Classical Theory of Atomic Scattering

Ordered Ni3Fe crystals possess a LI2 type superlattice similar to the Cu3Au structure. The difference in slip behavior of the superlattice as compared with that of a disordered phase has been well established. Cottrell first postulated that the increase in resistance for slip in the superlattice structure is attributed to the presence of antiphase domain boundaries. Following Cottrell's domain hardening mechanism, numerous workers have proposed other refined models also involving the presence of domain boundaries. Using the anomalous X-ray diffraction technique, Davies and Stoloff have shown that the hardness of the Ni3Fe superlattice varies with the domain size. So far, no direct observation of antiphase domain boundaries in Ni3Fe has been reported. Because the atomic scattering factors of the elements in NijFe are so close, the superlattice reflections are not easily detected. Furthermore, the domain configurations in NioFe are thought to be independent of the crystallographic orientations.

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Multislice calculations for quasi-periodic and non-periodic objects

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100173820 ◽

1990 ◽

Vol 48 (4) ◽

pp. 138-139

Author(s):

R. Herrera ◽

A. Gómez

Keyword(s):

Electron Diffraction ◽

Computer Simulations ◽

Periodic Table ◽

Amorphous Materials ◽

Space Group ◽

Essential Step ◽

Shape Effects ◽

Atomic Scattering ◽

Diffraction Patterns ◽

Periodic Continuation

Computer simulations of electron diffraction patterns and images are an essential step in the process of structure and/or defect elucidation. So far most programs are designed to deal specifically with crystals, requiring frequently the space group as imput parameter. In such programs the deviations from perfect periodicity are dealt with by means of “periodic continuation”.However, for many applications involving amorphous materials, quasiperiodic materials or simply crystals with defects (including finite shape effects) it is convenient to have an algorithm capable of handling non-periodicity. Our program “HeGo” is an implementation of the well known multislice equations in which no periodicity assumption is made whatsoever. The salient features of our implementation are: 1) We made Gaussian fits to the atomic scattering factors for electrons covering the whole periodic table and the ranges [0-2]Å−1 and [2-6]Å−1.

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Long-period modulated superstructures in Pd-12.5 at.%Ce and Pd-15 at.%Ce alloys

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100173959 ◽

1990 ◽

Vol 48 (4) ◽

pp. 164-165

Author(s):

Noriyuki Kuwano ◽

Masaru Itakura ◽

Kensuke Oki

Keyword(s):

Electron Microscopy ◽

Mean Value ◽

Heavy Elements ◽

Arc Furnace ◽

X Ray ◽

Long Period ◽

Ultra High Purity ◽

Heat Treated ◽

Atomic Scattering ◽

The Mean

Pd-Ce alloys exhibit various anomalies in physical properties due to mixed valences of Ce, and the anomalies are thought to be strongly related with the crystal structures. Since Pd and Ce are both heavy elements, relative magnitudes of (fcc-fpd) are so small compared with <f> that superlattice reflections, even if any, sometimes cannot be detected in conventional x-ray powder patterns, where fee and fpd are atomic scattering factors of Ce and Pd, and <f> the mean value in the crystal. However, superlattices in Pd-Ce alloys can be analyzed by electron microscopy, thanks to the high detectability of electron diffraction. In this work, we investigated modulated superstructures in alloys with 12.5 and 15.0 at.%Ce.Ingots of Pd-Ce alloys were prepared in an arc furnace under atmosphere of ultra high purity argon. The disc specimens cut out from the ingots were heat-treated in vacuum and electrothinned to electron transparency by a jet method.

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Let all social partners in the social support process count: New perspectives on classical theory

PsycEXTRA Dataset ◽

10.1037/e577572014-567 ◽

2013 ◽

Author(s):

Liu-Qin Yang ◽

Robert R. Wright ◽

Liu-Qin Yang ◽

Lisa M. Kath ◽

Michael T. Ford ◽

...

Keyword(s):

Social Support ◽

Classical Theory ◽

The Social ◽

Social Partners

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The Calder´on-Zygmund Theory I: Ellipticity

10.23943/princeton/9780691162515.003.0001 ◽

2017 ◽

Author(s):

Brian Street

Keyword(s):

Classical Theory ◽

Singular Integral ◽

Singular Integrals ◽

Differential Operators ◽

Integral Operators ◽

Singular Integral Operators ◽

Single Parameter ◽

Partial Differential ◽

Translation Invariant ◽

Partial Differential Operators

This chapter discusses a case for single-parameter singular integral operators, where ρ‎ is the usual distance on ℝn. There, we obtain the most classical theory of singular integrals, which is useful for studying elliptic partial differential operators. The chapter defines singular integral operators in three equivalent ways. This trichotomy can be seen three times, in increasing generality: Theorems 1.1.23, 1.1.26, and 1.2.10. This trichotomy is developed even when the operators are not translation invariant (many authors discuss such ideas only for translation invariant, or nearly translation invariant operators). It also presents these ideas in a slightly different way than is usual, which helps to motivate later results and definitions.

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