Introduction

Generation a large variety of structural defects under high-energy ball mechanical milling (MM) [1,2,3,4,5] is known as an alternative technological resolution allowing approaching high-entropy amorphous state of parent crystalline substances, even those possessing extremely low glass-forming ability [6]. To a great extent, this unique phenomenon concerns a large group of overstoichiometric arsenic sulfides As-S with promising anticancer functionality guided due to MM-induced nanostructurization, also termed in biomedicine as arsenicals (nanoarsenicals) [7,8,9,10,11]. Different types of crystallization–vitrification processes in arsenical-based crystalline–amorphous systems were successfully studied employing the DSC method [12,13,14,15]. Recently [16], some of current authors reported first results on complete amorphization in partially crystalline As45S55 alloy prepared by direct synthesis from pure elements, this research being performed employing multifrequency DSC TOPEM® method. Amorphous substance appeared due to high-energy MM was shown to possess double-Tg relaxation originated from intrinsic separation on distinct high-temperature (Tg1 ≅ 200 °C) and low-temperature (Tg2 ≅ 155.5 °C) glassy-like components. This amorphous phase was identified with DSC TOPEM® as close to nominal alloy composition As45S55. Structural inspection with X-ray powder diffraction (XRPD) related to the first sharp diffraction peak (FSDP) revealed this phase as extension of melt-quenched As-rich glassy states stretching far beyond As2S3 stoichiometry.

Amorphous phase appeared in addition to crystalline counterpart has been detected when dealing with high-temperature polymorph of tetra-arsenic tetra-sulfide β-As4S4 prepared by direct synthesis from elemental constituents under high-energy wet or dry MM [17,18,19]. But chemical and thermodynamic authenticity of this phase has not been clarified up to now, and many controversies left in respect of its microstructure origin. In this work, we shall parameterize the amorphization effect in β-As4S4 arsenical, driven by high-energy MM under different rotational speeds, exploring heat capacity measurements with temperature-modulated DSC TOPEM®.

Experimental

Commercial arsenic sulfide β-As4S4 prepared by direct synthesis from elemental constituents (98% in purity, purchased in Sigma-Aldrich, USA) was used as a precursor for high-energy MM. Small pieces of this arsenical were coarse-grained powdered and sieved under 200 μm. Then, this powder (3 g) was subjected to MM in a dry mode under a protective Ar atmosphere, using planetary rotational ball mill Pulverisette 6 (Fritsch, Germany) loaded with 50 tungsten carbide balls of 10 mm in diameter. (The milling conditions were described elsewhere [18].) The overall MM duration was 60 min for each sample at different rotational speed n of the planet carrier, e.g., REHE-0 (non-milled or coarse-grained powdered sample sieved through 200 μm taken as a reference), REHE-100 (n = 100 min−1), REHE-200 (n = 200 min−1), REHE-500 (n = 500 min−1) and REHE-600 (n = 600 min−1). There was no possibility to measure directly the averaged temperature inside milling vial. Nevertheless, in respect of our estimates for other similar compounds, the highest temperature at n = 600 min−1 did not exceed 50 °C. In final, all samples were compressed by compacting inside a stainless steel die under the same pressure of ~ 0.7 GPa to prepare disk pellets (having 6 mm in a diameter and 1 mm in a thickness).

The calorimetric heat capacity measurements were taken with multifrequency DSC TOPEM® using DSC-1 calorimeter (Mettler-Toledo, Switzerland). In this method, the stochastic temperature modulations are superimposed on underlying rate of conventional DSC scans, resulting in distinguished frequency-dependent and frequency-independent phenomena [20, 21]. This provides more information concerning thermodynamic stability of the revealed phases, which is expected to be important in the case of phase-changed nanoarsenicals affected by high-energy MM. The DSC TOPEM® instrument was equipped with FRS5 + sensor and HT100 (Huber, Germany) intracooler, the STARe ver. 13a software being used to control experimental conditions and process the data. The calorimeter was multi-point calibrated using n-octane, Hg, In and Zn standard samples. The tested samples (ca. 9.5–12.0) were encapsulated in sealed 40-μL aluminum pans kept in protective N2 atmosphere and scanned at the rate of 1.0 K min−1 stochastically modulated in pulses between 20 s and 60 s, the pulse height being 0.75 K. All TOPEM evaluations were adjusted using sapphire reference curve, the width and shift of calculation window being 60 s and 1 s, respectively. The heat capacity Cp measurements were taken in the range of 70–360 °C, each experiment protocol being averaged in triplicate.

