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Hybrid Phonons in Nanostructures$
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Brian K. Ridley

Print publication date: 2017

Print ISBN-13: 9780198788362

Published to Oxford Scholarship Online: April 2017

DOI: 10.1093/acprof:oso/9780198788362.001.0001

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Prelude to Part 1

Prelude to Part 1

Chapter:
(p.6) Prelude to Part 1
Source:
Hybrid Phonons in Nanostructures
Author(s):

B. K. Ridley

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198788362.003.0002

Space is three dimensional, and so is the matter that resides in it. Matter is made up of atoms, so it has a point-like structure, but it can also behave is if it were a continuum. It therefore has microscopic and macroscopic properties. As a consequence, the physical properties of matter are written in terms of scalar, vector, and tensor quantities that obey differential equations, involving many of the transcendental functions of mathematics, all of which can reach a high degree of complexity, even in the well-ordered structure of crystals. Or it can be described in terms of that well-ordered structure, taking into account the dynamic properties of atoms. The description of the vibrational modes of crystals is no exception, especially when those crystals have nanometre dimensions. Fortunately, it is possible to discover some vital properties of three-dimensional crystals quite simply by considering the vibrational properties of a linear chain of atoms, and this provides a useful prelude to ...

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