Vapor-deposited ultrastable metallic glasses (UMGs) occupy unusually deep minima of the potential energy landscape, yet X-ray photon correlation spectroscopy (XPCS) on Cu50Zr50 UMGs showed that a one-minute anneal near the glass transition accelerates their atomic-scale dynamics ('anti-aging'), the reverse of the physical aging of conventional metallic glasses, while the relaxation retains a compressed exponential shape with exponent beta approximately 2 that is universal across all metallic glasses studied and insensitive to ultrastability and thermal treatment. The microscopic mechanism of anti-aging (the specific atomic rearrangements, and the quantitative validity of the proposed promotion of the glass to higher energy-landscape basins), the origin of the universal compressed exponent (in particular its persistence despite the low internal stress expected in UMGs), and the long-term aging behavior of the non-equilibrium stationary regime all remain unexplained. The problem is to provide a microscopic, quantitative account of atomic-scale relaxation in ultrastable metallic glasses that explains these observations.

Background

Metallic glasses (MGs) are amorphous alloys produced by quenching a melt so quickly that crystallization is bypassed. They combine high elasticity, hardness and corrosion resistance, but like all glasses they are out of thermodynamic equilibrium and slowly evolve toward the supercooled-liquid state; this drift of mechanical and thermodynamic properties, called physical aging, is a main obstacle to their technological use. The glass transition temperature TgT_g marks the softening point below which this evolution becomes extremely slow.

A route to far more stable glasses was discovered in molecular systems by Swallen et al. (Science 315, 353 (2007)): building a glass up by physical vapor deposition onto a substrate held at a temperature TsubT_{sub} between roughly 0.7 and 0.9 TgT_g lets atoms at the free surface, which are orders of magnitude more mobile than in the bulk, find low-energy packings during growth. The resulting 'ultrastable' glasses have higher TgT_g, lower fictive temperature (the temperature at which the frozen structure would be in equilibrium) and higher density than ordinary quenched glasses, a state otherwise reachable only after impractically long aging. The first ultrastable metallic glass (UMG), a vapor-deposited Zr65_{65}Cu27.5_{27.5}Al7.5_{7.5} film, was reported by Yu, Luo and Samwer (Adv. Mater. 25, 5904 (2013)). The standard interpretive framework is the potential energy landscape (PEL): configuration space viewed as an energy hypersurface whose local minima ('basins') correspond to metastable glass structures; deeper basins are more stable, with higher barriers and slower structural relaxation.

Whether ultrastability changes the atomic-scale dynamics themselves was addressed by Lüttich et al. (Phys. Rev. Lett. 120, 135504 (2018)) using X-ray photon correlation spectroscopy (XPCS): a partially coherent x-ray beam scattered off the sample produces a speckle pattern that fingerprints the instantaneous atomic configuration, and the time autocorrelation function g(2)(q,t)g^{(2)}(q,t) of the scattered intensity measures how fast density fluctuations at the probed length scale (a few angstroms, at the first maximum of the amorphous structure factor) decorrelate. In free-standing Cu50_{50}Zr50_{50} films sputter-deposited at Tsub=0.89TgT_{sub}=0.89T_g and temperature-cycled between 476, 456 and 436 K (about 0.65-0.71 TgT_g), they found: (i) the as-deposited UMG relaxes more slowly than both a rapidly quenched ribbon of the same composition and UMGs pre-annealed for one minute at 0.97Tg0.97T_g or 1.03Tg1.03T_g; that is, near-TgT_g annealing accelerates the atomic dynamics, the reverse of conventional aging, which the authors termed 'anti-aging'; (ii) the relaxation time grows with TsubT_{sub}, confirming ultrastability at the atomic scale; (iii) after about two temperature cycles the dynamics of most samples become stationary under further cycling (the UMG pre-annealed at 1.03Tg1.03T_g is fully reversible), but the stationary regime is not thermodynamic equilibrium; and (iv) in every sample, at every temperature and cycle, the correlation functions decay with a compressed Kohlrausch-Williams-Watts (KWW) form, g(2)(q,t)=1+A exp⁡[−2(t/τ)β]g^{(2)}(q,t)=1+A\,\exp[-2(t/\tau)^{\beta}] with β=2.0(2)\beta=2.0(2). Here τ\tau is the structural relaxation time and β\beta the shape parameter: β<1\beta<1 ('stretched') is typical of heterogeneous diffusive relaxation in liquids, while β>1\beta>1 ('compressed') signals faster-than-exponential decay.

