Glass-to-liquid transition in metallic glasses: thermodynamic phase transition or kinetic freezing, and the microscopic basis of sub-$T_g$ atomic mobility and kinetic stability

A 2006/2007 study of zirconium- and palladium-based metallic glasses by Ichitsubo, Matsubara and Numakura's group measured how the calorimetric glass-transition temperature $T_g$ and the crystallization temperature $T_x$ shift with heating rate β, showing that the extrapolated $T_g(β)$ and $T_x(β)$ curves intersect at a critical heating rate $β_c$ and intersection temperature $T_c$ that separate thermally stable metallic glasses (reversible glass→liquid transition observable) from less-stable ones (crystallization preempts it). The study acknowledged as unsettled: the physical meaning of the intersection temperature $T_c$ — whether the glass→liquid transition classified by the heating-rate criteria reflects an underlying thermodynamic transition (including the controversial proximity of $T_c$ to the Kauzmann temperature $T_K$) or kinetic freezing; the microscopic mechanism by which appreciable single-atom (tracer) diffusion proceeds below $T_g$ in less-stable glasses and its relation to the β relaxation and to the high-mobility regions that nucleate crystallization; and the microscopic foundation and range of validity of the proposed heating-rate measure of kinetic stability (the magnitude of $β_c$) across metallic glasses. The core remains open: the β-relaxation–diffusion link is now empirically established at the correlation level, structural heterogeneity has been mapped, and ultrastable and hyperaged metallic glasses sharpen the kinetic character of the transition, but no quantitative microscopic theory connects these to the heating-rate criteria, and the thermodynamic-versus-kinetic question remains unresolved.

Background

A metallic glass is an alloy whose atoms are frozen in a disordered, liquid-like configuration, typically produced by very rapid cooling of the melt; bulk metallic glasses are compositions such as Pd$_{42.5}$Ni$_{7.5}$Cu$_{30}$P$_{20}$ that can be cast in millimetre thicknesses because their supercooled liquid (liquid below its melting point) is extremely viscous and slow to crystallize. On heating in a differential scanning calorimeter (DSC) at rate β, a metallic glass shows a calorimetric glass→liquid transition at $T_g$ — a step-like increase in heat capacity — followed, at $T_x$, by crystallization. Whether this glass→liquid transition reflects an underlying thermodynamic phase transition (an ideal glass transition, for example at a Kauzmann-like temperature where the extrapolated liquid entropy equals the crystal entropy) or is purely kinetic — the arrest of atomic rearrangement on the observation timescale — is the classic, still-unresolved question of glass physics; leading microscopic theories (free-volume, Adam–Gibbs entropy, random-first-order-transition, elastic, and interstitialcy models) differ precisely in whether they invoke such a thermodynamic singularity (Berthier and Biroli, 2011).

Empirically, the apparent $T_g$ rises roughly linearly with log β (the Lasocka relation), and $T_x$ also shifts with β. Ichitsubo, Matsubara, Numakura and coworkers measured both curves for a stable metallic glass (SMG, Pd$_{42.5}$Ni$_{7.5}$Cu$_{30}$P$_{20}$, which shows a reversible glass↔liquid transition at ordinary heating rates) and a less-stable metallic glass (LMG, Zr$_{70}$Ni$_{30}$, which crystallizes before any glass transition at ordinary rates) (Ichitsubo et al., 2005). The extrapolated $T_g(β)$ and $T_x(β)$ curves intersect at a critical heating rate $β_c$ — about $10^{-4}$ °C/min for the SMG but about 10 °C/min for the LMG — at an intersection temperature $T_c$, so the observability of the glass→liquid transition and the kinetic stability of the glassy state are quantified by these heating-rate criteria. In the source framework, $T_c$ is the temperature at which the extrapolated $T_g$–$\log β$ and $T_x$–$\log β$ (Lasocka-type) curves cross at $β_c$, and $T_x^*$ is the crystallization temperature extrapolated to small laboratory heating rates (of the order of 1–10 °C/min), corresponding to the temperature at which atoms start to lose/acquire mobility on cooling/heating; the classification inequalities are $T_c<T_g<T_x^*$ for a stable metallic glass such as Pd$_{42.5}$Ni$_{7.5}$Cu$_{30}$P$_{20}$ versus $T_x^*<T_c$ for a less-stable metallic glass such as Zr$_{70}$Ni$_{30}$, so that the relative location of $T_c$ against $T_x^*$ gives a measure of the thermal stability of metallic glasses (Ichitsubo et al., Phys. Rev. B 72, 052201 (2005), Eqs. (1)–(3)).

