Thermodynamic response functions in Group IV, V, and VI liquid alloys

Density and thermal expansivity anomalies

Three elements and many Group IV, V, and VI alloys exhibit temperatures of maximum density (T _MD) in their liquid states, an anomaly often mistakenly thought to be unique to water. In Figure 2,^{Reference Hosokawa, Sakaguchi and Tamura19–Reference Betts, Bienenstock, Keating and deNeufville26} liquid densities are plotted against T _m-scaled temperature for the elements and several alloys. The elements and alloys exhibiting a density (ρ) maximum include Te (direct measurement), Si and Ge (by computer simulation extension of experimental data), GeTe₁₂, GeTe₆ (i.e., Ge₁₅Te₈₅), As₂Se₃, As₂Te₃, and Ga₂Te₃ as well as In₂Te₃²⁷ and Te_x-Se_1−x²⁸ (not shown). The T _MD is ∼0.9 T _m for tellurium. Liquid silicon undergoes a first-order liquid-liquid transition during supercooling seen as a sharp density decrease at around 0.65 T _m in computer simulations.^{Reference Sastry and Angell29} Most observable density maxima are above T _m (i.e., T _MD > T _m). Those with compositions typical of PCMs such as GeTe, Sb₂Te₃, and Ge₁Sb₂Te₄, Ge₂Sb₂Te₅ on the Yamada line, do not display a density maximum above T _m.^{Reference Otjacques, Raty, Gaspard, Tsuchiya and Bichara20} But when we include the measured density of the glassy phase obtained by sputtering or hyperquenching (i.e., excessively fast cooling) and compare with the behavior of nearby compositions that do exhibit density maxima, it is highly plausible to interpolate the curves for temperature-dependence of density with maxima.

Figure 2.

Liquid densities versus melting point (T _m)-scaled temperature for Group IV, V, and VI elements and their alloys. The low-temperature data points are for glassy states, and dashed lines are interpolations of the density traces in the supercooled liquid regime based on evidence from the cases of As₂Te₃² and As₂Se₃¹⁹ that the density follows a negative slope with respect to temperature below the temperature of maximum density, T _MD. Data for GeTe, Sb₂Te₃, and Ge₁Sb₂Te₄, Ge₂Sb₂Te₅ are from Reference Reference Otjacques, Raty, Gaspard, Tsuchiya and Bichara20. Data for Te, GeTe₁₂, GeTe₆ (Ge₁₅Te₈₅) are from Reference Reference Tsuchiya21. For the glassy states, Ge₁Sb₂Te₄: ρ = 5.88 g/cm³,^{Reference Steimer, Coulet, Welnic, Dieker, Detemple, Bichara, Beuneu, Gaspard and Wuttig22} Ge₂Sb₂Te₅: ρ = 5.88g/cm³,^{Reference Njoroge, Wöltgens and Wuttig23} GeTe: ρ = 5.6 g/cm³,^{Reference Chopra and Bahl24} As₂Te₃: ρ = 5.53g/cm³,^{Reference Quinn25} and Ge₁₅Te₈₅: ρ of Ge₁₇Te₈₃ is available and assumed to be approximately the same 5.53 g/cm³.^{Reference Betts, Bienenstock, Keating and deNeufville26}

Note that between the density maximum and the density minimum, there lies an extremum in thermal expansivity, α_p = V ^–1(∂V/∂T), where V is the volume. The temperature of the peak in α_p corresponds to the peak in the heat capacity (see next section). It also corresponds closely with temperature of the closing of the bandgap (see Figure 3^{Reference Hosokawa, Sakaguchi and Tamura19,Reference Hosokawa, Yamada and Tamura28} ), and other properties that relate to a M-SC. It is obvious that the width of the α_p(T) peak will be correlated with the sharpness of the maximum in ρ(T).

Figure 3.

The metal-semiconductor transition (M-SC). (a) Upper plot: The C _p maximum is ∼80 K above the liquidus T _L in As₂Te₃. Dotted line indicates the onset of melting (T _m^onset). T _x is the crystallization temperature during cooling. Lower plot: the density maximum and minimum of liquid As₂Te₃.^{Reference Tveryanovich, Ushakov and Tverjanovich2} (b) Upper: Densities of liquid As₂Se₃ at various mild pressures. Lower: Optical bandgap (E _g) of liquid As₂Se₃ closes at ∼1280 K, and that of As₂S₃ would close at a higher temperature.^{Reference Hosokawa, Sakaguchi and Tamura19,Reference Hosokawa, Yamada and Tamura28} (c) Electronic conductivity (σ) as a function of inverse temperature for (As₂Se₃)_1–x(As₂Te₃)_x alloys. σ drops from a plateau of ∼10³ S cm^–1 through a M-SC. The temperature at which the M-SC occurs (T _M-SC) corresponds to the maximum in apparent activation energy (E _a) of σ. The arrow indicates T _M-SC of liquid As₂Te₃.^{Reference Nagels, Rotti and Vikhrov30,Reference Alekseev, Andreev and Sadovskii32}

