Molecular-Network Transformations in Tetra-Arsenic Triselenide Glassy Alloys Tuned within Nanomilling Platform

Abstract

Polyamorphic transformations driven by high-energy mechanical ball milling (nanomilling) are recognized in a melt-quenched glassy alloy of tetra-arsenic triselenide (As₄Se₃). We employed XRPD analysis complemented by thermophysical heat-transfer and micro-Raman spectroscopy studies. A straightforward interpretation of the medium-range structural response to milling-driven reamorphization is developed within a modified microcrystalline model by treating diffuse peak-halos in the XRPD patterns of this alloy as a superposition of the Bragg-diffraction contribution from inter-planar correlations, which are supplemented by the Ehrenfest-diffraction contribution from inter-atomic and/or inter-molecular correlations related to derivatives of thioarsenide As₄Se_n molecules, mainly dimorphite-type As₄Se₃ ones. These cage molecules are merely destroyed under milling, facilitating the formation of a polymerized network with enhanced calorimetric heat-transfer responses. Disruption of intermediate-range ordering, due to weakening of the FSDP (the first sharp diffraction peak), accompanied by an enhancement of extended-range ordering, due to fragmentation of structural entities responsible for the SSDP (the second sharp diffraction peak), occurs as an interplay between medium-range structural levels in the reamorphized As₄Se₃ glass alloy. Nanomilling-driven destruction of thioarsenide As₄Se_n molecules followed by incorporation of their remnants into a glassy network is proved by micro-Raman spectroscopy. Microstructure scenarios of the molecular-to-network polyamorphic transformations caused by the decomposition of the As₄Se₃ molecules and their direct destruction under grinding are recognized by an ab initio quantum-chemical cluster-modeling algorithm.

1. Introduction

Nowadays, the nm-scaled substances functionalized through a plethora of nanostructurization technologies, such as high-energy mechanical milling (MM, also referred to as nanomilling), compose one of the most promising challenges in contemporary nanomaterials science and engineering [1]. Employing mechanochemistry [2,3], the thermodynamically stable materials can be transformed into out-of-equilibrium high-entropy prototypes, with this transition being simply observable in crystals possessing regular interatomic ordering, while merely hidden in amorphous substances, such as glasses derived by conventional melt-quenching (MQ). Nevertheless, even in the latter case, many glassy materials are modified irreversibly because of the MM-driven nanostructurization metastability [4].

In past decades, this conceptual approach has been convincingly proved for MQ-derived substances, like chalcogenide glasses (ChG) [5,6], with their archetypal representatives from a binary As-Se system (hereafter referred to as glassy arsenoselenides g-As_xSe_100−x) possessing a great variety of molecular-network conformations in a whole glass-forming region from ‘pure’ Se (x = 0) to As-rich alloys with x~65–75 [5,6,7]. The stoichiometric arsenic triselenide As₂Se₃ has a characteristically layered network composed of corner-sharing trigonal AsSe_3/2 pyramids interlinked by -Se- bridges, which can be classified as optimal in view of the average number of mechanical constraints per atom n_c exactly approaching space dimensionality (3D), representing the principal glass-former in As-Se systems. In this stoichiometric glass-former and under-stoichiometric Se-bearing g-As_xSe_100−x alloys from moderated compositional domains (20 < x < 40) dominated by the transition from layer-type structures characteristic of As₂Se₃ to a 2D-network of Se-chains bridging AsSe_3/2 pyramids [3], the effects of nanomilling-driven nanostructurization are merely hidden [8,9]. With a trend further towards ‘pure’ Se, that is, under-stoichiometric g-As_xSe_100−x enriched in Se content (x < ~10–15), where the molecular Se₈ ring-like species consist of cis-configurated Se linkages typical for α- and β-monoclinic Se are stabilized, in addition to spiral trans-configurated Se_n chains typical for trigonal t-Se [10], nanomilling induces molecular-to-network reamorphization transformations of Se chains bridging AsSe_3/2 pyramids from preferential cis- to trans-configurated arrangements [11]. Especially attractive for the glass manufacturing community is the recently justified possibility to modify g-As_xSe_100−x in over-stoichiometric compositional domain (x > 40), tuning them by cage-like molecules such as As₄Se₄, As₄Se₃ or As₄ incorporated in covalent-bonded As-Se networks [3]. In these over-stoichiometric As-bearing arsenoselenides, nanomilling-driven escape from the macro- to the nanoscopic state is expected for tetra-arsenic selenide compounds having stable crystalline counterparts (alternatively, thioarsenides As₄Se_n where n = 4, 3) [1,3,9]. Recently, the transition from the initial to final amorphous states (that can be considered as a manifestation of amorphous-I-to-amorphous-II or reamorphization transition) has been realized under nanomilling in MQ-derived arsenic monoselenide, g-AsSe (viz. tetra-arsenic tetraselenide, g-As₄Se₄), contributing to considerable progress in the engineering of special glass media with guided functionality [12].

The objective of this research is to justify the molecular-to-network nature of the nanomilling-driven polyamorphic transition in glassy arsenoselenides g-As_xSe_100−x of other remarkable compositions equivalent to tetra-arsenic triselenide, such as g-As₄Se₃ (corresponding to x = 57, g-As₅₇Se₄₃), having the orthorhombic As₄Se₃ as the high-temperature crystalline counterpart [13,14,15]. The microstructure of the MQ-derived and nanomilled specimens will be recognized by employing X-ray powder diffraction (XRPD) analysis in application to diffuse peak-halos responsible for medium-range ordering in ChG. This study on molecular-network disproportionality in arsenoselenide alloys compositionally approaching As₄Se₃ will be complemented with calorimetric heat-transfer measurements and micro-Raman scattering (micro-RS) spectroscopy studies, and ab initio quantum-chemical modeling of thioarsenide As₄Se_n molecules and their network-forming derivatives using the cluster-simulation code CINCA (the cation-interlinked network cluster approach [16,17]).

