How to Play with Springs and Pulses in a Classical Harmonic Crystal View Full Text


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Chapter Info

DATE

1991

AUTHORS

M. Dominoni , N. Terzi

ABSTRACT

The classical dynamics of a harmonic lattice is presented. The aim of these lectures is not that of explaining once more the elements of the lattice dynamics. On the subject there is infact a large number of excellent treatises, either extended or short, starting from the milestone book of Born and Huang. Here we examine how pulses, locally generated inside a crystal, propagate into the surrounding harmonic crystal, when the whole system of dispersion curves is taken into account. We focus attention on the process of propagation and not on that of pulse generation. A pulse is assumed to be already present at t=0 with a given shape and very localized. At t>0 it relaxes into the sourrounding threedimensional crystal with which it interacts through harmonic springs. This is the socalled regime of ballistic propagation when any source of scattering is disregarded. We consider the propagation inside both a perfect and an imperfect crystal. For the last case we examine the effects due to a very localized change of force constants induced by a substitutional imperfection. The plan of these lectures is the following. First, the lattice dynamics of a harmonic nonconducting crystal is briefly reviewed, mainly in order to define useful quantities. The equation of motion is discussed in terms of normal modes. Both the perfect and the imperfect crystal, containing a low concentration of substitutional impurities, are considered (Section I, II). In order to follow the propagation of a pulse inside the crystal, a specific case must be studied, by solving numerically the equation of motion inside a specific crystal. We have chosen the diatomic KI and LiF ionic crystals as our model crystals, and the very reliable Breathing Shell Model as our lattice dynamics model. We have considered a very localized initial pulse, as that generated, within the limits of the classical approximation, by excitating a bound electron in the Condon approximation. The relaxation of the lattice around the excited electron (i.e. the time dipendent dynamics of the n.n. ions), is numerically evaluated, for the cases of the thallium impurity in KI and the F 2 + color center in LiF (Section III, IV). The relaxation time deduced for the last case is compared with the experiments reported in the literature (Knox, Fork, Mollenauer ‘86:) a good agreement is found. More... »

PAGES

443-482

Book

TITLE

Advances in Nonradiative Processes in Solids

ISBN

978-1-4419-3219-8
978-1-4757-4446-0

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-1-4757-4446-0_15

DOI

http://dx.doi.org/10.1007/978-1-4757-4446-0_15

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1025362953


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