Calorimetry shows that the β-relaxation of metallic glasses has two parts: a reversible component, seen as an endothermic sub-TgT_\text{g} peak with activation energy of about 26RTg26RT_\text{g} that can be restored by a brief excursion to near the glass-transition temperature, and an irreversible component that appears as ordinary enthalpy recovery and is annihilated by sub-TgT_\text{g} annealing. The microscopic origin of this decomposition is not understood. The open problem is to identify the local atomic configurations and the nature of their activation-energy barriers that distinguish the two components, and to determine the conditions under which they fully decouple, including the role of the near-TgT_\text{g} activation step. Recent in-situ synchrotron and simulation work has tied β-relaxation to specific cluster motifs and fast atoms in free-volume-rich environments, but explicitly leaves the mechanism and the distinction between the two components unresolved.

Background

Metallic glasses are amorphous alloys produced by cooling fast enough to bypass crystallization; like other glasses they show a glass-transition temperature TgT_\text{g} below which the structure is kinetically frozen but still evolves slowly (physical aging). When probed periodically, glasses display a hierarchy of relaxation modes: the slow α-relaxation, associated with cooperative structural rearrangement and the glass transition itself, and the faster β-relaxation, a localized secondary process (the metallic analogue of the Johari–Goldstein relaxation of molecular glasses). In dynamic mechanical analysis (DMA), which measures the storage and loss moduli of a sample under periodic strain while scanning temperature or frequency, β-relaxation appears in most metallic glasses only as a broad excess wing or shoulder on the α-loss peak; only in a few families, notably La- and Pd-based glasses, does it appear as a distinct loss peak. β-relaxation matters practically because it is linked to physical aging, ductility, and the ductile-to-brittle transition of metallic glasses. In differential scanning calorimetry (DSC), which measures heat flow during controlled heating, sub-TgT_\text{g} annealing produces an endothermic overshoot at TgT_\text{g} (enthalpy recovery); theoretical work on the physics of glasses had long predicted, and fast-scanning calorimetry later confirmed, an additional weaker endothermic signal below TgT_\text{g} for very rapidly quenched ('hyper-quenched') glasses, the so-called shadow glass transition, whose temperature–time dependence was shown to track β-relaxation. Zhao et al. (Phys. Rev. B 101, 094203 (2020)) studied a metallic glass by conventional calorimetry and found that long-time sub-TgT_\text{g} annealing induces a distinct endothermic peak below TgT_\text{g} with an activation energy of about 26RTg26RT_\text{g}. Using an annealing–scanning–annealing thermal protocol (anneal below TgT_\text{g}, heat while recording, re-anneal or briefly activate near TgT_\text{g}, and scan again), they showed that this sub-TgT_\text{g} peak is a reversible β-relaxation signal, whereas the ordinary enthalpy-recovery overshoot reflects an irreversible component: β-relaxation thus comprises both reversible and irreversible parts, which can be separated by combining calorimetry with the designed thermal protocol. The paper interprets the carriers of the two components in terms of flow units — nanoscale, defect-like soft regions of the glass that carry localized rearrangement — distinguishing annealing-susceptible ('defectlike') units from intrinsic ones; this flow-unit attribution is not part of the required answer. Subsequent work has added probes and structural evidence: the sub-TgT_\text{g} calorimetric signal was connected to the shadow-glass-transition phenomenology of hyper-quenched glasses; in-situ synchrotron X-ray diffraction and absorption plus molecular-dynamics simulation on Pd-based glasses linked β-relaxation to tricapped-trigonal-prism-like first-shell clusters and to fast atoms sitting in specific Voronoi polyhedra (the geometric cells used to index local atomic packing) that carry excess free volume, and showed that the irreversible event decays during sub-TgT_\text{g} annealing and can be reactivated by rejuvenation near TgT_\text{g}; electrical-resistivity measurements detect the irreversible but not the reversible component. What no study has yet provided is the microscopic account that would complete this picture: which atomic configurations carry each component, what energy barriers distinguish them, and when exactly they decouple.