2. Results and Discussion

2.1. Medium-Range Structural Correlations in MQ-Derived g-As₄Se₃

The XRPD patterns collected for MQ-derived g-As₅₇Se₄₃ before and after high-energy MM in a dry mode are depicted in Figure 1.

These patterns clearly demonstrate a so-called three-peak structure [18] composed of separated peak-halos responsible for the first sharp diffraction peak (FSDP), second sharp diffraction peak (SSDP) and third diffraction peak (TDP), supplemented by some features related to pre-FSDP, post-FSDP and post-SSDP (unreproducible in the reduced structure factor determination) positioned near diffraction angles 2θ and scattering vectors Q character for g-As₆₀Se₄₀ [9]. Thus, the FSDP position in the MQ-derived g-As₄Se₃ (viz. characteristic distance R~5.7 Å) is found to be in excellent agreement with the most pronounced Bragg-diffraction line (I = 100%) arising from (111) plane in the orthorhombic As₄Se₃ (equiv. to inter-planar distance d = 5.243 Å) [13]. As it follows from Figure 1, one of the strongest (I = 91.3%) lines arising from the (120) plane at ~16.07°2θ (d = 5.512 Å) in other molecular thioarsenide (monoclinic As₄Se₄ [19,20,21]) occurs to be very close to the FSDP, although the other line (I = 91.2%) ascribed to (020) plane in layer-type monoclinic As₂Se₃ [19,22] is positioned at higher angle (~17.9°2θ) corresponding to d = 4.950 Å. Assuming equal contributions to the FSDP from these lines (ascribed to As₄Se₃-, As₄Se₄- and As₂Se₃-structures), the FSDP-related characteristic distance R was expected near ~5.64 Å, which is slightly below the characteristic value derived from the Bragg-diffraction positioning of the FSDP. This testifies in favor of the essential contribution to the FSDP from inter-planar correlations belonging to some remnants of crystalline arsenoselenide structures.

Other input to the FSDP is expected from inter-atomic and/or inter-molecular correlations, which belong to these remnants. Indeed, as was pointed out in [5,6,7], the structure of over-stoichiometric As-rich g-As_xSe_100−x (x > 40) could be imagined as a stacking of network-type entities based on Se-linked AsSe_3/2 pyramids and molecular-type entities based on thioarsenide cages (such as As₄Se₄, As₄Se₃, and even As₄). The spatial arrangement of such cages could be parameterized by introducing a ‘dummy atom’ B serving as a geometrical barycentre for each molecule [23]. The dense random packing of such thioarsenide molecules (viz. inter-molecular correlations) contributes to diffuse peak-halos in the XRPD patterning of arsenoselenides through the Ehrenfest diffraction [24,25,26,27].

Figure 1. The XRPD patterns of unmilled MQ-derived and dry-milled g-As₅₇Se₄₃ alloys showing regions of the three most prominent diffuse peak-halos corresponding to the FSDP (~15–25°2θ), SSDP (~28–33°2θ) and TDP (~50–60°2θ). Theoretical Bragg-diffraction reflexes of monoclinic As₂Se₃ (JCPDS No. 65-2365) [27,28], monoclinic As₄Se₄ (JCPDS No. 71-0388), orthorhombic As₄Se₃ (JCPDS No. 04-4979), trigonal Se (JCPDS No. 73-0465) and rhombohedral As (JCPDS No. 72-1048) are reproduced below for comparison (see text for more details).

Figure 1. The XRPD patterns of unmilled MQ-derived and dry-milled g-As₅₇Se₄₃ alloys showing regions of the three most prominent diffuse peak-halos corresponding to the FSDP (~15–25°2θ), SSDP (~28–33°2θ) and TDP (~50–60°2θ). Theoretical Bragg-diffraction reflexes of monoclinic As₂Se₃ (JCPDS No. 65-2365) [27,28], monoclinic As₄Se₄ (JCPDS No. 71-0388), orthorhombic As₄Se₃ (JCPDS No. 04-4979), trigonal Se (JCPDS No. 73-0465) and rhombohedral As (JCPDS No. 72-1048) are reproduced below for comparison (see text for more details).

A typical fragment of orthorhombic As₄Se₃ structure visualized from crystallographic data of Bastow and Whitfied [13] using the DIAMOND and VESTA programs is shown in Figure 2. The arrangement of As₄Se₃ molecules is reproduced with respect to the strongest Bragg-diffraction line arising from the (111) plane in the orthorhombic As₄Se₃, with an inter-planar distance d = 5.243 Å (Figure 2a). Each As₄Se₃ molecule is surrounded by 12 neighbors forming B[B₁₂] anticubooctahedron, corresponding to hexagonal close packing of a Mg structure type (see Figure 2b), with inter-molecular centroid-centroid distances deviated from 5.651 Ǻ to 7.910 Ǻ (Figure 2c), corresponding in average to d_B-B = ~6.650 Ǻ. This distance, accepted as the radius of the first coordination sphere in the dense packing of As₄Se₃ cage-like molecules obeying the Ehrenfest relation [27], corresponds to the FSDP position in the MQ-derived (unmilled) g-As₄Se₃ approaching d_s~7.0 Å (see Figure 1).

Thus, the FSDP in g-As₄Se₃ at Q₁ = Q_FSDP~1.11 Ǻ⁻¹ can be attributed to equal contributions from both inter-planar correlations corresponding to some remnants ascribed to As₄Se₃-, As₄Se₄- and As₂Se₃-type crystalline structures with an averaged Bragg-diffraction distance R = ~5.7 Å and respective inter-molecular correlations with averaged Ehrenfest-diffraction distance d_s~7.0 Å.

Noteworthy, because of the Ehrenfest diffraction due to pair inter-atomic correlations within some remnants of crystalline structures, the diffuse peak-halos in the XRPD patterning of ChG reveal non-elementary satellite nature supplemented by some humps and asymmetric extensions [9,12]. Thus, in g-As₄Se₃, the shoulder near ~1.5 Ǻ⁻¹ (viz. d_s~5.1 Å), referred to as the post-FSDP, is revealed at the high-angular side of the FSDP, so that both peak positions obey interrelation:

κ(FSDP) = Q_post-FSDP/Q_FSDP = d_s^FSDP/d_s^post-FSDP = 1.38,

(1)

which occurs very close to the Ehrenfest number (1.23) [27].

