Background

Nowadays, nanoparticle (NP)-based substances have attracted high attention due to advances of their implementation in various spheres of human activity (Roduner 2006). Tremendous efforts have been done to prepare such media composed of NP consolidated in multicomponent systems referred to as multiparticulate nanocomposites, which utilize combination of important properties unachievable in one-component materials. The multiparticulate approach grounded on variation of different NP formulations has been very promising for contemporary drug-delivery systems extending frontiers of their promising pharmaceutical developments (Fatima et al. 2006).

To a great extent, the above materials’ engineering strategy concerns wide group of arsenicals, which are representative arsenic (As) based compounds preferentially of natural mineral origin applied in anti-cancer therapy (Dilda and Hogg 2007; Liu et al. 2021). Poor bioavailability of some arsenicals like realgar As4S4 (the As4S4-bearing arsenicals) resulting from limited solubility in water has been eliminated in NP-based formulations (Tian et al. 2014), particularly, treated by high-energy mechanical milling sometimes called nanomilling (Baláž et al. 2013). Nanomilling-derived arsenicals (nanoarsenicals) have attained excellent medicinal efficacy allowing their usage as promising anti-cancer drugs (see Bujňáková et al. 2015; Baláž et al. 2017). In the past decade, achievements on this path have been so impressive that even emergence the novel branch of anti-cancer therapy (realgar nanotherapeutics) has been declared recently (see Wang and Xu 2020).

In biomedicinal applications, nanoarsenicals possessing improved anti-cancer functionality are often combined with NP of other nature to form multiparticulate pharmaceutical systems possessing additional advances, such as fluorescent emission due to nanostructured zinc sulfide ZnS (Fang et al. 2011; Baláž et al. 2016) and magnetically addressable drug-delivery functions owing to magnetite Fe3O4 (Cabrera et al. 2008). The groups of novel biparticulate nanocomposites such as anti-cancer-magnetic As4S4/Fe3O4 (see Shpotyuk et al. 2017a; Bujňáková et al. 2020), anti-cancer-fluorescent As4S4/ZnS (see Bujňáková et al. 2017; Shpotyuk et al. 2017b) and magnetically fluorescent Fe3O4/ZnS (see Liu et al. 2014; Roychowdhury et al. 2014; Bujňáková et al. 2016) have been emerged. The functioning principles of these multiparticulate nanocomposites occurred to be rather complicated, since they embrace diverse levels of materials organization including atomic-specific and atomic-deficient structural entities. That is why understanding of such nanomaterials’ engineering routines has a pivotal importance for contemporary biomedicine.

The objective of current research is to identify sub-nm volumetric nanostructuralization effects in multiparticulate As4S4-bearing nanocomposites within quasi-ternary As4S4–ZnS–Fe3O4 system in transitions between different hierarchical derivatives originated from parent anti-cancer-fluorescent-magnetic nanocomposite (1⋅As4S4/4⋅ZnS/1⋅Fe3O4) prepared by nanomilling (Lukáčová Bujňáková et al. 2020; Shpotyuk et al. 2020c), employing positron annihilation lifetime (PAL) spectroscopy developed within the Positronics approach, serving as advanced instrumentation tool probing space-time continuum correlations for electrons annihilating with their anti-particles (the positrons) in nanostructuralized substance at extremely low sub-nm level, far below measuring possibilities available for conventional microstructural probes (Shpotyuk et al. 2015b; 2022).

Methods

Nanocomposite preparation route

To prepare As4S4-bearing nanocomposites of quasi-ternary As4S4–ZnS–Fe3O4 system, the ZnS precursors (zinc acetate (CH3COO)2Zn·2H2O, 99%, Ites; and sodium sulfide Na2S·9H2O, 98%, Acros Organics) were co-milled with commercial arsenic sulfide β-As4S4 of 95% purity (purchased in Sigma-Aldrich, USA) and natural mineral magnetite Fe3O4 (supplied from the mine Kiruna, Sweden) according to the following disproportionality equation:

$$ {{\text{As}}_4} {\text{S}}_4 + ( {{\text{CH}}_3 }{\text{COO}} )_2 {\text{Zn}}\cdot{\text{2H}}_2 {\text{O}} + {\text{Na}}_{{2}} {\text{S}}\cdot 9{\text{H}}_2 {\text{O}} + {\text{Fe}}_3 {{\text{O}}_4 }\to \{ {{\text{As}}_4} {\text{S}}_4 /{\text{ZnS}}/{\text{Fe}}_3 {\text{O}}_4 \} + 2{\text{CH}}_3 {\text{COONa}} + 11{\text{H}}_2 {\text{O}}. $$
(1)

