Toward an understanding of disequilibrium dihedral angles in mafic rocks

[1] The median dihedral angle at clinopyroxene-plagioclase-plagioclase junctions in mafic rocks, Θcpp, is generally lower than equilibrium (109° ± 2°). Observation of a wide range of mafic bodies demonstrates that previous work on systematic variations of Θcpp is incorrect in several important respects. First, the spatial distribution of plagioclase compositional zoning demonstrates that the final geometry of three-grain junctions, and hence Θcpp, is formed during solidification (the igneous process): sub-solidus textural modification in most dolerites and gabbros, previously thought to be the dominant control on Θcpp, is insignificant. Θcpp is governed by mass transport constraints, the inhibiting effects of small pore size on crystallization, and variation in relative growth rates of pyroxene and plagioclase. During rapid cooling, pyroxene preferentially fills wider pores while the narrower pores remain melt-filled, resulting in an initial value of Θcpp of 78°, rather than 60° which would be expected if all melt-filled pores were filled with pyroxene. Lower cooling rates create a higher initial Θcpp due to changes in relative growth rates of the two minerals at the nascent three-grain junction. Low Θcpp (associated with cuspate clinopyroxene grains at triple junctions) can also be diagnostic of infiltration of previously melt-free rocks by late-stage evolved liquids (the metasomatic process). Modification of Θcpp by sub-solidus textural equilibration (the metamorphic process) is only important for fine-grained mafic rocks such as chilled margins and intraplutonic chill zones. In coarse-grained gabbros from shallow crustal intrusions the metamorphic process occurs only in the centers of oikocrysts, associated with rounding of chadacrysts

Hysteresis and the dynamic phase transition in thin ferromagnetic films

Hysteresis and the non-equilibrium dynamic phase transition in thin magnetic films subject to an oscillatory external field have been studied by Monte Carlo simulation. The model under investigation is a classical Heisenberg spin system with a bilinear exchange anisotropy in a planar thin film geometry with competing surface fields. The film exhibits a non-equilibrium phase transition between dynamically ordered and dynamically disordered phases characterized by a critical temperature Tcd, whose location of is determined by the amplitude H0 and frequency w of the applied oscillatory field. In the presence of competing surface fields the critical temperature of the ferromagnetic-paramagnetic transition for the film is suppressed from the bulk system value, Tc, to the interface localization-delocalization temperature Tci. The simulations show that in general Tcd < Tci for the model film. The profile of the time-dependent layer magnetization across the film shows that the dynamically ordered and dynamically disordered phases coexist within the film for T < Tcd. In the presence of competing surface fields, the dynamically ordered phase is localized at one surface of the film.Comment: PDF file, 21 pages including 8 figure pages; added references,typos added; to be published in PR

Growth, microstructure, and failure of crazes in glassy polymers

We report on an extensive study of craze formation in glassy polymers. Molecular dynamics simulations of a coarse-grained bead-spring model were employed to investigate the molecular level processes during craze nucleation, widening, and breakdown for a wide range of temperature, polymer chain length $N$, entanglement length $N_e$ and strength of adhesive interactions between polymer chains. Craze widening proceeds via a fibril-drawing process at constant drawing stress. The extension ratio is determined by the entanglement length, and the characteristic length of stretched chain segments in the polymer craze is $N_e/3$. In the craze, tension is mostly carried by the covalent backbone bonds, and the force distribution develops an exponential tail at large tensile forces. The failure mode of crazes changes from disentanglement to scission for $N/N_e\sim 10$, and breakdown through scission is governed by large stress fluctuations. The simulations also reveal inconsistencies with previous theoretical models of craze widening that were based on continuum level hydrodynamics

Test of the Kolmogorov-Johnson-Mehl-Avrami picture of metastable decay in a model with microscopic dynamics

The Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory for the time evolution of the order parameter in systems undergoing first-order phase transformations has been extended by Sekimoto to the level of two-point correlation functions. Here, this extended KJMA theory is applied to a kinetic Ising lattice-gas model, in which the elementary kinetic processes act on microscopic length and time scales. The theoretical framework is used to analyze data from extensive Monte Carlo simulations. The theory is inherently a mesoscopic continuum picture, and in principle it requires a large separation between the microscopic scales and the mesoscopic scales characteristic of the evolving two-phase structure. Nevertheless, we find excellent quantitative agreement with the simulations in a large parameter regime, extending remarkably far towards strong fields (large supersaturations) and correspondingly small nucleation barriers. The original KJMA theory permits direct measurement of the order parameter in the metastable phase, and using the extension to correlation functions one can also perform separate measurements of the nucleation rate and the average velocity of the convoluted interface between the metastable and stable phase regions. The values obtained for all three quantities are verified by other theoretical and computational methods. As these quantities are often difficult to measure directly during a process of phase transformation, data analysis using the extended KJMA theory may provide a useful experimental alternative.Comment: RevTex, 21 pages including 14 ps figures. Submitted to Phys. Rev. B. One misprint corrected in Eq.(C1

Dynamic Phase Transition, Universality, and Finite-size Scaling in the Two-dimensional Kinetic Ising Model in an Oscillating Field