In a similar manner, it is found that a slight hump near ~2.4 Ǻ⁻¹ (viz. d_s~3.2 Å) appears as satellite doublet to the SSDP, justifying its asymmetry (reasonably referred to as the post-SSDP), with both peaks obeying similar interrelation, which is also very close to the Ehrenfest number [27]:

κ(SSDP) = Q_post-SSDP/Q_SSDP = d_s^SSDP/d_s^post-SSDP = 1.15.

(2)

Thus, the asymmetry observed in both peak-halos (the FSDP and the SSDP) is presumably caused by the superposition of the broadened Bragg-diffraction reflections from remnants of quasi-crystalline inter-planar correlations superimposed by the Ehrenfest-diffraction reflections from the most prominent inter-atomic and/or inter-molecular correlations belonging to these remnants. In contrast, the TDP at the higher diffraction angles, corresponding to Q₃ = Q_TDP~3.6 Å⁻¹, associated with direct nearest-neighbor correlations approaching d_s~2.1 Ǻ, does not show any doublet structure.

The Ehrenfest diffraction is a suitable approach to explain other features in the XRPD patterning of ChG, known as pre-FSDP [28] and related to an additional peak-halo appearing at ~(5–7)°2θ, i.e., in the region free of any inter-planar reflections from all possible crystalline counterparts. This peak-halo (unreproducible with respect to the structure factor determination and compositional variations [9,12]) arises from prolonged inter-atomic correlations in g-As₄Se₃ approaching d_s~16.5 Ǻ.

2.2. Medium-Range Structure Response in g-As₄Se₃ on Nanomilling-Driven Reamorphization

As emerged from Figure 1, high-energy MM does not alter the principal appearance of diffuse peak-halos in the XRPD pattern of g-As₅₇Se₄₃, testifying in favor of a nanomilling-driven polyamorphic transition between respective states of unmilled and milled alloys. Following Propenzi et al. [29], this effect can be classified as MM-induced polyamorphism, whereas the transition between respective states of glass before and after MM can be referred to as nanomilling-driven reamorphization transition [12].

Changes observed in diffuse peak-halos in g-As₄Se₃ undergoing nanomilling-driven reamorphization are well understood, even from the visual inspection of Figure 1. Indeed, after MM, the FSDP loses intensity and gets to be (i) more weakened, (ii) shifted to higher Q₁ = Q_FSDP~1.14Ǻ⁻¹ and (iii) broadened in width to ΔQ₁ = ΔQ_FSDP~0.32 Ǻ⁻¹. Therefore, the spacing of the FSDP-responsible quasi-periodicity R in g-As₃Se₄ slightly decreases after MM to ~5.5 Ǻ, while correlation length L (over which this quasi-periodicity is maintained) gradually decreases to ~19.5 Ǻ. This means the MM fragmentation impact that occurs in the correlation length L of the quasi-periodic entities is responsible for the FSDP.

Similar, albeit reduced, changes are observed in the SSDP (increase in the position of this peak-halo, Q₂ = Q_SSDP, broadening in the width and ΔQ₂ = ΔQ_SSDP), signifying the nanomilling-driven fragmentation of the correlation length of the structural entities is responsible for this peak-halo. Since the XRPD analysis is arranged following the normalization procedure with respect to the maximum peak, these changes should be accepted as a signature of increased ERO.

In contrast, as can be also inferred from previous research [8,9,12], no changes were found in the TDP, presumably due to invariant nearest-neighbor interatomic correlations in these arsenoselenides.

Thus, disruption of IRO due to weakening of the FSDP (when the FSDP loses intensity, becomes more broadened in width and shifted towards higher diffraction angles, as follows from Figure 1) is accompanied by an enhancement of ERO due to fragmentation of the SSDP responsible entities (when the SSDP becomes broadened and shifted towards higher angles; this also follows from Figure 1). This occurs as a manifestation of the interplay between IRO and ERO in the examined molecular-network glassy alloy (g-As₃Se₄) undergoing nanomilling-driven reamorphization. Ultimately, structural correlations responsible for IRO (presumably of inter-molecular and inter-atomic nature) are substantially destroyed under MM at a cost of competitive inter-planar quasi-crystalline correlations, taking the nanomilled glassy arsenoselenides closer to layer-type stoichiometric g-As₂Se₃ [8,15].

A similar competition at different levels of medium-range structural organization associated with IRO and ERO is characteristic of pressure-induced polyamorphism in glassy substances [30,31,32,33]. Thus, under applied pressure to molecular-network ChG [30,32,33], changes in IRO dominate, and inter-molecular spacing decreases because of increased packing of molecular units (causing gradual densification of a glass). As a result, the FSDP shifts to higher Q₁ and reduces dramatically until completely disappearing at higher pressures (~10–20 GPa), signalizing IRO breaking or collapse. The weakening of the FSDP under pressurization is accompanied by a growth in the SSDP, and its shift to higher Q₂ is indicative of an ERO increase. Despite FSDP and SSDP being restored under pressure release, changes in these halos serve as a signature of elementary pressure-induced IRO-to-ERO interplay, which also occurs in nanomilled molecular-network ChG like g-AsSe [12] or g-As₃Se₄. So high-energy MM (as in this case) is an effective way to stabilize such changes in molecular-network glass as a result of nanomilling-driven irreversible reamorphization.

