Phase field modeling of electrochemistry II: Kinetics

The kinetic behavior of a phase field model of electrochemistry is explored for advancing (electrodeposition) and receding (electrodissolution) conditions in one dimension. We described the equilibrium behavior of this model in [J. E. Guyer, W. J. Boettinger, J.A. Warren, and G. B. McFadden, ``Phase field modeling of electrochemistry I: Equilibrium'', cond-mat/0308173]. We examine the relationship between the parameters of the phase field method and the more typical parameters of electrochemistry. We demonstrate ohmic conduction in the electrode and ionic conduction in the electrolyte. We find that, despite making simple, linear dynamic postulates, we obtain the nonlinear relationship between current and overpotential predicted by the classical ``Butler-Volmer'' equation and observed in electrochemical experiments. The charge distribution in the interfacial double layer changes with the passage of current and, at sufficiently high currents, we find that the diffusion limited deposition of a more noble cation leads to alloy deposition with less noble species.Comment: v3: To be published in Phys. Rev. E v2: Attempt to work around turnpage bug. Replaced color Fig. 4a with grayscale 13 pages, 7 figures in 10 files, REVTeX 4, SIunits.sty, follows cond-mat/030817

A Model for Solid 3^3He: II

We propose a simple Ginzburg-Landau free energy to describe the magnetic phase transition in solid $^3$He. The free energy is analyzed with due consideration of the hard first order transitions at low magnetic fields. The resulting phase diagram contains all of the important features of the experimentally observed ph ase diagram. The free energy also yields a critical field at which the transition from the disordered state to the high field state changes from a first order to a second order one.Comment: This paper has been accepted for publication in Journal of Low Temperature Physics. Use regular Tex, with the D. Eardley version of Macros called jnl.tex. 10 pages, 4 figs available from [email protected]

Phase field modeling of electrochemistry I: Equilibrium

A diffuse interface (phase field) model for an electrochemical system is developed. We describe the minimal set of components needed to model an electrochemical interface and present a variational derivation of the governing equations. With a simple set of assumptions: mass and volume constraints, Poisson's equation, ideal solution thermodynamics in the bulk, and a simple description of the competing energies in the interface, the model captures the charge separation associated with the equilibrium double layer at the electrochemical interface. The decay of the electrostatic potential in the electrolyte agrees with the classical Gouy-Chapman and Debye-H\"uckel theories. We calculate the surface energy, surface charge, and differential capacitance as functions of potential and find qualitative agreement between the model and existing theories and experiments. In particular, the differential capacitance curves exhibit complex shapes with multiple extrema, as exhibited in many electrochemical systems.Comment: v3: To be published in Phys. Rev. E v2: Added link to cond-mat/0308179 in References 13 pages, 6 figures in 15 files, REVTeX 4, SIUnits.sty. Precedes cond-mat/030817

Epitaxial growth in dislocation-free strained alloy films: Morphological and compositional instabilities

The mechanisms of stability or instability in the strained alloy film growth are of intense current interest to both theorists and experimentalists. We consider dislocation-free, coherent, growing alloy films which could exhibit a morphological instability without nucleation. We investigate such strained films by developing a nonequilibrium, continuum model and by performing a linear stability analysis. The couplings of film-substrate misfit strain, compositional stress, deposition rate, and growth temperature determine the stability of film morphology as well as the surface spinodal decomposition. We consider some realistic factors of epitaxial growth, in particular the composition dependence of elastic moduli and the coupling between top surface and underlying bulk of the film. The interplay of these factors leads to new stability results. In addition to the stability diagrams both above and below the coherent spinodal temperature, we also calculate the kinetic critical thickness for the onset of instability as well as its scaling behavior with respect to misfit strain and deposition rate. We apply our results to some real growth systems and discuss the implications related to some recent experimental observations.Comment: 26 pages, 13 eps figure

The spatiotemporal evolution of granular microslip precursors to laboratory earthquakes

Laboratory earthquake experiments provide important observational constraints for our understanding of earthquake physics. Here we leverage continuous waveform data from a network of piezoceramic sensors to study the spatial and temporal evolution of microslip activity during a shear experiment with synthetic fault gouge. We combine machine learning techniques with ray theoretical seismology to detect, associate, and locate tens of thousands of microslip events within the gouge layer. Microslip activity is concentrated near the center of the system but is highly variable in space and time. While microslip activity rate increases as failure approaches, the spatiotemporal evolution can differ substantially between stick-slip cycles. These results illustrate that even within a single, well-constrained laboratory experiment, the dynamics of earthquake nucleation can be highly complex

