Griffiths-like region explains the dynamic anomaly in metallic glass-forming liquids

Technical Summary: Griffiths-like Region Explains Dynamic Anomaly in Metallic Glass-Forming Liquids

Problem Statement
Complex fluids, particularly water, exhibit anomalous behavior frequently attributed to critical fluctuations near a critical point of a liquid-liquid phase transition (LLCP). Although liquid-liquid transitions (LLTs) have been identified in various systems, including certain amorphous alloys (e.g., cesium-based), their existence in metallic glass-forming liquids with high atomic coordination numbers remains an open question. In these high-coordination-number systems, clear first-order phase transitions driven by significant density variations are rare, and existing explanations for dynamic anomalies—such as the breakdown of the Stokes-Einstein (SE) relation—rely primarily on dynamic heterogeneity or structural reorganization rather than thermodynamic fluctuations. A perspective based on thermodynamic fluctuations has been little explored due to the difficulty of detecting density-driven phase transitions in these systems.

Methodology
The authors performed molecular dynamics (MD) simulations using the LAMMPS package to investigate a prototypical metallic glass-forming system: the Cu$_{50}$Zr$_{50}$ alloy. Interatomic interactions were modeled using a realistic EAM potential (Embedded-Atom Method). The study employed a system of 10,000 atoms with periodic boundary conditions.

• Protocols: Two cooling protocols were applied: isochoric (constant volume) and isobaric (constant pressure) cooling.
• Initialization: Samples were equilibrated at 3500 K under zero pressure, followed by the generation of 20 independent atomic configurations for statistical analysis.
• Analysis: The study tracked pressure, density, enthalpy, and isobaric heat capacity ($C_p$) as a function of temperature. Dynamic properties were analyzed via the diffusion coefficient ($D$) and structural relaxation time ($\tau_\alpha$), extracted from the self-intermediate scattering function $F_s(q, t)$ at $q = 2.8$ Å$^{-1}$. The breakdown of the SE relation ($D \sim (\tau_\alpha/T)^{-1}$) was examined at various pressures, including negative pressures.

Main Results

1. Pressure Discontinuities and Bubble Formation: During isochoric cooling, a discontinuous pressure jump corresponding to cavitation (bubble formation) was observed at lower particle densities ($\rho = 50$ nm$^{-3}$). At higher densities ($\rho = 52$ nm$^{-3}$), pressure evolved continuously, indicating a homogeneous liquid-glass transition. At intermediate densities ($\rho = 51$ nm$^{-3}$), a "coexistence" of liquid, bubble, and glass-like states was observed, characterized by probabilistic bubble formation.
2. Thermodynamic Fluctuations: Under isobaric cooling, pronounced peaks in the isobaric heat capacity ($C_p$) were observed. As pressure decreased, the magnitude of the $C_p$ peak increased, and the peak temperature shifted to lower values.
3. Correlation with Dynamic Anomalies: The onset temperature for the breakdown of the SE relation closely followed the temperature of the $C_p$ maximum across various pressures.
4. Convergence to a Specific Region: Both the $C_p$ maximum and the onset temperatures for the SE breakdown asymptotically approach a distinct thermodynamic region, defined by the intersection of the kinetic glass transition line and the gas-liquid spinodal line.
5. Griffiths-like Behavior: The study identifies this intersection region as a "Griffiths-like" singularity. In contrast to a sharp critical point, this region exhibits a "smeared" singularity, where rare, metastable clusters (local heterogeneities in density or structure) dominate the response. The Kohlrausch exponent ($\beta_{KWW}$) showed a systematic drift as state points approached this region, rather than saturating, consistent with a broad distribution of relaxation times characteristic of Griffiths phenomena.

Main Contributions

• Thermodynamic Perspective: The paper provides a thermodynamic-fluctuation-based explanation for the breakdown of the SE relation in high-coordination-number metallic liquids, linking it to enhanced fluctuations near a specific thermodynamic region, rather than relying solely on kinetic constraints.
• Identification of a Griffiths-like Region: The authors propose that dynamic anomalies in undercooled metallic liquids arise from a Griffiths-like regime located near the intersection of the kinetic glass transition line and the liquid-gas spinodal. This region is characterized by rare, anomalously dynamic domains that favor large thermodynamic fluctuations.
• Mechanistic Link: The work establishes a direct connection between the violation of the SE relation and the extrema of thermodynamic response functions ($C_p$), suggesting that proximity to a spinodal-like instability under negative pressure amplifies the influence of these rare regions.

Significance and Claims
The authors claim that their results offer a "fresh Griffiths-like perspective" on dynamic anomalies in undercooled metallic liquids. By identifying a region where thermodynamic and dynamic anomalies converge, the study suggests that the breakdown of the SE relation in these systems can be understood through the lens of rare-region effects, akin to Griffiths phenomena, rather than requiring a conventional liquid-liquid critical point with a sharp phase transition.

The paper emphasizes that this "Griffiths-like" description is a phenomenological framework rooted in stability under negative pressure and proximity to spinodal instabilities. It distinguishes this region from a conventional triple point and notes that the involved phases (liquid, vapor, and glass) do not exhibit the symmetry breaking typical of crystalline solids. The authors conclude that this thermo-mechanically oriented viewpoint offers a useful interpretative window for transport anomalies in metallic glass-forming liquids, although they acknowledge that a detailed microscopic characterization of the underlying rare domains remains a direction for future work.