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All issues Volume 2 / No 3 (2023) Natl Sci Open, 2 3 (2023) 20220049 Full HTML
Issue
Natl Sci Open
Volume 2, Number 3, 2023
Special Topic: Glasses—Materials and Physics
Article Number 20220049
Number of page(s) 28
Section Physics
DOI https://doi.org/10.1360/nso/20220049
Published online 25 April 2023

© The Author(s) 2023. Published by Science Press and EDP Sciences

Licence Creative CommonsThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Introduction

A novel type of glass has been discovered in a variety of alloys originally from metallic glasses (MGs) [1–4]. Unlike the ordinary MGs that are formed by rapid cooling the metallic melt, these novel glasses are made by vitrifying the second liquid of the liquid-to-liquid transition (LLT). An exothermic peak developing immediately after the onset of glass transition of their as-cast MG is discovered when the sample is heated in differential scanning calorimetry, indicating an LLT as confirmed by in-situ structural analyses [1–4]. If the liquid is heated further, crystallization occurs; however, if the liquid is cooled to room temperature, new glass forms (Figure 1). After a first-order LLT, the new glass has an amorphous structure, higher glass-transition temperature, greater mechanical strength, increased hardness and enhanced thermodynamic stability [1–4], demonstrating an engineering potential. Furthermore, the structural alteration of these new glasses is of critical scientific importance. Considering the long-range disordered structure of glasses [5], the short-range ordered structure is the only feasible location for a first-order transition to happen yet the most difficult part to characterize. Unless specified, here short-range ordering also includes medium-range ordering [6–8]. On the other hand, the arrival of this new type of MG raises severe questions about alternative explanations, such as nanocrystallization [9,10], quasicrystallization [11,12], and phase separation [13], all of which need to be clarified. This review is about to make clarifications and comparisons between diverse studies.

thumbnail Figure 1

Metallic glacial glass (MGG) formation (Reproduced from ref. [3]). Upon heating the metallic glass (MG) passing the glass transition temperature (Tg), a primary exothermic peak representing glaciation with a peak temperature (Tp) is detected, which is followed by the onsets of crystallization (at Tx) and melting (at Tm). By summarizing the characteristic temperatures with the heating rates, a continuous-heating-transformation diagram showing MG, MGG, crystal and supercooled liquid (SCL) regions is constructed. The green open symbol represents the reversal of glaciation, i.e., the transition from MGG-forming liquid to MG-forming liquid.

In 1996, a discovery was made in the triphenyl phosphite (TPP), i.e., a single-component molecular liquid [14,15]. Instead of rapid vitrification, a first-order LLT takes place when TPP is rapidly cooled to 213–225 K and kept at this temperature. The structural change is discernible under an optical microscope, where the sample gradually becomes turbid, then nearly opaque (in a matter of hours) and eventually clear again. Kivelson and his colleagues [14,15] who first made the observation named such an LLT as the glaciation. Glaciation is a term that originally represents a landscape reformation by a massive mass of ice covering the land and is employed here because the opaque TPP appears similarly to the ice cover, we wonder. Despite the fact that no such visual alterations are seen, we decide to call the LLT (including liquid-to-liquid, liquid-to-glass and glass-to-glass transitions) of MG-forming liquids as the glaciation, too, as the resulting new type of glass, i.e., so-called metallic glacial glass (MGG) [3], has many similarities in thermodynamics and kinetics to the glacial phases of TPP.

In the literature, there is a rival term called reentrant glass [16–18]. The term stems from the “reentrant glass transition”, which is extensively used in the colloidal-glass field. The reentrant glass transition is a structural transformation from a repulsive to an attracting glass [19] in which a liquid state may or may not be at an intermediate stage bridging the transition [17,20]. Despite the fact that the term “reentrant glass transition” has been used to characterize the LLT of some MGs [1,2], it is unclear if this change is from repulsion to attraction in their short-range atomic bonding. To put it another way, a reentrant glass transition may capture the spirit of vitrifying a new type of glass from a liquid but fail to specify whether or not the liquid is structurally altered. A reentrant glass transition is usually considered as a pure kinetics phenomenon [17].

Pressure-induced poly-amorphism [21–24] is another way to obtain a new glassy state. When loaded up to a particular high pressure at room temperature, poly-amorphous transformations have been seen in numerous MG compositions where the most notable feature is an abrupt change of the density or bulk modulus at the phase-transition pressure [25–27]. However, such high-pressure triggered product distinguishes with the MGG. MGG is energetically more favorable than MG since MGG had a lower enthalpy than MG [1–4]; on the contrary, the pressure-induced poly-amorphic phase is unstable after the decompression as it will revert to its former state [21–23]. Despite the fact that pressure and temperature are sometimes equivalent thermodynamic variables that can induce phase transformations, existing MGs capable of poly-amorphic transformation are not necessarily MGG candidates.

The review is organized in the following manner. In Section The glaciation and glacial phase of TPP, a brief history regarding the researches of glaciation and glacial phase of TPP is introduced. In Section First order exothermic transitions in metallic glasses, comparisons are made on the calorimetry curves of principal crystallization, phase separation, quasicrystallization, short-range ordering, mesophase formation and glaciation, highlighting their differences in the primary exothermic peak. In Section Glaciation, kinetics and properties of MGG, identification requirements, kinetics and properties of MGGs are summarized. In Section Unresolved issues, scientific concerns about glaciation and alloy candidates for future MGGs are described.