The energy transfer to fine-grained powder estimated over specific grinding work performed in the ball mill Pulverisette 6, was estimated to approach ~ 105 kJ/g (see Tkacova 1989; Heegn 2001). Milling was performed in a 250-mL chamber with 50 balls (each having ~ 10 mm in diameter) made of tungsten carbide WC. This treatment lasting 20 min was performed in protective argon atmosphere at the rotational speed of planet carrier of ~ 500 rpm. After reaction (1), the resultant sodium acetate was removed from product by washing in distilled water and drying at 70 °C during 180 min to separate solid remainder keeping 1:4:1 ratio between molar fractions of components (β-As4S4, ZnS, and Fe3O4). Finally, the fine-grained powder was compressed by compacting inside stainless-steel die under ~ 0.7 GPa pressure to produce disc-like pellets having ~ 6 mm in diameter and ~ 1 mm in thickness.

More details on technological preparation route for these multiparticulate nanocomposites can be found elsewhere (see, e.g., Shpotyuk et al. 2020c). This mechanochemical technology was used to obtain parent triparticulate 1⋅As4S4/4⋅ZnS/1⋅Fe3O4 nanocomposite referred hereafter as AZF-141 (in respect to the first letters in the chemical formula and number of the respective molecules), and its compositionally equivalent As4S4-bearing derivatives, these being biparticulate AF-11 (1⋅As4S4/1⋅Fe3O4) and AZ-14 (1⋅As4S4/4⋅ZnS) ones addressed in Shpotyuk et al. (2017a, b), and recently studied monoparticulate A-1 (As4S4) nanocomposite addressed in Baláž et al. (2017) and Shpotyuk et al. (2018a, 2019a, b).

Preliminary microstructure characterization of As4S4-bearing nanocomposites

Crystallographic specificity of the prepared nanocomposites was identified by the X-ray powder diffraction (XRPD) method in transmission mode employing STOE STADI P diffractometer (STOE & Cie GmbH, Darmstadt, Germany) with a linear position-sensitive detector (Cu-Kα1 radiation), as was described in more details elsewhere (Baláž et al. 2017; Shpotyuk et al. 2017a, 2018a, 2020c). The microstructure of the crystallites (average apparent crystallite size D and average maximum strain ε) of arsenic monosulfide β-As4S4 (JCPDS card No. 72-0686; see Porter et al. 1972; Bonazzi and Bindi 2008), magnetite Fe3O4 (JCPDS card No. 74-0748; see Fleet 1981), low-temperature cubic ZnS (sphalerite, JCPDS card No. 05-0566; see Fang et al. 2011) and high-temperature hexagonal ZnS (wurtzite, JCPDS card No. 70-2204; see Fang et al. 2011) were defined by Rietveld refinement using the FullProf.2k (v.5.40) program (Rodriguez-Carvajal 2001) in terms of isotropic line broadening (see Rodriguez-Carvajal and Roisnel 2004).

The experimental XRPD profiles of some As4S4-bearing nanocomposites derived in quasi-ternary As4S4–ZnS–Fe3O4 system compared with calculated Bragg-diffraction reflexes from constituent crystalline phases are shown in Fig. 1. The results of nanophase analysis for the studied nanocomposites are summarized in Table 1 with D and ε values calculated from the broadening of the most pronounced Bragg-diffraction lines ascribed to the respective nanocrystalline (nc) phases.

Fig. 1
figure 1

XRPD profiles of As4S4-bearing nanocomposites derived in quasi-ternary As4S4–ZnS–Fe3O4 system in a sequence of decaying As4S4 content: a monoparticulate A-1 (As4S4); b biparticulate AF-11 (1⋅As4S4/1⋅Fe3O4); c triparticulate AZF-141 (1⋅As4S4/4⋅ZnS/1⋅Fe3O4), as compared with calculated Bragg-diffraction reflexes from constituent crystalline phases (d): β-As4S4 (red-colored, JCPDS card No. 72-0686), magnetite Fe3O4 (blue-colored, JCPDS card No. 74-0748), high-temperature ZnS wurtzite (green-colored, JCPDS card No. 79-2204) and room-temperature ZnS sphalerite (brown-colored, JCPDS card No. 05-0566)

