respectively, (i) the thioarsenide molecular cluster in the form of a regular four-atom pyramid-shaped As 4 tetrahedron and (ii) the thioarsenide-type network-forming cluster in the form of a flattened pyramid-shaped unit derived through distortion from this regular As 4 -tetrahedrallike molecule by breaking in one of three As-As bonds at each As atom composed of a two-dimensional double-layer network of chair-configurated six-fold rings (As 6•(2/3) = As 4 ).These blocks within the arrangement of the three nearest neighbors can be differentiated by the E f energies derived from the CINCA modelling, while distortion pathways beyond the three nearest neighbors explain the emergence of As allotropes in orthorhombic and rhombohedral structures [30], but this specificity cannot be accounted for within this cluster modelling routine.The under-constrained configuration of the tetrahedral As 4 molecule (n c = 2.25) in Figure 10a is found to be very unfavorable in realistic structures in view of E f ~−4.31 kcal/mol.This finding is in line with the fact that yellow As (also named insulator, γ-As) consisting of As 4 tetrahedra exists only in the gaseous state [71,72].In contrast, the E f energy of over-constrained network clusters (n c = 4.5) composed of a double-layer honeycomb structure of chair-configurated (As 6•(2/3) = As 4 ) rings (see Figure 10b) typical of both rhombohedral (grey or metallic, α-As) and orthorhombic (black or semiconducting, β-As) allotropes [30,31,71,72] seems very promising in view of E f ~−2.46 kcal/mol.This finding explains the appearance of the rhombohedral As phase as the most stable allotrope under crystallization in MQ-derived As-Se alloys.
the Ef energy of over-constrained network clusters (nc = 4.5) composed of a double-layer honeycomb structure of chair-configurated (As6⋅(2/3) = As4) rings (see Figure 10b) typical of both rhombohedral (grey or metallic, α-As) and orthorhombic (black or semiconducting, β-As) allotropes [30,31,71,72] seems very promising in view of Ef ~ −2.46 kcal/mol.This finding explains the appearance of the rhombohedral As phase as the most stable allotrope under crystallization in MQ-derived As-Se alloys.Let us parameterize molecular-network disproportionality at the border of the glassforming region in the As-Se system (close to As 4 Se 2 ) based on the cluster-forming energies E f calculated for the components of most expected decomposition scenarios, sketched in Figure 11.
The first scenario (Figure 11a) involves the decomposition of x2-As 4 Se 2 -I networkforming clusters (shown in Figure 8e) on dimorphite-type As 4 Se 3 molecules [59] supplemented by the extraction of As 6•(2/3) ring-like network-forming clusters (see Figure 10b), which occurs with a negative energetic barrier (∆E f ) corresponding to the spontaneous decomposition of the examined arsenoselenide alloy under MQ: By removing down from As 4 Se 2 stoichiometry, the second disproportionality scenario involving the spontaneous decomposition of x2-As 4 Se 2 -I network-forming clusters (Figure 8e) on realgar-type As 4 Se 4 molecules [23] supplemented by the extraction of As 6•(2/3) ring-like network clusters (Figure 10b) occurring also with a negative barrier becomes clear (see Figure 11b): Further approaching stoichiometric arsenic triselenide As 2 Se 3 , the third molecularnetwork disproportionality scenario, which involves the decomposition of x2-As 4 Se 2 -I network-forming clusters (Figure 8e) on layer-type As 2 Se 3 network clusters composed of two corner-shared AsSe 3/2 pyramids (as shown in [61,62]) supplemented by the extraction of As 6•(2/3) ring-like network clusters (Figure 10b), occurring with a positive energetic barrier, can be validated (see Figure 11c): The positive value of the energetic barrier ∆E f in Equation ( 3) means that this decomposition scenario cannot be realized spontaneously but, rather, as activated thermal or milling-driven decomposition.
The spontaneous nature of molecular-network disproportionality in As x Se 100−x alloys from the border of the glass-forming region (65 < x < 70), obeying reactions (1) and ( 2), is proved by a large amount of molecular thioarsenides in these alloys stabilized under MQ with respect to the micro-RS spectra of unmilled samples (see Figures 4a,b and 5a) and the crystalline inclusions of the rhombohedral As phase in these samples revealed by the XRPD analysis (see Figures 1-3).Thus, from this disproportionality analysis, the compositional location of the border of the glass-forming region in the As-Se system nearby the As 4 Se 2 thioarsenide composition (CN = 2.67) becomes completely understandable.
Molecules 2024, 29, x FOR PEER REVIEW 17 of 27 Let us parameterize molecular-network disproportionality at the border of the glassforming region in the As-Se system (close to As4Se2) based on the cluster-forming energies Ef calculated for the components of most expected decomposition scenarios, sketched in Figure 11.The first scenario (Figure 11a) involves the decomposition of x2-As4Se2-I networkforming clusters (shown in Figure 8e) on dimorphite-type As4Se3 molecules [59] supplemented by the extraction of As6⋅(2/3) ring-like network-forming clusters (see Figure 10b), which occurs with a negative energetic barrier (ΔEf) corresponding to the spontaneous decomposition of the examined arsenoselenide alloy under MQ: The nanomilling-driven molecular-to-network transition in As 4 Se 2 -bearing alloys is described by decomposition reaction (3), with a positive energetic barrier (∆E f = 0.375 kcal/mol) comparable to the decomposition of As 4 Se 3 molecules in As 4 Se 4 ones and accompanying amorphous products (∆E f = 0.41 kcal/mol) [59].The transition towards more network conformations is accompanied by interplay between medium-range structure levels in As-Se alloys subjected to nanomilling (see Figure 1) and the respective broadening of their micro-RS spectra (see Figures 4c,d and 5b).Since the remnants of thioarsenides destructed under grinding interact with oxygen, especially in PVP water solution, the cubic arsenolite As 2 O 3 phase is intensively formed in these alloys subjected to nanomilling in combined dry-wet mode (see Figure 3).Because of the enhanced heterogeneity in the atomic-deficient microstructure, the superposition of the PAL spectra collected for PVP and MQ-derived umilled, dry-milled and dry-wet-milled samples shows a spectacular smoothly decaying trend over superimposed PAL spectra peaks and tails (highlighted in Figure 7).