The glaciation and glacial phase of TPP

A first-order LLT was found in a single-component molecular liquid called triphenyl phosphite (TPP) in 1996 [14,15]. For TPP, when its liquid was cooled slowly, crystals developed, and when it was quenched rapidly, glass was obtained; but, if TPP was rapidly cooled to a temperature at around 213–225 K avoiding crystallization and maintained there (Figure 2), the transparent sample would progressively turn turbid, then almost opaque (within a few hours), and finally return transparent [14,15]. These samples appeared to be amorphous since X-ray diffraction (XRD) did not exhibit any Bragg peaks. A significant drop in enthalpy of 7 kJ mol−1 occurred along with the conversion, indicating a phase change [28]. Phase separation was ruled out because TPP was a single-component molecular liquid. This led them to conclude that the phase change was an LLT. Glaciation and the glacial phase were then used to describe the specific LLT and the ending product, respectively. When compared with the 17.5 s of original liquid and 83.9 s of crystal, the glacial phase had a 31P spin-lattice relaxation period of 28.4 s at 200 K [14,15]. Although the peak strength between the original liquid and the glacial phase was equivalent in terms of α-relaxation, the peak temperature at the same frequency increased, for example, from 102 K (of the original liquid) to 114 K (of the glacial phase) at 1 Hz [29]. In other words, glaciation lengthened the 31P spin-lattice relaxation time at the same temperature or increased the relaxation temperature at the same α-relaxation time [30]. Because β-relaxation of the glacial phase was unchanged compared with the original liquid, it was believed that glaciation was accompanied by cooperative molecular changes instead of local molecular motions [29,30]. The original liquid of TPP was fragile [31] because its glass transition temperature (Tg) significantly shifted with heating rate, and the fragility index of the initial liquid was as large as 160 [32]. The glacial phase was strong as supported by its large temperature range between the onset and end of the glass transition in calorimetry [33,34], as well as by nuclear-magnetic-resonance [35] and dielectric-relaxation signatures [31,35,36]. Thus, glacial phase and initial liquid of TPP have significantly different dynamics.

thumbnail Figure 2

A schematic temperature-time-transformation (TTT) diagram of triphenyl phosphite (TPP). Crystallization (blue curve) occurs at higher annealing temperature (Ta) and shorter annealing time (ta), while glaciation (red curve) occurs at lower Ta and longer ta.

The glacial phase was envisioned as a “defect-ordered crystal” in which the supercooled liquid was divided into domains placed in a crystal array [14,15]. Geometric frustration prevented the spatial extension of domains that was generated by locally-favored non-crystalline molecular clusters, inhibiting crystallization. Further researches, however, refuted the “defect-ordered crystal” theory. From synchrotron X-ray diffraction [35,37], inelastic neutron scattering [38], Raman scattering [38,39], and neutron diffraction [37], Hédoux discovered a number of counterexamples. Firstly, on the structural factor of the glacial phase, there existed a pre-peak at 1.1 Å−1 that was likely a signature of nanocrystals [36,37]. Secondly, in the density of vibrational states (VDOS) spectra and Raman susceptibility of the glacial phase, a low-frequency shoulder was visible at a location corresponding to a crystal’s low-frequency peak [38]. Thirdly, neutron diffraction demonstrated that the glaciation coincided with a sharpening of the second main peak and a smoothing of the shoulder at 2.8 Å−1; the latter matched an envelope of a set of Bragg peaks in the diffraction pattern of crystal [37]. Using these data, Hédoux et al. [36] considered the glacial “domains” microcrystallites, envisioned the glaciation an “aborted” crystallization, and attributed the apparent amorphous structure of the glacial phase to the slow growth and fast nucleation of the microcrystallites [40]. These results, as well as those collected from the repeating experiments, made Demirjian et al. [41,42] agree that glaciation was poor crystallization.

It would be less fascinating if glaciation were “aborted” or poor crystallization as the glacial phase would then be considered as a composite of liquid and nanocrystals, instead of a second liquid phase. However, Kurita and Tanaka [43] contended that the glacial phase was a new liquid phase created by glaciation, and the nanocrystals were merely by-products. On one hand, when the TPP liquid was annealed at a higher temperature, such as 220 K, it underwent a nucleation-growth (NG) type LLT that was frequently accompanied by nanocrystalline by-products; on the other hand, when it was annealed at a lower temperature, such as 215 K, it underwent a spinodal-decomposition (SD) type LLT that made the corresponding glacial phase purely amorphous [43,44]. A pure sample of the glacial phase being fully amorphous lent LLT substantial support. An explanation of the concepts of NG and SD here is necessary. NG and SD are two mechanisms of phase transformation involved in a pair of partially miscible liquids, that is, the liquids are not completely mixed. When the second derivative of the free energy of mixing (ΔG″mix) is positive, NG occurred; when ΔG″mix is negative, SD happened [45]. Usually, there is no thermodynamic barrier to phase separation for compositions inside the spinodal since a homogenous solution is unstable against fluctuations in density or composition. The term SD in this context, on the contrary, refers to structural alterations rather than compositional differences because TPP, being a single-component molecular liquid, lacks phase separation. In place of the order-parameter density, which was often employed for gas-to-liquid transition, Tanaka et al. [44] established a new order-parameter, S, referring to the volume fraction of locally favored clusters in the liquid, to represent the structural changes between the two liquids of TPP. They argued that even though the density of the glacial phase was 1.288 g cm−3 at 218 K, which was 2.5% higher than the 1.256 g cm−3 of the original liquid and 0.4% lower than the 1.293 g cm−3 of the crystal [41], it was unlikely that the small density change would correspond to the big enthalpy change of glaciation (about 7 kJ mol−1 [28]). On the other hand, the volume fraction of locally favored clusters could increase by the liquid particles cooperative motions at low temperatures, resulting in an increase of S. As a result, the glaciation was likely a transition involving an increment of the volume fraction of locally-favored clusters, and hence better described as a transition from low S to high S states. For NG-type LLT, S changed discontinuously, and for SD-type LLT, S evolved continuously [33,43,44].

Comprehending the glaciation of metallic liquids should utilize the studies of the LLT and glacial phase of TPP stated before. First of all, since the glaciation temperature is lower than the nose temperature of crystallization, i.e., a condition that nucleation of crystals predominates, nanocrystals may be accessories to glaciation. Therefore, a structural analysis that is only partially sensitive to nanocrystal detection may not actually reveal the nature of glaciation. Second, whereas phase separation might not be a problem for TPP made of a single-component molecule, it might be a problem for multi-component alloys, necessitating compositional checking.

First-order exothermic transitions in metallic glasses

The understanding of the calorimetry behavior of MG is important for distinguishing various exothermic transitions. While some exothermic peaks on the calorimetry heating curves of MGs are indicators of glaciation [1–4], other exothermic peaks having different origins may show up and need to be classified. Despite the fact that other techniques, such as X-ray diffraction, are useful in resolving the origins, calorimetry curves may contain hints, particularly on the peak temperature and peak area of the exothermic peaks, which are helpful for preliminary screening. A comparison based on the calorimetry curves of different exothermic events is given in this section.

