Mechanochemically driven amorphization of nanostructurized arsenicals, the case of β-As₄S₄

The MM-driven nanonization in the arsenicals at growing rotational speed n is accompanied by progressive appearance of amorphous halos (typical for As–S glasses [32, 33]) in the XRPD patterns near 13°–19°, 26°–34°, and 52°–60° 2θ, superimposed on crystalline reflexes ascribed to β-As₄S₄ (Fig. 1). According to Fourier-transform formalism [34], the first of these halos can be reproduced in a reciprocal space (in the structure factor determination) as the FSDP, corresponding to a real-space ordering with R “quasi-periodicity” and L correlation length, defined, respectively, by Eqs. (3) and (4).

The FSDP is an obvious manifestation of medium-range order in glass-forming systems [35]; however, its strict microstructure origin remains controversial (see, e.g., [36] and literature therein). Nevertheless, the Gaskell’s concept on crystalline-like order in MQ glasses [37] modified with Wright’s justification on the FSDP as arising from periodicity in the distribution of some “pseudo-planes” for Bragg diffraction (“quasi-periodicity”) separating succession of randomly packed network cages [38] seems convenient for interpretation of crystalline-to-amorphous transition in MM nanoarsenicals. The flattened cage structure of network glasses produces inner equivalent planes at the opposite sides of these cages forming necessary contribution to reciprocal space Fourier component generating the FSDP [38]. Within this model, the FSDP can be ascribed to variations in the underlying cage structure of glass-forming network defined by interlinked polyhedrons forming multiple cycles (like random atomic array within Zachariasen’s diagram [39]). So, the cages keep some elements of interplanar “ordering” in network glasses, character for most stable crystalline counterparts of close chemical compositions.

Detailed inspection of XRPD profile after subtracting the overlapping β-As₄S₄ reflexes (Fig. 2) allows the FSDP parameterization using Eqs. (1)–(4), these data being gathered in Table 1. With increase in speed n, the FSDP parameters reach saturation, so that the FSDP is indeed sharp (in a reciprocal space) in REHE-600 due to low width of scattering vector ΔQ = 0.23 Å⁻¹ centered at Q = 1.14 Å⁻¹, thus corresponding to R = 5.49 Å in “quasi-periodicity” and L = 27.0 Å in correlation length (in a real space). These parameters are well fitted to monotonic compositional dependence in amorphous As–S as going from MQ As₄₀S₆₀ glass [33], MQ As₄₂S₅₈ glass [33] (both being within glass-forming region in binary As–S system [2‐4]) and completely amorphized As₄₅S₅₅ alloy [7] toward As-rich compositions. Therefore, it can be assumed that under current MM conditions, we deal with continuous generation of compositionally authentic amorphous phase in β-As₄S₄ arsenical. The most stabilized amorphous substance appeared in REHE-600 sample differs substantially in its medium-range ordering from stoichiometric MQ As₂S₃ glass. Within Gaskell–Wright’s microscrystalline concept [37, 38], the smooth shift in the FSDP position to lower Q (respectively, 2θ) with rotational speed n can be treated as domination in the MM products; some structural derivatives arise from cage-type entities of crystalline β-As₄S₄. Indeed, the most intensive (11\( \bar{1} \)) reflex of this β-As₄S₄ crystal phase (possessing C2/c space group) corresponds just to interplanar distance \( d_{{(11\bar{1})}} \) = 5.76 Å; that is the highest one within all possible over-stoichiometric As–S polymorphs [7]. Simultaneously, the FSDP becomes sharper with increased n, as it is character to longer correlation lengths L of networks built of these cage-type molecular derivatives (Table 1).

The PAL spectra of pelletized MM arsenicals are depicted in Fig. 3 with insert showing depressed and right-shifted peaks in a sequence of REHE-0, REHE-200, REHE-500, REHE-600. This depressing and time-enhancing trend correlates with degree of amorphization in these samples as determined from FSDP-related XRPD, and, thus, can be used as indicative of the appeared amorphous phase, whichever its occurrence (composition, sizes, shapes, morphologies, etc.).

