🔬 materials science

Linking the pressure dependence of the structure and thermal stability to α- and \b{eta}-relaxations in metallic glasses

This study utilizes high-pressure experiments on Zr-based metallic glasses to reveal that $\beta$ -relaxation is driven by reduced atomic mobility and enhanced disorder, while $\alpha$ -relaxation promotes density-driven structural ordering and improved thermal stability, with the transition between these regimes occurring at a constant $T/T_{g,P}$ ratio independent of pressure.

Original authors: Jie Shen, Antoine Cornet, Alberto Ronca, Eloi Pineda, Fan Yang, Jean-Luc Garden, Gael Moiroux, Gavin Vaughan, Marco di Michiel, Gaston Garbarino, Fabian Westermeier, Celine Goujon, Murielle Legendre

Published 2026-02-18

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Jie Shen, Antoine Cornet, Alberto Ronca, Eloi Pineda, Fan Yang, Jean-Luc Garden, Gael Moiroux, Gavin Vaughan, Marco di Michiel, Gaston Garbarino, Fabian Westermeier, Celine Goujon, Murielle Legendre, Jiliang Liu, Daniele Cangialosi, Beatrice Ruta

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a metallic glass not as a shiny, hard metal, but as a frozen crowd of people at a concert.

In a normal metal (like steel), the atoms are like people standing in perfect, orderly rows (a crystal). In a metallic glass, the atoms are like a mosh pit that suddenly froze in place. They are jumbled, chaotic, and stuck in a messy arrangement. This "frozen mess" gives the material its unique strength and flexibility, but it also makes it tricky to predict how it will behave when you squeeze it or heat it up.

This paper is like a detective story where scientists squeezed this "frozen crowd" with massive pressure (like a giant hydraulic press) to see how the atoms rearrange themselves. They discovered that the crowd has two different ways of reacting depending on how hot the "concert" is.

Here is the breakdown of their findings using simple analogies:

1. The Two Types of "Crowd Movement"

The scientists found that the atoms in the glass have two distinct modes of moving, which they call $\beta$ -relaxation and $\alpha$ -relaxation.

$\beta$ -relaxation (The "Wiggly Neighbors"):
- The Analogy: Imagine the crowd is cold. People can't move their whole bodies, but they can wiggle their elbows or shift their weight slightly. They are jostling their immediate neighbors but not changing the overall shape of the crowd.
- What happens under pressure: When you squeeze the glass while it's "cold" (in the $\beta$ -regime), the atoms get squeezed tighter locally, but they don't settle into a better order. In fact, they get more chaotic and disordered, like a crowd that gets so squished they start bumping into each other in a panic. The material becomes slightly less stable.
$\alpha$ -relaxation (The "Dancing Crowd"):
- The Analogy: Now imagine the crowd is warm (or the glass is heated). People can now move their whole bodies. They can dance, swap places, and find a more comfortable spot.
- What happens under pressure: When you squeeze the glass while it's "warm" (in the $\alpha$ -regime), the atoms use that extra energy to shuffle around and find a perfectly packed, orderly arrangement. It's like a crowd finding a way to stand shoulder-to-shoulder without gaps. The material becomes denser, stronger, and much more stable.

2. The "Magic Switch" (The Transition)

The most exciting discovery is that there is a magic switch that separates these two behaviors.

The scientists found that this switch doesn't happen at a specific temperature (like 500°C). Instead, it happens at a specific ratio of the current temperature to the "melting point" of the glass under that specific pressure.
The Metaphor: Think of it like a video game level. Whether you are playing on "Easy Mode" (low pressure) or "Hard Mode" (high pressure), the level boss (the transition from wiggling to dancing) always appears when you reach 85% of the way to the finish line. It doesn't matter how hard the level is; the rule stays the same.

3. Why This Matters (The "Recipe" for Better Glass)

Before this study, scientists knew that squeezing glass changed it, but they didn't know how or why it changed so differently depending on the temperature.

The Problem: If you squeeze a glass at the wrong time (too cold), you might accidentally make it weaker and more prone to breaking (rejuvenation).
The Solution: If you squeeze it at the right time (when the atoms are "dancing" or in the $\alpha$ -regime), you can create a super-dense, ultra-stable glass.