Principal crystallization (l-to-x)

Under the condition of undercooling, i.e., at temperatures below the melting point (Tm), the liquids have a tendency to crystallize. This liquid-to-crystal (l-to-x) transformation is known as principal crystallization, often manifested as a sharp exothermic peak, defined as main exo in this context, on the calorimetry curve [46]. Figure 3A provides a typical illustration of principal crystallization. The beginning of crystallization, however, requires an incubation period that depends on the undercooling temperature, which means that crystallization is also constrained by kinetic parameters like cooling rate [47,48]. Rapid cooling of the melts down to temperatures below Tg results in the formation of MGs for some alloys. On the calorimetry heating curve scanned at a modest heating-rate, e.g., at 20 K min−1, the MGs undergo a glass transition, which is represented by a specific-heat step on the calorimetry curve, entering a supercooled-liquid state manifested as a plateau, before crystallization that is reflected by a sharp main exo with an onset temperature called the crystallization temperature (Tx), occasionally followed by several exothermic peaks. The thermal-stability range of supercooled liquid, often defined as ΔTx-g = Tx−Tg, is an evaluation of glass forming ability in avoiding crystallization, and a large ΔTx-g is necessary for thermally plastic forming of MGs [49].

thumbnail Figure 3

Calorimetry heating curves of various metallic glasses or amorphous alloys. Primary exo (triangles) and main exo (circles) are shown on samples undergone (A) principal crystallization [46], (B) phase separation [50], (C) amorphous-to-quasicrystal (a-to-q) quasicrystallization [51], (D) liquid-to-quasicrystal (l-to-q) quasicrystallization [52], (E) short-range ordering [53] and (F) glaciation [3].

Although the principal crystallization event is often indicated by a sharp main exo in many MGs, multiple exothermic peaks have been seen in many other MGs, e.g., off-eutectic metallic liquids have a tendency of precipitation, that is, to nucleate crystalline precipitates out of the undercooled liquids. The primary crystallization representing precipitation (x1) is shown by the first exothermic peak (or primary exo) on the calorimetry curve, whereas the principal crystallization (x2) is indicated by the second exothermic peak or the main exo. The crystallites formed during the primary crystallization may work as the heterogeneous nuclei of the principal crystallization, rendering these two exothermic peaks overlapped. However, the remaining liquid after primary crystallization could be metastable with the existence of the crystalline precipitates, leaving the two exothermic peaks separated (Figure 3B) [50–53]. The separation of the exothermic peaks allows for an easy distinction of their origins. An “up-quench” approach [54] enables the preservation of the modified structure from the primary crystallization, which involves heating the sample to the end or peak temperature of the primary exo (Te and Tp) and then rapidly cooling the sample back to room temperature. Energy dispersive spectroscopy (EDS) and X-ray or electron diffraction can be used to determine the compositions and microscopic structures of the up-quenched sample, respectively.

Primary crystallization (l-to-x1/x2)

For alloys comprising one pair of the elements with a positive enthalpy of mixing, liquid-phase separation is a potential outcome [13]. The phase diagram displays a miscibility gap that identifies the temperature at which a particular mixture begins to decompose [45]. The miscibility gap can be found in either supercooled liquids or metallic melts. Phase-separated glass can be created by vitrifying the phase-separated liquid structure [13]. At least two exothermic peaks may be seen on the calorimetry heating curve of the phase-separated MG, which signify the crystallization of one liquid and another, respectively.

Quasicrystallization (a-to-q or l-to-q)

Other than crystallization, another example of exothermic peaks on the calorimetry curves is quasicrystallization. Due to the absence of translational order and the presence of icosahedral order, quasicrystals are not technically crystals [55]. Al86Mn14 is the first ever-reported quasicrystalline composition [56,57]. Through rapid quenching the metallic melts, the Al86Mn14 melt-spun ribbon displays remarkable quasicrystalline peaks in its X-ray diffraction pattern. On the other hand, heating metallic glasses or amorphous alloys can trigger quasicrystallization. While the term “glassy” highlights both an amorphous structure and the presence of a glass transition, the term “amorphous” only stresses that the alloys have a halo structure without Bragg crystalline peaks on the diffraction pattern [58]. For instance, a deposited Al83Mn17 thin film formed by tiny quasicrystalline grains exhibits an amorphous halo under X-ray diffraction [59]. The lack of a glass-transition signal on the calorimetry heating curve suggests that the initial substance is amorphous prior to quasicrystallization. Additionally, the heating curve for the amorphous alloys displays an exothermic peak with small peak-area covering a wide temperature range, representing quasicrystallization, before the onset of a sharp and large exothermic peak (Figure 3C). The quasicrystallization peak appears asymmetrical with the leading edge of the peak being steeper than the trailing edge, which yields a typical calorimetry signature of a grain-growth type quasicrystallization [51]. Similar calorimetry curves are evident in other thin-film-deposited amorphous alloys, particularly for the Al-based compositions [59–73].

The liquid-to-quasicrystal transition (l-to-q) is distinguished from the a-to-q transition by the glass-transition signal on the calorimetry heating curve (Figure 3). In contrast to the grain-growth type quasicrystallization of the a-to-q transition, the l-to-q transition goes through a nucleation and growth type quasicrystallization during isothermal annealing [74,75]. The Johnson-Mehl-Avrami analysis [76] gives the volume fraction (xf) of material transformed in an isothermal nucleation-and-growth process as xf = 1 – exp (–Ktn), where K incorporates the rates of nucleation and growth, and the Avrami exponent n depends on the nucleation mechanism and the growth morphology: an n in the range of 3–4 implies that the quasicrystallization is in nucleation-and-growth kinetics [52,77–79]. Having a sharp peak-shape and a large peak-area comparable to that of the main exo, the exothermic peak occurs immediately after Tg corresponding to a l-to-q transition (Figure 3D). This corresponding structural origin is once more investigated by firstly creating a sample using an up-quench method and then performing structural investigations on it. The X-ray diffraction pattern of these samples exhibits multiple peaks with large peak width [80]; bright-field high-resolution transmission electron microscopy (TEM) images exhibit distinct dark-and-white contrasts of the 5–50 nm in diameter nanoquasicrystals [61,78,81–86]; selective area electron diffraction reveals the five-order, three-order, and two-order symmetries of these nanograins [87]. All of these data point to the samples being quasicrystals.

