Nucleation in systems with elastic forces

Dynamic hysteresis at a noisy saddle node shows power-law scaling but nonuniversal exponent

Dynamic hysteresis, viz., delay in switching of a bistable system on account of the finite sweep rate of the drive, has been extensively studied in dynamical and thermodynamic systems. Dynamic hysteresis results from slowing of the response around a saddle-node bifurcation. As a consequence, the hysteresis area increases with the sweep rate. Mean-field theory, relevant for noise-free situations, predicts power-law scaling with the area scaling exponent of 2/3. We have experimentally investigated the dynamic hysteresis for a thermally driven metal-insulator transition in a high-quality NdNiO_{3} thin film and found the scaling exponent to be about 1/3, far less than the mean-field value. To understand this, we have numerically studied Langevin dynamics of the order parameter and found that noise, which can be thought to parallel finite temperature effects, influences the character of dynamic hysteresis by systematically lowering the dynamical exponent to as small as 0.2. The power-law scaling character, on the other hand, is unaffected in the range of chosen parameters. This work rationalizes the ubiquitous power-law scaling of the dynamic hysteresis as well as the wide variation in the scaling exponent between 0.66 and 0.2 observed in different systems over the last 30 years.

Critical Slowing Down at the Abrupt Mott Transition: When the First-Order Phase Transition Becomes Zeroth Order and Looks Like Second Order

We report that the thermally induced Mott transition in vanadium sesquioxide shows critical slowing down and enhanced variance ("critical opalescence") of the order parameter fluctuations measured through low-frequency resistance-noise spectroscopy. Coupled with the observed increase of the phase-ordering time, these features suggest that the strong abrupt transition is controlled by a critical-like singularity in the hysteretic metastable phase. The singularity is identified with the spinodal point and is a likely consequence of the strain-induced long-range interaction.

Morphogenetic Transition in Weak Gelation of Crystallizable Linear Polymers

Fibrillar networks and spherulite assemblies are the two most frequently observed textures in weak gelation of crystallizable linear polymers. We find such two textures in response to the kinetic distinction between instability/spinodal and metastability/nucleation of the polymer crystallization and prove the morphogenetic transition in between. Moreover, it comes as a surprise when such a transition exhibits a spinodal singularity that reveals a mean-field-like "mesoscopic" phase transition behavior.

Structure of fluctuations near mean-field critical points and spinodals and its implication for physical processes

We analyze the structure of fluctuations near critical points and spinodals in mean-field and near-mean-field systems. Unlike systems that are non-mean-field, for which a fluctuation can be represented by a single cluster in a properly chosen percolation model, a fluctuation in mean-field and near-mean-field systems consists of a large number of clusters, which we term fundamental clusters. The structure of the latter and the way that they form fluctuations has important physical consequences for phenomena as diverse as nucleation in supercooled liquids, spinodal decomposition and continuous ordering, and the statistical distribution of earthquakes. The effects due to the fundamental clusters implies that they are physical objects and not only mathematical constructs.

Simulations of spinodal nucleation in systems with elastic interactions

Systems with long-range interactions quenched into a metastable state near the pseudospinodal exhibit nucleation that is qualitatively different from classical nucleation near the coexistence curve. We observe nucleation droplets in Langevin simulations of a two-dimensional model of martensitic transformations and determine that the structure of the nucleating droplet differs from the stable martensite structure. Our results, together with experimental measurements of the phonon dispersion curve, allow us to predict the nature of the droplet. The results have implications for nucleation in many solid-solid transitions and the structure of the final state.

Heterogeneous nucleation of supercooled water, and the effect of an added catalyst

The statistics of liquid-to-crystal nucleation are measured rigorously by using a recently developed automated lag-time apparatus (ALTA). A single sample, in this case a sample of pure water both with and without an (insoluble) AgI crystal, is repeatedly cooled, nucleated, and thawed. Analysis of the data, coupled with a second kind of experiment, shows that the statistics of nucleation are consistent with a first-order kinetic mechanism over a wide range of supercooling temperatures. The limitations of classical nucleation theory are exhibited. Our analysis unifies many related experiments in biology, physics, chemistry, and chemical engineering.