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

TL;DR

The paper addresses why dynamic anomalies such as Stokes-Einstein breakdown occur in high-coordination metallic glass-forming liquids. It employs molecular dynamics simulations of Cu$_{50}$Zr$_{50}$ to connect thermodynamic fluctuations, evidenced by peaks in the isobaric heat capacity $C_p$, with dynamic decoupling near a Griffiths-like smeared region ($G$-region) formed at the intersection of the kinetic glass-transition line and the gas–liquid spinodal, verified by the concurrent drift of the Kohlrausch exponent $eta_{ m KWW}$. The onset of SE breakdown tracks $C_p$ maxima and both move toward the $G$-region as pressure decreases, supporting a thermodynamic-fluctuation mechanism for anomalous transport. This framework offers a path to interpret rare-region dynamics in metallic glasses and motivates experimental tests under negative pressure and extension to other glass-forming compositions.

Abstract

Complex fluids such as water exhibits many anomalous phenomena, and research suggests these properties are closely tied to critical fluctuations near the liquid-liquid phase transition critical point (LLCP). However, whether a similar LLCP exists in metallic glass-forming liquids, which are notable for their high atomic coordination, remains an open question. Although dynamic anomalies such as the breakdown of the Stokes-Einstein (SE) relation have often been attributed to dynamic heterogeneity or structural changes, relatively few studies have analyzed these anomalies from a thermodynamic-fluctuation perspective. This gap probably stems from the challenges in detecting density-driven phase transitions in such systems. Here, we use numerical simulations to explore the thermodynamic mechanisms behind dynamic anomalies in a prototypical metallic glass-forming melt. We observe substantial thermodynamic fluctuations near a particular region, which likely corresponds to a frustration state of liquid, vapor, and glass. These fluctuations may contribute to the violation of the SE relation. Our findings offer a fresh Griffiths-like perspective on the dynamic anomalies seen in supercooled metallic liquids, and shed new light on their underlying mechanisms.

Figures (7)

• Figure 1: (a-c) Variation of pressure with temperature during isodensity cooling at different number densities: (a) $\rho = 50$, (b) $\rho = 51$, and (c) $\rho = 52$ (in units of $\text{nm}^{-3}$). Each curve represents one of the 20 independent configurations. The definition of $T_s$ and $T_g$ used in this work was also given in the panel accordingly. (d-e) Snapshots of atomic configurations at the end of the cooling process ($T=500$K): (d) $\rho = 50$, showing bubble formation; (e) $\rho = 52$, exhibiting a homogeneous glassy state. Note that here the reported $T_{\rm s}$ is the locus of spinodal points where the the homogeneous liquid approaches its mechanical stability limit.
• Figure 2: (a) A diagram indicating the occurrence of pressure discontinuities for 20 independent configurations prepared at various target number densities and temperatures. The color of each point denotes the probability of observing a pressure discontinuity at the corresponding state point. Blue triangles represent the characteristic temperatures ($T_s$) at which pressure jumps occur during the isodensity cooling processes, as described in detail in the main text. Variation of (b) number density and (c) enthalpy as a function of temperature during isobaric cooling at various pressures. (d) Corresponding temperature dependence of the isobaric heat capacity $C_p$ with error bars (using the method described in the Appendix), highlighting pronounced maxima at specific pressures.
• Figure 3: Relationship between the diffusion coefficient $D$ and relaxation time $\tau_{\alpha}$ (scaled by $T$) during the isobaric cooling process at five different pressures. The dashed grey line represents the Stokes-Einstein relation, $D \propto (\tau_{\alpha}/T)^{-1}$. The arrows indicate the temperatures below which the SE relation breaks down. Curves for $P<0$ GPa are shifted downward by multiple factors of 0.1 for visibility. Specifically, at $P = -6\,\text{GPa}$, we include error bars to represent statistical variability arising from cavitation events.
• Figure 4: Summary of characteristic temperatures near the Griffiths-like singularity, a smeared point representative by a red solid circle. Empty blue triangles denote the temperature $T_s$ at which pressure discontinuities occur, and solid blue triangles represent the glass-transition temperature $T_g$ identified in this study. Green squares indicate the temperature corresponding to the maximum isobaric heat capacity $C_p$, while black crosses mark the onset temperature for breakdown of the Stokes-Einstein (SE) relation. Gray lines represent the variation of number density with temperature, as previously shown in Fig. \ref{['Fig:thermo']}(b). Grey circles denote data obtained from a step-by-step cooling-equilibration process, demonstrating that our conclusions are robust against minor variations in the cooling protocol. The yellow star represents the melting temperature $T_{\mathrm{m}}$ measured at zero pressure using the two-phase coexistence method.
• Figure 5: The Kohlrausch exponent $\beta_{\rm KWW}$ at different temperatures and pressures is obtained by fitting the corresponding $F_{\rm s}(q,t)$ with the Kohlrausch–Williams–Watts (KWW) function. Panels (a)–(f) show $\beta_{\rm KWW}(T,P)$ at pressures (a) –1 GPa, (b) –2 GPa, (c) –3 GPa, (d) –4 GPa, (e) –5 GPa, and (f) –6 GPa. Panel (g) displays $\beta_{\rm KWW}$ along the SE-violation line as the state points approach the $G$-region. Error bars in panels have been obtained from the KWW-fit.