Preliminary XRPD results [18] testified that MM-driven nanostructurization in β-As4S4 arsenical was revealed through extensive generation and interaction of nanoparticles (NPs) with character crystallite sizes of d ~ 30 nm for non-milled REHE-0 and REHE-100 samples, d ~ 19–21 nm for REHE-200–500 samples, and increased to d ~ 25–26 nm for REHE-600 sample. At the same time, within this sequence of samples, the average maximum strain demonstrated only growing tendency from 0.0043–0.0044‰ (REHE-0 and REHE-100) to 0.0082‰ (REHE-600) [18]. Thus, the arsenicals were not affected by MM under low rotational speed (n = 100 min−1), while fragmentation of β-As4S4 crystallites (due to NPs aggregation) was prevailed under n = 200–500 min−1 speed. Finally, at n = 600 min−1, the most energetically treated β-As4S4 crystallites agglomerated together, resulting in partially decreased (but not completely restored) specific surface area. It worth mentioning that evident growing tendency was observed with rotational speed n in amorphous halos in the experimental XRPD profiles of milled arsenicals starting from REHE-200 sample.

Results and discussion

Interphase transformations in binary As-S system have been in sphere of hot disputes for a long time, starting from first experimental observation addressed to Jonker more than a century ago [22]. In the earliest 1970s, the comprehensive calorimetric studies on overstoichiometric As-S alloys were performed by Hruby [23], who discovered the second glass-forming region in this system ranging from 51 to 66 at.% of As. These experiments testified that crystalline As4S4 alloy as prepared by direct synthesis from elements is not chemically well-defined compound, but rather mixture of some phases. The melting process was shown to be incongruent [23], but it became congruent after annealing at 250 °C for 48 h, when this alloy was transformed in stable red-colored As4S4 crystalline modification with considerable amount of additional amorphous phase. This phase was ascribed to melt-quenched (MQ) glassy As2S3, as was suggested by Hruby [23], but without strict evidences (noteworthy, appearance of stoichiometric As2S3 is not allowed by simple chemical transformations in this alloy occurring only between overstoichiometric As4S4 compounds).

The variation of specific heat capacity Cp0 in the reference (non-milled) coarse-grained powdered REHE-0 and MM REHE-500 pellets in high-temperature 295–320 °C and low-temperature 100–240 °C regions is depicted in Figs. 1 and 2, respectively. In the first heating run, two endothermic thermally induced melting effects are revealed in both samples, near ~ 305 °C and ~ 315 °C, testifying in a favor of incongruent melting (like it was suggested by Hruby [23]). The first of these effects is well detectable in Cp0 due to strong peak Tm1 at 304.1 °C observed in reference REHE-0 (black-solid curve, Fig. 1a), and more reduced peak at 303.2 °C detected in MM REHE-500 sample (red-dashed curve, Fig. 1a), i.e., at the liquidus of this alloy near arsenic monosulfide line [23]. The shape analysis testifies this peak is rather asymmetric in the reference sample, being completed from low-temperature side by evident shoulder near ~ 303.1–303.3 °C. Whichever the case, this endothermic effect occurs at peak temperature Tm1, which is less than Tm = 318 °C defined as melting point for As4S4 by Blachnik [24], but very close to Tm = 307 °C defined by Street et al. [25] and Tm = 309 °C defined by Chattopadhya et al. [26] for this compound.

Fig. 1
figure 1

Modulated DSC profile (TOPEM®) showing high-temperature variation of specific heat Cp0 for coarse-grained powdered REHE-0 (black-solid curve) and MM REHE-500 (red-dashed curve) samples in the first (a) and second (b) heating runs

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Fig. 2
figure 2

Modulated DSC profile (TOPEM®) showing low-temperature variation of specific heat Cp0 for coarse-grained powdered REHE-0 (black-solid curve) and MM REHE-500 (red-dashed curve) samples in the first (a) and second (b) heating runs

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The second endothermic effect is less pronounced, but still quite detectable due to Cp0 peak at Tm2 in the same reference and MM β-As4S4 samples revealed themselves, respectively, at 314.0–315.0 °C. Noteworthy, the MM REHE-500 pellet possesses an obviously decreased first melting peak at Tm1, but increased second melting peak at Tm2 as compared with the same in the reference sample (Fig. 1a). Hence, considerable redistribution in the intensities of these peaks accompanied by smaller changes in peaks positions (~ 1 °C decrease in Tm1 and increase in Tm2) is the main result of high-energy MM effect on β-As4S4 arsenical.