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Table 1 Nanophase parameterization in triparticulate AZF-141 (1⋅As4S4/4⋅ZnS/1⋅Fe3O4) nanocomposite and its direct hierarchical derivatives: biparticulate AZ-14 (1⋅As4S4/4⋅ZnS), biparticulate AF-11 (1⋅As4S4/1⋅Fe3O4) and monoparticulate A-1 (As4S4)
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In the XRPD patterns of all As4S4-bearing nanocomposites, the nc-β-As4S4 phase was revealed due to broadened reflections from (\(\overline{1 }\)11), (\(\overline{2 }\)22) and (221) planes (Porter et al. 1972; Bonazzi and Bindi 2008). In nanocomposites prepared under current nanomilling conditions (see Shpotyuk et al. 2020c), the apparent crystallite size of coherently diffracting domain for this monoclinic phase calculated from broadening of the most pronounced d(\(\overline{1 }\)11) = 5.745 Å line was close to D ~ 20–23 nm, while maximum strain ε was estimated to be around ~ 0.010–0.005 (see Table 1).

The amorphous phase iso-compositional to nanocrystalline tetra-arsenic tetra-sulfide (a-AsS) was always detected in nanomilling-activated As4S4-bearing nanocomposites (Baláž et al. 2017; Shpotyuk et al. 2018a, 2020c). In the XRPD patterns of these arsenicals, this phase was revealed due to diffuse peak-halos at 13–19o 2θ, 26–34o 2θ and 52–60o 2θ, superimposed on the reflexes from nc-β-As4S4 phase (see Fig. 1). The first of these halos ascribed to so-called first sharp diffraction peak (FSDP) is accepted as an adequate manifestation of intermediate-range ordering in glass structure (Elliott 1995). In As4S4-based composites, the FSDP is always shifted to 2θ angles almost completely coincided with broadened Bragg-diffraction line from d(\(\overline{1 }\)11) plane in nc-β-As4S4 (see Shpotyuk et al. 2020c). The intermediate-range ordering in a-AsS phase derived by nanomilling in biparticulate and monoparticulate As4S4-bearing nanocomposites can be described through the FSDP position QFSDP1.14 Å−1 and width ΔQFSDP0.3 Å−1 (Table 1) as composed of inter-planar Bragg-diffraction correlations originated from crystalline remnants having characteristic distance R ~ 5.46–5.49 Å and correlation length L ~ 23–27 Å, complemented by prominent inter-atomic Ehrenfest-diffraction correlations approaching ~ 6.7–7.2 Å (Shpotyuk et al. 2019a). Specifically, in grinding media composed by hard nanoparticles biased by their sizes in respect to 20:1 rule (Zhao and Jimbo 1991) such as triparticulate AZF-141 nanocomposite, the FSDP parameters somewhat differ due to additional nc-ZnS-assisted milling-driven amorphization (Shpotyuk et al. 2020c).

In the XRPD patterns of nanomilling-driven Fe3O4-containing nanocomposites AF-11 (Fig. 1b) and AZF-141 (Fig. 1c), the nc-Fe3O4 phase was revealed due to broadened Bragg-diffraction reflexes ascribed to Fd \(\overline{3 }\) m structure of mineral magnetite (Fleet 1981). The average crystallite size D was determined from broadening of the most intensive d(311) = 2.531 Å line resulting in ~ 22.4 nm, this value being complemented with more than twice lower strain ε ~ 0.0057 as compared with corresponding values in nc-β-As4S4 (see Shpotyuk et al. 2017a, 2020c).

The both nanocrystalline nc-ZnS phases (sphalerite and wurtzite) were found in ZnS-containing AZ-14 and AZF-141 nanocomposites. Accepting overlapping between Bragg-diffraction lines of nc-β-As4S4 phase and diffuse peak-halo ascribed to a-AsS (Shpotyuk et al. 2018a, 2019a, 2020c), the D values reaching ~ 1.2–1.4 nm, which could be extracted in calculations for broadened reflections originated from (220) plane in sphalerite and (110) plane in wurtzite structure (Fang et al. 2011), seems most suitable for ZnS nanocrystallites. Respectively, the values of maximum strain were found to be substantially increased to ε ~ 0.077–0.092, as compared with other phases.