The doublet structure of the FSDP, revealed through satellite high-angular post-FSDP, is more expressed after MM because κ(FSDP)~1.34 in Equation (1) better approaches the Ehrenfest number (1.23) [27]. It means that inter-atomic correlations contributing to the FSDP (d_s^FSDP) prevail over inter-atomic correlations connected with inter-planar arrangement responsible for this peak-halo (d_s^post-FSDP). Concisely, disruption of intermediate-range ordering in the glasses subjected to nanomilling is dominated as compared with the destruction of inter-atomic correlations belonging to remnants of quasi-crystalline planes contributing to the FSDP. So, it seems reasonable that asymmetry in the FSDP is reduced after MM (Figure 1). In contrast, the doublet structure of the SSDP revealed in the satellite post-SSDP is depressed after MM, which resulted in κ(SSDP) approaching only ~1.12.

Thereby, remnants of crystalline entities in g-As₄Se₃, responsible for inter-molecular correlations with inter-centroid distances between As₄Se₃ cages d_B-B(α-As₄Se₃)~6.650 Ǻ contributing to the FSDP through the Ehrenfest diffraction, are destroyed under MM, similarly to more depressed inter-planar quasi-crystalline correlations contributing to the FSDP through the Bragg-diffraction lines ascribed to the (111) plane in orthorhombic As₄Se₃ (I = 100%), the (120) plane in monoclinic As₄Se₄ (I = 91.3%) and the (020) plane in monoclinic As₂Se₃ (I = 91.2%). As a result, the FSDP in g-As₄Se₃, obeying such molecular-to-network reamorphization, becomes gradually weakened in intensity, broadened in width and shifted towards higher scattering vector positions (see Figure 1).

Noteworthy, changes in medium-range structure in the examined molecular-network glassy alloy (g-As₄Se₃) associated with nanomilling-driven reamorphization obey clearly an irreversible scenario. This is in contrast to the pressure-induced reversible amorphous-to-amorphous transition observed by Ahhmad et al. [31] in network glasses (like g-As₂Se₃) under compression-decompression cycling below ~40 GPa, which became amorphous-to-crystalline (also reversible) as the pressure was increased to ~53.5 GPa. However, XRD patterns in [31] were not parameterized, leaving room to consider that this was only based on visual inspection of XRD profiles for glasses before and after compression. Thus, it was obvious that under the increasing pressure (up to ~13.5 GPa) applied to g-As₂Se₃, changes in peak-halos were similar and commensurable to those observed in MM-driven reamorphization [8,9,12], while after decompression to the initial state, a gradual difference still remained.

2.3. Thermophysical Heat-Transfer Phenomena and Micro-RS Response in g-As₄Se₃ Undergoing Nanomilling-Driven Molecular-to-Network Transition

Temperature variations in non-reversing heat flow HF_nrev in g-As₄Se₃ in initial (melt-quenched) and final (reamorphized) states in MQ-derived alloy subjected to nanomilling collected in the dynamic heating-run regime are reproduced by, respectively, the colored black and red thermograms in Figure 3. Under heating, the principal calorimetric heat-transfer event in these alloys derived by MQ represents a glass transition [34,35]. In molecular-network g-As₄Se₃, this thermal-alteration event is revealed as a sharp endothermic step-like jump near ~130–140 °C in temperature behavior of non-reversing heat flow HF_nrev depicted by the black curve in Figure 3. More precise parameterization of this phenomenon using the multifrequency DSC-TOPEM^® method for As-Se alloys of close composition such as g-As₅₅Se₄₅ [35] provides the values of the onset of the glass transition temperature T_g ~134.6 °C, heat capacity variation ΔC_p~0.11 J·g⁻¹·K⁻¹ and specific enthalpies difference ΔH~5.57 J·g⁻¹.

This calorimetric response originated from temperature variation in DSC heat flow HF_nrev gets to be changed drastically in g-As₄Se₃ subjected to nanomilling, this effect being revealed as a pronounced exothermic event within broad 100–200 °C region highlighted by the red curve in Figure 3. Undoubtedly, this phenomenon is due to the relaxation of inner strength generated in the examined glass under high-energy MM. Slight features observed in HF_nrev variation near 165–175 °C testify in favor of enhanced glass transition temperature in this glass undergoing MM-driven molecular-to-network transition, in contrast to T_g reduction observed in network glasses such as g-As₅Se₉₅ [35]. Parameterization of this calorimetric response for g-As₅₅Se₄₅ specified with DSC-TOPEM^® method shows the onset glass-transition temperature T_g increased to ~170.0 °C, ΔC_p~0.13 J·g⁻¹·K⁻¹ and ΔH~−29.7 J·g⁻¹ [35].

The network directionality in reamorphization is also confirmed by micro-RS response observed in MQ-derived g-As₄Se₃ subjected to MM, with respective micro-RS spectra being reproduced in Figure 4. The most prominent RS-active modes in a non-milled sample are represented by a few more or less resolved low-frequency bands (at ~109, 143, 154, 168, 190 cm⁻¹) and high-frequency bands (at ~203, 218, 235, 253, 278 cm⁻¹). The high-frequency bands (strong and very strong) are ascribed to overlapped bond-stretching modes of AsSe_3/2 pyramids (227 cm⁻¹ [35,36,37]) and cage-like thioarsenide molecules, such as As₄Se₄ (190 and 248 cm⁻¹ [38]), As₄Se₃ (196, 242, 256, 266 and 280 cm⁻¹ [39]) and As₄ (~200 cm⁻¹ [40]). The low-frequency bands (preferentially weak and medium) are ascribed to bond-bending modes of molecular cages, such as As₄Se₄ (106, 136, 144, 190, 207 cm⁻¹ [40,41]) and As₄Se₃ (140 and 166 cm⁻¹ [39]). These features are merely broadened and depressed in g-As₄Se₃ subjected to nanomilling (see Figure 4, red curve), testifying in favor of nanomilling-driven destruction of thioarsenide As₄Se_n molecules and their incorporation in newly polymerized As-Se backbone.

Thus, the structure of g-As₄Se₃ becomes notably stressed under MM being affected by defects. As a result, the remainder of destroyed thioarsenide molecules became more incorporated in a network, changing essentially calorimetric heat-transfer response from the glass-transition event in this alloy.