Metal-semiconductor transition versus metallicity in PCMs

The maxima in thermodynamic response functions are, in each case, accompanied by conductivity transitions in Group IV, V, and VI alloys in which conductivities σ decrease from almost temperature-independent values slightly above σ = 1000 S cm^–1 (Mott’s “minimum metallic conductivity”), to the lower and temperature-dependent values characteristic of semiconductors^{Reference Alekseev, Andreev and Sadovskii32} (Figure 3c). The transition, designated M-SC, is also evident in the closing of the optical bandgap E _g as shown for the case of As₂Se₃ liquid^{Reference Hosokawa, Sakaguchi, Hiasa and Tamura33} (Figure 3b).

Considering the series As₂S₃, As₂Se₃, and As₂Te₃, in Figure 3, it is clear that the M-SC transition moves to lower temperatures as the chalcogenide becomes more metallic, and the same is true for the series Sb₂S₃, Sb₂Se₃, and Sb₂Te₃ (the latter of which actually melts to the metallic phase, see Figure 8 of Reference Reference Wei, Coleman, Lucas and Angell11). Finally, the trend holds for the binary solutions Se-Te.^{Reference Kakinuma and Ohno34} In an attempt to quantify this trend, we introduce a new parameter, the “metallicity,” which we define as the inverse of the composition-averaged electronegativity of the alloy, according to:

$${M_P} = {1 / {\left( {{x_1} \cdot {\chi _{P1}} + {x_2} \cdot {\chi _{P2}} + .. + {x_i} \cdot {\chi _{Pi}}} \right)}},$$

where 0 < x _i < 1 is the atomic fraction of the alloy component i, and χ_Pi is available for each element in any Table of revised Pauling electronegativities^{Reference Allred35} (hence, the subscript P).

In Figure 4a,^{Reference Kakinuma, Ohno and Suzuki36–Reference Bhat, Molinero, Soignard, Solomon, Sastry, Yarger and Angell38} we use this parameter to rationalize the variation of the temperature of the M-SCs when scaled by the alloy melting points (or liquidus for Te-Se), referred to as the reduced M-SC temperature:

$${t_{M - SC}} &#x003D; {{{T_{M - SC}}} / {{T_{m}}}}.$$

Figure 4.

Correlations of T _M-SC/T _m (= t _M-SC) and T _M-SC values with the metallicity parameter, M _P for various alloys. (a) The t _M-SC of Group IV, V, and VI alloys (red dots) and Group III, VI alloys (green diamonds). The phase-change material (PCM) compositions on the Yamada line, and (Ag, In)-doped Sb₂Te (AIST) and Ge₁₅Sb₈₅ have metallicity ranging from M _P = 0.48–0.49, marked by the shadowed pink area, which corresponds to t _M-SC < 1.0. (b) The absolute T _M-SC relation to metallicity M _P. This shows a V-shape with respect to M _P with a minimum zone (shadowed pink zone), where all known PCMs are located. Data sources: As₂Se₃ and As₂S₃;^{Reference Hosokawa, Sakaguchi, Hiasa and Tamura33} T _M-SC of As₂S₃ is an extrapolation to optical bandgap closing; Te-Se,^{Reference Kakinuma and Ohno34} SbSe,^{Reference Kakinuma, Ohno and Suzuki36} Ge₄₅As₃₀Se₂₅.³⁷ The T _M-SC is assigned to the temperature of maximum slope of density curve ∼750°C = 1023 K. As₂Te₃,^{Reference Tveryanovich, Ushakov and Tverjanovich2} Te,^{Reference Quinn25} Ge₁₅Te₈₅,^{Reference Wei, Lucas and Angell10,Reference Tsuchiya21} In-Te,^{Reference Thurn and Ruska27} Ge,^{Reference Bhat, Molinero, Soignard, Solomon, Sastry, Yarger and Angell38} Si,^{Reference Sastry and Angell29} AIST and Ge₁₅Sb₈₅.^{Reference Zalden, Quirin, Schumacher, Siegel, Wei, Koc, Nicoul, Trigo, Andreasson, Enquist, Shu, Pardini, Chollet, Zhu, Lemke, Ronneberger, Larsson, Lindenberg, Fischer, Hau-Riege, Reis, Mazzarello, Wuttig and Sokolowski-Tinten39}