The similar double-peak behavior was recently observed in melting of other overstoichiometric alloy in this As-S system, As45S55 composed of crystalline β-As4S4 and some amount of compositionally unknown amorphous phase with glass transition temperature Tg close to 165 °C [16]. The corresponding melting peak temperatures in this alloy were measured to be Tm1 = 303.8 °C and Tm2 = 317.4 °C, these effects being essentially non-elemental showing additional features from low-temperature side. Thus, the first Cp0 peak (at Tm1) was completed with slight shoulder near 303.9 °C overlapped with broader hump in 302.7–305.5 °C domain, while second peak (at Tm2) revealed additional slight satellite pre-peak at 316.2 °C. The heating–cooling run allowed elimination second melting event (which therefore could be classified as irreversible), and all additional attributes from first one remaining only sharp single endothermic peak shifted to Tm1 = 303.5 °C. (Similar changes were produced by MM resulting in complete amorphization of As45S55 alloy [16].) The double-peak Cp0 effects were assumed to originate from non-equilibrium melting of some crystalline compounds in principally different environments like crystalline and amorphous [27, 28]. Respectively, the melting of β-As4S4 in amorphous environment was accepted as responsible for endothermic peak at Tm2 in As45S55 alloy [16]. This process was supplemented by strong effect at Tm1 owing to melting of this well-separated phase near liquidus (mainly in its own environment). These interphase equilibria were essentially disturbed under high-energy MM, when β-As4S4 phase disappeared at a cost of amorphous substance, representing a mixture of two glassy phases possessing double-Tg relaxation at low- (Tg1 = 155.5 °C) and high-temperature (Tg2 = 197.9 °C) glass transition midpoints [16].

The modulated DSC profiles (TOPEM®) in Figs. 3 and 4 demonstrate respective first-run high-temperature variation of specific heat Cp0 and non-reversing heat flow HFnrev for MM REHE-200 (with fine aggregated crystalline NPs, d = ~19–21 nm [18]) and REHE-600 samples (with more agglomerated NPs, d = ~26 nm [18]) as compared with non-milled coarse-grained powdered REHE–0 probe (d ~ 30 nm [18]). The high-energy MM is always revealed in the melting temperature Tm1 decrease, the effect, which is in strong dependence on average crystallite sizes d. Such melting-point depression is known to be most evident for nanostructurized substances with increased surface-to-volume ratio occurring under critical NPs sizes d (usually d < 50 nm) [29,30,31]. Assuming inverse quadratic nature of NPs size dependence in the melting equation, as it was accepted for covalently bonded semiconductor NPs by Farrell and Van Siclen [30]:

$$T_{{\text{m}}} = T_{{\text{m}}}^{\infty } \times \left( {1 - \left( {d_{o} /d} \right)^{2} } \right),$$
(1)

it can be calculated, accepting the data (Fig. 1) for REHE-0 (Tm1 = 304.1 °C, d ~ 30 nm) and REHE-500 samples (Tm1 = 303.2 °C, d ~ 20 nm), the melting temperature is close to 303.8 °C for MM sample with d ~ 25 nm crystallites, which is in excellent agreement with experimental melting peak position Tm1 = 303.7 °C for REHE-600 sample (Figs. 3 and 4). With these data, the parameter T ∞m in Eq. (1) which can be accepted as melting peak point for the bulk arsenical is estimated to be 304.8 °C, that is in very close proximity to Tm1 = 304.5 °C, experimentally detected in the second heating run (i.e., after first melting) for REHE-500 pellet (Fig. 1b), when MM-driven nanostructurization is fully destroyed (due to re-melting). This melting-point depression effect in MM arsenicals parameterized in the extrapolated position Tm1 and specific heat capacity ΔCp0 of the first melting peak in dependence on crystallite sizes d is illustrated by diagram in Fig. 5.