Preparation, Preliminary Testing and Nanomilling of the Examined Arsenoselenides
The border of the glass-forming region in As x Se 100−x system from As-rich side is exemplified by MQ-derived alloys compositionally deviated around tetra-arsenic biselenide (As 4 Se 2 ) thioarsenide stoichiometry, corresponding in coordination number CN = 2.67, these being under-stoichiometric glassy g-As 65 Se 35 (CN = 2.65), stoichiometric glassycrystalline g/c-As 67 Se 33 (or g/c-As 4 Se 2 ) and over-stochiometric glassy-crystalline g/c-As 70 Se 30 (CN = 2.70).These alloys were synthesized via vibrational MQ from elemental precursors (As and Se of 5N purity), as described in more detail elsewhere [11,12,15,18].The density ρ (±0.005 g•cm −3 ) of coarse-grained pieces of samples defined by the Archimedes displacement method in ethanol was lower in the glassy state (4.448 g•cm −3 for g-As 65 Se 35 ) and higher in the glassy-crystalline state, approaching 4.654 g•cm −3 for g/c-As 70 Se 30 .The mean inter-atomic spacing d s m derived from the density of g/c-As 67 Se 33 alloy was ~3.79 Å. Mechanical treatment of the prepared alloys was performed in two stages.Firstly, the MQ-derived ingots were subjected to nanostructurization by dry MM in a protective argon atmosphere in a planetary ball mill Pulverissete 6 (Fritsch, Idar-Oberstein, Germany).This grinding route was performed under a rotational speed of 500 rpm in 250 mL tungsten carbide chamber loaded with 50 tungsten carbide balls (each 10 mm in diameter) using 3 g of preliminary coarse-grained material sieved under 200 µm.Then, the fine-grained powder was pelletized in a stainless-steel die via ~0.7 GPa compressing, stabilizing dry-milled samples for further research.
In the second stage, part of the powder (prepared in a dry mode) was subjected to additional attrition in wet mode using a laboratory MiniCer mill (Netzsch, Germany), operational under a rotational speed of 3500 rpm.This 90-minute route was performed in 300 mL of 0.5% PVP water solution, milling shaft being loaded on 85% with yttriumstabilized ZrO 2 balls (each 0.6 mm in diameter).The PVP of ~40,000 g•mol −1 molecular weight purchased from Sigma-Aldrich Co. LLC (St. Louis, MO, USA) was used to prepare compositionally authentic nanosuspensions.Finally, they were dried at 70 • C and pelletized via compressing (under ~0.7 GPa) in stainless-steel die, stabilizing a set of the As x Se 100−x /PVP nanocomposites as plane-parallel disc-like pellets (~6 mm in diameter, ~1 mm in thickness), the most suitable shape for micro-RS and PAL measurements.
The particle size distribution was recognized for nanosuspensions of powdered As-Se alloys, employing photon cross-correlation spectroscopy with Nanophox particle size analyzer (Sympatec, Clausthal-Zellerfeld, Germany).The unimodal particle size distribution centered around ~180-190 nm was monitored in all cases.As an example, the particle size distribution in the suspension of nanomilled g-As 65 Se 35 showing (x50)~182 nm (meaning that 50% of particles are smaller than 182 nm) and (x99)~291 nm (meaning that 99% of particles are smaller than 291 nm) is shown in Figure 12.
Se alloys, employing photon cross-correlation spectroscopy with Nanophox particle size analyzer (Sympatec, Clausthal-Zellerfeld, Germany).The unimodal particle size distribution centered around ~180-190 nm was monitored in all cases.As an example, the particle size distribution in the suspension of nanomilled g-As65Se35 showing (x50)~182 nm (meaning that 50% of particles are smaller than 182 nm) and (x99)~291 nm (meaning that 99% of particles are smaller than 291 nm) is shown in Figure 12.