For low M _P chalcogenides such as As₂Se₃ and Te₄₀Se₆₀, the t _M-SC is larger than 1.0. With increasing metallicity, t _M-SC decreases, approaching the value of 1.0 around M _P = 0.47–0.48. For any IV, V, and VI alloy with M _P > 0.48, t _M-SC, the M-SC transition falls below T _m. While the correlation is clear for Group IV, V, and VI alloys, the Group III, VI alloys (e.g., In-Te, green diamonds) are displaced, suggesting that a volume scaling might also be a needed addition.

For PCM compositions on the Yamada line (e.g., Ge₁Sb₂Te₄ and Ge₂Sb₂Te₅), M _P lies between 0.481 and 0.487 (pink shadow area), and the Figure 4 correlation line suggests their M-SCs, should all be “submerged” below T _m (t _M-SC < 1.0), as our earlier study suggested.^{Reference Wei, Coleman, Lucas and Angell11} Note that the PCM compositions Ge₁₅Sb₈₅ and (Ag, In-doped) Sb₂Te are not on the Yamada line, but they have similar values of M _P, namely in the range 0.48–0.49.^{Reference Zalden, Quirin, Schumacher, Siegel, Wei, Koc, Nicoul, Trigo, Andreasson, Enquist, Shu, Pardini, Chollet, Zhu, Lemke, Ronneberger, Larsson, Lindenberg, Fischer, Hau-Riege, Reis, Mazzarello, Wuttig and Sokolowski-Tinten39}

In Figure 4b, the absolute values of T _M-SC are plotted against M _P, showing a V-shape, where all known PCM compositions are located in the minimum zone around M _P = 0.48–0.49. This zone appears to be crucial for Group IV, V, and VI PCMs, as it corresponds to a lowest T _M-SC, and meanwhile, ensures t _M-SC < 1. Their relevance to fast switching lies on a transition in kinetic properties at the same temperature T _M-SC, known as a fragile-strong transition (which is discussed in detail in the next section). Only when t _M-SC < 1, the temperature window of the fragile liquid is below T _m. As such, the fragile liquid provides high atomic mobility, which facilitates crystallization that can only occur below T _m.

Following these successes, we have noted that the element bismuth (Bi) has nearly the same metallicity as Ge (0.495 and 0.498, respectively), which might be predicted to replace Ge in PCM formulations. We find that Bi₂Te₃ has been identified by atomic probe tomography as having the bonding of a PCM,^{Reference Zhu, Cojocaru-Mirédin, Mio, Keutgen, Küpers, Yu, Cho, Dronskowski and Wuttig40} and Bi₂Te₃ nanowires exhibit memory switching behavior.^{Reference Han, Kim, Yang, Lee, Sohn, So, Ahn and Yoo41} It raises the question, “is there perhaps an equivalent of the “Yamada line” in the Bi-Sb-Te system (Ge-free) (e.g., along much of the Bi₂Te₃-Sb₂Te₃ join)?” Both are in the weak metal state at their melting temperatures, as for PCMs. Attention has already been drawn to the analog of the GST Yamada line provided by the (Ge-containing) Ge-Bi-Te system^{Reference Lee, Kim, Kang, Suh, Kim and Khang42} and to the similarity of the various crystalline structures along that line to those in the GST system. In that case, it was reported that the presence of Bi “significantly enhances the crystallization of the GBT layers.”

Finally, we caution that the use of the metallicity parameter should be limited to the covalent alloys based on the Group IV, V, and VI elements. These elements are metalloid or close to metalloid, where the inverse electronegativity gives a quantitative measure of how “metallic” the element is. Those alloys with a higher metallicity are usually associated with higher conductivities. This may explain why, for liquid PCMs (with high metallicities), the conductivity upon heating usually reaches the value of 10²–10³ S cm^–1 of a “weak-metal” state earlier at a relatively low temperature (often below T _m), at which the semiconductor-to-metal transition occurs. By contrast, non-PCM chalcogenides need to be heated to higher temperatures, usually above T _m, so as to reach the weak-metal state for the semiconductor-to-metal transition to occur.