PAL spectra recording, treatment and parameterization

The PAL spectra of the studied nanocomposites were collected in triplicate employing fast–fast coincidence system ORTEC (having 230 ps in resolution) with 22Na source of ~ 50 kBq activity operational in normal statistics (~ 1 M coincidences), as described elsewhere (Shpotyuk O et al. 2015b, 2017a, b, 2018b, 2020b). The fitting of just-collected PAL spectra was achieved with LT computer program (Kansy 1996) using unconstrained decomposition into three negative exponentials obeying normalization by component intensities (I1 + I2 + I3 = 1) and stabilizing model-independent average positron lifetime τavΣ as mass center of the whole PAL spectrum. Under this fitting procedure, the reconstructed PAL spectra allow error-bar in positron lifetimes τi and component intensities Ii at the level of ± 0.005 ns and 0.5%, respectively.

In nanocomposites, this approach covers contributions originated from positrons annihilating in defect-free bulk states, trapped in intrinsic free-volume defects and decaying bound positron–electron (Ps, positronium) states. In such a case, one of the most simplified approaches is based on canonical two-state simple trapping model (STM) ignoring Ps-related contribution (see, e.g., West 1973; Krause-Rehberg and Leipner 1999; Tuomisto and Makkonen 2013; Shpotyuk et al. 2015b). Within this approach, positron-trapping modes (such as average lifetime for trapped positrons τavtr, defect-specific τ2 and defect-free bulk τb lifetimes, trapping rate in defects κd and fraction of trapped positrons ηd, and (τ2–τb) difference ascribed to size and (τ2/b) ratio ascribed to nature of positron traps) can be simply parameterized.

The highly heterogeneous multinanoparticulate substances obey selective localization of traps (Shantarovich and Goldanskii 1998), so that annihilation occurs through interconnected channels of positron trapping in vacancy-type volumetric defects (preferentially, negatively charged) and Ps-decaying in free-volume holes (preferentially, neutral). In case when Ps-decaying holes are the only sites which could be converted in positron traps (and vice versa), the volumetric effects in the substance under nanostructuralization obey generalized two-state simple trapping model (STM) modified for Ps-positron conversion known as x3-x2-CDA (coupling decomposition algorithm; see Shpotyuk et al. 2015b, 2022). Within this model, the differential two-component PAL spectrum with well defined (n⋅In) and (int⋅Iint) inputs derived from unconstrained three-component PAL spectra of nanostructuralized (final) and unstructuralized (initial) substance is ascribed to hypothetical medium where conversion between trapping channels (positron trapping in vacancy-type defects and Ps-decaying in free-volume holes) occurs in addition to annihilation from defect-free bulk states (see Shpotyuk et al. 2015b, 2017a, b, 2018b, 2019b, 2020b). In this case, the nanostructuralization-driven transformation between Ps-decay holes and positron-trapping sites can be parameterized employing conventional two-state STM, where derived trapping-conversion modes being as follows: defect-specific τint and defect-free bulk bNP lifetimes, trapping rate in defects κdNP, and some characteristics relevant to size of these traps in terms of equivalent number of vacancies defined by (τint – τbNP) difference and nature of these traps defined by (τint/τbNP) ratio.

Within this approach (the x3-x2-CDA), the directionality in the nanostructuralization-driven trapping-conversion process is defined by sign of both In and Iint components. However, this approach becomes meaningless in case of competitive inputs in the overall trapping-modification process from other alternative sources or unsaturated component contributions (n⋅In) and/or (int⋅Iint) due to uncorrelated positron-trapping and Ps-decaying channels.

Results and discussion

In multiparticulate nanostructured media composed of contacting crystalline grains, essential role belongs to interfacial free-volume elements stabilized at the intersections of three or more adjoining grain boundaries, known as inter-particle junctions between neighboring three (triple junctions, TJ), four (quadruple junctions) or more NP (Palumbo G et al. 1990, 2022; Chakraverty et al. 2005; Shpotyuk et al. 2018a, b, 2020b). In case of contacting nanosized grains (sub-nm-scaled grains), these defects act as preferential positron traps, while for greater grains preferentially in polymer environment (polymer-filler composites) they are functionalized rather as sites available for Ps-decay owing to pick-off interaction between positron and one of electrons from surrounding.

The raw PAL spectra collected from pelletized As4S4-bearing nanocomposites can be adequately reconstructed under unconstrained fitting into three negative exponentials (Shpotyuk et al. 2017a, b, 2018a, 2019b). As example, the raw PAL spectrum of triparticulate AZF-141 (1⋅As4S4/4⋅ZnS/1⋅Fe3O4) nanocomposite reconstructed from constraints-free three-component fitting is shown in Fig. 2 with bottom insert demonstrating statistical scatter of variance, i.e., mean square deviations between experimentally measured points and modeling curve grouped around horizontal axis (thus speaking in a favor of applied fitting procedure).