Atomic-Specific Phase Composition and Medium-Range Structure via Xrpd Analysis
The phase composition and medium-range structure of the arsenoselenides were recognized with the XRPD analysis using the STOE STADI P diffractometer operational in transmission mode of Cu Kα1-radiation (for details of the XRPD analysis, see [20][21][22][23][24]).
The phase diagram of As-Se alloys contains three stable crystalline compounds corresponding to different thioarsenide As4Sen stoichiometry, such as arsenic triselenide

Atomic-Specific Phase Composition and Medium-Range Structure via Xrpd Analysis
The phase composition and medium-range structure of the arsenoselenides were recognized with the XRPD analysis using the STOE STADI P diffractometer operational in transmission mode of Cu Kα1-radiation (for details of the XRPD analysis, see [20][21][22][23][24]).
The amorphous phase in the examined alloys was identified due to diffuse peak halos in their XRPD patterning, in part, the FSDP (the first sharp diffraction peak), which is believed to be a signature of structural entities forming intermediate-range ordering in glass over a few tens Å reproduced in a reciprocal space near scattering vector [75], and the SSDP (the second sharp diffraction peak, in terms of Elliott [76]) or PDP (the principal diffraction peak, in terms of Zeidler and Salmon [77]) serving as signature of extended-range order at Q 2 ~(1.8-2.2) Ǻ−1 .In the XRPD patterning of As-rich As x Se 100−x alloys (x > 40), the FSDP-related peak halo at ~(15-22) • 2θ reflects correlations between some polyhedrons like thioarsenide As 4 Se n molecules, while the SSDP-related halo shifted to ~(28-33) • 2θ reflects orientational specificity of these polyhedrons ascribed to the second-order pair atomic correlations close to the mean inter-atomic spacing, d s m [35].At ~(50-60) • 2θ (equivalent to Q 3 ~3.3-4.0Ǻ−1 ), the third diffraction peak (TDP) is observed as manifestation of shortest (~2.1-2.3Ǻ) interatomic separation in a glass [35,77].Thus, the XRPD measurement reveals three-peak structure of the patterns, which reflects a succession of single pairwise correlations defined by Q 3 = Q TDP and multi-pairwise correlations determined by Q 1 = Q FSDP and Q 2 = Q SSDP responsible for medium-range ordering [77].Arrangement of diffuse peak halos in the XRPD patterns responsible for amorphous phase was analyzed using the STOE WinXPOW 3.03 [78] and PowderCell 2.4 [79] program packages, following normalization procedure with respect to the maximum.The error bar in the peak halo position (2θ) and full width at half maximum (FWHM) was not worse, ±0.05 • 2θ; the scattering vector position and width were calculated as Q = (4π/λ)•sinθ and ∆Q = (4π/λ)•sin(FWHM/2), respectively.The characteristic distance R (the spacing of peak halo responsible quasi-periodicity) and the correlation length L over which this quasi-periodicity were maintained and defined as for the Bragg diffraction (R = 2π/Q, L = 2π/∆Q).Within modified microcrystalline approach [20][21][22][23][24], the diffuse peak-halo arrangement in the XRPD patterning in chalcogenide glass was also treated as arising from diffraction of coordination spheres, i.e., the shortest inter-atomic distances like in randomly packed multiparticulate systems (see [80] and literature therein), when the XRPD is governed by the Ehrenfest relation [81]: where d s is the average distance between scatterers (the radius of the coordination sphere).Noteworthily, the error bar in the above parameters (R, L, d s ) does not exceed ±0.1 Å.