The collected PAL spectra were fitted using three unconstrained exponentials, proving a decreasing tendency in mean positron lifetime \( \tau_{{{\text{av}}.}}^{\varSigma} \) as it follows from data gathered in Table 2. Since only low contribution in the PAL spectra arises from third component (no more 3%), we tried to resolve the physically realistic annihilation channels exploring two-state STM [18‐20] in addition to Ps-decaying modes [21] (Table 3). Despite simplification, it is clearly seen that free-volume changes associated with nanostructurization of β-As₄S₄ arsenicals due to MM notably differ in dependence on rotational speed n. Under small n (REHE-200), there are no changes in free volumes responsible for positron and Ps trapping (unchanged τ₂ and τ₃ lifetimes), apart from amount of positron traps, which demonstrates rather growing trend in view of higher I₂, thus resulting in increased positron-trapping rate in defects κ_d. With further n increase resulting in aggregation of NPs and increased specific surface area in REHE-500 pellet, this trapping-enhancing trend is missed, leading to decreased fractional free volumes f_v. In contrast, in REHE-600 pellet dominated by agglomerated NPs, the free-volume voids responsible for positron trapping also agglomerate (thus giving increased τ₂ and decreased I₂), but fractional volume f_v increases notably due to both volume and amount of Ps-trapping holes (drastic increase in both τ₃ and I₃, Table 3).

Noteworthily, the evolution trends in positron- and Ps-trapping modes in MM β-As₄S₄ arsenicals are mutually correlated. This allows assuming that at MM with increased rotational speed n, only Ps traps are transformed into positron traps and vice versa. Hence, we can try to parameterize this trapping-conversion process employing the x3–x2-CDA [22‐26] for tested MM probes in respect of non-milled (coarse-grained) REHE-0 one, the results being gathered in Table 4. These data clarify that at n = 200–500 min⁻¹, the free-volume changes in MM arsenicals correspond to the scheme of direct Ps-to-positron trapping conversion due to positive both I_n and I_int intensities.

In REHE-200 pellet, the spherical Ps traps with R₃ = 0.286 nm disappear (see Table 3), being replaced by positron traps with defect-specific lifetime τ_int = 0.335 ns (see Table 4). These sites can be identified as interfacial free-volume holes between neighboring crystallite grains forming so-called triple junctions (TJs) [10, 22‐26, 40]. With known semiempirical correlations for As–S compounds [41‐43], these positron traps can be ascribed to bi-/tri-atomic vacancies characterized by (τ_int −  τ _b ^NP ) = 0.09 ns and τ_int/τ _b ^NP  = 1.37 (Table 4). These defects are stabilized in preferential crystalline environment, as it follows from τ _b ^NP approaching defect-free bulk lifetime in crystalline arsenic sulfides [41, 44]. Amorphization is inessential in REHE-200 sample, in full respect of low amorphization degree derived from the FSDP-related XRPD.

The MM-driven amorphization is enhanced in REHE-500 sample subjected to MM under higher speed. Despite general direction of free-volume evolution which does not change in this sample, the Ps-to-positron trapping conversion is more suppressed (due to κ _d ^NP  = 1.20 ns⁻¹) as compared with REHE-200 (κ _d ^NP  = 1.59 ns⁻¹). The positron-trapping defects appeared instead of Ps traps with R₃= 0.286 nm (Table 3) are characterized by higher volumes in respect of τ_int = 0.369 ns (Table 4), which can be ascribed rather to quadruple vacancies in As–S alloys [41‐43]. The chemical environment of these positron-trapping TJs is preferentially amorphous in view of τ _b ^NP  = 0.281 ns, which closely approaches the defect-free bulk lifetime in glassy As–S [41, 42].

Conceptually, despite the same initial state, the studied MM arsenicals are not linked by sole technology (because of changed rotational speeds n, resulting in different structural transformations in the milled substance). Nevertheless, we can apply the developed approach for REHE samples to clarify the microstructural picture of their differentiation, assuming unchanged origin of responsible free-volume elements. The results of such comparison employing x3–x2-CDA for REHE-500 pellet in respect of REHE-200 one are also given in Table 4. It is evident that greater speed n leads to more amorphous structure of MM arsenical, possessing positron-trapping sites with defect lifetime τ_int = 0.372 ns (proper to multi-atomic vacancies [41‐43]) appeared instead of Ps traps in an amorphous environment (due to τ _b ^NP = 0.289 ns correlated with bulk lifetime in glassy As–S [41, 42]).

