Homogenization of Harmonic Maxwell Equations with Allowance for Interphase Surface Currents: Layered Structure

Author(s):  
Tai D. Nguyen ◽  
Ronald Gronsky ◽  
Jeffrey B. Kortright

Nanometer period Ru/C multilayers are one of the prime candidates for normal incident reflecting mirrors at wavelengths < 10 nm. Superior performance, which requires uniform layers and smooth interfaces, and high stability of the layered structure under thermal loadings are some of the demands in practical applications. Previous studies however show that the Ru layers in the 2 nm period Ru/C multilayer agglomerate upon moderate annealing, and the layered structure is no longer retained. This agglomeration and crystallization of the Ru layers upon annealing to form almost spherical crystallites is a result of the reduction of surface or interfacial energy from die amorphous high energy non-equilibrium state of the as-prepared sample dirough diffusive arrangements of the atoms. Proposed models for mechanism of thin film agglomeration include one analogous to Rayleigh instability, and grain boundary grooving in polycrystalline films. These models however are not necessarily appropriate to explain for the agglomeration in the sub-nanometer amorphous Ru layers in Ru/C multilayers. The Ru-C phase diagram shows a wide miscible gap, which indicates the preference of phase separation between these two materials and provides an additional driving force for agglomeration. In this paper, we study the evolution of the microstructures and layered structure via in-situ Transmission Electron Microscopy (TEM), and attempt to determine the order of occurence of agglomeration and crystallization in the Ru layers by observing the diffraction patterns.


PIERS Online ◽  
2008 ◽  
Vol 4 (5) ◽  
pp. 546-550 ◽  
Author(s):  
João R. Canto ◽  
Sérgio A. Matos ◽  
Carlos R. Paiva ◽  
Afonso M. Barbosa
Keyword(s):  

2019 ◽  
Vol 485 (4) ◽  
pp. 428-433
Author(s):  
V. G. Baydulov ◽  
P. A. Lesovskiy

For the symmetry group of internal-wave equations, the mechanical content of invariants and symmetry transformations is determined. The performed comparison makes it possible to construct expressions for analogs of momentum, angular momentum, energy, Lorentz transformations, and other characteristics of special relativity and electro-dynamics. The expressions for the Lagrange function are defined, and the conservation laws are derived. An analogy is drawn both in the case of the absence of sources and currents in the Maxwell equations and in their presence.


1993 ◽  
Vol 18 ◽  
pp. 27-32
Author(s):  
Yasuaki Nohguchi ◽  
Takashi Ikarashi ◽  
Osamu Abe ◽  
Atsushi Sato

A striped pattern can be seen by spraying ink on a vertical wall of a snow pit to observe the layered structure of a snow cover. This pattern is caused by variations of snowfall in time, particularly pauses in snowfall, and its structure is related to a kind of fractal. In this paper, we consider snowfall and snow cover from a viewpoint of fractals and show that the layered structure of snow cover is a record of fractals on atmospheric-turbulence phenomena through the time variation of snowfall.


2012 ◽  
Vol 27 (7) ◽  
pp. 726-730 ◽  
Author(s):  
Li-Chao ZONG ◽  
Jiang-Tao ZENG ◽  
Su-Chuan ZHAO ◽  
Wei RUAN ◽  
Guo-Rong LI

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