Problem Statement

Provide a microscopic account of the two-component β-relaxation of metallic glasses established by calorimetry. Concretely: (1) identify the specific local atomic configurations and the nature of their activation-energy barriers that carry the reversible component (the sub-TgT_\text{g} endothermic peak, restorable by a brief excursion to near TgT_\text{g}) and the irreversible component (the enthalpy-recovery signal annihilated by sub-TgT_\text{g} annealing), and explain what structurally distinguishes the two types of carriers, since current in-situ structural evidence correlates with β-relaxation as a whole but does not discriminate between the two components; and (2) determine the conditions under which the two components fully decouple — i.e. the regime and alloy conditions under which the reversible sub-TgT_\text{g} signal and the irreversible enthalpy recovery can be varied independently by the thermal protocol — including the role of the near-TgT_\text{g} activation/rejuvenation step that reactivates the irreversible component after sub-TgT_\text{g} annealing.

References

  1. R. Zhao, H. Y. Jiang, P. Luo, L. Q. Shen, P. Wen, Y. H. Sun, H. Y. Bai, W. H. Wang, "Reversible and irreversible β-relaxations in metallic glasses", Phys. Rev. B 101, 094203 (2020), DOI 10.1103/PhysRevB.101.094203, https://doi.org/10.1103/PhysRevB.101.094203
  2. Tianding Xu, Jinquan Zhou, Xiao-Dong Wang, Ke Yang, Qing-Ping Cao, Dong-Xian Zhang, Chih-Wen Pao, Jian-Zhong Jiang, "Atomic-Level Structural Characteristics of β-Relaxation in Metallic Glasses", Advanced Science 13, e18424 (2025), DOI 10.1002/advs.202518424, https://doi.org/10.1002/advs.202518424
  3. Jianyu Chen, Shuai Ren, Zhe Chen, Jie Dong, Lixing Zhu, Yangguang Zhan, Wenxue Wang, Shenghao Zeng, Jing Xiao, Xiong Liang, Jiang Ma, "Unveiling Irreversible β-Relaxations in Metallic Glasses via Electrical Resistivity", Metals 15, 196 (2025), DOI 10.3390/met15020196, https://doi.org/10.3390/met15020196
  4. Qun Yang, Si-Xu Peng, Zheng Wang, Hai-Bin Yu, "Shadow glass transition as a thermodynamic signature of β relaxation in hyper-quenched metallic glasses", National Science Review 7, nwaa100 (2020), DOI 10.1093/nsr/nwaa100, https://doi.org/10.1093/nsr/nwaa100
  5. Y. Ding, F. Shi, X. Wang, Y. Bai, Z. Wang, L. Hu, "Evolution of coupling modes between α and β relaxations in metallic glass-forming liquids revealed by nano-calorimetry", Acta Materialia 266, 119698 (2024), DOI 10.1016/j.actamat.2024.119698, https://doi.org/10.1016/j.actamat.2024.119698
  6. Q. Sun, W. Wang, M. Huang, X. Zhao, J. Lv, G. Zhang, L. Liu, J. Yi, "Probing the decoupling degree between α and β relaxations in metallic glasses through differential scanning calorimetry", Journal of Non-Crystalline Solids 641, 123089 (2024), DOI 10.1016/j.jnoncrysol.2024.123089, https://doi.org/10.1016/j.jnoncrysol.2024.123089
  7. Adit Sharma, M. V. Gorshenkov, Vladislav Yu. Zadorozhnyy, "Thermomechanical relaxation and aging dynamics in La55Al25Co20 metallic glass", The Journal of Chemical Physics 163, 144509 (2025), DOI 10.1063/5.0291893, https://doi.org/10.1063/5.0291893
  8. J. Wang, W. Zhou, Z. Luo, J. Li, D. Wang, J. Xie, H. Yu, Z. Wu, Y. Li, "Repeated rejuvenation from relaxed metallic glasses through the memory effect", Acta Materialia 303, 121732 (2026), DOI 10.1016/j.actamat.2025.121732, https://doi.org/10.1016/j.actamat.2025.121732