However, the character of trapping conversion changes drastically in REHE-600 pellet, where crystallite agglomeration associated with decreased specific surface area prevails. Both I_n and I_int intensities occur to be negative (in respect of REHE-0, Table 4), testifying in a favor of positron-to-Ps trapping conversion (which can be considered as inverse Ps-to-positron trapping conversion), associated with more intensive free-volume generation due to increased \( \tau_{{{\text{av}}.}}^{\varSigma } \) = 0.334 ns (see Table 2). The NPs agglomeration under these MM conditions is accompanied by elimination of positron-trapping TJs between contacting crystallites (with defect lifetime τ_int= 0.338 ns character for bi/tri-atomic vacancies) and appearance of extended Ps-trapping holes. Irrespective of enhanced degree of amorphization, this process prevails mainly in crystalline environment of REHE-600 pellet (due to τ _b ^NP = 0.243 ns close to non-defect bulk lifetimes in crystalline arsenic sulfides [41, 44]).

Again, by assuming that REHE samples are interlinked only by physically correlated states, which can be validated for unchanged origin of respective free-volume elements responsible for their PAL spectra, the difference in free-volume structure can be unambiguously parameterized for REHE-600 pellet taken in respect of REHE-500 as a reference. Within such comparative consideration, it seems that less amount of positron traps with τ_int= 0.358 ns (corresponding to multiatomic vacancy clusters) are stabilized in REHE-600 pellet affected by MM at n = 600 min⁻¹. These free-volume entities disappear from mixed crystalline–amorphous environment proper to more amorphized REHE-500 sample, as it can be expected from calculated τ _b ^NP = 0.263 ns, which is higher than τ_b in crystalline, but lower than in glassy As–S alloys [41‐44]).

So in contrast to substances possessing poor glass-forming ability, and thus obeying MM-driven size-dependent pressure-induced amorphization [1] in respect of crystalline destabilization model [45], the directly synthesized β-As₄S₄-based arsenicals are distinguished by continuous generation of amorphous phase under speed-increased high-energy MM. These findings as it follows from above research (especially, the PAL spectroscopy data on responsible free-volume elements) testify rather in a favor of “shell” kinetic model [46], treated this phenomenon in terms of intensive defect accumulation in parent β-As₄S₄ crystalline phase. Such defects appear firstly at grain boundaries, and amorphous phase nucleates heterogeneously followed by stretching into interior, thus creating mixed crystalline–amorphous environment for TJs between contacting grains.

These PAL-responsible elements are sketched in Fig. 4. Under MM with n = 200–500 min⁻¹, the NPs aggregation is accompanied by transformation of free-volume entities within Ps-to-positron trapping-conversion scheme. The Ps-trapping holes between loosely packed crystalline–amorphous grains and positron-trapping TJs between β-As₄S₄ crystallites (depicted in Fig. 4b, c) are character for non-milled REHE-0. Under low amorphization (due to MM at n = 200 min⁻¹), the Ps-holes transform into positron traps in mainly crystalline environment (see Fig. 4c). With increased rotational speed (n = 500 min⁻¹), this process occurs in an amorphous environment (see Fig. 4d). Finally, under highest rotational speed in REHE-600, the NPs agglomeration starts, this process being accompanied by disappearing of TJs between grains in both crystalline (Fig. 4c) and crystalline–amorphous environment (Fig. 4d) into inter-NPs Ps-trapping holes (see Fig. 4b).

The cage-type As₄S₄ molecule character for realgar α-As₄S₄ structure [44] can be accepted as starting element for MM-driven amorphization of directly synthesized β-As₄S₄-based REHE arsenicals. This is well confirmed by obviously reduced intensities of all bands corresponding to this molecular unit in the Raman scattering spectra of MM REHE-200 and REHE-600 samples, especially as compared with non-milled REHE-0 and REHE-100 pellets [9].