Note that there are density functional theory (DFT)-based parameter maps proposed for crystalline phase properties of PCMs.^{Reference Raty, Schumacher, Golub, Deringer, Gatti and Wuttig43,Reference Pries, Cojocaru-Miredin and Wuttig65} However, they are not available for amorphous phases. It remains to be seen whether and how they are related to the metallicity parameter introduced here and the M-SC behaviors.

Double-kink and smeared-out fragile-strong transitions in viscosity

In their classic 1965 paper,^{Reference Adam and Gibbs44} Adam and Gibbs presented a molecular kinetic theory in which the temperature dependence of relaxation time τ(T) is determined by the probability of cooperative rearrangement of mobile units in the system. The latter can be expressed in terms of configurational entropy, S _c:

$$\tau &#x003D; {\tau _0}\,exp\left[ {{{ - C} / {\left( {T{S_C}} \right)}}} \right]$$

where τ₀ is the pre-exponent near the phonon cycle time (10^–14 s) and C is a constant. In treating experimental data, S _c has been shown to be proportional to the excess entropy S _ex of liquid over crystal, which can be derived from C _p.^{Reference Wei, Lucas and Angell10} Thus, the C _p maximum leads to a transition in τ(T) and therefore the viscosity η(T) (through the Maxwell relation η = G _∞∙τ, where G _∞ is the infinite-frequency shear modulus.)

The drastic change in the temperature dependence of viscosity from a high-temperature fragile liquid to a low-temperature strong liquid near T _g is the so-called fragile-strong transition (FST). According to the liquid fragility concept,^{Reference Angell45} some liquids, exhibiting a near-Arrhenius rise in viscosity on approaching T _g, are classified as “strong” liquids, while others, showing a range of non-Arrhenius behavior, are referred to “fragile” liquids. Fragility is commonly characterized by measuring the slope of the T _g-scaled Arrhenius plot (fragility plot) at T _g, called “steepness index” or “m-fragility,” m = d log η/d(T _g/T) |_T=Tg.^{Reference Angell45}

A clear FST is demonstrated in Ge₁₅Te₈₅ (Figure 5)^{Reference Orava, Greer, Gholipour, Hewak and Smith8,Reference Wei, Lucas and Angell10–Reference Wei, Evenson, Stolpe, Lucas and Angell12,Reference Angell45,Reference Orava, Weber, Kaban and Greer47,Reference Orava, Hewak and Greer48,Reference Weber, Orava, Kaban, Pries and Greer53,Reference Schumacher, Weber, Jóvári, Tsuchiya, Youngs, Kaban and Mazzarello57–Reference Rhim and Ohsaka64} as a “double-kink” in η(T)-curve near its eutectic temperature, which is verified by a direct differential scanning calorimetry (DSC) measurement near T _g.^{Reference Wei, Lucas and Angell10} The corresponding structural change is shown as a stepwise rise in the second to first peak position ratio r ₂/r ₁ of reduced pair distribution functions G(r) from in situ x-ray scattering.^{Reference Wei, Stolpe, Gross, Hembree, Hechler, Bednarcik, Busch and Lucas46} In As₂Te₃, the FST is so smeared-out that no “double-kink” is discerned. The C _p anomaly spans ∼300 K (Figure 3a). The viscosity of As₂Te₃ drops smoothly by ∼3 orders of magnitude in the transition range. The sharpness of the FST depends on the sharpness of the C _p maximum and the associated loss of S _ex across the transition.

Figure 5.