Fig. 3
figure 3

Modulated DSC profile (TOPEM®) showing first-run high-temperature variation of specific heat Cp0 for coarse-grained powdered REHE-0 (black curve), MM REHE-200 (red curve) and REHE-600 (blue curve) samples

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Fig. 4
figure 4

Modulated DSC profile (TOPEM®) showing first-run high-temperature variation of non-reversing heat flow HFnrev for coarse-grained powdered REHE-0 (black curve), MM REHE-200 (red curve) and REHE-600 (blue curve) samples

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Fig. 5
figure 5

Melting-point depression effect in directly synthesized β-As4S4 affected high-energy MM determined in the extrapolated position Tm1 and specific heat capacity ΔCp0 of the first melting peak in dependence on crystallite sizes d

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The appearance of additional amorphous phase was always detected in β-As4S4 prepared by direct synthesis from elements [25], as well as in many other MQ and MM composites based on this arsenical [16,17,18,19, 32, 33]. This amorphization trend is clearly revealed in REHE-0 and MM REHE-500 pellets due to heat capacity Cp0 variation in low-temperature 100–240 °C region (see Fig. 2). The first of these samples (coarse-grained powdered β-As4S4 arsenical) demonstrates strong relaxation effect with ΔCp0 = ~0.160 J·g−1·K−1 amplitude at glass transition midpoint Tg = ~190.0 °C. The second sample affected to high-energy MM shows double-Tg relaxation effect, the corresponding glass transitions obeying more fragile behavior at Tg1 = ~208.3 °C (ΔCp0 = ~0.072 J g−1 K−1) and only slight specific heat Cp variation at Tg2 = ~130–140 °C (ΔCp0 = ~0.020 J g−1 K−1).

Such double-Tg relaxation is known to be indicative of incomplete mixing or intrinsic phase separation in glassy systems [34, 35]. So it quite reasonable to assume appearance of two amorphous phases in MM β-As4S4 with high-temperature midpoint Tg1 very close to that proper to MQ As2S3 [36, 37] and low-temperature midpoint Tg2 near solidus of metastable melting in overstoichiometric As-S alloys determined by Hruby [23]. In general, an actual ratio between these amorphous phases reflects disturbance in a system due to created structural defects, so that different nature of the amorphized products follows from thermodynamic driven forces emerged under MM. That is why it seems only high-temperature amorphous phase with Tg1 is reliably detectable in many experiments (as it occurred, e.g., in thermally annealed As4S4 alloy [23]), while full balance in the amorphized system is maintained by glassy phase with lower glass transition midpoint Tg2. Since the maximum Tg in binary As-S glassy system is achieved for stoichiometric As2S3 glass [36, 37], this additional amorphous phase is evidently also As-rich one (like it was in case of completely amorphized MM As45S55 alloy [16]).

With increased agglomeration of β-As4S4 crystallites, as it occurs at higher rotational speed n in REHE-600 sample (Fig. 6), the low-temperature relaxing glassy phase cannot be further simply determined, being masked by substantial growing trend in the low-temperature variation of specific heat Cp0 just before glass transition (Tg1 = ~200.7 °C, ΔCp0 = ~0.144 J g−1 K−1). This growing trend in the slope of specific heat Cp0 curve is well observed as compared with DSC profiles for other samples shown in Fig. 5, such as REHE-0 (Tg1 = ~189.2 °C, ΔCp0 = ~0.144 J g−1 K−1) and REHE-200 (Tg1 = ~189.8 °C, ΔCp0 = ~0.113 J g−1 K−1). Correspondingly, the inner stress accumulated under high-energy MM relaxes more efficiently at higher rotational speeds n due to agglomeration of crystallites, as it can be well revealed from obviously decreasing low-temperature pre-Tg exotherm in non-reversing heat flow HFnrev in Fig. 7 detected for REHE-600 pellet having larger β-As4S4 crystallites (d values approaching ~ 25 nm [18]).

Fig. 6
figure 6

Modulated DSC profile (TOPEM®) showing first-run low-temperature variation of specific heat Cp0 for coarse-grained powdered REHE-0 (black curve), MM REHE-200 (red curve) and REHE-600 (blue curve) samples

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Fig. 7
figure 7

Modulated DSC profile (TOPEM®) showing low-temperature pre-Tg exotherms in non-reversing heat flow HFnrev for coarse-grained powdered REHE-0 (black curve), MM REHE-200 (red curve) and REHE-600 (blue curve) samples

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The observed decaying trend in ΔCp0 for amorphous phase with high-Tg1 glass transition midpoint (with growing rotational speed n) testifies that low-Tg2 amorphous phase is formed under MM from this high-Tg1 phase (which exist just before MM in REHE-0 sample) in addition to amorphous phase vitrified from β-As4S4 crystallites. Thus, the overall solid-state amorphization in commercial arsenic sulfide subjected to high-energy MM occurs from two sources, these being high-to-low-Tg amorphous phase transformation and direct vitrification of β-As4S4 crystallites.