2.4. Cluster Modeling of Molecular-Network Conformations Related to As₄Se₃ Thioarsenide

There are three conformations for tetra-arsenic triselenide molecule (As₄Se₃) in dependence on the arrangement of four As atoms, forming three (As-As) bonds. These include triangular-pyramidal (As₃)-As conformation due to basal (As₃) triangular neighboring with AsSe₃ pyramid by sharing three -Se- bridges along adjacent apical edges (see Figure 5a), open chain-like As4 conformation due to three (As-As) bonds in zig-zag sequence of As atoms (Figure 5b) and star-like As(As)3 conformation due to three (As-As) bonds having the same origin on As atom (Figure 5c).

In view of average cluster-forming energies (E_f) calculated for these conformations employing the CINCA algorithm [16,17], the most plausible is As₄Se₃-I molecule composing triangular-pyramidal (As₃)-As arrangement (shown in Figure 5a) possessing E_f = 0.33 kcal/mol with respect to the energy of single AsSe_3/2 pyramid [17]. This cage-like molecular cluster is isostructural with the molecule refined in α- and β-modifications of mineral dimorphite As₄S₃ by Whitfield [23,41,42,43]. Topologically, this molecule includes four small rings (three pentagons and one triangle) in idealized under-constrained geometry of C_3v symmetry because of the average number of constraints n_c = 2.71, which is evidently less than space dimensionality (3D). All seven atoms of almost spherical shape are positioned at the same sphere, resulting in a 0D structure with unusually low calorimetric heat transfer and strong thermal expansion responses, which are characteristic features of the plastically crystalline As₄Se₃ phase [15,30]. With respect to the CINCA modeling, the optimized configuration of this As₄Se₃-I molecule is defined by slightly deviated (As-Se) and (As-As) bond lengths approaching 2.37 Å and 2.46 Å, respectively, and bond angles on apical As atoms ∠(Se-As-Se) = 99.4°, on basal As atoms in linking to AsSe₃ pyramid ∠(As-As-Se) = 104.1°, on basal As atoms within (As₃) triangular ∠(As-As-As) = 60.0°, and angles of -Se- bridges between apical and basal As atoms ∠(As-Se-As) = 101.9°.

Other molecular clusters corresponding to As₄Se₃ stoichiometry are unfavorable as compared with this dimorphite-type As₄Se₃-I molecule. Thus, the estimated E_f energy approaches −0.94 kcal/mol for the As₄Se₃-II molecule arranged in chain-like As4 configuration (as shown in Figure 5b) and −2.44 kcal/mol for the As₄Se₃-III molecule arranged in star-like As(As)3 configuration (as shown in Figure 5c), both molecules being under-constrained in view of the large number of small rings involved.

Thus, in MQ-derived glasses compositionally approaching As₄Se₃, the molecular clusters of the first type (dimorphite-type As₄Se₃-I molecule) are obviously dominant. But not only these clusters are governing in these alloys. As it follows from the above results of calorimetric measurements and micro-RS studies, the examined glassy arsenoselenides are also enriched in realgar-type As₄Se₄ molecules and amorphous As-bearing network substance of unidentified composition obeying the concept of preferential molecular-network disproportionality [44,45]. By analogy with As-S alloys [45], these products are expected in the MQ-derived As-Se alloys near As₄Se₃ stoichiometry, as a result of the decomposition of most energetically favorable As₄Se₃-I cage-like molecules.

In glassy-crystalline As-S alloys, where multiphase equilibria are disturbed by the transformation of dimorphite As₄S₃ phase into realgar-type β-As₄S₄ phase [15], the supplemented amorphous substance is compositionally close to a-As₄S₂ and decomposition reaction is activated under high energetic barrier ΔE_f~1.5 kcal/mol [44]:

2·(As₄S₃-I) → β-As₄S₄ + a-As₄S₂ + (ΔE_f = +1.53 kcal/mol).

(3)

Let us parameterize the decomposition reaction in glassy arsenoselenide g-As₄Se₃ on the basis of cluster-forming energies E_f calculated for the respective components.

The ball-and-stick presentation in Figure 6a highlights the main features of optimized tetra-arsenic tetraselenide As₄Se₄ molecule [12,46]. This realgar-type molecule of D_2d symmetry is composed of a maximum number of small rings (four pentagons and four hexagons) built of eight As-Se and two As-As bonds in evidently under-constrained (floppy) topology possessing n_c~2.875. The E_f energy for this molecule is 0.40 kcal/mol (which is dominant among all As₄Se₄-bearing polymorphs [46]), and intramolecular parameters are in good agreement with those refined from XRD analysis for monoclinic As₄Se₄ [19,20,21].

Since molecular clusters undergoing decomposition become As-deficient (because of the transition from coordination number CN = 2.57 corresponding to As₄Se₃ to CN = 2.50 in As₄Se₄), the appeared amorphous substance is expected to be As-enriched. Among different network clusters related to the As₄Se_n thioarsenide molecules with n_c < 3, only one can be derived from the under-constrained (n_c = 2.67) tetra-arsenic biselenide As₄Se₂ molecule by double x2-breaking the Se atom positions, possessing reasonable E_f energy approaching −0.72 kcal/mol. The optimized ball-and-stick presentation of the H-saturated molecular prototype of this cluster keeping a closed tetragon-like As₄ arrangement of four (As-As) bonds is shown in Figure 6b. Because of such topology with only one small ring involved (As₄ tetragon), the network built of such clusters corresponding to a-As₄Se₂ (with CN = 2.67) is topologically over-constrained in view of n_c = 3.33.

Finally, the complete decomposition reaction in glassy arsenoselenides that are compositionally close to tetra-arsenic triselenide (g-As₄Se₃) can be schematically presented as follows:

2·As₄Se₃-I → As₄Se₄ + a-As₄Se₂   +(ΔE_f = +0.41 kcal/mol).