In addition to the heating approach [88–90], the quasicrystals can also be made by annealing MGs for a period of time at or close to, mostly the onset temperature (To) of the primary exo [9,12,74,75,77,79,81,83, 86,90–116]. If the onset temperature of the main crystallization peak of the annealed sample stays unchanged, then the presence of quasicrystals has no impact on crystallization. The size of the resulting quasicrystal grains after hours of annealing at To is in the magnitude of 10 nm [61,78,81–86], indicating a sluggish kinetics of quasicrystallization. Most compositional investigations have found no differences in composition between glass and quasicrystal nanograins [60,63,68,112], except when quasicrystal grains reach a certain size, or the volume percentage of quasicrystals in the material surpasses 35% [74,98].

Short-range ordering (l1-to-l2)

In 1976, Chen and colleagues [117] investigated how the metalloid element phosphor affected the capacity of (Pd0.5Ni0.5)1−xPx (x = 17–25 in at.% hereinafter) MGs to produce glass. The MG at x = 20 has typical calorimetric behavior, similar to that of good glass formers with large supercooled liquid region. In contrast, a tiny exothermic peak appears before the main crystallization peak when x is lowered to 17–19 (Figure 3E). Two specific-heat steps that are seen in the heating curve during this time are eliminated by heating after the terminal temperature of the exothermic peak. According to Chen [117], the two stages are glass transitions of the two phase-separated liquids, and the minor exothermic peak is due to the liquid-phase separation. Phase-separation argument is supported by a number of articles [118–121] but refuted by others [53,112]. The second step of the specific heat (Cp) on the calorimetry heating curve is later discovered to be an endothermic peak, contrary to what is initially believed to be the glass transition of a second glass [1].

The Pd-Ni-P MG series underwent structural investigations after the first research [117], which focused solely on calorimetry. Ex-situ TEM and XRD tests are performed on the transformed samples that have been preheated to the Te and then cooled to room temperature. Despite that connected patterns in the bright-field TEM pictures of such samples are reported, it is soon discovered that they are artifacts of sample processing [122,123]. According to in-situ high-energy X-ray diffraction, no discernible crystalline or quasicrystalline peaks are seen at the exothermic peak [1,2], indicating a purely amorphous nature of the resultant sample. However, a sudden decrease of the peak width of the first diffraction halo is found at the exothermic peak [2], pointing to the possibility of short-range ordering.

In terms of distinguishing phase transformation from phase separation, the phrase “short-range ordering” may sound unclear. Structural and chemical short-range orderings are two different categories for short-range ordering. The former speaks about effective atomic packing, whilst the latter assesses the bonding between atomic species [124]. Unfortunately, the X-ray scattering data are insufficient for clarification because narrowing of the first XRD halo can result from either structural or chemical short-range ordering. In fact, MG compositions that are said to have phase separation have a similarity: each of these MG compositions has at least one pair of alloying elements with negative heat of mixing [13], indicating chemical ordering. However, because effective packing based on atomic radius of the constituent elements likely involves modification of the chemical species at the short range, one could also consider chemical short-range ordering as a natural consequence of structural short-range ordering induced by, for example, an LLT. Therefore, the essential query about the concept is: should phase separation be considered the cause or consequence of short-range ordering? This question is challenging to address, due to the tiny heat release of the primary exo. A glass with the chemically-different inhomogeneities taken a small volumetric percentage as suggested by the tiny heat release in the phase-separation scenario leads to a weak glass-transition signal that is uneasy to be detected by standard DSC. An MG with a primary exo whose area is greater than that considered to be short-range ordering is necessary for the answer.

Formation of non-glassy mesophases (l-to-m)

On metallic melts that are rapidly quenched, mesophases are frequently recorded [125,126]. These mesophases usually have a potential energy that lies between glass and crystal, making them thermodynamically metastable. An et al. [127–129] found a first-order transition in addition to crystallization on cooling in the molecular dynamics (MD) simulations of Ag and Ag-Cu liquids, resulting in new glassy states. This transition begins in a homogeneous supercooled liquid phase (L-phase) and ends in a heterogeneous mesophase (G-phase). The short-range order is more prominent in G-phase than L-phase, despite the fact that the long-range order is absent in G-phase. Additionally, the G-phase develops an elastic stiffness with a persistent and finite shear modulus, demonstrating the solidity.

On the nature of the G-phase, however, there are modest disagreements. When annealing a Cu50Zr50 specimen in the lower-temperature regime below the nose temperature of crystallization in its TTT diagram using MD simulation, during which an abrupt drop of the energy per atom (similar to that of G-phase Ag) is observed, amorphous/crystalline nano-composite microstructures with strong interface stability is discovered [130]. Unlike L-phase Cu, G-phase Cu is found lack of glass transition signals in MD simulation [58]. Furthermore, it is shown that the radial distribution function of G-phase Cu at long atomic distances exhibited weak oscillations rather than no characteristics, implicating a modest ordering at long atomic range. Moreover, five-fold twining structures consisting of face-center-cubic or hexagonal-cubic-packed Cu atoms are discovered. At least for Cu50Zr50 and pure Cu, G-phase is not a real glass but a mesophase.

There is no claim that all mesophases must not be glassy, despite some counter-evidence pointing to alternative explanations. However, in order for the initiation of the glass transition and the elimination of weak structural oscillations at long atomic range, these glassy mesophases, or the MGGs, should only be present in a limited range of alloying compositions, we think. This is due to the fact that MGG has a stronger short-range ordering than its original MG, which ought to show in the constrained choices of constituents. Optimal space-filling of the atomic clusters is unlikely a universal solution to all alloy compositions. How glass transition is made achievable is then a problem of which composition has the smallest scale of the short-range ordering. Following this point, new glassy mesophases depend on how much the structural ordering can be constrained in the short-range.

Liquid-to-liquid transition (l1-to-l2) or glaciation

In the supercooled liquid of MG-forming compositions, LLTs or glaciations have recently been reported. The key characteristic of the calorimetry curve is an enlarged peak-area of the primary exo (Figure 3F), also known as the anomalous exothermic peak (AEP). In Pd41.25Ni41.25P17.5, the released heat of its AEP is 0.75 kJ mol−1, about 10.5% of its heat of crystallization [1]. In Pd42.5Ni42.5P15, the released heat of AEP is 0.9–1.1 kJ mol−1 [2,3], and the reversed LLT is demonstrated on fast heating, with the absorbed heat comparable to the released heat of AEP [131]. In La32.5Ce32.5Ni20Al13Co2, the released heat of AEP is 1.33 kJ mol−1, about 35% of the total heat of crystallization [3]. In a high-entropy Nb20Ni20Zr20Ti20Co20 MG, the released heat of AEP is 1.65 kJ mol−1, roughly 58%1) of its total heat of crystallization [4].

