Edge misfit dislocation formation at the interface of a nanopore and infinite substrate with surface/interface effects

The model of an edge misfit dislocation at the interface of the hollow nanopore and the infinite substrate with surface/interface stress is investigated. Using the complex variable method, analytical solutions for complex potentials of a film due to an edge misfit dislocation located in the film with surface/interface effect are derived, and the stress fields of the film and the edge misfit dislocation formation energy can be obtained. The critical conditions for edge misfit dislocation formation are given at which the generation of an edge misfit dislocation is energetically favourable. The influence of the ratio of the shear modulus between the film and the infinite substrate, the misfit strain, the radius of the nanopore and the surface/interface stress on the critical thickness of the film is discussed.     

Capillary-driven interdiffusion along interphase boundaries in solids

We consider chemical interdiffusion along interphase boundary (IB) between two immiscible solid phases. We derive explicit expressions for capillary-related excess chemical potentials of the atoms diffusing along the IB. The obtained expressions contain both a local term which depends on local curvature of the IB, and a non-local one which depends on overall system geometry and on energy of all surfaces and interfaces in the system. The obtained expressions are employed for describing the sintering of two immiscible two-dimensional solid particles controlled by surface and IB diffusion processes. We demonstrate that the sintering of particles is accompanied by relative rigid-body rotation of the particles even for fully isotropic surfaces and interphase boundaries.     

Surface/interface effects on the formation of misfit dislocation in a core–shell nanowire

The misfit strain within the core of a two-phase free-standing core–shell nanowire resulting in the generation of an edge misfit dislocation or an edge misfit dislocation dipole at the core–shell interface is considered theoretically within both the classical and surface/interface elasticity approaches. The critical conditions for the misfit dislocation generation are studied and discussed in detail with special attention to the non-classical surface/interface effect. It is shown that this effect is significant for fine cores of radius smaller than roughly 20 interatomic distances. The positive and negative surface/interface Lamé constants mostly make the generation of the misfit dislocation easier and harder, respectively. Moreover, the positive (negative) residual surface/interface tensions mostly make the generation of the misfit dislocation harder (easier). The formation of individual misfit dislocation is energetically more preferential in finer two-phase nanowires, while the formation of misfit dislocation dipole is more expectable in the coarser ones.     

Doping dependence of charge order in electron-doped cuprate superconductors

Abstract

In the recent studies of the unconventional physics in cuprate superconductors, one of the central issues is the interplay between charge order and superconductivity. Here the mechanism of the charge-order formation in the electron-doped cuprate superconductors is investigated based on the t-J model. The experimentally observed momentum dependence of the electron quasiparticle scattering rate is qualitatively reproduced, where the scattering rate is highly anisotropic in momentum space, and is intriguingly related to the charge-order gap. Although the scattering strength appears to be weakest at the hot spots, the scattering in the antinodal region is stronger than that in the nodal region, which leads to the original electron Fermi surface is broken up into the Fermi pockets and their coexistence with the Fermi arcs located around the nodal region. In particular, this electron Fermi surface instability drives the charge-order correlation, with the charge-order wave vector that matches well with the wave vector connecting the hot spots, as the charge-order correlation in the hole-doped counterparts. However, in a striking contrast to the hole-doped case, the charge-order wave vector in the electron-doped side increases in magnitude with the electron doping. The theory also shows the existence of a quantitative link between the single-electron fermiology and the collective response of the electron density.     

Generalized exterior boundary-value problems and optimization for the Helmholtz equation

A class of radiation problems is considered for the Helmholtz equation in exterior domains bounded by a smooth surface on which Dirichlet, Neumann, or Robin boundary conditions are imposed. The problem of finding the boundary data which maximizes far field power in a restricted subset of far field directions is formulated as a constrained maximization problem. Existence of an optimal solution in a variety of control domains is established. The particular case when the boundary is circular and the control domain is the unit ball inL ² is treated in detail. An algorithm for constructing the optimal solution is derived and used to obtain explicit numerical results.This work was supported by the US Air Force under Grant No. AFOSR 81-0156. The work was completed while the first author was on leave to the Institut für Numerische und Angewandte Mathematik, Universität Göttingen, Göttingen, BRD.     

pH‐sensing nanostar probe using surface‐enhanced Raman scattering (SERS): theoretical and experimental studies

Local pH environment has been considered to be a potential biomarker for tumor diagnosis because solid tumors contain highly acidic environments. A pH‐sensing nanoprobe based on surface‐enhanced Raman scattering (SERS) using nanostars under near‐infrared excitation has been developed for potential biomedical applications. To theoretically investigate the effect of protonation state on SERS spectra of p‐mercaptobenzoic acid (pMBA), we used the density functional theory (DFT) with the B3LYP functional to calculate Raman vibrational spectra of pMBA‐Au/Ag complex in both protonated and deprotonated states. Vibrational spectral bands were assigned with DFT calculation and used to investigate SERS spectral changes observed from experiment when varying pH value between five and nine. The SERS peak position of pMBA at ~1580 cm⁻¹ was identified to be a novel pH‐sensing index, which has small but noticeable downshift with pH increase. This phenomenon is confirmed and well‐explained with theoretical simulation. The study demonstrates that SERS is a sensitive tool to monitor minor structural changes due to local pH environment, and DFT calculations can be used to investigate Raman spectra changes associated with minor differences in molecular structure. Copyright © 2013 John Wiley & Sons, Ltd.     

Vibrational properties of the F A (Li+) center in alkali halides

Abstract

The on- or off-axis behavior and the vibrational properties of the F _A (Li⁺) center are investigated in several alkali halides by means of polarized resonant Raman scattering. The observed Raman modes are interpreted and classified according to their nature and frequency. A comparison between on- and off-axis systems and between the vibrational modes of the isolated Li⁺ and the F _A (Li⁺) center reveals a displacement of the Li⁺ equilibrium position parallel to the F _A (Li⁺) defect axis and, due to the small impurity size, away from the adjacent F center.     

Quasi-isometries of groups, graphs and surfaces

We give a characterization of virtual surface groups as groups quasi-isometric to complete simply-connected Riemannian surfaces. Results on the equivalence up to quasi-isometry of various bounded geometry conditions for Riemannian surfaces are also obtained. Received: January 18, 2000