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

Thermodynamics of non-local materials: extra fluxes and internal powers

The most usual formulation of the Laws of Thermodynamics turns out to be suitable for local or simple materials, while for non-local systems there are two different ways: either modify this usual formulation by introducing suitable extra fluxes or express the Laws of Thermodynamics in terms of internal powers directly, as we propose in this paper. The first choice is subject to the criticism that the vector fluxes must be introduced a posteriori in order to obtain the compatibility with the Laws of Thermodynamics. On the contrary, the formulation in terms of internal powers is more general, because it is a priori defined on the basis of the constitutive equations. Besides it allows to highlight, without ambiguity, the contribution of the internal powers in the variation of the thermodynamic potentials. Finally, in this paper, we consider some examples of non-local materials and derive the proper expressions of their internal powers from the power balance laws.Comment: 16 pages, in press on Continuum Mechanics and Thermodynamic

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

Phases of Josephson Junction Ladders

We study a Josephson junction ladder in a magnetic field in the absence of charging effects via a transfer matrix formalism. The eigenvalues of the transfer matrix are found numerically, giving a determination of the different phases of the ladder. The spatial periodicity of the ground state exhibits a devil's staircase as a function of the magnetic flux filling factor $f$. If the transverse Josephson coupling is varied a continuous superconducting-normal transition in the transverse direction is observed, analogous to the breakdown of the KAM trajectories in dynamical systems.Comment: 12 pages with 3 figures, REVTE

Critical dimensions for random walks on random-walk chains

The probability distribution of random walks on linear structures generated by random walks in $d$-dimensional space, $P_d(r,t)$, is analytically studied for the case $\xi\equiv r/t^{1/4}\ll1$. It is shown to obey the scaling form $P_d(r,t)=\rho(r) t^{-1/2} \xi^{-2} f_d(\xi)$, where $\rho(r)\sim r^{2-d}$ is the density of the chain. Expanding $f_d(\xi)$ in powers of $\xi$, we find that there exists an infinite hierarchy of critical dimensions, $d_c=2,6,10,\ldots$, each one characterized by a logarithmic correction in $f_d(\xi)$. Namely, for $d=2$, $f_2(\xi)\simeq a_2\xi^2\ln\xi+b_2\xi^2$; for $3\le d\le 5$, $f_d(\xi)\simeq a_d\xi^2+b_d\xi^d$; for $d=6$, $f_6(\xi)\simeq a_6\xi^2+b_6\xi^6\ln\xi$; for $7\le d\le 9$, $f_d(\xi)\simeq a_d\xi^2+b_d\xi^6+c_d\xi^d$; for $d=10$, $f_{10}(\xi)\simeq a_{10}\xi^2+b_{10}\xi^6+c_{10}\xi^{10}\ln\xi$, {\it etc.\/} In particular, for $d=2$, this implies that the temporal dependence of the probability density of being close to the origin $Q_2(r,t)\equiv P_2(r,t)/\rho(r)\simeq t^{-1/2}\ln t$.Comment: LATeX, 10 pages, no figures submitted for publication in PR

Stress-driven instability in growing multilayer films

We investigate the stress-driven morphological instability of epitaxially growing multilayer films, which are coherent and dislocation-free. We construct a direct elastic analysis, from which we determine the elastic state of the system recursively in terms of that of the old states of the buried layers. In turn, we use the result for the elastic state to derive the morphological evolution equation of surface profile to first order of perturbations, with the solution explicitly expressed by the growth conditions and material parameters of all the deposited layers. We apply these results to two kinds of multilayer structures. One is the alternating tensile/compressive multilayer structure, for which we determine the effective stability properties, including the effect of varying surface mobility in different layers, its interplay with the global misfit of the multilayer film, and the influence of asymmetric structure of compressive and tensile layers on the system stability. The nature of the asymmetry properties found in stability diagrams is in agreement with experimental observations. The other multilayer structure that we study is one composed of stacked strained/spacer layers. We also calculate the kinetic critical thickness for the onset of morphological instability and obtain its reduction and saturation as number of deposited layers increases, which is consistent with recent experimental results. Compared to the single-layer film growth, the behavior of kinetic critical thickness shows deviations for upper strained layers.Comment: 27 pages, 11 figures; Phys. Rev. B, in pres

Momentum distributions in ^3He-^4He liquid mixtures

We present variational calculations of the one-body density matrices and momentum distributions for ^3He-^4He mixtures in the zero temperature limit, in the framework of the correlated basis functions theory. The ground-state wave function contains two- and three-body correlations and the matrix elements are computed by (Fermi)Hypernetted Chain techniques. The dependence on the ^3He concentration (x_3) of the ^4He condensate fraction $(n_0^{(4)})$ and of the ^3He pole strength (Z_F) is studied along the P=0 isobar. At low ^3He concentration, the computed ^4He condensate fraction is not significantly affected by the ^3He statistics. Despite of the low x_3 values, Z_F is found to be quite smaller than that of the corresponding pure ^3He because of the strong ^3He-^4He correlations and of the overall, large total density \rho. A small increase of $n_0^{(4)}$ along x_3 is found, which is mainly due to the decrease of \rho respect to the pure ^4He phase.Comment: 23 pages, 7 postscript figures, Revte