Atomic-Specific Microstructure by Micro-Rs Spectroscopy
The microstructure peculiarities of the arsenoselenides were also identified with RS microscopy using the Horiba Xplora apparatus equipped with CCD detector, all micro-RS spectra being collected at ambient temperature.The CW 785 nm laser of 90 mW output power was employed for excitation, the 10% power option being used to avoid photostructural effects.Other measurement options applied were as follows: x100 objective, 1800 1/mm grating, 500 µm hole and 50 µm slit.The spectral resolution was ~2 cm −1 , and the spatial resolution was near ~2 µm.Number of scans was chosen depending on the surface of the samples to be sure that RS spectra processed with Horiba LabSpec 6 software were reasonably identical.The milled and unmilled samples were compared through normalization by matching the spectral areas of interest.The RS active bands were identified using the known data for chalcogenide compounds [3,[41][42][43][44][45][46].

Atomic-Deficient Microstructure by Revised PAL Analysis
The PAL spectra were recorded with the fast-fast coincidence system ORTEC (230 ps in resolution) using 22 Na isotope of ~50 kBq activity operated in normal measuring statistics (~1 M coincidences), as described in more detail elsewhere [29].The best fitting of the PAL spectra was achieved with the LT 9.0 program [82] under decomposition into three negative exponentials obeying normalization (I 1 + I 2 + I 3 = 1) and stabilizing the model-independent average positron lifetime τ av Σ as the mass center of a whole PAL spectrum.
Under this measuring set-up, the reconstructed three-component PAL spectra allow for error bars in the lifetimes τ i and intensities I i at the level ±0.005 ns and 0.5%, respectively.This approach covers different channels in nanostructured substances arising from positrons annihilating in defect-free bulk states, intrinsic trapping sites (such as vacancy-type defects) and Ps-hosting holes (free-volume voids).
In nanostructured substances dominated by annihilation from positron-and Ps-related states, unconstrained three-component PAL spectra can be interpreted employing different mathematical algorithms based on canonical STM [28, 29,57,83,84].But this model is valid only for solids with one kind of trap having two-component PAL spectra.So, multichannel spectra of nanosubstances originating from a great variety of free-volume elements should be processed with STM modified for some restrictions.One of the most simplified is two-state STM ignoring Ps decaying.Within this approach, the positron-trapping modes (such as defect-specific τ 2 and defect-free bulk τ b lifetimes, positron trapping rate κ d and a fraction of trapped positrons η) can be parameterized [57,83,84].The most plausible free-volume void modification processes in nanostructured materials can be hypothesized as suggested by Shpotyuk M. et al. [84].Finally, the 'remainder' over positron trapping in the PAL spectrum is ascribed to the Ps-decay channel owing to positrons annihilating as free particles or interacting with electrons from the environment [85].The Ps localized in holes give indication on their radii R in terms of the longest τ 3 lifetime with respect to the semiempirical Tao-Eldrup equation with material constants [85].The fractional free volume (f v ) of Ps-hosting sites can be calculated accepting the I 3 intensity and some constants validated for materials without structural groups inhibiting Ps formation.
Alternatively, in substances obeying three-component PAL spectra with essential input of the third component, which cannot be recompensated by source contribution, two Psdecay scenarios can be resolved in terms of fitting parameters only [56].The prevailing trend in the Ps formation probability would result to iso-typical changes in both I 1 and I 3 intensities accompanied by opposite changes in I 2 intensity.On the contrary, the prevailing trend in the hole density would result to iso-typical changes in both I 2 and I 3 intensities counterbalanced by opposite changes in I 1 intensity.
In heterogeneous substances obeying selective localization of traps, positron annihilation occurs through mixed positron-trapping and Ps-decaying channels.The low-electron density holes with maximum free volume and minimum surface tension should fit to confine Ps stabilization owing to its repulsive exchange potential, while regions of higher negative electron density and polarization such as sub-nm voids are more suitable to capture electrically charged positrons [86].So, positron annihilation is expected via interconnected positron-Ps-related channels, so that Ps-decay sites are the only free-volume holes which could be converted into positron traps (and vice versa).In this case, the generalized two-state STM modified for Ps-positron trapping conversion (known as the x3-x2-CDA, Coupling Decomposition Algorithm, or the Positronics approach [28,29]) can be used.Firstly, this algorithm is applied to an unstructured substance characterized by unconstrained three-component PAL spectrum, transforming it to generalized two-component form where all trapping inputs are gathered in the second component.Then, this procedure is performed for nanostructured substances (often modified by embedded nanoparticles, NP, thus defining respective nomenclature in parameterization).Nanostructurizationdriven interplay between Ps-and positron-related sites can be refined by transition to differential spectrum with the first (τ n •I n ) and second (τ int •I int ) components defined under condition of full inter-channel balance in nanosubstance.Parameterization of the Pspositron trapping conversion is performed within canonical two-state STM [28, 29,57,83,84] applied to this differential PAL spectrum.Finally, trapping modes such as defect-specific τ int and defect-free bulk τ b NP positron lifetimes, trapping rate in defects κ d NP , and some characteristics relevant to the size of these traps in terms of equivalent number of vacancies (τ int −τ b NP ) and nature of these traps in terms of (τ int /τ b NP ), can be determined.Within this approach, directionality in trapping conversion (Ps-to-positron or positron-to-Ps) is defined by sign of both I n and I int intensities.So, this approach can be used as indicator separating meaningful nanostructurization-driven processes from simple interplay between uncorrelated positron-trapping and Ps-decaying channels.

