Luan et al. (Nature Communications 13, 2183, 2022) reported that a melt-spun equiatomic NbNiZrTiCo high-entropy metallic glass transforms on heating into a distinctly lower-energy amorphous state of the same composition, releasing more heat (~130% of the subsequent crystallization exotherm) than any previously known anomalous exothermic event in a metallic glass, and correlated the occurrence of this glass-to-glass transition with a high total mixing entropy ST=SC+SES_T = S_C + S_E. Four years of follow-up work has materially extended the phenomenon (continuous polyamorphous transitions in other high-entropy metallic glasses, ultrastable-glass production via glass-to-glass transition in a conventional alloy, and competing pathway interpretations) but has not delivered a species-resolved atomistic mechanism, nor a validated quantitative criterion predicting for which multicomponent compositions and processing conditions the transition occurs before crystallization. This record states that problem: identify the atomic rearrangements and transition pathway underlying entropy-induced glass-state selection, and thereby establish the mechanism-level foundation for predicting when the transition occurs before crystallization.

Background

Metallic glasses (MGs) are metal alloys frozen in an amorphous, non-crystalline state, usually by cooling a melt so fast that crystallization is bypassed (here, melt-spinning onto a cold copper wheel produces thin ribbons at roughly 10410^4–10610^6 K s−1^{-1}). A melt cooled below its melting point without crystallizing is a supercooled liquid; at the glass-transition temperature TgT_g — the temperature at which the liquid's structural relaxation time outgrows the experimental timescale — it freezes kinetically into the glass. A glass is not a unique state: depending on cooling rate and thermal history it is trapped at different depths of the potential energy landscape (the multi-valley surface governing atomic configurations), so glasses of identical composition can hold different energies, structures, and properties. Differential scanning calorimetry (DSC) measures heat flow on heating; a glass settling into a lower-energy state releases heat (an exotherm) before any crystallization occurs. Most known MGs show only weak structural relaxation with small heat release, and genuine transitions between two amorphous states of the same composition — glass-to-glass transitions, a metallic analogue of polyamorphism (the existence of two distinct amorphous states of the same substance, the disordered counterpart of allotropy in crystals) — are rare: high pressure can induce them but the high-pressure state is usually not recoverable at ambient pressure, and a few Pd-Ni-P and related alloys show anomalous exothermic peaks attributed to still-debated amorphous-amorphous reorganizations.

A separate thread, high-entropy alloys, studies multicomponent alloys of five or more elements in near-equiatomic ratios, whose large entropy of mixing stabilizes disordered configurations. The relevant thermodynamic quantities are the ideal configurational entropy of mixing SC=−R∑iciln⁡ciS_C = -R\sum_i c_i \ln c_i for atomic fractions cic_i (gas constant RR), and the excess configurational entropy of mixing SES_E, the departure from the ideal-solution value caused by atomic-size misfit and chemical interactions, estimated from the atomic packing fraction and atomic-size differences through the hard-sphere (Carnahan–Starling/Mansoori) excess-entropy model used in ref. 1; the total is ST=SC+SES_T = S_C + S_E. High-entropy metallic glasses (HEMGs) combine both ideas.

Luan et al. (2022) melt-spun the equiatomic five-element NbNiZrTiCo HEMG (SC=13.38S_C = 13.38, SE=−2.75S_E = -2.75, ST=10.63S_T = 10.63 J mol−1^{-1} K−1^{-1}) and found on heating three exotherms at 781, 911, and 1016 K releasing 1.65, 1.27, and 1.59 kJ mol−1^{-1}; the first, unusually, exceeds the crystallization exotherms (for other MGs with anomalous exothermic peaks the ratio is below 16%), and the sample heated past it (to 855 K) remains fully amorphous by X-ray diffraction and electron microscopy while its hardness rises from 6.78 to 9.46 GPa. In-situ synchrotron X-ray diffraction tracks the structure through the transition via the reduced pair distribution function G(r)G(r), the Fourier transform of the scattering structure factor giving the distribution of interatomic distances: both sub-peaks of the first G(r)G(r) peak contract on heating (contrary to thermal expansion) with a redistribution of intensities, and the second peak splits. But for a five-component alloy fifteen atomic-pair correlations overlap in each peak, so the observed changes could not be attributed to specific atomic pairs or local motifs. Comparing entropies, the transition-bearing HEMGs sit in a region of high SCS_C and high (less negative) SES_E whereas previously known HEMGs without any transition (e.g. SrCaYbMgZn with SE=−6.73S_E = -6.73 J mol−1^{-1} K−1^{-1}) have low SES_E; substituting Co by Cu or adding Cu reproduced the transition in NbNiZrTiCu and NbNiZrTiCoCu. The authors' physical picture is kinetic: many elements enlarge configuration space and slow configurational sampling, so fast quenching traps a high-energy glass that, on reheating, finds a lower-energy glass basin. Atom-probe tomography (APT, an atomic-scale composition-mapping technique) detected no compositional inhomogeneity at either nanometer or sub-nanometer scales before or after the transition, excluding spinodal decomposition, but its limited spatial resolution could not detect the detailed structural change, and the authors themselves state that how high entropy induces the transition is the key unresolved question, with no quantitative entropy threshold or occurrence criterion established.

Problem Statement

Establish a mechanism-level, predictive understanding of entropy-induced glass-state selection in multicomponent metallic glasses, as posed by the open issues of Luan et al. (2022) and sharpened by the subsequent literature. A complete answer requires all three of the following results, and no single result on its own resolves the task. First, a species-resolved atomistic account of the high-energy to low-energy transition in the NbNiZrTiCo-family high-entropy metallic glasses — which atomic-pair rearrangements and local motifs carry the documented G(r)G(r) first-peak sub-peak contractions and intensity redistributions and the second-peak splitting, with their activation barriers and kinetics; an adequate account is one whose proposed atomic-pair rearrangements quantitatively reproduce the documented G(r)G(r) first-peak contractions, intensity redistribution, and second-peak splitting and are consistent with the calorimetric and hardness observations. Second, a determination of the transition pathway (direct glass-to-glass, versus proceeding through transient supercooled-liquid states or a fragile-to-strong transition — a crossover from fragile behavior, where viscosity rises very steeply on cooling, to strong behavior, where it rises slowly — the currently competing interpretations); this must go beyond the first result by adjudicating among those competing interpretations from the same species-resolved rearrangements and kinetics and stating which one the mechanism supports, rather than merely restating the authors' kinetic picture. This is the open question Luan et al. (2022) explicitly pose: 'How the high-entropy induces the unusual glass-to-glass transition is the key to a deeper understanding of the high-entropy effect in glass formation.' Third, a quantitative criterion — expressed through the configurational entropy of mixing SCS_C, the excess configurational entropy of mixing SES_E (or equivalent measures), and the relevant kinetic variables such as quench rate and thermal history — that predicts, for a given multicomponent composition and processing route, whether a high-energy glass basin is trapped during vitrification and whether the glass-to-glass transition occurs on heating before crystallization; an adequate criterion is one whose predicted boundary is tested against the experimentally reported behavior of the transition across element classes, concentrations, and preparation routes — that is, validated against existing experimental data, not new experiments by the solver. Together, these results serve the broader objective of converting the empirically observed high-entropy effect into a predictive, mechanism-grounded tool for selecting glass states.

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