Arrhenius plots scaled by the glass-transition temperature (T _g) for the viscosity (η) of Group IV, V, and VI alloys. Phase-change materials (PCMs), which have the highest metallicity, exhibit the lowest viscosities at T _m (where T _g/T _m ∼ 0.5). On the T _g-reduced scale, they overlap the elemental Te data. Alloys of lower metallicity exhibit systematically higher viscosities, and lower m fragilities. The lowest metallicity case, As₂O₃, with m = 19 (according to light-scattering relaxation time data) is even stronger than the archetypal strong liquid, SiO₂. Apart from this interesting case, Figure 5 contains only directly measured experimental viscosities. The crystal-growth-derived viscosities are not shown. The bold colored arrows indicate T _M-SC (660 K) of AIST (purple) below T _m, and that of As₂Te₃ (green), Ge₁₅T₈₅ (red), and As₂Se₃ (orange) above T _m, respectively. Data sources: Ge₂Sb₂Te₅;^{Reference Schumacher, Weber, Jóvári, Tsuchiya, Youngs, Kaban and Mazzarello57} T _g = 430 K,^{Reference Kalb, Wuttig and Spaepen58} although the value is still under debate;^{Reference Orava, Greer, Gholipour, Hewak and Smith8} AIST (Ag-In-doped Sb₂Te),^{Reference Orava, Weber, Kaban and Greer47} (its T _g = 443 K^{Reference Kalb, Wuttig and Spaepen58}) is also under debate;^{Reference Orava, Hewak and Greer48} Te;^{Reference Herwig and Wobst59} T _g = 350 K;^{Reference Wei, Coleman, Lucas and Angell11} Ge₁₅Te₈₅: viscosity data;^{Reference Neumann, Herwig and Hoyer60} Adam–Gibbs fitting line;^{Reference Wei, Lucas and Angell10} GeTe^{Reference Weber, Orava, Kaban, Pries and Greer53} assigned T _g = 470 K; As₂Te₃;^{Reference Tverjanovich61} T _g = 375 K is the value at which calculated viscosity reaches 10¹² Pa s; As₂Se₃;^{Reference Tverjanovich62} As₂S₃.^{Reference Angell45} For As₂O₃, relaxation times were directly measured using light scattering, from which the precise Vogel–Fulcher–Tammann (VFT) parameters were obtained. The viscosity is represented by a VFT fit in the similar temperature range of relaxation time data using the parameters in Reference Reference Yannopoulos, Papatheodorou and Fytas63; SiO₂, and o-terphenyl (OTP);^{Reference Angell45} Si^{Reference Rhim and Ohsaka64} (the T _g of Si is unknown and here assigned as 900 K).^{Reference Wei, Lucas and Angell10}

The viscosity of PCM compositions has been measured directly for (e.g., Ge₂Sb₂Te₅, [Ag, In]-doped Sb₂Te [AIST], and GeTe) at high temperatures above their T _m, as shown in Figure 5. Those data nearly overlap the high-temperature viscosity of Te (orange triangles) and that of the fragile state of Ge₁₅Te₈₅ above its FST (open circles) at T _g/T < 0.5. Thus, liquid PCMs above T _m exhibit a “fragile” behavior, as expected from their weak-metal states in the equilibrium melt.

Insofar as the predicted FSTs (also M-SC transitions) always occur below T _m in PCMs, they cannot be directly observed due to the interference of fast crystallization, but have only been inferred. Orava et al.^{Reference Orava, Weber, Kaban and Greer47,Reference Orava, Hewak and Greer48} measured the temperature-dependence of crystallization kinetics using ultrafast DSC, and inferred an “Arrhenius”-like behavior of viscosity between 383 K and ∼490 K for as-deposited AIST. They proposed a broad crossover from a high-temperature fragile liquid (m = 74) to a low-temperature strong liquid (m = 37). Zalden et al.^{Reference Zalden, von Hoegen, Landreman, Wuttig and Lindenberg49} identified a crossover temperature in AIST (∼570 K for melt-quenched samples and ∼540 K for as-deposited samples) through the kinetics of subnanosecond laser induced crystallization. In the same composition, Salinga et al.^{Reference Salinga, Carria, Kaldenbach, Bornhöfft, Benke, Mayer and Wuttig50} revealed a nearly constant activation energy for the temperature-dependence of crystal-growth-derived viscosity below ∼570 K, which they referred to as Arrhenius-like behavior. This was attributed to the falling out of equilibrium into glassy states due to extremely fast cooling rates (∼10⁹–10¹⁰ K/s) by laser-melt-quench on the small beam spot.

An ab initio calculation by Zhang et al. for AIST^{Reference Zhang, Ronneberger, Zalden, Xu, Salinga, Wuttig and Mazzarello51} successfully produced reasonable temperature-dependence of diffusivity at high temperature above T _m, though it did not give a reasonable account for the supercooled liquid state at much lower temperatures. For Ge₂Sb₂Te₅, the ultrafast DSC study of Orava et al.^{Reference Orava, Greer, Gholipour, Hewak and Smith8} implied a single fragility parameter (m ≈ 90) for the entire liquid regime, while the ab initio simulation of Flores-Ruiz and Micoulaut^{Reference Flores-Ruiz and Micoulaut52} proposed a FST from m ≥ 129 to m = 90 at 792 K. An ultrafast DSC study of Ge₂Sb₂Te₅ nanoparticles suggested a broad FST.^{Reference Weber, Orava, Kaban, Pries and Greer53} In another PCM GeTe, a single fragility (m = 76) is suggested, partially based on ultrafast DSC measurements, to describe the liquid without a FST,^{Reference Chen, ten Brink, Palasantzas and Kooi54} which is in contrast to the extrapolation from reference Reference Wei, Coleman, Lucas and Angell11 and this work.

