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PHONONS

J. M. Ziman

in Electrons and Phonons: The Theory of Transport Phenomena in Solids

Published in print:
2001
Published Online:
September 2007
ISBN:
9780198507796
eISBN:
9780191709937
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507796.003.0001
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses the basic properties of phonons. Topics covered include solid matter as a gas of excitations, the crystal lattice, dynamics of a linear lattice, dynamics of space lattices, the ... More


Lattices and Crystal Structures

J. B. Ketterson

in The Physics of Solids

Published in print:
2016
Published Online:
December 2016
ISBN:
9780198742906
eISBN:
9780191821523
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198742906.003.0008
Subject:
Physics, Condensed Matter Physics / Materials

This chapter begins with a definition of space lattice. For most pure materials, the lowest energy state at low temperatures is a crystalline solid, where the atoms or molecules making up the ... More


The Various Approaches to the Concept of Space Lattice

André Authier

in Early Days of X-ray Crystallography

Published in print:
2013
Published Online:
September 2013
ISBN:
9780199659845
eISBN:
9780191748219
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199659845.003.0002
Subject:
Physics, Crystallography: Physics

The various approaches to the concept of space lattices are described in this chapter. The first one is the space-filling approach, which dates back to Aristotle and Kepler. It was applied to the ... More


Significance of the Discovery of X‐Ray Diffraction

André Authier

in Early Days of X-ray Crystallography

Published in print:
2013
Published Online:
September 2013
ISBN:
9780199659845
eISBN:
9780191748219
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199659845.003.0001
Subject:
Physics, Crystallography: Physics

This chapter stresses the significance of the discovery of X-ray diffraction by Laue, Friedrich, and Knipping, at the time of the discovery and afterwards. The discovery confirmed the wave nature of ... More


Quantitative Nondivergence and Diophantine Approximation on Manifolds: Dedicated to G. A. Margulis, with admiration

Victor Beresnevich and Dmitry Kleinbock

in Dynamics, Geometry, Number Theory: The Impact of Margulis on Modern Mathematics

Published in print:
2022
Published Online:
May 2022
ISBN:
9780226804026
eISBN:
9780226804163
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226804163.003.0010
Subject:
Mathematics, Geometry / Topology

The goal of this survey is to discuss the Quantitative non-Divergence estimate on the space of lattices and present a selection of its applications. The topics covered include extremal manifolds, ... More


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