Quantum-Chemical Modeling of Molecular-Network Clustering
The optimized configurations of thioarsenide As 4 Se n cage-like molecules (n = 6-0) and network-forming clusters derived from these molecules by breaking in available Se atom positions were reconstructed using ab initio quantum-chemical atomic cluster-modeling algorithm CINCA (Cation Interlinked Network Cluster Approach) [60,61].The HyperChem Release 7.5 program based on restricted Hartree-Fock self-consistent field method with split-valence double-zeta basis set and single polarization function 6-311G* [87][88][89] was used.Optimization and single-point energy calculations were performed by the Fletcher-Reeves conjugate gradient method until a root-mean-square gradient of 0.1 kcal/(Å•mol) was reached.The cluster-forming energy (E f ) was corrected on the energy of terminated H atoms transforming network-forming cluster into molecular one [89,90] and recalculated with respect to the energy of a single AsSe 3/2 pyramid (E f = −72.309kcal/mol [61]).This modelling route allows for the characterization of both molecular and network-forming conformations in covalent-bonded systems like chalcogenide glasses characterized by CN (coordination number), thus parameterizing the most energetically favorable molecularnetwork decomposition scenarios.To compare clusters accounting for small rings involved, the average number of constraints per atom n c was calculated following the Phillips-Thorpe constraint-counting algorithm with stretching and bending forces ascribed to intra-molecular bonds within the cluster [65][66][67].

