Phase transitions, as thermodynamic first-order or continuous transformations that occur when the control parameters of condensed‑matter systems cross critical thresholds, have critical dynamical behaviors that directly determine the macroscopic properties of functional materials. This paper focuses on three prototypical phase‑transition systems—thermoelastic martensitic transformations, electric‑field‑induced resistive switching, and metastable liquid–solid phase transitions—systematically elucidating the non‑equilibrium evolution of their order parameters near the critical point, while thoroughly analyzing the multiscale, multiphysics‑coupled measurement challenges inherent in achieving precise characterization of these transient processes.

1. The Reconstruction Mechanism of the Order Parameter in Phase-Transition Systems

1.1 Evolution of the Structural Order Parameter in Thermoelastic Martensitic Phase Transformations
The shape memory effect arises from the reversible crystallographic transformation between the martensitic and austenitic phases in an alloy system. This first-order phase transition is governed by a competitive interplay between chemical driving forces and elastic strain energy, with its transformation onset temperatures (Ms, Af) exhibiting sub‑Kelvin‑level sensitivity to compositional segregation, grain boundary constraints, and thermal history. In situ high‑resolution transmission electron microscopy reveals that the velocity of the phase‑transformation front can approach the speed of sound, while the orientation evolution of the habit plane conforms to the Wechsler–Lieberman–Read (WLR) crystallographic description.

1.2 Electronic Order Parameter Transitions in Resistive Random Access Memory

RRAM devices operate through either a field‑induced local metal–insulator phase transition (Mott transition) or the formation and rupture of conductive filaments driven by anion migration. This non‑equilibrium phase transition is governed by the coupled effects of multiple physical phenomena, including Schottky barrier modulation, the activation energy for oxygen vacancy migration (typically 0.5–1.2 eV), and Joule heating dissipation. Recent synchrotron radiation studies have revealed that, during the critical filament‑formation stage, the conductive filaments exhibit fractal growth, with diameter fluctuations conforming to the Kardar–Parisi–Zhang dynamical scaling law.

1.3 Nucleation Kinetics of Metastable Systems
As a typical metastable system, supercooled liquids exhibit solid–liquid phase transitions that conform to classical nucleation theory (CNT):

Among them, the critical nucleation energy barrier $\mathrm{Delta}{G}^{\ast }$ G Interfacial energy $\mathrm{gamma}$ gamma It exhibits a cubic dependence. As the system approaches the glass transition temperature Tg, diffusion‑controlled nucleation and growth display non-Arrhenius behavior, and the growth rate can be described by the Doremus equation:

2. Technical bottlenecks in characterizing critical processes

2.1 The Measurement Paradox of Spatiotemporal Resolution
The propagation speed of the phase‑transition front—reaching up to 100 m/s—and the timescale of lattice reconstruction—on the order of 10⁻¹² s—demand that characterization techniques simultaneously offer nanoscale spatial resolution and picosecond temporal resolution. Conventional scanning probe methods are constrained by their mechanical response bandwidth (typically below 1 MHz), whereas ultrafast pump–probe techniques, despite achieving femtosecond time resolution, lack the capability to track local structural evolution in real space.

2.2 Measurement Interference Due to Multiphysics Coupling
During electric-field‑induced phase transitions, the probe beam required for characterization—such as an electron beam or X-rays—can induce additional radiation damage or localized heating. Experiments have shown that a 300 keV electron beam in conventional TEM can generate displacement damage exceeding 10^8 Gy in resistive switching materials, which is already close to the threshold fluence for phase transitions in certain perovskite oxide materials.

2.3 Perturbation Sensitivity of Metastable Systems
The waiting-time distribution of a supercooled system prior to nucleation follows Poisson statistics:

Among them, the nucleation rate $\mathrm{lambda}$ λ exhibits exponential sensitivity to the Zeta potential of interfacial contaminants, the amplitude spectrum of container-wall roughness, and even the muon flux from cosmic rays. Under extreme supercooling conditions (ΔT > 50 K), the probability of nucleation events induced solely by background radiation already reaches 0.01 s⁻¹·cm⁻³.

3. Advances in Cutting-Edge Characterization Paradigms

3.1 Four-Dimensional Electron Microscopy Technology
A 4D-STEM system integrating femtosecond laser pumping with single-electron detection now achieves a dose efficiency of 10^7 electrons per pixel per frame, enabling nanosecond‑scale temporal resolution while preserving atomic‑scale spatial resolution. This technique has successfully captured the cascade growth of martensitic transformation domains in Fe–Pd alloys, and measurements reveal that phase‑boundary migration is strongly modulated by anisotropic stress waves.

3.2 Synchrotron Radiation Multimodal Correlation Measurements
A synchrotron radiation source based on a diffraction-limited storage ring, combined with a multi‑technique approach integrating X-ray photon correlation spectroscopy (XPCS), Bragg coherent diffraction imaging (BCDI), and X-ray absorption fine structure (XAFS), enables three‑dimensional, real‑time reconstruction of order‑parameter fluctuations, strain‑field evolution, and local coordination‑environment changes during phase transitions, with a sensitivity down to 10⁻⁶ strain.

3.3 Low-Temperature Scanning Tunneling Spectroscopy
A 4K-STM system equipped with atomic force feedback enables the observation of a pseudogap in the electronic density of states near the phase-transition critical point via dI/dV spectroscopy. In studies of the VO2 metal–insulator transition, this technique has revealed V–V dimerization fluctuations that precede the structural phase transition, with a correlation length that remains on the order of 2 nm—representing short-range order—even 100 K above the transition temperature, Tc.

Conclusion:
The essence of critical dynamics in phase transitions lies in the coupling between non-equilibrium statistical physics and microscopic quantum processes. The central challenge facing current characterization techniques is this: macroscopic thermodynamic measurements cannot resolve fluctuations and correlations on the nanosecond timescale, while atomic‑scale probes struggle to capture the micron‑scale cooperative evolution of phase domains. Future breakthroughs will hinge on developing a next‑generation characterization platform that combines the following features: (1) parallel spatial multiprobe measurement capabilities; (2) active noise suppression and quantum nondestructive detection; and (3) machine‑learning‑based real‑time inversion algorithms. Only by achieving complete resolution of these decisive moments can we truly establish a predictive design framework that bridges electronic‑level microscopic dynamics and device‑level macroscopic performance.

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