The structural evidence for glaciation seems more plausible with an increase in the heat change of AEP, denoting a larger volumetric amount of phase change. When ΔHAEP is around 10% of the ΔHX, peak sharpening is only noticed on the second peak of structural factor S(q), and intensity changes of the pair-correlation function g(r) peaks are seen on the 5th rather than the 1st atomic shell. When ΔHAEP reached 30% or more of the ΔHX, peak sharpening and peak-position shift are both discovered on the 1stS(q) peak, along with the peak splitting of the second g(r) peak. These facts imply that the structural modifications brought on by glaciation are not limited to the medium-range [1], but involved the short-range below 5 Å [2–4], too.

Glaciation, kinetics and properties of MGG

In addition to the traditional differential scanning calorimetry methods, there are other methods to distinguish glaciation from, in particular, nanocrystalization or quasicrystallization and phase separation (Figure 4). This section also discusses the reversibility of glaciation and the transition kinetics of glaciation, including nucleation-growth and spinodal decomposition. The mechanical performance, electrical properties and thermal stability of MGG are also compared with those of its forming MG.

thumbnail Figure 4

The procedures for identifying a primary exo. The abbreviations are explained in the Glossary.

Glaciation vs. nanocrystallization or quasicrystallization

High-resolution structural analysis techniques have been used to look at the structural change caused by glaciation or the structure of MGG. Under high-energy synchrotron X-ray scattering, in-situ studies are carried out on Pd-, La-, and Ni-based MGs that go through glaciation upon heating [1–4,131]. The absence of crystal-indicating Bragg reflections until the start of the main exo emphasizes the amorphous nature of the primary exo implying glaciation. Only amorphous halos are seen in MGG samples under selected-area electron diffraction and synchrotron XRD at room temperature [3]. MGGs lack crystallinities or quasicrystallinities, according to nanobeam electron diffraction [3]. When using high-resolution TEM at an imaging mode, periodic or quasiperiodic atomic configurations are not found [2–4]. Since the large heat-release of the primary exo should correspond to a large volume fraction of nanocrystals or quasicrystals, the absence of their signals under these high-resolution structural-analysis techniques rules out the possibilities of nanocrystallization and quasicrystallization.

Another indicator that distinguishes glaciation from nanocrystallization and quasicrystallization is the signal of glass transition on calorimetry. Glaciation is supported when Tg is detected from the heating curve of the transformed sample (Figure 5A). Tg is largely increased after glaciation, typically by 18–75 K if measured at 10–20 K min−1 in DSC [2–4]. The shift in Tg by glaciation is much larger than what is anticipated for thermal annealing [132], indicating a major change in the glassy structure. Information about the residual glassy structure in the sample is contained in the height change of Cp during glass transition (ΔCp). For example, metallic liquids have a Cp 1.5R bigger than that of metallic solids [133]. If a drop in the amount of ΔCp is seen for the transformed sample, it is likely that the specimen contains nanocrystalline or quasicrystalline solids [134]. If ΔCp of the transformed sample stays identical, glaciation may be the dominant mechanism.

thumbnail Figure 5

Calorimetry responses in glaciation [3,131]. (A) A primary exo appears after the glass transition on heating, resembling glaciation (red curve); upon heating-quenching by the end of the primary exo, the MGG shows increased glass transition temperature and no changes in crystallization exothermic peaks. (B) Reversal of glaciation is demonstrated by firstly heating the MG up to the end of the primary exo (green curve), quenching and reheating the MGG up to the end of the endothermic peak (red curve). Further quenching and reheating show collapse in the heating curve (blue curve), indicating that MGG is fully transformed back to MG. (C) Reversible specific-heat (Cp, rev.) change reveals two glass transitions and two separated glass transition temperatures (Tg1 and Tg2), indicating nucleation-growth kinetics. (D) Cp, rev. change reveals two glass transitions yet one glass transition temperature (Tgs) shifting continuously with the annealing time, implying spinodal-decomposition kinetics. (E) For NG-type kinetics, two endothermic peaks emerge simultaneously in annealing. (F) For SD-type kinetics, the second endothermic peak appears only after the intensity of the first endothermic peak is saturated.

Glaciation vs. phase separation

Phase separation is yet another reason against glaciation. Energy-dispersive spectroscopy (EDS) mapping, 3D reconstruction atomic probe tomography (APT) and small-angle x-ray or neutron scattering (SAXS or SANS) have been frequently used for compositional analysis. For the La32.5Ce32.5Ni20Al13Co2 MGG, which was tested by EDS within a detection region of 20 nm×20 nm, no chemical variation is identified at a length scale above 1 nm [3]. For the Pd42.5Ni42.5P15 MGG, no obvious chemical segregation is detected by SAXS and SANS [2]. For both Pd42.5Ni42.5P15 and Nb20Ni20Zr20Ti20Co20 MGGs, a uniform distribution of all the constituent elements in the samples is concluded from the APT experiments [2,4]. It could be argued that phase separation below a length scale of 1 nm might be unnoticed by EDS. However, it is useless to address the chemical variation at this length scale because the MGs are chemically heterogeneous within a length scale of 2.5 nm [135]. Similarly, no compositional difference between quasicrystals and the material surrounding them can be seen at length scales smaller than 10 nm [74].

Structural analysis can quickly validate the crystallization of a separated liquid phase if a primary exo suggests it has occurred. The 1st amorphous halo would break into two halos following the exothermic event if the primary exo signals liquid-phase separation rather than crystallization [13]. Also, the lower the decomposition-temperature, the larger the composition variation, according to the “dome” shape of the miscibility gap [13]. Such structural and chemical variations would be simple to find using XRD and EDS, respectively. If not, the primary exo is probably due to glaciation.