The optimized configuration of this monomer As₄S₄ molecule nominating geometrical positions of all atoms which is as follows from CINCA simulation is shown in Fig. 5, the bond distances and angles (which occur to be in an excellent agreement with known experimental data [47]) being given previously in [44]. To estimate network-forming ability of amorphized network, the forming energy of this molecule (E_f = − 0.58 kcal/mol) is defined in respect of the energy of single AsS_3/2 pyramidal unit (− 79.404 kcal/mol), as it is typically accepted in CINCA modeling [13]. The network-forming clusters can be derived from this As₄S₄ molecule by breaking corresponding sulfur atoms, linking them with surrounding environment through S_1/2…S_1/2 chains. For modeling purpose, these dangling bonds are terminated by hydrogen H atoms (allowing full saturation of covalent bonding), and thus overall forming energies for such molecular self-closed clusters can be simply calculated. By subtracting the energy of H-based terminated atomic groups, the proper energy of network clusters can be recalculated as it is demonstrated in more details elsewhere [13, 29, 30].

Full structural diversity for starting As₄S₄ molecule (see Fig. 5), composed of four S and four As atoms linked in D_2d symmetry (thus evolving maximum number of short-ring entities, i.e., four pentagons and four hexagons), is described by four types of network clusters formed due to single breaking in (S1) position, two types of double breaking in (S1)–(S3) and (S1)–(S4) positions, and triple breaking in (S1)–(S2)–(S3) positions. The geometrically optimized configurations of these clusters are shown in Fig. 6, the character-forming energies (in respect of the energy of AsS_3/2 pyramid) being given in Table 5.

It is seen that destruction of As₄S₄ molecule due to single breaking in (S1) position (Fig. 5) followed by network polymerization due to two S–H bonds (thus forming As₄S₅H₂ molecular cluster, see Fig. 6a) is energetically plausible. Indeed, this process needs only E_f = − 1.29 kcal/mol energy to be realized (i.e., twice more as forming energy of monomer As₄S₄ molecule, see Table 5). Under such destruction–polymerization transformation, only three short-ring entities remain, these being two pentagons and one hexagon (Fig. 6a). Previously, such changes in As₄S₄ clusters were considered by Musgraves et al. [48] to explain the mechanism of photo-induced effects in As-rich arsenicals. Double breaking in (S1)–(S3) and (S1)–(S4) positions (see Fig. 5) followed by network polymerization remains only one short-ring entity in the remnants of As₄S₄ molecule (i.e., As₄S₆H₄ molecules), this being pentagon (Fig. 6b) or hexagon (Fig. 6c). The former (the pentagon-based As₄S₄ derivative) was considered in [49] as resulting from broken chemical ordering in arsenic sulfide glasses. Nevertheless, the energetic costs for such transformations seem to be too expensive (see Table 5) to be considered as realistic competitive scheme of MM-driven amorphization of β-As₄S₄ arsenical. Triple breaking in (S1)–(S2)–(S3) positions (see Fig. 5) destroys all short-ring entities, transforming monomer As₄S₄ molecule into network of two (As–S) bonds interlinked by homonuclear (As–As) bonds (the corresponding As₄S₇H₆ molecular cluster is shown in Fig. 6d). This destruction–polymerization process needs only E_f = − 1.72 kcal/mol energy, and, correspondingly can be accepted as quite possible for realization in As₄S₄-based network.

So, in respect of CINCA modeling, the structural matrix of directly synthesized β-As₄S₄ can be imagined as admixture of crystalline phase composed of monomer cage-type As₄S₄ molecules and some amount of isocompositional amorphous phase, built of network-forming fragments, mainly single- and triple-broken As₄S₄ derivatives. This phase equilibrium is responsible for the FSDP-related XRPD in (Fig. 1a) and free-volume distribution governing the PAL spectrum of REHE-0 sample (Fig. 3). The effect of high-energy MM can be identified as destructive action on As₄S₄ molecules and existing amorphous phase, transforming them into the network of triple-broken As₄S₄-molecule derivatives. The topologically changed amorphous phase possessing no short-ring entities modifies the FSDP parameters of β-As₄S₄ arsenicals milled with increasing speed n as shown in Table 1. This structurally inhomogeneous amorphous phase (composed preferentially of single- and triple-broken As₄S₄ derivatives) is also responsible for modified environment of PAL-detectable free-volume elements (inter-grain Ps-trapping holes and inter-crystallite positron-trapping TJs schematically shown in Fig. 4) in MM β-As₄S₄ arsenicals.