Prabhat K. Jaiswal

Mechanical Yield in Amorphous Solids: A First-Order Phase Transition.

Amorphous solids yield at a critical value of the strain (in strain-controlled experiments); for larger strains, the average stress can no longer increase-the system displays an elastoplastic steady state. A long-standing riddle in the materials community is what the difference is between the microscopic states of the material before and after yield. Explanations in the literature are material specific, but the universality of the phenomenon begs a universal answer. We argue here that there is no fundamental difference in the states of matter before and after yield, but the yield is a bona fide first-order phase transition between a highly restricted set of possible configurations residing in a small region of phase space to a vastly rich set of configurations which include many marginally stable ones. To show this, we employ an order parameter of universal applicability, independent of the microscopic interactions, that is successful in quantifying the transition in an unambiguous manner.

Shear Transformation Zones: State determined or protocol dependent?

The concept of a Shear Transformation Zone (STZ) refers to a region in an amorphous solid that undergoes a plastic event when the material is put under an external mechanical load. An important question that had accompanied the development of the theory of plasticity in amorphous solids for many years now is whether an STZ is a {\em region} existing in the material (which can be predicted by analyzing the unloaded material), or is it an {\em event} that depends on the loading protocol (i.e., the event cannot be predicted without following the protocol itself). In this Letter we present strong evidence that the latter is the case. Infinitesimal changes of protocol result in macroscopically big jumps in the positions of plastic events, meaning that these can never be predicted from considering the unloaded material.

Hydrodynamic crossovers in surface-directed spinodal decomposition and surface enrichment

We present comprehensive molecular dynamics results for the kinetics of surface-directed spinodal decomposition and surface enrichment in binary mixtures at wetting surfaces. We study the surface morphology and the growth dynamics of the wetting and enrichment layers. The growth law for the thickness of these layers shows a crossover from a diffusive regime to a hydrodynamic regime. We provide phenomenological arguments to understand this crossover.

Kinetics of spinodal phase separation in unstable thin liquid films.

We study universality in the kinetics of spinodal phase separation in unstable thin liquid films, via simulations of the thin film equation. It is shown that, in addition to morphology and free energy, the number density of local maxima in the film profile can also be used to identify the early, late, and intermediate stages of spinodal phase separation. A universal curve between the number density of local maxima and rescaled time describes the kinetics of the early stage in d=2 and 3. The Lifshitz-Slyozov exponent of -1/3 describes the kinetics of the late stage in d=2 even in the absence of coexisting equilibrium phases.

Kinetics of surface enrichment: A molecular dynamics study

We use molecular dynamics to study the kinetics of surface enrichment (SE) in a stable homogeneous mixture (AB), placed in contact with a surface which preferentially attracts A. The SE profiles show a characteristic double-exponential behavior with two length scales: ξ(-), which rapidly saturates to its equilibrium value, and ξ(+), which diverges as a power-law with time (ξ(+)∼t(θ)). We find that hydrodynamic effects result in a crossover of the growth exponent from θ≃0.5 to θ≃1.0. There is also a corresponding crossover in the growth dynamics of the SE layer thickness.

Stochastic Approach to Plasticity and Yield in Amorphous Solids

We focus on the probability distribution function (PDF) P(Δγ;γ) where Δγ are the measured strain intervals between plastic events in a athermal strained amorphous solids, and γ measures the accumulated strain. The tail of this distribution as Δγ→0 (in the thermodynamic limit) scales like Δγ(η). The exponent η is related via scaling relations to the tail of the PDF of the eigenvalues of the plastic modes of the Hessian matrix P(λ) which scales like λ(θ), η=(θ-1)/2. The numerical values of η or θ can be determined easily in the unstrained material and in the yielded state of plastic flow. Special care is called for in the determination of these exponents between these states as γ increases. Determining the γ dependence of the PDF P(Δγ;γ) can shed important light on plasticity and yield. We conclude that the PDFs of both Δγ and λ are not continuous functions of γ. In slowly quenched amorphous solids they undergo two discontinuous transitions, first at γ=0(+) and then at the yield point γ=γ(Y) to plastic flow. In quickly quenched amorphous solids the second transition is smeared out due to the nonexisting stress peak before yield. The nature of these transitions and scaling relations with the system size dependence of 〈Δγ〉 are discussed.

Phase separation in antisymmetric films: a molecular dynamics study.

We have used molecular dynamics (MD) simulations to study phase-separation kinetics in a binary fluid mixture (AB) confined in an antisymmetric thin film. One surface of the film (located at z = 0) attracts the A-atoms, and the other surface (located at z = D) attracts the B-atoms. We study the kinetic processes which lead to the formation of equilibrium morphologies subsequent to a deep quench below the miscibility gap. In the initial stages, one observes the formation of a layered structure, consisting of an A-rich layer followed by a B-rich layer at z = 0; and an analogous structure at z = D. This multi-layered morphology is time-dependent and propagates into the bulk, though it may break up into a laterally inhomogeneous structure at a later stage. We characterize the evolution morphologies via laterally averaged order parameter profiles; the growth laws for wetting-layer kinetics and layer-wise length scales; and the scaling properties of layer-wise correlation functions.

Amplification of fluctuations in unstable systems with disorder.

We study the early stage kinetics of thermodynamically unstable systems with quenched disorder. We show analytically that the growth of initial fluctuations is amplified by the presence of disorder. This is confirmed by numerical simulations of morphological phase separation in thin liquid films and spinodal decomposition in binary mixtures. We also discuss the experimental implications of our results.

Modeling Barkhausen Noise in magnetic glasses with dipole-dipole interactions

Long-ranged dipole-dipole interactions in magnetic glasses give rise to magnetic domains having labyrinthine patterns. Barkhausen Noise is then expected to result from the movement of domain boundaries which is supposed to be modeled by the motion of elastic membranes with random pinning. We propose an atomistic model of such magnetic glasses in which we measure the Barkhausen Noise which indeed results from the movement of domain boundaries. Nevertheless the statistics of the Barkhausen Noise is found in striking disagreement with the expectations in the literature. In fact we find exponential statistics without any power law, stressing the fact that Barkhausen Noise can belong to very different universality classes. In this glassy system the essence of the phenomenon is the ability of spin-carrying particles to move and minimize the energy without any spin flip. A theory is offered in excellent agreement with the measured data without any free parameter.

Scaling Theory of the Mechanical Properties of Amorphous Nano-Films

Numerical Simulations are employed to create amorphous nano-films of a chosen thickness on a crystalline substrate which induces strain on the film. The films are grown by a vapor deposition technique which was recently developed to create very stable glassy films. Using the exact relations between the Hessian matrix and the shear and bulk moduli we explore the mechanical properties of the nano-films as a function of the density of the substrate and the film thickness. The existence of the substrate dominates the mechanical properties of the combined substrate-film system. Scaling concepts are then employed to achieve data collapse in a wide range of densities and film thicknesses.