The reversal of glaciation

Any exothermic peak, including the primary exotherm of glaciation, should have a corresponding endothermic peak on the calorimetry curve at a higher temperature. The lack of an endothermic peak on the calorimetry curve [2], which leads some to conclude that glaciation was irreversible, is actually a heating-rate (ϕh) artifact. When the sample is measured using differential scanning calorimetry (DSC) at a ϕh of 20 K min−1, the main exo is detected on heating passing the exothermic peak of glaciation; however, when the sample is measured using fast differential scanning calorimetry (FDSC) at a ϕh of 1200 K s−1, the main exo representing crystallization is postponed, while the endothermic peak reversing glaciation appears [3]. Additionally, the onset temperature of this endothermic peak (Tendo) is lower than the Tm of the sample, for example, Tendo is 50 K smaller than the Tm of La32.5Ce32.5Co25Al10 [3], indicating that this peak is not the result of melting crystals. The discovery of this endothermic peak offers a way to reverse glaciation in the FDSC. The MG has been successfully recast from MGG by rapidly heating the sample until it approached the end temperature of the endothermic peak and then rapidly quenching it (Figure 5B). The as-cast MG and the re-cast MG’s heating curves look identical, ruling out the possibility of crystallinities that cannot be eliminated until Tm.

The kinetics of MGG formation

Depending on the annealing temperature (Ta), the kinetics of glaciation for metallic liquids can be either NG or SD type [131], similar to that of TPP molecular liquid [33,34]. Glaciation of a Pd42.5Ni42.5P15 metallic liquid has been investigated using FDSC by examining the reheating curves of the sample that is repeatedly vitrified and pre-annealed at different Ta. Following the abrupt rise of Cp indicative of the glass transition, two endothermic peaks are seen, the first of which correlates with the structural relaxing of the initial MG and the second of which is predominated by the reversed glaciation of MGG. For an NG-type glaciation enabled at higher Ta, the glass-transition temperature of MG (Tg1) is separated from that of MGG (Tg2) (Figure 5C); and the first and second endothermic peaks emerge concurrently (Figure 5E). Contrarily, for an SD-type glaciation that proceeds at lower Ta, only one glass-transition temperature (Tgs), which climbs steadily with increasing annealing time (ta), is identified (Figure 5D); additionally, the second endo appeared 100 s after the first endo (Figure 5F). The glass-to-glass transition is possible by SD-type glaciation because Ta can be smaller than the conventional Tg (or Tg1 in this case) measured at 20 K min−1.

The volume fraction of MGG in the MG/MGG composite or the progress of glaciation can be determined using the area of the 2nd endo, which represents the heat absorbed by the reversal of glaciation. This makes it possible to investigate the physical characteristics of MG/MGG composites with a variety of variables, such as volume percentages of MGG and the NG- or SD-type micro-morphologies. Numerous composite materials with intriguing features, based on an MG matrix and nanocrystalline embedment, have been discovered, for example, the outstanding soft-magnetic Fe-Si-B MG/BCC-Fe nanocrystals composite [136] and the Cu-Zr-Al MG/B2 nanocrystals composite [137,138]. Phase-separated glass/glass composites have shown compressive plasticity [13]. The pure glassy structure of the MG/MGG composite, which has the same composition in two glasses, may display various mechanical properties that need to be explored.

Properties of MGG

For MGGs and their parent MGs, mechanical similarities and discrepancies coexist. The 2% elastic-strain limit of MGG is the same as MG, whereas the Young’s modulus of MGG is 7%–22% larger than that of its MG [2–4]; the plastic deformation of MGG occurs via shear banding that is identical to MG [3], but the yield strength of MGG is 18% greater than that of its MG [3]; at room temperature, the nanohardness of MGG is 30%–40% larger than that of its MG [2–4]. However, similar property changes are expected for structural relaxation of MG, too, so a comparison between glaciation and structural relaxation should be made because MG is unavoidably relaxed on heating in the calorimetry before glaciation. By structural relaxation, the increase in Young’s modulus is 10%–50% [139] and the enhancement in nanohardness is 10% [140]; the yield strength is often decreased because of nanocrystallization caused embrittlement [141]. Therefore, it appears that only the extra hardening, not stiffening, is a direct consequence of glaciation. On the other hand, the hardening effect of glaciation resembles the l-to-q type quasicrystallization. It has been found that after quasicrystallization, the mechanical strength of MG-based quasicrystals is increased by 18% [101,142]. By adjusting the volume fraction of the quasicrystals, one can change the attributes of quasicrystals. For instance, the yield strength is increased from 1.7 GPa of the as-cast to 2.4 GPa when 20%–30% of the MG is converted into quasicrystals [142].

The electrical resistivity has been reported to drop during glaciation, e.g., a 15% decrease by glaciation is found in Pd42.5Ni42.5P15 [2]. However, such a 15% decrease in electrical resistivity may not necessarily represent glaciation since similar change in the electrical resistivity is found during the glass transition of Pd40Cu30Ni10P20 [143], a composition that is not capable of glaciation. Also, the electrical resistivity of quasicrystals is significantly larger than that of its amorphous sample. For example, the room-temperature electrical resistivity of Al55Si25Mn20 is 970 μΩ cm in amorphous state and 1830 μΩ cm for quasicrystals [61]. The electrical-resistivity of MGGs matters the interpretation of their bonding nature. Covalent bonds are likely to form when electrical resistivity rises, yet metallic bonds are likely to form when electrical resistivity falls. There is a need for further measurements on this topic to provide clarification due to the limited number of studies currently available.

The MGGs were thought to have an ultrastable-glass appeal. The ultrastable glasses (both in molecular and metallic glass systems) have been created in the past using physical vapor deposition on substrates pre-heated to temperatures around the Kauzmann temperature [144–147]. The ultrastable glasses are thought to be both thermodynamically and kinetically stable since they have lower enthalpy and higher Tg than rapidly quenched glasses. MGGs are regarded as ultrastable glasses because they have an enhanced Tg as high as 48 K more than the original MG [2] and a reduced enthalpy as low as 36% the heat of crystallization [4]. MGGs are not size restricted, making them more appealing than the ultrastable thin-film MGs. A direct comparison between MGG and the ultrastable MG, however, may be deceptive since MGG is quenched from another equilibrium liquid that is distinct from the equilibrium liquid that forms MG, and so far there is no direct evidence to prove whether the ultrastable glass originated from LLT or not. Because the enthalpy reduction is achieved through glaciation rather than structural relaxation, for instance, the atomic structure of MGGs might not be well-relaxed due to the subsequent quenching; in addition, despite the fact that Tg is heavily increased, there is no hint that MGG is more resistant to sub-Tg nanocrystallization than MG [148]. In order to find out whether its enthalpy is not further reduced and whether its structure is more resistant to nanocrystallization, annealing experiments of MGGs are necessary.