Conclusions
Changes in the atomic-specific and atomic-deficient microstructure of binary As x Se 100−x arsenoselenides from the border of the glass-forming region (65 < x < 70) driven by nanomilling in dry and dry-wet modes are examined by multiexperimental characterization probes, including the X-ray powder diffraction (XRPD) in terms of the modified microcrystalline model, micro-Raman scattering (micro-RS) and revised positron annihilation lifetime (PAL) spectroscopy within the Positronics approach, complemented with molecular-network disproportionality analysis employing the ab initio quantumchemical cluster-modeling algorithm CINCA (the Cation Interlinked Network Cluster Approach).The studied alloys are considered with respect to tetra-arsenic biselenide As 4 Se 2 thioarsenide stoichiometry corresponding to coordination number CN = 2.67, these being glassy g-As 65 Se 35 (CN = 2.65), glassy-crystalline g/c-As 67 Se 33 (CN = 2.67) and g/c-As 70 Se 30 (CN = 2.70).
Due to XRPD analysis, the crystalline inclusions in the examined alloys are ascribed to two phases enhanced under milling, especially in PVP (polyvinylpyrrolidone) water solution, such as rhombohedral As and cubic arsenolite As 2 O 3 .A straightforward interpretation of the observed changes in the amorphous structure of these alloys is developed by analyzing diffuse peak halos in their XRPD patterning recognizing the medium-range structure within the modified microcrystalline model.Disruption of the intermediate-range order due to weakening of the FSDP (the first sharp diffraction peak) responsible entities accompanied by an enhancement of the extended-range order due to fragmentation of the SSDP (the second sharp diffraction peak) responsible entities compose principal interplay between medium-range structure levels in arsenoselenides subjected to nanomilling.Since remnants of thioarsenide As 4 Se n molecular entities destructed under grinding interact with oxygen, a cubic arsenolite As 2 O 3 phase is formed in the alloys subjected to nanomilling in wet mode.
Due to micro-RS spectroscopy, the examined alloys are stabilized by thioarsenide As 4 Se n molecules (preferentially with n = 3, 4) incorporated in the As-Se network.Nanomilling-driven molecular-to-network (amorphization) transitions occur due to the destruction of molecular thioarsenides followed by their incorporation in the network undergoing polyamorphic (reamorphization) transition.The examined arsenoselenides affected by generated defects become notably stressed, the respective defect-formation transformations being realized independently on crystalline inclusions in them.
Due to revised PAL analysis for direct conversion of bound positron-electron (Ps, positronium) states into positron traps, nanomilling-driven volumetric changes in PVPstabilized alloys are identified with respect to dry-milled ones.Under wet milling, the Ps-hosting holes in a preferential PVP environment appear instead of positron traps with ~0.36-0.38 ns lifetimes corresponding to multiatomic vacancies in the As-Se matrix.Superposition of the PAL spectra collected for PVP, melt-quenching-derived, dry-and dry-wetmilled As-Se samples shows spectacular smoothly decaying behavior over superimposed PAL spectra peaks and tails.

Figure 4 .
Figure 4.The normalized micro-RS spectra of MQ-derived g/c-As67Se33 reproduced in a sequence from the bottom to the top: (a) unmilled bulk pieces (unpelletized); (b) pelletized coarse-grained sample; (c) pelletized dry-milled sample; (d) pelletized dry-wet-milled sample.The most prominent features in the micro-RS spectrum of the bulk unmilled sample (a) are marked by vertical arrows, and traced by dotted lines to the respective micro-RS spectra of the pelletized samples (b-d).

Figure 4 .
Figure 4.The normalized micro-RS spectra of MQ-derived g/c-As 67 Se 33 reproduced in a sequence from the bottom to the top: (a) unmilled bulk pieces (unpelletized); (b) pelletized coarse-grained sample; (c) pelletized dry-milled sample; (d) pelletized dry-wet-milled sample.The most prominent features in the micro-RS spectrum of the bulk unmilled sample (a) are marked by vertical arrows, and traced by dotted lines to the respective micro-RS spectra of the pelletized samples (b-d).

Figure 5 .
Figure 5.The normalized micro-RS spectra of MQ-derived g-As65Se35 in unmilled state (a) and after nanomilling in a single dry mode (b).The most prominent features in the micro-RS spectrum of the bulk sample (a) are marked by arrows and traced by dotted lines to that of dry-milled sample (b).

Figure 5 .
Figure 5.The normalized micro-RS spectra of MQ-derived g-As 65 Se 35 in unmilled state (a) and after nanomilling in a single dry mode (b).The most prominent features in the micro-RS spectrum of the bulk sample (a) are marked by arrows and traced by dotted lines to that of dry-milled sample (b).