(4)

This reaction is schematically depicted in Figure 7 using a molecular presentation of the constituents. The energetic barrier of this decomposition ΔE_f is close to ~0.41 kcal/mol. It means that in contrast to the glassy-crystalline g/c-As₄S₃, where such reaction occurs under the barrier ΔE_f ~1.5 kcal/mol [44,45], the decomposition of the As₄Se₃ molecular phase becomes more plausible. As a result, thermally activated crystallization in As-Se alloys is merely inhibited by the amorphous phase (a-As₂Se₄) which appears to extend their glass-forming ability to more As-rich compositions approaching As₇₀Se₃₀ [5,6,7].

By analogy with As-S alloys [44,45], the decomposition reaction (4) can be initiated by breaking one of three (As-Se) bonds within the AsSe₃ pyramid of the most plausible dimorphite-type As₄Se₃-I molecule (see Figure 7). This results in a local disturbance due to the release of one Se atom from this molecule. Interacting with another such molecule, this disturbance is stabilized by forming an As-deficient with respect to As₄Se₃ stoichiometry (CN = 2.57) with a realgar-type As₄Se₄ molecule (under-constrained in view of n_c = 2.875 (CN = 2.50) and the over-constrained As-enriched remainder a-As₄Se₂ (with n_c = 3.33, CN = 2.67) is left as the destroyed As₄Se₃-I molecule. Specifically, the cluster contributing to such an amorphization scenario can be considered as a network-forming derivative reconstructed from the As₄Se₂ molecule by double x2-breaking in Se atom positions (x2-As₄Se₂-I cluster shown in Figure 6b).

As an alternative to this reamorphization scenario (4), the decomposition of As₄Se₃-I molecules into a realgar-type As₄Se₄ phase supplemented by a more As-enriched substance, such as tetra-arsenic monoselenide (As₄Se) or arsenic (As₄), can be considered. The latter is undoubtedly more essential for the above reaction (4), while not equally competitive to this decomposition reaction in view of under-estimated cluster-forming energies E_f beyond the glass-forming region in binary As-Se system [5,6,7].

Under high-energy MM, products of molecular-to-network transition in As-Se glass alloys can be also stabilized as the most favorable network conformations derived by direct destruction from all possible As₄Se₃ thioarsenide molecules. These conformations include network clusters reconstructed from these molecules by breaking in all Se atom positions (Figure 5), which appear due to an extremely large portion of mechanically transferred energy. By CINCA modeling, it was found that triple-broken derivatives of each molecule possessed better cluster-forming energy and therefore could be considered as possible in the MQ-derived alloys subjected to nanomilling. The H-saturated molecular prototypes of these network clusters conserving triangular-, chain- and star-like arrangement of neighboring As-As bonds are, respectively, reproduced in Figure 8a–c.

In realistic arsenoselenide glass structures composed of the most favorable As₄Se₃-I molecules, as shown in Figure 5a (E_f = 0.33 kcal/mol), the network clusters are possible in a reverse sequence to energetic barriers ΔE_f calculated with respect to the cluster-forming energies E_f provided in the captions in Figure 8. The most plausible are chain-like (ΔE_f = 0.93 kcal/mol) and star-like (ΔE_f = 1.21 kcal/mol) clusters. Because of the absence of small rings, both clusters are over-constrained (n_c = 3.43; CN = 2.57), counterbalancing the effect from molecular dimorphite-type As₄Se₃-I (n_c = 2.71; CN = 2.57) and realgar-type As₄Se₄ (n_c = 2.875; CN = 2.50) clusters. Noteworthy, the optimally constrained network clusters derived from As₄Se₃-I molecule by triple x3-breaking in all Se atom positions (n_c = 3.00), keeping basal (As₃) triangle as a small ring (see Figure 7, are rather impossible in realistic As-Se structures because of very unfavorable cluster-forming energy E_f~−1.47 kcal/mol, resulting in an unrealistically high energetic barrier of direct destruction (ΔE_f = 1.80 kcal/mol).

3. Materials and Methods

3.1. Glass Samples Preparation, Nanomilling Treatment and Preliminary Characterization

Glass samples of tetra-arsenic triselenide g-As₄Se₃ (viz. g-As₅₇Se₄₃) and some alloys slightly deviated from this composition (g-As₅₅Se₄₅ and g-As₆₀Se₄₀) were obtained by vibrational MQ from elemental precursors (the As and Se of 5N purity stored in argon atmosphere) [8,9,12].

The sealed ampoules filled with As and Se were placed in a rocking furnace, heated to 650 °C and homogenized for 10 h. Then, they were placed vertically, cooled to 500 °C for 1.5 h and quenched in water. To eliminate residual stress possible under cooling, the ingots were annealed for 1 h at 125 °C, which was below the glass-transition temperature of the samples defined from calorimetric scanning under 10 K/min heating rate (T_g~140 °C for g-As₅₇Se₄₃). The ingots extracted from the ampoules were completely amorphous, as observed from their XRPD patterns, showing diffuse peak-halos typical for amorphous substances, conchoidal fracture and IR transparency of fresh cut-sections.

The macroscopic density ρ (±0.005g·cm⁻³) of g-As₄Se₃ defined by the Archimedes displacement method in ethanol was 4.447 g·cm⁻³, this being in good agreement with the known counterparts [5,6,7]. The mean inter-atomic spacing for this glass d_s^m~3.80 Å was the maximum among all over-stoichiometric As-rich glassy arsenoselenides g-As_xSe_100−x (40 < x < 65) [9].

The nanomilling treatment in the high-energy planetary ball mill Pulverisette 6 (Fritsch, Germany) was employed to transform coarse-grained pieces of the prepared glasses (~3 g) sieved under 200 μm into a fine-grained (nanostructured) state. Mechanical attrition was performed in a mill for 60 min under a protective Ar atmosphere with 500 min⁻¹ rotational speed in 250 mL tungsten carbide chamber loaded with 50 tungsten carbide balls (each having 10 mm in diameter). Under such MM conditions, the energy transfer to the powder estimated through specific grinding work performed in a rotational mill of this type was as high as ~300–320 kJ/g [47,48,49], justifying a novel branch of contemporary materials science and engineering, the chalcogenide mechanochemistry [2,50]. The particle size distribution was recognized for nanosuspentions prepared on the basis of powdered alloys, employing photon cross-correlation spectroscopy with Nanophox particle size analyzer (Sympatec, Germany). The unimodal particle size distribution was monitored for examined samples, showing the averaged (x50) parameter approaching ~180 nm (meaning that 50% of particles were smaller than 180 nm) and (x99) parameter close to ~330 nm (meaning that 99% of the particles were smaller than 330 nm).