Annual Summary of Vital Statistics-1997

Many positive trends in the health of Americans continued into 1997. In 1997, the preliminary birth rate declined slightly to 14.6 births per 1000 population, and the fertility rate, births per 1000 women 15 to 44 years of age, was unchanged from the previous year (65.3). These indicators suggest that the downward trend in births observed since the early 1990s may have abated. Fertility rates for white, black, and Native American women were essentially unchanged between 1996 and 1997. Fertility among Hispanic women declined 2% in 1997 to 103.1, the lowest level reported since national data for this group have been available. For the sixth consecutive year, birth rates dropped for teens. Birth rates for women 30 years or older continued to increase. The proportion of births to unmarried women (32.4%) was unchanged in 1997. The trend toward earlier utilization of prenatal care continued for 1997; 82.5% of women began prenatal care in the first trimester. There was no change in the percentage with late (third trimester) or no care in 1997. The cesarean delivery rate rose slightly to 20.8% in 1997, a reversal of the downward trend observed since 1989. The percentage of low birth weight (LBW) infants rose again in 1997 to 7.5%. The percentage of very low birth weight was up only slightly to 1.41%. Among births to white mothers, LBW increased for the fifth consecutive year, to 6.5%, whereas the rate for black mothers remained unchanged at 13%. Much, but not all, of the rise in LBW for white mothers during the 1990s can be attributed to an increase in multiple births. In 1996, the multiple birth rate rose again by 5%, and the higher-order multiple birth rate climbed by 20%. Infant mortality reached an all time low level of 7.1 deaths per 1000 births, based on preliminary 1997 data. Both neonatal and postneonatal mortality rates declined. In 1996, 64% of all infant deaths occurred to the 7.4% of infants born at LBW. Infant mortality rates continue to be more than two times greater for black than for white infants. Among all the states in 1996, Maine, Massachusetts, and New Hampshire had the lowest infant mortality rates. Despite declines in infant mortality, the United States continues to rank poorly in international comparisons of infant mortality. Expectation of life at birth reached a new high in 1997 of 76.5 years for all gender and race groups combined. Age-adjusted death rates declined in 1997 for diseases of the heart, accidents and adverse affects (unintentional injuries), homicide, suicide, malignant neoplasms, cerebrovascular disease, chronic liver disease and cirrhosis, and diabetes. In 1997, mortality due to HIV infection declined by 47%. Death rates for children from all major causes declined again in 1997. Motor vehicle traffic injuries and firearm injuries were the two major causes of traumatic death. A large proportion of childhood deaths continue to occur as a result of preventable injuries

The natural history of regional wall motion in the acutely infarcted canine ventricle

Two-dimensional echocardiography was employed to define the natural history of regional wall motion abnormalities in a canine model of acute experimental myocardial infarction. Serial short-axis two-dimensional echocardiograms were recorded in 11 closed chest dogs before coronary occlusion and 10, 30, 60, 180 and 360 minutes after permanent coronary ligation. Radiolabeled microsphere-derived blood flows were obtained in each study period and the histochemical (triphenyltetrazolium chloride) extent of infarction was determined at 6 hours. Previously published methods were used to quantitate field by field (every 16.7 ms) excursion of 36 evenly spaced endocardial targets. The circumferential extent of abnormal wall motion was followed sequentially using previously published definitions of abnormality: 1) systolic fractional radial change of less than 20%; 2) dyskinesia (systolic bulging) at the point in time (echocardiographic field) in which there is maximal dyskinesia; and 3) correlation with composite normal ray motion falling outside the 95 % confidence limits defined in the control period. On the basis of the triphenyltet razolium chloride staining pattern, the ventricle was divided into five zones: central infarct zone, zone with greater than 25% transmural infarction, total infarct zone, border zones and normal zone. Mean systolic fractional radial change was calculated for each zone and used as an index of the magnitude of abnormal wall motion.Regardless of the definition of abnormality employed, the circumferential extent of abnormal wall motion manifested at 10 minutes after occlusion did not significantly change, even up to 6 hours later. Similarly, 10 minutes after coronary occlusion the three infarct zones and border zones demonstrated significantly reduced systolic fractional radial change. This remained stable over the remainder of the 6 hour study period.It is concluded that once established at 10 minutes after coronary occlusion, the circumferential extent and magnitude of abnormal wall motion do not significantly change in the immediate postinfarct (6 hour) period