Unresolved issues

The order parameter governing glaciation

The order parameter, whose change affects the ordering and symmetry of the physical system and subsequently causes phase transformation, is a fundamental premise in the phase-transformation theory. For characterizing the polymorphous transition of water and the general liquid-to-gas (l-to-g) transition, density (ρ) was used as the order parameter. However, due to the small density variations between MG and MGG, density might not be an appropriate order parameter to describe glaciation [3,131]. For instance, the density difference between MGG and MG is less than 0.3% [2,4]. It is improbable that a change in density this minor causes glaciation to release so much energy. Alternatively, Kurita et al. [33,34,43,44] proposed a new order-parameter S, which they defined as the volume fraction of locally favored clusters (LFCs) within the liquid. Glaciation was then defined as a shift in S from low to high values (Figure 6): the change in S is abrupt by nucleation-growth type glaciation, yet continuous by the spinodal-decomposition glaciation. In Pd42.5Ni42.5P15 metallic liquids, similar characteristics are reported except that the spinodal-decomposition glaciation can take place at temperatures below Tg implying a glass-to-glass transition [131].

thumbnail Figure 6

The temperature (T) vs. order parameter (S) phase diagram of the glaciation (Reproduced from ref. [131]). The two black arrows suggest the reversibility of glaciation. TBN (red and blue open circles), TSD (red and blue solid circles) represent the binodal temperature and the spinodal temperature, respectively. The critical point is marked by the black solid circle where the liquid coexistence line is ended.

Selecting S as the order-parameter to describe the glaciation of metallic liquids raises questions, especially as ρ has been widely recognized as the order parameter to describe the polymorphism of water [149]. We believe that, particularly for thick liquids with limited space for big density-change, ρ may not be an exclusive one for defining the structural state of liquids. Viscosity characterizes a liquid’s instantaneous transformation. The simplest approach to discern between two bottled liquids, both of which are assumed to be odorless and colorless, is probably to rotate the bottle. If a swirl forms, the liquid in this bottle is less viscous; if not, the liquid in that bottle is viscous. The point here is that ordering is another factor that affects viscosity [150] in addition to density. As a result, it should be possible to characterize glaciation using parameters other than ρ, as long as the ordering can be quantified.

Quantifying the ordering of liquids remains difficult. The LFCs in metallic liquids and glasses have been known to exist for decades. When compared with face-centered cubic and hexagonal close-packed clusters, the icosahedrons are the potentially most densely packed atomic clusters in atomic liquid with the lowest energy [151]. The existence of icosahedron clusters in liquids is energetically and geometrically favorable because they have a 5-fold symmetry that cannot be stretched to 3D. From MD simulations, icosahedron and non-icosahedron LFCs are reported [152–154]. Additionally, the angstrom-size electron beam diffraction provided evidence for their existence [155]. However, neither the volume fraction of the LFCs in any MGs can be determined by experimental studies, nor a first-order change in the volume fraction of any LFCs are observed by MD simulations. It remains a challenge to testify S for MGGs from both experiments and simulation.

Where to look for MGGs?

The glacial phases seem to exist in both molecular [14,15] and metallic liquids [1–4], making them appear universal in disordered systems. MGGs, however, stand apart from other glacial phases because they may be preserved at ambient conditions, and hence capable for materials engineering. Vitrification preserves the structure of the glacial liquid because the Tg of MGG is above room temperature [3]. MGGs can therefore be thought of as valuable materials convenient for applications. Due to their increased strength and hardness following glaciation, MGGs may serve as abrasive materials. A slightly safer usage of MGGs at a somewhat higher temperature than their original MGs is another benefit, thanks to the better thermal stability of MGGs. However, the compositions of MGGs so far are very limited, and a roadmap for future MGGs is needed.

The MGGs and quasicrystals are fundamentally different. In contrast to quasicrystals, MGGs undergo a glass transition exhibiting an unchanged amount of ΔCp, which is compelling evidence for glaciation [131]. However, there are some similarities between glaciation and the l-to-q type quasicrystallization, such as the calorimetric appearance of the primary exo, the amount of enthalpy released, and the extent of the hardness enhancement (Figures 3 and 4). These similarities lead us to speculate about a possible connection between glaciation and quasicrystallization.

The aforementioned criterion of quasicrystallization is based on structural evidence from diffraction or imaging, relaying on the grain size of quasicrystals. Most quasicrystalline samples investigated were pre-annealed at To (see Table 1). However, there appears to exist a lower limit of grain size, below which the quasicrystals are not detectable using current methods of structural investigation. It is also unclear what would be the smallest size of quasicrystalline grains or alternatively, how atoms are packed for a “1 nm” quasicrystal. These “invisible” quasicrystals can be produced under annealing circumstances that call for a low Ta and a short ta, but the enthalpy released, as determined by the calorimetry curves, is substantial. Are amorphous alloys or MGGs made of these “invisible” quasicrystals? The calorimetry heating curves of these partially-annealed materials may provide answers. In the absence of any glass transition, the sample would be amorphous (in analogy to the amorphous thin-film [51]); in the presence of glass transition but with a reduced ΔCp (because quasicrystals have a lower Cp than liquid), the sample would be an MG/amorphous alloy composite; and in the presence of distinct glass transition but with a ΔCp that is comparable to that of the original MG, the sample would be an MGG. In this regard, there may be a few MGGs buried in Table 1 [1–4,9,12,50–53,59–75,77,79,81–105,122,107–117,131,156–188], which were initially thought to be quasicrystals due to the fact that many structural analyses were done on the well-annealed, waiting for a relook of their calorimetry heating curves for the transformed samples. Thus, future research on the compositions listed under the column of quasicrystallization in Table 1 is necessary.

Table 1

Summary on the origin of primary exothermic peaks on the calorimetry curve. To, Tp and Te represent the onset, peak and end temperatures of the primary exo, respectively. Amorphous thin-film, quasicrystals, liquids and glasses are represented by a, q, l and g; l1’ and l2’ stand for phase-separated liquids; l1 and l2 denote phase-changed liquids

Short-range order engineering?