3.2. Medium-Range Structural Research in Molecular-Network Glassy Arsenoselenides

Medium-range structure of glassy arsenoselenides was recognized with the XRPD analysis using STOE STADI P diffractometer operational in transmission mode with Cu Kα₁-radiation and curved Ge monochromator on primary beam (more details in [8,9]). The XRPD patterns were collected under 0.015°2θ step, detector increment of 0.480°2θ and 500s scanning time per step in the whole range of angles (2θ). The amorphous phase was identified parameterizing diffuse peak-halos in the XRPD patterns of the examined substances (Figure 9), in part, the FSDP, serving as a signature of structural entities forming a so-called intermediate-range ordering (IRO) in a glass over a few tens Å reproduced in a reciprocal space near scattering vector Q₁~1–1.5 Ǻ⁻¹ [51], and the SSDP (according to Elliott [52]) or the PDP (the principal diffraction peak according to Zeidler and Salmon [18]) serving as the signature of extended-range ordering (ERO) near Q₂~1.8–2.2 Ǻ⁻¹.

Specifically, in the XRPD patterns of over-stoichiometric g-As_xSe_100−x (x > 40), the FSDP related peak-halo at ~15–22°2θ reflects IRO, corresponding to predominant correlations between some polyhedrons such as thioarsenide As₄Se_n molecules, while the SSDP shifted to higher diffraction angles of ~28–33°2θ reflects ERO, corresponding to orientational arrangement of these polyhedrons (related to the second-order pair atomic correlations close to mean inter-atomic spacing in a glass, d_s^m [24]). At ~50–60°2θ (viz. Q₃~3.3–4.0 Ǻ⁻¹), the third peak-halo (not so sharp as the previous) known as the TDP (the third diffraction peak) is observed in XRPD patterns as a manifestation of the shortest interatomic separation in a glass related to the nearest-neighbor As-Se and As-As distances of ~2.1–2.3 Ǻ [54,55].

Thus, the XRPD measurements reveal the three-peak structure of the collected diffraction patterns as shown in Figure 9, which reflects a succession of single pairwise correlations defined presumably by Q₃ = Q_TDP, and multi-pairwise correlations defined by Q₁ = Q_FSDP and Q₂ = Q_SSDP responsible for medium-range ordering [18].

Equilibrium phase diagram of binary As-Se alloys derived with thermodynamic optimization [56] contains three stable ambient-temperature compounds, such as stoichiometric arsenic triselenide As₂Se₃ (corresponding to tetra-arsenic hexaselenide As₄Se₆) and two over-stoichiometric selenides, tetra-arsenic tetraselenide As₄Se₄ (arsenic monoselenide AsSe) and tetra-arsenic triselenide As₄Se₃, the latter existing in two modifications nominated in somewhat nonfusing nomenclature of Bastow and Whitfield [13] as high-temperature orthorhombic α-As₄Se₃ and ambient-temperature monoclinic β-As₄Se₃ phase [13,14]. Blachnik and Wickel [15] renamed β-As₄Se₃ and α-As₄Se₃ polymorphs of Bastow and Whitfield [13] in normal crystalline α-As₄Se₃ and α′-As₄Se₃ modifications stable at ambient and high temperatures, and introduced “β” symbol for plastically crystalline modification appeared under heating. As was reported by Blachnik and Wickel [15], under heating above 412 K (with 1.25 K·min⁻¹ rate), the ambient-temperature normal crystalline As₄Se₃ modification (monoclinic α-As₄Se₃) transforms in high-temperature modification (orthorhombic α′-As₄Se₃), and under further heating above 447 K, the latter transforms into plastically crystalline β-As₄Se₃ phase and unidentified amorphous substance, while only orthorhombic α′-As₄Se₃ phase could be obtained in metastable form at ambient temperature by quenching.

Since the examined arsenoselenides are matched within polymorphic α–α′–β phase transitions, the remainders of As₄Se₃ crystalline phases are expected in these alloys under nanostructurization. Hence, preliminary processing of the XRPD patterns was performed using the databases [57,58] and available resources on the crystallography of As-Se polymorphs of close compositions, in part, the JCPDS cards No. 65-2365 for monoclinic As₂Se₃ (space group P2₁/n, structure type α-As₂S₃, orpiment [19,22]); No. 71-0388 for monoclinic As₄Se₄ (space group P2₁/n, structure type α-As₄S₄, realgar [19,20,21]); No. 04-4979 for orthorhombic As₄Se₃ (space group Pnma, structure type α-As₄S₃, dimorphite [13]), and terminated elemental constituents in As-Se system, in part, the JCPDS cards No. 73-0465 for trigonal t-Se (space group P3121 [59]), and No. 72-1048 for rhombohedral (grey) As (space group $R\overline{3}m$ [60,61]). To visualize crystallographic details of the above phases, well known programs, such as DIAMOND [62] and VESTA [63], were employed.

