Random trees between two walls: Exact partition function

We derive the exact partition function for a discrete model of random trees embedded in a one-dimensional space. These trees have vertices labeled by integers representing their position in the target space, with the SOS constraint that adjacent vertices have labels differing by +1 or -1. A non-trivial partition function is obtained whenever the target space is bounded by walls. We concentrate on the two cases where the target space is (i) the half-line bounded by a wall at the origin or (ii) a segment bounded by two walls at a finite distance. The general solution has a soliton-like structure involving elliptic functions. We derive the corresponding continuum scaling limit which takes the remarkable form of the Weierstrass p-function with constrained periods. These results are used to analyze the probability for an evolving population spreading in one dimension to attain the boundary of a given domain with the geometry of the target (i) or (ii). They also translate, via suitable bijections, into generating functions for bounded planar graphs.Comment: 25 pages, 7 figures, tex, harvmac, epsf; accepted version; main modifications in Sect. 5-6 and conclusio

Structural properties and cation ordering in layered hexagonal CaxCoO2

A series of CaxCoO2 (0.15 <= x <= 0.40) materials have been prepared by means of ion exchange reaction from NaxCoO2. Transmission electron microscopy (TEM) measurements revealed a rich variety of structural phenomena resulting from cation ordering, structural distortion and twinning. Systematical structural analysis, in combination with the experimental data of NaxCoO2 (0.15 <= x <= 0.8) and SrxCoO2 (1.5 <= x <= 0.4) systems, suggests that there are two common well-defined cation ordered states corresponding respectively to the orthorhombic superstructure at around x = 1/2 and the 31/2a&#61620;31/2a superstructure at around x = 1/3 in this kind of system. Multiple ordered states, phase separation, and incommensurate structural modulations commonly appear in the materials with 0.33 < x < 0.5. The TEM observations also reveals an additional periodic structural distortion with q2 = a* / 2 in materials for x <= 0.35. This structural modulation also appears in the remarkable superconducting phase Na0.33CoO2 1.3H2O.Comment: 22 pages, 6 figure

Localized versus itinerant magnetic moments in Na0.72CoO2

Based on experimental 59Co-NMR data in the temperature range between 0.1 and 300 K, we address the problem of the character of the Co 3d-electron based magnetism in Na0.7CoO2. Temperature dependent 59Co-NMR spectra reveal different Co environments below 300 K and their differentiation increases with decreasing temperature. We show that the 23Na- and 59Co-NMR data may consistently be interpreted by assuming that below room temperature the Co 3d-electrons are itinerant. Their magnetic interaction appears to favor an antiferromagnetic coupling, and we identify a substantial orbital contribution corb to the d-electron susceptibility. At low temperatures corb seems to acquire some temperature dependence, suggesting an increasing influence of spin-orbit coupling. The temperature dependence of the spin-lattice relaxation rate T1-1(T) confirms significant variations in the dynamics of this electronic subsystem between 200 and 300K, as previously suggested. Below 200 K, Na0.7CoO2 may be viewed as a weak antiferromagnet with TN below 1 K but this scenario still leaves a number of open questions.Comment: 8.7 pages, 6 Figures, submitted to Phys. Rev.

Searching for Stable Na-ordered Phases in Single Crystal Samples of gamma-NaxCoO2

We report on the preparation and characterization of single crystal gamma phase NaxCoO2 with 0.25 < x < 0.84 using a non-aqueous electrochemical chronoamperemetry technique. By carefully mapping the overpotential versus x (for x < 0.84), we find six distinct stable phases with Na levels corresponding to x ~ 0.75, 0.71, 0.50, 0.43, 0.33 and 0.25. The composition with x ~0.55 appears to have a critical Na concentration which separates samples with different magnetic behavior as well as different Na ion diffusion mechanisms. Chemical analysis of an aged crystal reveals different Na ion diffusion mechanisms above and below x_c ~ 0.53, where the diffusion process above x_c has a diffusion coefficient about five times larger than that below x_c. The series of crystals were studied with X-ray diffraction, susceptibility, and transport measurements. The crystal with x = 0.5 shows a weak ferromagnetic transition below T=27 K in addition to the usual transitions at T = 51 K and 88 K. The resistivity of the Curie-Weiss metallic Na0.71CoO2 composition has a very low residual resistivity, which attests to the high homogeneity of the crystals prepared by this improved electrochemical method. Our results on the various stable crystal compositions point to the importance of Na ion ordering across the phase diagram.Comment: 9 pages, 9 figure

Size-dependent spinodal and miscibility gaps for intercalation in nano-particles

Using a recently-proposed mathematical model for intercalation dynamics in phase-separating materials [Singh, Ceder, Bazant, Electrochimica Acta 53, 7599 (2008)], we show that the spinodal and miscibility gaps generally shrink as the host particle size decreases to the nano-scale. Our work is motivated by recent experiments on the high-rate Li-ion battery material LiFePO4; this serves as the basis for our examples, but our analysis and conclusions apply to any intercalation material. We describe two general mechanisms for the suppression of phase separation in nano-particles: (i) a classical bulk effect, predicted by the Cahn-Hilliard equation, in which the diffuse phase boundary becomes confined by the particle geometry; and (ii) a novel surface effect, predicted by chemical-potential-dependent reaction kinetics, in which insertion/extraction reactions stabilize composition gradients near surfaces in equilibrium with the local environment. Composition-dependent surface energy and (especially) elastic strain can contribute to these effects but are not required to predict decreased spinodal and miscibility gaps at the nano-scale

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

Need and importance of health protection training in Nepal

By investing in health protection, the health of the nation can be safeguarded from future threats of uncontrolled infectious disease epidemics and disasters

Suppression of Phase Separation in LiFePO4 Nanoparticles During Battery Discharge

Using a novel electrochemical phase-field model, we question the common belief that LixFePO4 nanoparticles separate into Li-rich and Li-poor phases during battery discharge. For small currents, spinodal decomposition or nucleation leads to moving phase boundaries. Above a critical current density (in the Tafel regime), the spinodal disappears, and particles fill homogeneously, which may explain the superior rate capability and long cycle life of nano-LiFePO4 cathodes.Comment: 27 pages, 8 figure