What structural change follows the first-order LLT is the central query of glaciation. Liquids are long-range disordered in atomic configuration, in contrast to the long-range ordered solids where phase transformations are taken from one definite crystal form to another. Phase transformations in liquids must be accompanied by short-range ordering (SRO) as there are no distinguishments for structural changes in a disordered structure. Efficient atomic packing and favored chemical bonding have long been acknowledged to describe the SROs of metals. Unfortunately, the present theoretical explanations are not adequate to define two clearly distinct SROs of the same alloy composition, and the available experimental approaches are unable to shed any light on their differences [7,53]. On the likely switch of SRO from MG to MGG, however, we could make a reasonable predication. Firstly, because MGG contains a higher volume proportion of LFCs, or high S, the correlation length of structural ordering is probably increased, making medium-range ordering achievable. Secondly, the transition from metallic to covalent bonding, which likely accounts for the enormous enthalpy release of glaciation, may occur in the short range. Thirdly, the SRO in MGG may not always have the same chemical constituents as the SRO in MG, allowing for atomic switching from short to long ranges to enable LLT.

Our knowledge on the SRO may lead us to an intriguing application: by designing the SRO, we might be able to adjust the properties of liquids and glasses. Viscosity, which determines the rheology of liquids, is the primary factor affecting liquid properties. Utilizing a change in liquid viscosity to harvest tensile ductility is an example, where the viscosity is increased by glaciation [189]. Strong-to-fragile transition in the liquid is also brought on by changing the fragility index, which describes how viscosity changes with temperature [190]. Glaciation changes the mechanical characteristics of glasses, reaching an extent larger than that achieved by annealing, while maintaining the amorphous structure and a large elastic-strain limit. Thermal stability will be enhanced because of an increased Tg and a reduced enthalpy. The composite materials made of MG and MGG using the same composition provide a range of properties determined by the volume fraction and transformation kinetics (nucleation-growth and spinodal-decomposition). The best technique to accomplish SRO engineering today is to choose the ideal alloy composition for glaciation and apply the proper thermal processing. New tactics of SRO engineering, like thermo-mechanical processing [191], may provide interesting outcomes.

Conclusions

This paper reviews the anomalous exothermic peak reported recently in metallic-glass forming liquids and discusses its link to the formation of metallic glacial glasses. The similarity of the formation kinetics for metallic glacial glass and the glacial phase of the triphenyl-phosphite molecular liquid provides a general understanding of the nature of glaciation. The calorimetry curves that are typical of principal crystallization, primary crystallization, quasicrystallization, short-range ordering, meso-phase formation and liquid-to-liquid transition are compared, highlighting their difference in the primary exothermic peak. Eliminating nanocrystals, quasicrystals, and amorphous mesophases, as well as excluding phase separation by multiple experimental methods, are necessary for the identification of metallic glacial glasses. The intriguing properties and prospective uses of metallic glacial glasses are described, and a road map for new metallic-glacial-glass compositions is outlined.

1)

The 58% is calculated by 1.65 kJ mol−1 dividing the sum of the enthalpy release by the two exothermic crystallization peaks (1.27 kJ mol−1 and 1.59 kJ mol−1) [4].

Funding

This work was supported by the National Natural Science Foundation of China (51971239 and 92263103), the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB30000000), the National Key Research and Development Plan (2018YFA0703603), and the Natural Science Foundation of Guangdong Province (2019B030302010).

Author contributions

All authors contributed to the research, writing and reviewing of the paper.

Conflict of interest

The authors declare no conflict of interest.

References

All Tables

Table 1

Summary on the origin of primary exothermic peaks on the calorimetry curve. To, Tp and Te represent the onset, peak and end temperatures of the primary exo, respectively. Amorphous thin-film, quasicrystals, liquids and glasses are represented by a, q, l and g; l1’ and l2’ stand for phase-separated liquids; l1 and l2 denote phase-changed liquids

In the text

All Figures

thumbnail Figure 1

Metallic glacial glass (MGG) formation (Reproduced from ref. [3]). Upon heating the metallic glass (MG) passing the glass transition temperature (Tg), a primary exothermic peak representing glaciation with a peak temperature (Tp) is detected, which is followed by the onsets of crystallization (at Tx) and melting (at Tm). By summarizing the characteristic temperatures with the heating rates, a continuous-heating-transformation diagram showing MG, MGG, crystal and supercooled liquid (SCL) regions is constructed. The green open symbol represents the reversal of glaciation, i.e., the transition from MGG-forming liquid to MG-forming liquid.

In the text
thumbnail Figure 2

A schematic temperature-time-transformation (TTT) diagram of triphenyl phosphite (TPP). Crystallization (blue curve) occurs at higher annealing temperature (Ta) and shorter annealing time (ta), while glaciation (red curve) occurs at lower Ta and longer ta.

In the text
thumbnail Figure 3

Calorimetry heating curves of various metallic glasses or amorphous alloys. Primary exo (triangles) and main exo (circles) are shown on samples undergone (A) principal crystallization [46], (B) phase separation [50], (C) amorphous-to-quasicrystal (a-to-q) quasicrystallization [51], (D) liquid-to-quasicrystal (l-to-q) quasicrystallization [52], (E) short-range ordering [53] and (F) glaciation [3].

In the text
thumbnail Figure 4

The procedures for identifying a primary exo. The abbreviations are explained in the Glossary.

In the text
thumbnail Figure 5

Calorimetry responses in glaciation [3,131]. (A) A primary exo appears after the glass transition on heating, resembling glaciation (red curve); upon heating-quenching by the end of the primary exo, the MGG shows increased glass transition temperature and no changes in crystallization exothermic peaks. (B) Reversal of glaciation is demonstrated by firstly heating the MG up to the end of the primary exo (green curve), quenching and reheating the MGG up to the end of the endothermic peak (red curve). Further quenching and reheating show collapse in the heating curve (blue curve), indicating that MGG is fully transformed back to MG. (C) Reversible specific-heat (Cp, rev.) change reveals two glass transitions and two separated glass transition temperatures (Tg1 and Tg2), indicating nucleation-growth kinetics. (D) Cp, rev. change reveals two glass transitions yet one glass transition temperature (Tgs) shifting continuously with the annealing time, implying spinodal-decomposition kinetics. (E) For NG-type kinetics, two endothermic peaks emerge simultaneously in annealing. (F) For SD-type kinetics, the second endothermic peak appears only after the intensity of the first endothermic peak is saturated.

In the text
thumbnail Figure 6

The temperature (T) vs. order parameter (S) phase diagram of the glaciation (Reproduced from ref. [131]). The two black arrows suggest the reversibility of glaciation. TBN (red and blue open circles), TSD (red and blue solid circles) represent the binodal temperature and the spinodal temperature, respectively. The critical point is marked by the black solid circle where the liquid coexistence line is ended.

In the text

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