Fig. 2
figure 2

PAL spectrum of triparticulate AZF-141 (1⋅As4S4/4⋅ZnS/1⋅Fe3O4) nanocomposite reconstructed from unconstrained  × 3-term fitting at the general background of source contribution (the bottom inset shows tightly grouped statistical scatter of variance)

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Volumetric changes in monoparticulate (As4S4) nanocomposite

Continuous generation of amorphous arsenic monosulfide a-AsS in addition to monoclinic β-As4S4 was found to be most striking feature of monoparticulate As4S4 nanocomposite affected to nanomilling at 100–600 rpm (Baláž et al. 2017). In respect to this parameter, the batch of samples prepared at 500 rpm (marked as A-1) is suitable candidate for As4S4-bearing monoparticulate derivative from triparticulate AZF-141 nanocomposite (1⋅As4S4/4⋅ZnS/1⋅Fe3O4). In respect to its chemistry, this nanocrystalline-amorphous substance is to be classified rather as phase-biased nanocomposite. Milling-driven amorphization occurs as transition from molecular structure of tetra-arsenic tetra-sulfide proper for monoclinic β-As4S4 to structural arrangement of network-forming derivatives originated from realgar-type As4S4 cage-like molecules, which appear due to breaking of some intra-molecular bonds and forming of inter-molecular ones instead (Shpotyuk et al. 2020b). Our recent data (see Shpotyuk et al. 2019b) testify in favor of “shell” kinetic model describing this process as continuous generation of different structural defects in nc-β-As4S4, accompanied by appearance of iso-compositional amorphous phase (arsenic monosulfide a-AsS) nucleated heterogeneously from grain boundaries deeply into grain interior (thus stabilizing crystalline-amorphous core–shell structure of the NP).

The PAL spectrum of monoparticulate As4S4 nanocomposite (A-1) can be reconstructed under unconstrained fitting into three negative exponentials (see, e.g., Shpotyuk et al. 2018a, 2019b), fitting parameters and trapping modes for this reconstruction calculated within two-state STM ignoring Ps-decaying being presented in Tables 2 and 3. In view of this analysis, the PAL spectrum of this monoparticulate A-1 nanocomposite dominates by trapping modes originated from bi-/tri-atomic vacancies in As–S matrix covering spherical spaces (~ 70–80 Ǻ3) responsible for defect-related positron lifetime τ2 ~ 0.36 ns (see Jensen et al. 1994; Shpotyuk et al. 2014). The defect-free bulk positron lifetime τb tends towards ~ 0.27 ns (see Table 3), which is above the character level of ~ 0.24 ns reported for τb in crystalline arsenic sulfide (Jensen et al. 1994), but below character level of ~ 0.28–0.30 ns characteristic for glassy g-As–S (Ingram et al. 2012). In nanomilling-activated compounds, these positron-trapping sites are stabilized preferentially near boundaries of amorphized nc-β-As4S4 grains forming interfacial TJ (Shpotyuk et al. 2019b). Only small contribution in the PAL spectrum arises from Ps-related fractional free volume (fv =0.10%) estimated for spherical holes of ~ 0.295 ns in radius (Table 3).

Table 2 Fitting parameters describing unconstrained three-term decomposed PAL spectra of multiparticulate nanocomposites of quasi-ternary As4S4–ZnS–Fe3O4 system
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Table 3 Positron trapping and Ps-decaying modes derived from three-component PAL spectra of multiparticulate nanocomposites of quasi-ternary As4S4–ZnS–Fe3O4 system calculated within two-state STM ignoring Ps-decay contribution
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Volumetric changes in biparticulate (1⋅As4S4/1⋅Fe3O4) and (1⋅As4S4/4⋅ZnS) nanocomposites

Compositional variations in atomic-deficient structure of biparticulate nanocomposites within quasi-binary As4S4–Fe3O4 system (with inter-component ratio towards Fe3O4 tuned as 5:0, 4:1, 1:1; 1:4, 0:5) were identified employing the Positronics, the collected PAL spectra being reconstructed under unconstrained three-component fitting and analyzed in respect to central 1:1 composition corresponding to AF-11 nanocomposite 1⋅As4S4/1⋅Fe3O4 (Shpotyuk et al. 2017a). The fitting parameters of this reconstruction are reproduced in Table 2, and trapping modes calculated within conventional two-state STM ignoring Ps-related contribution are given in Table 3.