We study the two-dimensional kinetic Ising model below its equilibrium critical temperature, subject to a square-wave oscillating external field. We focus on the multi-droplet regime where the metastable phase decays through nucleation and growth of many droplets of the stable phase. At a critical frequency, the system undergoes a genuine non-equilibrium phase transition, in which the symmetry-broken phase corresponds to an asymmetric stationary limit cycle for the time-dependent magnetization. We investigate the universal aspects of this dynamic phase transition at various temperatures and field amplitudes via large-scale Monte Carlo simulations, employing finite-size scaling techniques adopted from equilibrium critical phenomena. The critical exponents, the fixed-point value of the fourth-order cumulant, and the critical order-parameter distribution all are consistent with the universality class of the two-dimensional equilibrium Ising model. We also study the cross-over from the multi-droplet to the strong-field regime, where the transition disappears

Stochastic Hysteresis and Resonance in a Kinetic Ising System

We study hysteresis for a two-dimensional, spin-1/2, nearest-neighbor, kinetic Ising ferromagnet in an oscillating field, using Monte Carlo simulations and analytical theory. Attention is focused on small systems and weak field amplitudes at a temperature below $T_{c}$. For these restricted parameters, the magnetization switches through random nucleation of a single droplet of spins aligned with the applied field. We analyze the stochastic hysteresis observed in this parameter regime, using time-dependent nucleation theory and the theory of variable-rate Markov processes. The theory enables us to accurately predict the results of extensive Monte Carlo simulations, without the use of any adjustable parameters. The stochastic response is qualitatively different from what is observed, either in mean-field models or in simulations of larger spatially extended systems. We consider the frequency dependence of the probability density for the hysteresis-loop area and show that its average slowly crosses over to a logarithmic decay with frequency and amplitude for asymptotically low frequencies. Both the average loop area and the residence-time distributions for the magnetization show evidence of stochastic resonance. We also demonstrate a connection between the residence-time distributions and the power spectral densities of the magnetization time series. In addition to their significance for the interpretation of recent experiments in condensed-matter physics, including studies of switching in ferromagnetic and ferroelectric nanoparticles and ultrathin films, our results are relevant to the general theory of periodically driven arrays of coupled, bistable systems with stochastic noise.Comment: 35 pages. Submitted to Phys. Rev. E Minor revisions to the text and updated reference

Dynamic phase transitions in thin ferromagnetic films

Monte Carlo simulations have been used to investigate the dynamic phase behavior of a classical Heisenberg spin system with a bilinear exchange anisotropy in a planar thin film geometry. Studies of the field amplitude, frequency and temperature dependence show dynamic phase transitions in films subject to a pulsed oscillatory external field. Thin films with competing surface fields show separate and distinct dynamic phase transitions for the bulk and surface layers of the film. Between the two transitions, a mixed state with coexisting dynamically ordered and dynamically disordered phases is observed in the film. In contrast, the free film with no surface fields shows a single dynamic phase transition as in a bulk system.Comment: 25 pages including figures in pdf format, to be published in PR

Spatiotemporal Stochastic Resonance in Fully Frustrated Josephson Ladders

We consider a Josephson-junction ladder in an external magnetic field with half flux quantum per plaquette. When driven by external currents, periodic in time and staggered in space, such a fully frustrated system is found to display spatiotemporal stochastic resonance under the influence of thermal noise. Such resonance behavior is investigated both numerically and analytically, which reveals significant effects of anisotropy and yields rich physics.Comment: 8 pages in two columns, 8 figures, to appear in Phys. Rev.

Solvable Kinetic Gaussian Model in External Field

In this paper, the single-spin transition dynamics is used to investigate the kinetic Gaussian model in a periodic external field. We first derive the fundamental dynamic equations, and then treat an isotropic d-dimensional hypercubic lattice Gaussian spin system with Fourier's transformation method. We obtain exactly the local magnetization and the equal-time pair correlation function. The critical characteristics of the dynamical, the complex susceptibility, and the dynamical response are discussed. The results show that the time evolution of the dynamical quantities and the dynamical responses of the system strongly depend on the frequency and the wave vector of the external field.Comment: 11 page

Direct observation of active material concentration gradients and crystallinity breakdown in LiFePO4 electrodes during charge/discharge cycling of lithium batteries

The phase changes that occur during discharge of an electrode comprised of LiFePO4, carbon, and PTFE binder have been studied in lithium half cells by using X-ray diffraction measurements in reflection geometry. Differences in the state of charge between the front and the back of LiFePO4 electrodes have been visualized. By modifying the X-ray incident angle the depth of penetration of the X-ray beam into the electrode was altered, allowing for the examination of any concentration gradients that were present within the electrode. At high rates of discharge the electrode side facing the current collector underwent limited lithium insertion while the electrode as a whole underwent greater than 50% of discharge. This behavior is consistent with depletion at high rate of the lithium content of the electrolyte contained in the electrode pores. Increases in the diffraction peak widths indicated a breakdown of crystallinity within the active material during cycling even during the relatively short duration of these experiments, which can also be linked to cycling at high rate