The heterogeneity of chemical environment over inner crystalline phase (β-As4S4) results in incongruent double-peak melting distinctly observed near ~ 305 °C and ~ 315 °C (see Fig. 1a). Because of shielding by amorphized surface, the melting of such crystallites proceeds at higher Tm2, as it can be expected from simple thermodynamic consideration. (The amorphous phase is firstly extracted at the grain surface and intergranular regions.) At the same time, the melting of β-As4S4 crystallites separated from amorphous phase occurs at lower Tm1 (near the liquidus in As-S system [23, 24]), strict position of this effect being defined by thermodynamics of a melting system (the effect of melting-point Tm1 depression in MM arsenicals as compared with non-milled coarse-grained one, see Fig. 5).

This crystal-glass equilibrium can be substantially disturbed due to initial melting (in the first heating–cooling run), when both parent crystalline and amorphous phases become well separated within alloy. Respectively, the specific heat capacity Cp0 in the second heating run attains character attribute of congruent melting with single-peak Tm1 approaching 303.4 °C for non-milled REHE-0 and 304.7 °C for MM REHE-500 samples (Fig. 1b). Amorphous phase in these samples becomes compositionally close to arsenic monosulfide (As4S4), being presented in the modulated DSC profiles (TOPEM®) in Fig. 2b by single-Tg relaxation event near ~ 190.3 °C (ΔCp0 = ~0.190 J g−1 K−1) and ~ 191.3 °C (ΔCp0 = ~0.100 J g−1 K−1) for REHE-0 and MM REHE-500 pellets, respectively. In other words, the effect of high-energy MM-driven depression in the melting temperature Tm1 is indeed gradually destroyed after samples re-melting.

Continuous generation of amorphous phase under speed-increased high-energy MM in directly synthesized β-As4S4 arsenicals testified rather in favor of “shell” kinetic model [4, 5] treated this phenomenon in terms of intensive generation and accumulation of different structural defects in parent crystalline phase. Under these high-energy MM (with speed n not exceeding 600 min−1), the appeared amorphous phase nucleates heterogeneously starting from crystallite grain boundaries, followed by stretching into crystallite grain interior. There were no any abrupt critical size effects in crystallite grains of MM β-As4S4 arsenicals allowing collapse of crystalline structure in respect of “the crystallite destabilization model” like in elemental Se [2, 3]. (Crystallites smaller than the critical grain size are transformed completely into amorphous phase, while those larger than the critical size remain crystalline.)

Conclusions

Continuous generation of amorphous phase in addition to parent crystalline β-As4S4 one was probed in directly synthesized high-temperature polymorph of tetra-arsenic tetra-sulfide under high-energy mechanical milling with 100–600 min−1 rotational speeds. The thermodynamic authenticity of generated amorphous phase was clarified exploring the temperature-modulated DSC TOPEM® method. The crystalline–amorphous heterogeneity of chemical environment proper to β-As4S4 results in incongruent double-peak melting revealed in the modulated DSC profiles (TOPEM®) through two endothermic effects at~ 305 °C and ~ 315 °C. The amorphized substance appeared under MM is of dual nature, being represented by As-rich glassy phases possessing high-temperature (~ 208.3 °C) and low-temperature (~ 130-140 °C) glass transition midpoints. Such double-Tg relaxation is accepted as indicative of intrinsic separation in the generated amorphized phase. The crystal-glass equilibrium in the milled arsenicals can be substantially modified with repeated melting, when crystalline and glassy phases become well separated, resulting in congruent melting near ~ 305 °C and single glass relaxation event near ~ 191 °C. The overall solid-state amorphization in commercial arsenic sulfide subjected to high-energy ball mechanical milling occurs from two sources, these being high-to-low-Tg transformation of existing amorphous phase and direct vitrification of parent β-As4S4 phase. These data testifies in favor of “shell” kinetic model treated solid-state amorphization in terms of intensive defect accumulation in β-As4S4 phase, the appeared amorphous phase being nucleated heterogeneously from grain boundaries followed by stretching into grain interior.