Under this simplified analysis, it can be concluded that annihilation occurs through defect-free bulk states and positron trapping in intrinsic volumetric defects of As4S4-bearing sub-system (composed of monoclinic nc-β-As4S4 and a-AsS) and TJ stabilized preferentially at the intersections of magnetite Fe3O4 crystallites. Thus, in AF-11 nanocomposite, the Ps-decaying sites have an obvious relation to Fe3O4 sub-system.

The crucial role of interfacial TJ in nanocomposites of other biparticulate cut-section (As4S4–ZnS) consisting of NP-biased constituents (~ 25–40 nm nc-β-As4S4 and ~ 2.4–3.4 nm ZnS crystallites, supplemented by amorphous a-AsS) was also proved by the Positronics. The fitting PAL spectrum parameters and calculated trapping modes for AZ-14 nanocomposite (1⋅As4S4/4⋅ZnS) are presented in Tables 2 and 3, respectively.

The void-evolution process governing mainly third component in the collected PAL spectrum of AZ-14 nanocomposite is connected with TJ dominated in the As4S4-bearing sub-system, due to occupancy of interparticulate spaces by the finest (~ 2.4–3.4 nm in sizes) ZnS nanocrystallites (see Shpotyuk et al. 2017b). Additional Ps-decay input is expected from multivacancy voids stabilized within agglomerates of ZnS grains. Thus, essential volumetric effects occur in 1⋅As4S4/4⋅ZnS nanocomposite caused by compacted ZnS nanocrystallites in looser environment of the amorphized nc-β-As4S4 phase (Shpotyuk et al. 2017b). The governing positron-trapping process in this nanocomposite is also shifted to ZnS-based sub-system, as it follows from calculated defect-free bulk lifetime τb ~ 0.226 ns (Table 3), which is very close to experimental and theoretical τb lifetimes in ZnS modifications (see Pareja et al. 1992; Adams et al. 1995; Krause-Rehberg et al. 1998; Plazaola et al. 1994).

Volumetric changes in triparticulate (1⋅As4S4/4⋅ZnS/1⋅Fe3O4) nanocomposite

The reconstructed PAL spectrum of pelletized triparticulate AZF-141 nanocomposite (1⋅As4S4/4⋅ZnS/1⋅Fe3O4) is reproduced in Fig. 2, and compared with respective PAL spectrum collected from biparticulate AF-11 nanocomposite (1⋅As4S4/1⋅Fe3O4) in Fig. 3. The narrow-grouped scatter of variance testifies this PAL spectrum can be adequately described by decomposition into three negative exponentials with best fitting parameters presented in Table 2, compared with those obtained for other As4S4-bearing nanocomposites (AF-11, AZ-14 and A-1). Preliminary analysis of this PAL spectrum is also performed within two-state STM ignoring Ps-decaying, the calculated positron-trapping and Ps-decaying modes being gathered in Table 3.

Fig. 3
figure 3

Comparison of the PAL spectra of triparticulate AZF-141 (1⋅As4S4/4⋅ZnS/1⋅Fe3O4) and biparticulate AF-11 (1⋅As4S4/1⋅Fe3O4) nanocomposites (the inset shows slightly depressed peak in AF-11 nanocomposite owing to nanomilling-derived generation of amorphous phase)

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In this triparticulate 1⋅As4S4/4⋅ZnS/1⋅Fe3O4 nanocomposite, the defect-specific lifetime τ2 approaching ~ 0.37 ns and bulk positron lifetime τb approaching ~ 0.26 ns testify that we deal with ~ 70–80 Ǻ3 imperfections, stabilized as TJ at the intersections of amorphized nc-β-As4S4 grains. Some of these TJ are more enriched in volume being suitable to allocate Ps atoms, albeit in preferential heterochemical environment. But the content of Ps-decaying holes in this triparticulate nanocomposite is rather low in view of I3 ~ 0.01 (nevertheless, the Ps-related component cannot be omitted in the collected PAL spectra without essential reduction in the fitting goodness).

To identify the governing annihilation channels in case of triparticulate 1⋅As4S4/4⋅ZnS/1⋅Fe3O4 nanocomposite, let us consider the trapping-conversion modes of hypothetical medium formed in transition from this parent AZF-141 nanocomposite (enriched in Ps-decay and positron-trapping sites) to its direct biparticulate and monoparticulate As4S4-bearing derivatives, employing formalism of the x3-x2-CDA (Shpotyuk et al. 2015b). The results of such parameterization related to the data taken from Table 1 are gathered in Table 4.