The Takeaway:
This paper gives engineers a new "recipe book." By controlling the pressure and the temperature together, they can now design metallic glasses with custom properties.

Want a glass that is tough and absorbs energy? Squeeze it while it's cold (to mess up the order).
Want a glass that is incredibly strong and stable for aerospace or medical implants? Squeeze it while it's warm (to pack the atoms perfectly).

Summary in One Sentence

By applying the right amount of pressure at the right "dance temperature," scientists can turn a chaotic, frozen atomic crowd into a perfectly organized, super-strong team, unlocking a new way to build better materials.

1. Problem Statement

The relaxation dynamics of glass-forming materials, specifically the primary $\alpha$ -relaxation (cooperative structural rearrangement) and secondary $\beta$ -relaxation (localized atomic mobility), dictate the thermal stability, aging, and mechanical properties of glasses. While the temperature dependence of these processes is well-established, their behavior under high hydrostatic pressure remains poorly understood, particularly in metallic glasses (MGs).

Key challenges include:

Experimental Difficulty: Performing in-situ high-pressure measurements on MGs is technically demanding due to their high packing density, which requires gigapascal (GPa) pressures to induce noticeable changes.
Decoupling Mechanisms: It is unclear how pressure independently affects $\alpha$ and $\beta$ relaxations and how these dynamic changes translate into irreversible structural rearrangements and thermodynamic stability in recovered samples.
Gap in Knowledge: Previous studies often relied on pre-compressed samples without distinguishing between the specific relaxation regimes active during compression, leading to ambiguous interpretations of pressure-induced rejuvenation vs. stabilization.

2. Methodology

The study employs a systematic approach combining thermo-mechanical processing, flash differential scanning calorimetry (FDSC), and synchrotron X-ray diffraction (XRD) on a prototypical Zr-based metallic glass (Vit4: Zr $_{46.8}$ Ti $_{8.2}$ Cu $_{7.5}$ Ni $_{10}$ Be $_{27.5}$ ).

Sample Preparation & Compression Protocols:
- Samples were compressed in a belt press under hydrostatic conditions (1–7 GPa).
- Variable Temperature ( $T_{comp}$ ): Compression was performed at temperatures ranging from 298 K (deep glassy state) to 693 K (supercooled liquid phase).
- Variable Pressure ( $P_{comp}$ ): Densification was tested at fixed temperatures across the 1–7 GPa range.
- Recovery: Samples were cooled under pressure and decompressed to ambient conditions to study the permanent structural and thermodynamic changes.
Characterization Techniques:
- FDSC (Flash DSC): Used at ultra-fast heating rates (up to 1000 K/s) to amplify endothermic peaks associated with relaxation processes. This allowed for the calculation of fictive temperature ( $T_f$ ) (a metric of thermodynamic stability) and activation energies ( $E_a$ ) via Kissinger analysis.
- Synchrotron XRD: High-resolution measurements (ID13 and ID15a beamlines, ESRF) to analyze the First Sharp Diffraction Peak (FSDP) parameters ( $q_1$ and FWHM) and Pair Distribution Functions (PDF) to probe short-to-medium range order.
- In-situ High-Pressure XRD: Conducted at PETRA III (DESY) using a diamond anvil cell (DAC) to distinguish between elastic deformation and permanent densification.

3. Key Contributions

Decoupling Relaxation Regimes: The study successfully identifies and separates the distinct structural responses of MGs to pressure in the $\beta$ -relaxation regime (low $T_{comp}$ ) versus the $\alpha$ -relaxation regime (high $T_{comp}$ ).
Master Curve Scaling: Demonstrates that activation energies for both $\alpha$ and $\beta$ relaxations across different pressures can be rescaled onto a single master curve when normalized by the pressure-dependent glass transition temperature ( $T_{g,P}$ ).
Structural Mechanism Identification: Links specific atomic-scale structural changes (bond redistribution, density changes) directly to the dominant relaxation mechanism active during compression.
Thermo-Mechanical Processing Guidelines: Establishes a framework for tailoring MG properties (stability vs. rejuvenation) by controlling the pressure-temperature path relative to the relaxation spectrum.