The arrangement of diffuse peak-halos in collected XRPD patterns responsible for amorphous phase was analyzed using the STOE WinXPOW 3.03 [64] and PowderCell 2.4 [65] program packages, following normalization procedure with respect to the maximum peak, which in the case of selenide ChG was related to the SSDP (in full harmony with the famous research of Vaipolin and Porai-Koshits from 1963 [53], see also insert in Figure 9). The accuracy in the peak-halo position (2θ) and full width at half maximum (FWHM) was no worse than ±0.05°2θ, the scattering vector Q = (4π/λ)·sinθ, and width ΔQ = (4π/λ)·sin(FWHM/2) corresponding to the peak-halo were calculated using the Bragg diffraction formalism (see, e.g., [8,9,12]). The characteristic distance R defined as spacing of quasi-periodicity responsible for diffuse peak-halo and correlation length L over which this quasi-periodicity was maintained in real space were defined as R = 2π/Q and L = 2π/ΔQ. The peak-halos in the XRPD patterns were also treated as arising from the diffraction of coordination spheres, i.e., closest inter-atomic distances like in randomly packed multiparticulate systems [24,25,26], when XRPD patterning is governed by the Ehrenfest relation [27]:

2d_s·sinθ = 1.23·λ,

(5)

where d_s is the average inter-atomic distance between scatterers (radius of coordination sphere). Note that a realistic error bar in the above parameters (R, L, d_s) does not exceed ±0.1 Å.

3.3. Complementary Microstructural Research on Glassy Arsenoselenides

Calorimetric heat-transfer measurements of non-reversing heat flow HF_nrev in the glasses were performed using possibilities of conventional heat-flux differential scanning calorimetry (hf-DSC) in a dynamic heating regime [34,35,66,67,68]. The instrument used for this analysis was the model DSC-1 calorimeter (Mettler-Toledo, Switzerland) equipped with a TC100 Huber intracooler. Temperature and heat calibration of the instrument was performed using a set of standard probes (water, In and Zn). For mass determination, the analytic balance model Ohaus AP250D with 0.01 mg resolution was used. The sample was encapsulated in sealed 20-μL Al pans in a N₂ atmosphere and scanned at 10 K·min⁻¹ rate.

The nature of nanomilling-driven structural changes in glassy arsenoselenides was identified by micro-RS spectroscopy using the Horiba Xplora spectrometer equipped with a CCD detector operational at room temperature [49]. The CW 785 nm laser of 90 mW power was used for excitation, the 10% power option being used to avoid photostructural effects. Other operational options were as follows: 100× objective, 1800 mm⁻¹ grating, 500 μm hole and 50 μm slit. The spectral resolution was maintained at the 2 cm⁻¹ level and spatial resolution was near 2 μm. Numerous scans were performed on the sample’s surface to be sure that the micro-RS-spectra processed with Horiba LabSpec 6 software were identical. The nanomilled and unmilled glasses were compared through normalization by matching spectral areas in the region of interest. The RS-active bands in the examined samples were identified using available data for ChG analogs [35,36,37,38,39,40].

3.4. Cluster Modeling of Molecular-Network Conformations in As-Se Compounds

The optimized configurations of As₄Se₃ cage-like molecule and network derivatives were reconstructed by breaking this molecule into separate fragments linked with surrounding by Se_1/2…Se_1/2 bridges were reconstructed using ab initio quantum-chemical atomic cluster-modeling code CINCA [16,17]. The HyperChem Release 7.5 program based on the restricted Hartree-Fock self-consistent field method with split-valence double-zeta basis set and single polarization function 6–311G* [69,70,71] was used. Geometrical optimization and single-point energy calculations were performed by the Fletcher-Reeves conjugate gradient method until the 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 the network-forming cluster in molecular one according to the known procedure [71,72], and recalculated with respect to the energy of AsSe_3/2 pyramid (E_f = −72.309 kcal/mol [17]). This modeling route (CINCA) [16,17] allows the characterization of both molecular and network configurations in saturated covalent-bonded systems like ChG [5,6], characterized by different coordination numbers (CN), parameterizing the most energetically favorable scenarios. To compare atomic clusters accounting for small rings in molecular thioarsenides As₄Se_n, the average number of Lagrangian constraints per atom n_c was calculated for different fragments derived by breaking in available positions of Se atoms (followed by H atoms saturation), using the Phillips-Thorpe constraint-counting algorithm with stretching and bending forces ascribed to intra-molecular bonds within the cluster [73,74,75].

4. Conclusions

Polyamorphic (amorphous-I-to-amorphous-II) transformations driven by high-energy mechanical milling (nanomilling) are recognized in a melt-quenched glassy alloy of tetra-arsenic triselenide As₄Se₃ employing a multiexperimental approach based on the X-ray powder diffraction (XRPD) analysis of diffuse peak-halos responsible for medium-range structure ordering in glassy chalcogenides, complemented with calorimetric heat-transfer and micro-Raman spectroscopy studies.

A straightforward interpretation of medium-range structure ordering response on nanomilling-driven reamorphization in this glassy alloy is developed within a modified microcrystalline model, treating diffuse peak-halos in the XRPD patterning of chalcogenide glasses as a superposition of the Bragg-diffraction contribution from inter-planar correlations supplemented by the Ehrenfest-diffraction contribution from prominent inter-atomic and/or inter-molecular correlations belonging to some derivatives of As₄Se_n thioarsenide molecules dominated by dimorphite-type As₄Se₃ ones. These cage-like molecules are merely destroyed under nanomilling, facilitating the formation of a polymerized covalent glass network with enhanced calorimetric heat-transfer responses. Disruption of intermediate-range ordering due to weakening of the first sharp diffraction peak (when the FSDP loses intensity, becomes broadened and shifted to higher diffraction angles), accompanied by an enhancement of extended-range ordering due to fragmentation of structural entities responsible for the second sharp diffraction peak (when the SSDP becomes broadened and shifted towards higher angles), an interplay takes place between the respective levels of medium-range structure in molecular-network As₄Se₃ glass undergoing reamorphization. The micro-Raman scattering spectra testify in favor of nanomilling-driven destruction of thioarsenide As₄Se_n molecules and incorporation of their derivatives in a more polymerized network. The microstructure scenarios of molecular-to-network disproportionality originating from decomposition and direct destruction of As₄Se₃ cage-like molecules are recognized by ab initio quantum-chemical modeling employing the cluster-simulation algorithm (CINCA).

From the point of view of the predominant microstructure, the nanomilling-driven amorphous-I-to-amorphous-II transition in glassy arsenoselenide alloys compositionally approaching tetra-arsenic triselenide As₄Se₃ is classified as the molecular-to-network reamorphization transition.