Table 4 Trapping-conversion modes in triparticulate parent AZF-141 (1⋅As4S4/4⋅ZnS/1⋅Fe3O4) nanocomposite calculated in respect to its biparticulate AF-11 (1⋅As4S4/1⋅Fe3O4) and AZ-14 (1⋅As4S4/4⋅ZnS) and monoparticulate A-1 (As4S4) derivatives employing the x3-x2-CDA
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Transition from biparticulate AF-11 to triparticulate AZF-141 nanocomposite is described by inverse (negative) positron-to-Ps trapping conversion, in view of both intensities In < 0 and Iint < 0 (see Table 4). The contributions from both trapping-conversion channels are slightly saturated, especially, the first one (n⋅In). Nevertheless, the governing trapping-conversion process in this transition can be recognized as disappearing of positron traps with defect-specific lifetime τint = 0.456 ns (Table 4) in AF-11 nanocomposite in environment having bNP approaching 0.266 ns (Table 2) at a cost of Ps-decaying holes with τ3 ~ 1.929 ns (see Table 1) in AZF-141 nanocomposite. In respect to these characteristics, the disappeared positron traps can be recognized as interfacial TJ in mixed arsenical-magnetite NP environment equivalent to multiatomic vacancies in a-As–S owing to τint–τbNP ~ 0.19 ns, and τint/τbNP ~ 1.7 (Jensen et al. 1994; Shpotyuk et al. 2014; Ingram et al. 2012). In contrast, the Ps-decaying holes newly formed instead of these positron traps are rather TJ stabilized in amorphized As4S4-bearing sub-system. The depressed peak of the collected PAL spectrum in this AF-11 nanocomposite (Fig. 3, inset) serves as confirmation on amorphous nature of the outer shell formed around nc-β-As4S4 grains (Shpotyuk et al. 2018b; 2019b).

Alternatively, we may consider the PAL spectra of both nanocomposites reproduced on Fig. 3 as completely uncorrelated. It means that there are no available trapping-conversion paths in transition from biparticulate AF-11 to triparticulate AZF-141 nanocomposite, so that trapping-conversion modes calculated in terms of  x3-x2-CDA have no physical meaning. Such obstacle can be caused by duplicate of reasons, these being (i) absence of any changes in annihilation channels speaking in a favor of simple inter-channel mixing or interplay, and/or (ii) principally different channels in the collected PAL spectra of nanostructured substance under compositional changes. Most plausibly, in the current case, we deal with the former condition (i), as it follows from nearly complete overlapping of the PAL spectra for these nanocomposites on Fig. 3, and very small (close to under-margin) values of both component inputs (n⋅In and int⋅Iint, Table 4). Therefore, the hypothetical medium obeying Ps-positron-trapping conversion cannot be reconstructed adequately from uncorrelated three-term decomposed PAL spectra of biparticulate (AF-11) and triparticulate (AZF-141) nanocomposites. However, such medium can be surely recognized in transition from other biparticulate nanocomposite AZ-14 (1⋅As4S4/4⋅ZnS) dominated by positron trapping in ZnS-based sub-system (see Shpotyuk et al. 2017b) to parent triparticulate AZF-141 nanocomposite.

Transition from biparticulate AZ-14 to triparticulate AZF-141 nanocomposite is governed by normal Ps-to-positron-trapping conversion, as it follows from positive intensities of components (In > 0 and Iint > 0) along with saturated component inputs n⋅In and int⋅Iint for these nanocomposites (see Table 4). Therefore, the resultant trapping-conversion process can be recognized as disappearing of Ps-related free-volume holes in AZ-14 nanocomposite (with τ3 ~ 1.804 ns, Table 2) at a cost of positron traps with defect-specific lifetime τint = 0.364 ns stabilized in an environment having bNP = 0.256 ns (see Table 4). In respect to calculated trapping-conversion modes, the disappeared Ps-related sites can be ascribed to interfacial TJ in the As4S4-bearing sub-system, which is to be recognized as interparticulate free-volume spaces between amorphized nc-β-As4S4 grains. The positron-trapping sites stabilized under this conversion have an obvious relation to free-volume spaces in ZnS-bearing sub-system, which can be identified as vacancy-type defects in packing of finest (~ 2–3 nm in sizes) ZnS nanocrystallites (Shpotyuk et al. 2017b).