4. Key Results

A. Thermal Stability and Relaxation Dynamics

Pressure Effect on $T_g$ : High pressure (7 GPa) increases the glass transition temperature ( $T_g$ ) by approximately 38 K (from ~596 K at 1 atm to ~634 K at 7 GPa). This shift is smaller than in molecular glasses due to the dense packing of MGs.
Activation Energy ( $E_a$ ):
- Two distinct regimes are observed: low $E_a$ (~~28 $RT_g$ ) corresponding to $\beta$ -relaxation and high $E_a$ (~~42 $RT_g$ ) for $\alpha$ -relaxation.
- The crossover between these regimes shifts to higher temperatures under pressure.
- Scaling: When temperature is normalized by $T_{g,P}$ , the activation energies collapse onto a single curve, indicating that the degree of equilibration required to activate $\alpha$ -relaxation is pressure-independent.
Fictive Temperature ( $T_f$ ) Anomalies:
- Unlike activation energies, $T_f$ does not scale with $T/T_{g,P}$ .
- Cold Compression ( $T < 400$ K): Causes slight "rejuvenation" (higher $T_f$ ) due to mechanical disordering without significant density change.
- $\beta$ -Regime ( $400 < T < 630$ K): High pressure leads to higher $T_f$ (less stable) compared to 1 atm samples at the same $T/T_{g,P}$ . This suggests pressure suppresses $\beta$ -relaxation, preventing structural relaxation and trapping the system in a higher energy state.
- $\alpha$ -Regime ( $T > 630$ K): High pressure leads to lower $T_f$ (more stable) and enhanced thermal stability, driven by pressure-induced densification.

B. Structural Evolution

FSDP Analysis ( $q_1$ and FWHM):
- $\beta$ -Regime: Compression results in a decrease in $q_1$ (indicating lower effective density/longer range correlations) and an increase in FWHM (increased structural heterogeneity). This confirms that $\beta$ -relaxation under pressure creates a more disordered local structure.
- $\alpha$ -Regime: Compression leads to an increase in $q_1$ and a decrease in FWHM, signifying a transition to a more packed, homogeneous, and ordered structure.
Pair Distribution Function (PDF) Insights:
- Cold/ $\beta$ -Compression: Minimal changes in bond lengths; primarily a redistribution of Zr-Zr and Cu-Zr bonds leading to local disorder.
- $\alpha$ -Compression: Significant shortening of Zr-Zr bond lengths and readjustment of Cu-Zr bonds. This reflects a transition from a covalent-like, directionally bonded structure to a dense random packed configuration.
Permanent Densification:
- In the $\alpha$ -regime (liquid state), compression induces permanent densification (~0.6–1%), whereas in the glassy state, deformation is largely elastic and recovered upon decompression.

5. Significance and Implications

Fundamental Physics: The study resolves the long-standing question of how pressure affects the competition between local ( $\beta$ ) and cooperative ( $\alpha$ ) dynamics. It reveals that pressure can suppress $\beta$ -relaxation (leading to destabilization) while promoting $\alpha$ -driven densification (leading to stabilization).
Material Design: The findings provide a "processing map" for metallic glasses. By selecting specific $P-T$ $P - T$ paths, engineers can intentionally design glasses with:
- Enhanced Stability: By compressing in the supercooled liquid regime ( $\alpha$ -dominated).
- Rejuvenated/High-Energy States: By compressing in the deep glassy or $\beta$ -dominated regimes.
Methodological Advance: The combination of fast-heating FDSC with high-pressure processing offers a robust method to decouple relaxation timescales that are difficult to separate at ambient pressure, applicable to other glass systems (polymeric, inorganic).
Polyamorphism: The results offer insights into pressure-induced glass-glass transitions, suggesting that the nature of the relaxation process dictates whether a glass transitions to a higher-density amorphous state or remains in a disordered, high-energy state.

In conclusion, this work establishes that the pressure dependence of metallic glass properties cannot be explained solely by density changes; rather, it is governed by the interplay between pressure-induced suppression of local mobility ( $\beta$ ) and the enhancement of collective structural ordering ( $\alpha$ ).