The microscopic side concerns atomic mobility below $T_g$. Tracer experiments established that diffusion in metallic glasses does not freeze at $T_g$ but proceeds by thermally activated, highly collective processes, unlike diffusion in crystalline metals (Faupel et al., 2003). Mechanical spectroscopy reveals a ubiquitous secondary (β, or Johari–Goldstein) relaxation — a faster, more local process than the structural (α) relaxation that underlies viscous flow — whose activation energy is close to the potential-energy barriers of shear transformation zones, the localized groups of atoms that rearrange inelastically as the elementary carriers of plastic flow in glasses (Zhao et al., 2007; Yu et al., 2010). Ichitsubo et al. further showed that ultrasonic excitation near or below $T_g$ induces crystallization preferentially in weakly bonded regions of a fragile Pd-based glass, through accumulation of atomic jumps associated with the β relaxation (Ichitsubo et al., 2005); metallic glasses are thus pictured as strongly bonded regions surrounded by weakly bonded, high-mobility regions — the same regions inferred to nucleate crystallization. Fragility — the steepness of the viscosity increase of the liquid on cooling toward $T_g$ — is intertwined with this structural heterogeneity. What has remained missing since the source paper is a quantitative microscopic account connecting β relaxation, sub-$T_g$ single-atom diffusion, and the mobility heterogeneity that nucleates crystallization to the heating-rate kinetic-stability criteria, and through them a decision on the thermodynamic-versus-kinetic character of the transition.

Problem Statement

The open core acknowledged by Ichitsubo, Matsubara and Numakura's study of zirconium- and palladium-based metallic glasses comprises three linked deliverables with one common objective — a quantitative microscopic account of the kinetic stability of the glassy state in metallic glasses expressed by the heating-rate criteria, clarifying in the source-given relation the thermodynamic-versus-kinetic character of the glass→liquid transition:

(1) Thermodynamic or kinetic? Clarify, in the source-given relation to the heating-rate criteria, whether the glass→liquid transition of metallic glasses observed calorimetrically on heating is the manifestation of an underlying thermodynamic phase transition (an ideal glass transition) or of kinetic freezing of atomic rearrangement — specifically the physical meaning of the intersection temperature $T_c$, including its controversial proximity to the Kauzmann temperature $T_K$, and what the classification inequalities $T_c<T_g<T_x^*$ versus $T_x^*<T_c$ imply. The field-wide ideal-glass-transition question is the acknowledged background, which the source itself explicitly does not settle; here it is tied to the measurable heating-rate phenomenology ($T_g(β)$, $T_x(β)$, their intersection $(β_c, T_c)$, and the classification inequalities between $T_c$ and $T_x^*$ defined above).

(2) Microscopic mechanism of sub-$T_g$ mobility. Establish quantitatively how appreciable single-atom (tracer) diffusion proceeds below $T_g$ in less-stable metallic glasses: the relation between the β relaxation, the spatially heterogeneous weakly bonded / enhanced-mobility regions, and the regions that nucleate crystallization — including whether one microscopic process underlies all three.

(3) Microscopic foundation and range of validity of the kinetic-stability criteria. Establish the microscopic foundation and range of validity of the heating-rate measures — the Lasocka-type log-β behavior of $T_g$ and $T_x$ (their near-linear rise with the logarithm of the heating rate), the critical heating rate $β_c$ at which the extrapolated curves intersect, and the associated $T_c$-versus-$T_x^*$ inequalities defined above — in relation to the microscopic mechanism of (2), and of the source's proposed general measure — that the magnitude of $β_c$ (equivalently, the relative location of $T_c$ against $T_x^*$) reflects the thermal stability of the glassy state — across metallic glasses, including the source's structural contrast between covalently bonded metal–metalloid cluster (network-like) stable glasses and metallic-bond-dominated less-stable glasses (the source study covered Pd$_{42.5}$Ni$_{7.5}$Cu$_{30}$P$_{20}$, Zr$_{70}$Ni$_{30}$, and Zr$_{70}$Cu$_{30}$).

Correlations alone (for example, the matched activation energies of β relaxation and small-atom diffusion) do not complete the account: the three deliverables above are jointly required, and an experimentally validated account that connects atomic-scale mobility to the macroscopic heating-rate criteria must be accompanied by an explicit interpretation, for deliverable (1) in the source-given relation, of the physical meaning of $T_c$ and of the classification inequalities $T_c<T_g<T_x^*$ versus $T_x^*<T_c$.

References

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