Transition from monoparticulate A-1 to triparticulate AZF-141 nanocomposite is described by inverse positron-to-Ps trapping conversion. As known (see Shpotyuk et al. 2015b), despite both components in the differential PAL spectrum are negative (In < 0 and Iint < 0), the derived trapping-conversion modes could be completely meaningful. The Ps-decaying sites with long-lived lifetime τ3 ~ 1.929 ns (Table 2) appear in triparticulate 1⋅As4S4/4⋅ZnS/1⋅Fe3O4 nanocomposite instead of positron traps with defect-specific lifetime τint = 0.355 ns stabilized in monoparticulate As4S4 nanocomposite having defect-free bulk positron lifetime bNP = 0.278 ns (Table 4). Therefore, in this case, the trapping-conversion components related to Ps-decaying and positron trapping are allocated in the As4S4-bearing sub-system. The disappeared positron-trapping sites are vacancy-type defects in a-As–S matrix, equivalent (in their sizes) to bi-/tri-atomic vacancies, as it follows from respective defect-specific lifetimes approaching the known values for a-AsS (see, e.g., Jensen et al. 1994; Shpotyuk et al. 2014, 2015a; Ingram et al. 2012), while the Ps-decaying sites formed instead are interparticulate free-volume holes like interfacial TJ between amorphized nc-β-As4S4 grains.

Thus, the hypothetical medium reconstructed (in terms of the x3-x2-CDA transition) to parent triparticulate AZF-141 nanocomposite (1⋅As4S4/4⋅ZnS/1⋅Fe3O4) from its derivatives dominated by positron-trapping in As4S4-bearing sub-system, such as biparticulate AF-11 (1⋅As4S4/1⋅Fe3O4) and monoparticulate A-1 (As4S4) ones, is governed by inverse positron-to-Ps trapping conversion. This effect originates from reduced fraction of As4S4 component in the parent AZF-141 nanocomposite. In contrast, the normal Ps-to-positron-trapping conversion prevails in the x3-x2-CDA transition to triparticulate (1⋅As4S4/4⋅ZnS/1⋅Fe3O4) nanocomposite from its derivative dominated by competitive Ps-decay channel in ZnS-based sub-system like biparticulate AZ-14 composite (1⋅As4S4/4⋅ZnS). Under current case, the changed directionality of conversion is explained by reduced content of this modificator in the parent triparticulate nanocomposite as compared with biparticulate derivative.

Conclusions

Employing the PAL spectroscopy in mixed positron-Ps trapping conversion mode obeying the x3-x2-CDA (the coupling decomposition algorithm), sub-nm-scaled volumetric changes are recognized in multiparticulate nanocomposites of quasi-ternary As4S4–ZnS–Fe3O4 system in transitions between their hierarchical As4S4-bearing derivatives prepared by nanomilling, such as parent triparticulate (1⋅As4S4/4⋅ZnS/1⋅Fe3O4), biparticulate (1⋅As4S4/1⋅Fe3O4), biparticulate (1⋅As4S4/4⋅ZnS) and monoparticulate (As4S4) ones. Coexistence of nanocrystalline nc-β-As4S4 supplemented by iso-compositional amorphous a-AsS phase is crucial feature of the studied nanocomposites, the a-AsS phase being generated continuously under nanomilling due to reamorphization of initial amorphous phase in arsenic monosulfide synthesized from elements or direct vitrification of nc-β-As4S4.

The inverse positron-to-Ps trapping conversion prevails in transition from biparticulate (1⋅As4S4/1⋅Fe3O4) and monoparticulate (As4S4) nanocomposites (both dominated by positron trapping in As4S4-bearing sub-system) to triparticulate (1⋅As4S4/4⋅ZnS/1⋅Fe3O4) one. In this case, the disappeared positron traps represent themselves as specific vacancy-type defects in a-As–S matrix equivalent in sizes to bi-/tri-atomic vacancies, while the Ps-decaying sites formed instead are interfacial triple junctions between amorphized nc-β-As4S4 grains. In contrast, the normal Ps-to-positron-trapping conversion takes place in transition from biparticulate (1⋅As4S4/4⋅ZnS) nanocomposite dominated by positron trapping in ZnS-based sub-system to parent triparticulate (1⋅As4S4/4⋅ZnS/1⋅Fe3O4) one. The disappeared Ps-decaying sites are identified as triple junctions between amorphized nc-β-As4S4 grains, while positron traps formed instead of these holes are vacancy-type defects in packing of the finest (~ 2–3 nm in sizes) ZnS crystallites.