Figure 6 .
Figure 6.The raw PAL spectra of pelletized g/c-As70Se30 in unmilled state (a) and after nanomilling in dry mode (b) and combined dry-wet mode (c) as compared with the spectrum of PVP pelletized under the same conditions (d).The collected PAL spectra are reconstructed from unconstrained three-term fitting and reproduced at background of source contribution with bottom insets showing statistical scatter of variance.The occupation of 'tail" states in unmilled and dry-milled samples grows notably under transition to dry-wet-milled sample approaching that in the pelletized PVP.

Figure 6 .
Figure 6.The raw PAL spectra of pelletized g/c-As 70 Se 30 in unmilled state (a) and after nanomilling in dry mode (b) and combined dry-wet mode (c) as compared with the spectrum of PVP pelletized under the same conditions (d).The collected PAL spectra are reconstructed from unconstrained three-term fitting and reproduced at background of source contribution with bottom insets showing statistical scatter of variance.The occupation of "tail" states in unmilled and dry-milled samples grows notably under transition to dry-wet-milled sample approaching that in the pelletized PVP.

Figure 7 .
Figure 7.The overlapping of the PAL spectra in the examined arsenoselenides g-As65Se35 (a), g/c-As67Se33 (b) and g/c-As70Se30 (c) pelletized before nanomilling (black points) and after nanomilling in dry mode (red points) and dry-wet mode (green points) as compared with the PAL spectrum in the PVP sample pelletized under the same conditions (blue points).The insets show a nearly invariant tendency in the PAL spectra peaks depressed in the right wing after nanomilling in dry-wet mode due to moderated Ps-formation probability and slightly changed average positron lifetime τav.

Figure 7 .
Figure 7.The overlapping of the PAL spectra in the examined arsenoselenides g-As 65 Se 35 (a), g/c-As 67 Se 33 (b) and g/c-As 70 Se 30 (c) pelletized before nanomilling (black points) and after nanomilling in dry mode (red points) and dry-wet mode (green points) as compared with the PAL spectrum in the PVP sample pelletized under the same conditions (blue points).The insets show a nearly invariant tendency in the PAL spectra peaks depressed in the right wing after nanomilling in dry-wet mode due to moderated Ps-formation probability and slightly changed average positron lifetime τ av .The changes in the PAL spectra tails of unmilled, dry-and dry-wet-milled samples are due to increase in density of o-Ps hosting holes.There is no evident empty gap between the PAL spectra tails for dry-milled and dry-wet-milled glassy samples as compared with glassy-crystalline samples caused by changes in Ps decaying states under transition to annihilation in PVP-bearing medium.
. But this situation cardinally changed in the transition to network clusters derived from these molecules by double breaking in both Se atom positions, with the H-saturated molecular prototypes of these clusters shown in Figure 8e,f.Surprisingly, the network-forming cluster (x2-As 4 Se 2 -I) derived from the As 4 Se 2 -I molecule, maintaining the closed tetragon-like As 4 arrangement built of four (As-As) bonds (Figure 8e), has E f ~−0.72 kcal/mol, which is the best among all clusters in this compositional range [59].Because of one small ring involved, the glassy network built of such clusters is rigid and stressed (n c = 3.33).These clusters facilitate the decomposition of dimorphite-type As 4 Se 3 molecules into realgar-type As 4 Se 4 ones, accompanied by the extraction of some amorphous products close to As 4 Se 2 [59].Molecules 2024, 29, x FOR PEER REVIEW 15 of 27 (a) As4Se2-I molecule composed by four (As-As) bonds in zigzag sequence: Ef = −4.42kcal/mol; nc = 2.67 (b) As4Se2-II molecule composed by (As-As) bond attached to As3 triangle: Ef = −3.59kcal/mol; nc = 2.50 (c) As4Se3H2 molecular prototype of network cluster derived by single break from As4Se2-I molecule (x1-As4Se2-I): Ef = −3.46kcal/mol; nc = 3.00 (d) As4Se3H2 molecular prototype of network cluster derived by single break from As4Se2-II molecule (x1-As4Se2-II): Ef = −3.27kcal/mol; nc = 2.83 (e) As4Se4H4 molecular prototype of network cluster derived by double break from As4Se2-I molecule (x2-As4Se2-I): Ef = −0.72 kcal/mol; nc = 3.33 (f) As4Se4H4 molecular prototype of network cluster derived by double break from As4Se2-II molecule (x2-As4Se2-II): Ef = −4.42kcal/mol; nc = 3.17