Each of these findings clashes with the accepted picture of conventional glasses. Prior XPCS work on rapidly quenched MGs (Ruta et al., Phys. Rev. Lett. 109, 165701 (2012); Evenson et al., Phys. Rev. Lett. 115, 175701 (2015)) had established that below TgT_g the atomic-scale structural relaxation is compressed, β>1\beta>1, with relaxation times that grow with sample age, sometimes intermittently. Theoretical and simulation work associates compressed decay with stress-driven, ballistic-like rearrangements in elastically frustrated disordered solids (reviewed by Cornet and Ruta, C. R. Physique 24, 165 (2023)), and simulations of metallic glass-forming melts link compressed exponentials to growing icosahedral local order (Wu et al., Nat. Commun. 9, 5334 (2018)). Ultrastable glasses, however, are precisely the glasses expected to carry the least internal stress, so the persistence of β≈2\beta\approx 2 in UMGs implies that either the stress interpretation or the assumption of stress-free ultrastability is wrong; the source paper could only speculate that a large β\beta is 'intrinsic to the out-of-equilibrium nature of the glassy state in metallic systems'. The anti-aging itself was interpreted only qualitatively, as the annealing energy boosting the glass from its exceptionally deep PEL basin into a higher one, without any identified structural change, and the stationary cycling regime was explicitly noted not to correspond to equilibrium, with aging expected to continue through intermittent jumps between stationary regimes of unknown nature and timescale. Structural studies of vapor-deposited metallic glasses (e.g. Luo et al., Nat. Commun. 9, 1389 (2018)) show that their structure differs from quenched glasses only subtly at the level of medium-range order (atomic correlations beyond nearest neighbors), and no atomic-level signature distinguishing the as-deposited and annealed UMG dynamics is known.

Problem Statement

The problem is to give a microscopic, quantitative account of the atomic-scale structural relaxation of ultrastable metallic glasses that explains the observations of the source experiment. The common objective is a mechanism-level understanding of how ultrastability changes out-of-equilibrium relaxation in metallic glasses; the following linked questions all serve that single objective.

  1. Anti-aging mechanism. Identify the specific atomic rearrangements or structural changes by which a brief anneal near TgT_g (one minute at 0.97Tg0.97T_g or 1.03Tg1.03T_g in the source experiment) accelerates the atomic dynamics of a vapor-deposited Cu50_{50}Zr50_{50} ultrastable glass, and determine quantitatively whether the proposed interpretation, that the anneal promotes the glass from a low potential-energy-landscape basin to a higher one, is correct. In particular: what structural observable distinguishes the annealed from the as-deposited UMG, and why do the dynamics accelerate where those of conventional metallic glasses slow down?

  2. Origin of the universal compressed shape. Establish the microscopic origin of the compressed exponential decay with β≈2\beta\approx 2 that is observed for all metallic glasses studied, independent of ultrastability, thermal treatment and measurement temperature, and explain why it persists in ultrastable metallic glasses despite the low internal stress expected there, for instance whether it arises from stress-driven ballistic-like atomic motion, from superposed liquid-like heterogeneous relaxation, or from another mechanism.

  3. Long-term aging. Characterize the aging behavior of the stationary regime reached after a few temperature cycles, which is not thermodynamic equilibrium: the nature and the timescales of the intermittent jumps between stationary regimes through which aging is expected to proceed at the atomic scale.

References

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