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

Kinetics governing phase separation of nanostructured Sn_xGe_(1–x) alloys

We have studied the dynamic phenomenon of Sn_xGe_(1–x)/Ge phase separation during deposition by molecular beam epitaxy on Ge(001) substrates. Phase separation leads to the formation of direct band gap semiconductor nanowire arrays embedded in Ge oriented along the [001] growth direction. The effect of strain and composition on the periodicity were decoupled by growth on Ge(001) and partially relaxed Si_yGe_(1–y)/Ge(001) virtual substrates. The experimental results are compared with three linear instability models of strained film growth and find good agreement with only one of the models for phase separation during dynamic growth

Testing Assumptions about Laboratory Protocol Fidelity

A recent focus of our Program for the Study of Infancy is the extent to which lab assistants retain fidelity when implementing experimental protocols. Dixon et al. showed that experimenters’ implementations of some aspects of standardized protocols can be influenced by infants’ temperaments. Ellefson and Oppenheimer further found that procedural deviations reduce effect sizes and lead to heterogeneity of findings. In this project, we evaluated archival videos involving experimenters’ implementations of two elicited imitation tasks, “Feed Bear” and “Make a Rattle.” In both tasks, experimenters were assumed to adhere to a narrative script and procedure, which included familiarizing infants with experimental stimuli for 60 seconds prior to infants engaging the tasks. Experimenters were also expected to adhere to a standardized narrative script that accompanied the modeling of “feeding the bear” or “making a rattle.” In this study we explored whether they did so, independent of infants\u27 temperament characteristics. Ten experimenters guided sixty-one 15-month-olds through the experimental procedure. We examined two types of dependent measures reflecting 1) whether experimenters adhered to the 60 second familiarization time protocol, and 2) whether experimenters adhered to the standardized scripts. We also tracked experimenter infant-directed speech (IDS) before the model (prologue IDS) and after the model (epilogue IDS), to see if experimenters’ speech was potentially influenced by infant temperament. Infant temperament was measured by parent-report using the Early Childhood Behavior Questionnaire (ECBQ). For familiarization times in the Feed Bear task, experimenters granted significantly longer times to the infants than they were supposed to [M = 68.72, SD = 17.14; t(28) = 2.74, p = .011]. But there were no differences among the experimenters in familiarization time. For Make a Rattle, experimenters were on-target with their familiarization times (M = 67.64, SD = 21.38). Infant temperament was not associated with familiarization times in either task. In terms of IDS, experimenters used more words in the standardized narratives of both tasks than they were supposed to [M = 123.90, SD = 18.03; t(28) = 7.73, p M = 109.00, SD = 9.52; t(27) = 15.01, p \u3c .001] respectively. There was no association between IDS during the narrative phase and infant temperament. However, there were associations between infant temperament and IDS during the prologue and epilogue phases; namely for effortful control (prologue r = .29, p p \u3c .05), impulsivity (prologue r = .23, p

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

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]

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

Capillary condensation in disordered porous materials: hysteresis versus equilibrium behavior

We study the interplay between hysteresis and equilibrium behavior in capillary condensation of fluids in mesoporous disordered materials via a mean-field density functional theory of a disordered lattice-gas model. The approach reproduces all major features observed experimentally. We show that the simple van der Waals picture of metastability fails due to the appearance of a complex free-energy landscape with a large number of metastable states. In particular, hysteresis can occur both with and without an underlying equilibrium transition, thermodynamic consistency is not satisfied along the hysteresis loop, and out-of-equilibrium phase transitions are possible.Comment: 4 pages, 4 figure