Figure 8 .
Figure 8.The ball-and-stick presentation of optimized configuration of tetra-arsenic biselenide thioarsenide As4Se2-I molecule composed by four (As-As) bonds in zig-zag sequence (a) and As4Se2-II molecule composed by (As-As) bond attached to As3 triangle (b), as compared with As4Se3H2 and As4Se4H4 molecular prototypes of network clusters derived from these molecules by single (x1-As4Se2-I-(c), x1-As4Se2-II-(d)) and double (x2-As4Se2-I-(e), x2-As4Se2-II-(f)) breaking in available Se atom positions.The cluster-forming energies Ef are given in respect to AsSe3/2 pyramid (Ef = −72.309kcal/mol [60]).The H, Se and As atoms are, respectively, grey-, blue-and red-colored, and chemical bonds between atoms are denoted by respectively colored sticks.The average number of constraints nc is given following the Phillips-Thorpe constraint-counting algorithm [65-67].

Figure 8 . 80 Figure 9 .
Figure 8.The ball-and-stick presentation of optimized configuration of tetra-arsenic biselenide thioarsenide As 4 Se 2 -I molecule composed by four (As-As) bonds in zig-zag sequence (a) and As 4 Se 2 -II molecule composed by (As-As) bond attached to As 3 triangle (b), as compared with As 4 Se 3 H 2 and

Figure 9 .
Figure 9.The ball-and-stick presentation of optimized configuration of tetra-arsenic monoselenide As 4 Se molecule composed by two edge-sharing As 3 triangles (a), as compared with As 4 Se 2 H 2 molecular prototype of network-forming cluster derived from this molecule by breaking in Se atom position x1-As 4 Se (b).The terminated H atoms are grey-colored, Se and As atoms are respectively blue-and red-colored, chemical bonds between atoms are denoted by, respectively, colored sticks.

80 Figure 10 .
Figure 10.The ball-and-stick presentation of optimized configuration of regular pyramid-shaped tetra-arsenic As4 thioarsenide molecule (a) and As6H6 molecular prototype of network-forming cluster derived by distortion from this molecule in a form of flattened pyramidal-shaped unit, which composes two-dimensional double-layer network of chair-configurated six-fold rings of As atoms (As6⋅(2/3) = As4).The H and As atoms are respectively grey-and red-colored, and chemical bonds between atoms are denoted by respectively colored sticks.

Figure 10 .
Figure 10.The ball-and-stick presentation of optimized configuration of regular pyramid-shaped tetra-arsenic As 4 thioarsenide molecule (a) and As 6 H 6 molecular prototype of network-forming cluster derived by distortion from this molecule in a form of flattened pyramidal-shaped unit, which composes two-dimensional double-layer network of chair-configurated six-fold rings of As atoms (As 6•(2/3) = As 4 ).The H and As atoms are respectively grey-and red-colored, and chemical bonds between atoms are denoted by respectively colored sticks.

Table 1 .
Parameterization of the FSDP-related diffuse peak halo in the examined MQ-derived arsenoselenides before and after nanomilling in dry and combined dry-wet mode.

Table 1 .
Parameterization of the FSDP-related diffuse peak halo in the examined MQ-derived arsenoselenides before and after nanomilling in dry and combined dry-wet mode.

Table 2 .
[50]best-fit PAL spectra parameterization in the pelletized arsenoselenide samples in unmilled state and after nanomilling in dry-and dry-wet modes compared with these parameters in the PVP samples pelletized under the same conditions[50].

Table 3 .
[50]positron trapping modes in the pelletized arsenoselenides in unmilled state and after nanomilling in dry and dry-wet modes compared with these parameters in the PVP samples pelletized under the same conditions[50], derived from their reconstructed three-component PAL spectra treated within two-state simple-trapping model (STM) ignoring Ps-decaying contribution.

Table 4 .
Trapping conversion modes calculated for pelletized dry-milled arsenoselenide sample respectively to the same sample subjected to nanomilling in combined dry-wet mode.
2.3.Molecular-Network Disproportionality at the Border of the Glass-Forming Region in As-SeSystem via Quantum-Chemical Cluster Modelling