Zhang et al.^{Reference Zhang, Mazzarello, Wuttig and Ma16} emphasized a “kinetic crossover,” defined as a large change in activation energy of viscosity, that occurs somewhat below T _m, as essential for fast crystal growth in PCMs. Note that a so-defined “kinetic crossover” is not the same concept as the FST discussed here (or fragile-strong crossover), because the former is expected during the undercooling of any fragile liquid that is described by mode coupling theory (MCT)^{Reference Götze55} at higher temperatures. It corresponds to the much-discussed crossover from MCT to “hopping” behavior (i.e., it does not imply a structural or heat capacity-based transition to a stronger liquid state).

Unlike the cases of good glass-formers (e.g., Ge₁₅Te₈₅ and As₂Te₃), the ambiguity and controversy of fragilities and FSTs in PCM compositions are no surprise because direct experiments cannot easily be carried out in the fast crystallization regime to determine the viscosity of supercooled liquid. In the literature, the reported crystal growth velocities themselves may differ by a few orders of magnitude, depending on different sample preparation processes and experimental approaches. Furthermore, since crystallization processes may occur in either glass or liquid, and since the glass-transition temperatures of PCMs are still debated, it is unclear whether the derived viscosity corresponds to the equilibrium viscosity, which is the meaningful quantity for discussion of liquid fragility, or something else. For instance, if a liquid falls out of equilibrium during cooling and forms a glass at a fictive temperature T _f, which depends on the cooling rate, a quantity with dimensions of viscosity can still be measured, and it usually follows the Arrhenius Law,^{Reference Angell, Ngai, McKenna, McMillan and Martin56} but this behavior should not be confused with that of a strong liquid, nor the transition to the strong state, a FST.

Zalden et al.^{Reference Zalden, Quirin, Schumacher, Siegel, Wei, Koc, Nicoul, Trigo, Andreasson, Enquist, Shu, Pardini, Chollet, Zhu, Lemke, Ronneberger, Larsson, Lindenberg, Fischer, Hau-Riege, Reis, Mazzarello, Wuttig and Sokolowski-Tinten39} recently conducted a femtosecond pump-probe x-ray laser experiment that enables resolution of structural changes within nanosecond time scales, which provided the first direct evidence of a structural transition in PCMs below T _m. This was observed at 660 K in AIST (Ag₄In₃Sb₆₇Te₂₆) and 610 K in Ge₁₅Sb₈₅, and is so far the most convincing evidence of liquid-liquid transitions (which are also M-SCs, as mentioned earlier) in the supercooled liquid PCMs. When the results are plotted in Figure 4, the data well support our prediction from the metallicity parameter.

We further comment on the significance of FSTs due to the sharp heat capacity anomalies in the PCM metallicity domain. The FST controls the kinetic factor (atomic mobility) of nucleation and growth of crystals. In the fragile state, a high kinetic factor facilitates crystallization (fast switching) at an elevated temperature between T _M-SC and T _m by a “set” pulse, while, in the strong state below T _M-SC, a low kinetic factor hinders crystallization at ambient temperature, which is favorable for data retention. Within limits, this transition should be tunable by change of metallicity. From the previously discussed analysis, this transition is also the origin of the additional entropy loss during vitrification of PCMs, as mentioned in the Introduction section.

A recent study suggested that imminence of a M-SC/FST transition is signaled well above T _m by the combination of viscosity with diffusivity data, known as the Stokes–Einstein relation (SER).^{Reference Wei, Evenson, Stolpe, Lucas and Angell12} In PCMs, unlike other liquids, the SER breaks down while in a high-fluidity state (τ ∼ ps) and even above T _m.^{Reference Wei, Evenson, Stolpe, Lucas and Angell12}

Summary and outlook

The liquid states of PCMs are shown to be anomalous in comparison with the majority of liquid (and glass-forming) chalcogenides. This appears to be due to the existence of M-SC transitions, hidden below T _m, which are driven by structure-related thermodynamic and kinetic anomalies. The knowledge of the transition-related property changes is essential for understanding of switching behaviors. The M-SC for a wide range of compositions seems to be confined to a narrow range of values of a new parameter, the metallicity M _P. Given that all PCMs are concentrated in a zone of M _P = 0.48–0.49, the metallicity concept may provide useful guidance for future PCM designs.