PLANE WAVE SPECTRAL REPRESENTATION FOR EM FIELDS

2021 ◽  
pp. 144-155
Author(s):  
J. M. Pankratz

It is often desirable in transmission electron microscopy to know the vertical spacing of points of interest within a specimen. However, in order to measure a stereo effect, one must have two pictures of the same area taken from different angles, and one must have also a formula for converting measured differences between corresponding points (parallax) into a height differential.Assume (a) that the impinging beam of electrons can be considered as a plane wave and (b) that the magnification is the same at the top and bottom of the specimen. The first assumption is good when the illuminating system is overfocused. The second assumption (the so-called “perspective error”) is good when the focal length is large (3 x 107Å) in relation to foil thickness (∼103 Å).


1997 ◽  
Vol 92 (3) ◽  
pp. 477-487 ◽  
Author(s):  
GERALD LIPPERT ◽  
JuRG HUTTER ◽  
MICHELE PARRINELLO

2002 ◽  
Vol 727 ◽  
Author(s):  
A. M. Mazzone

AbstractFull Potential Linearized Augmented Plane Wave calculations have been performed for epitaxial multilayers formed by the noble metals Ag and Cu with a thickness n up to 10 layers. The multilayers have a fcc lattice and are pure or compositionally modulated with a structure of the type Agn Cun or (AgCu)n. For n in the range 2,3 the density of states, evaluated at paramagnetic level, exhibits a sharp reduction of the bandwidth which is consistent with the reduced coordination of these structures. For n ≤ 5 the density of states in the central layers converges to the bulk value while the outer layers retain the narrow bandwidth found at n=2. Due to the absence of charge intermixing and hybridization, these features are shared by multilayers of all composition.


2020 ◽  
Author(s):  
Daniel Koch ◽  
Sergei Manzhos

<p></p><p>The generalized gradient approximation (GGA) often fails to correctly describe the electronic structure and thermochemistry of transition metal oxides and is commonly improved using an inexpensive correction term with a scaling parameter <i>U</i>. We tune <i>U</i> to reproduce experimental vanadium oxide redox energetics with a localized basis and a GGA functional. We find the value for <i>U</i> to be significantly lower than what is generally reported with plane-wave bases, with the uncorrected GGA results being in reasonable agreement with experiments. We use this computational setup to calculate interstitial and substitutional <a>insertion energies of main group metals in vanadium pentoxide</a> and find <a>interstitial doping to be thermodynamically favored</a>.</p><p></p>


Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan

This chapter examines solutions to the Maxwell equations in a vacuum: monochromatic plane waves and their polarizations, plane waves, and the motion of a charge in the field of a wave (which is the principle upon which particle detection is based). A plane wave is a solution of the vacuum Maxwell equations which depends on only one of the Cartesian spatial coordinates. The monochromatic plane waves form a basis (in the sense of distributions, because they are not square-integrable) in which any solution of the vacuum Maxwell equations can be expanded. The chapter concludes by giving the conditions for the geometrical optics limit. It also establishes the connection between electromagnetic waves and the kinematic description of light discussed in Book 1.


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