By Pines D.
This ebook has grown from lectures given in a complicated direction within the concept of solids on the collage of Illinois in the course of the fall semester 1961-1962. It was once assumed that the scholar possessed a data of quantum mechanics such as a years direction in that subject; no earlier wisdom of box thought was once assumed. The direction used to be designed to stick with one within the one-electron or band theorv of solids. although, within the view of the vast applicability (to plasma physics, nuclear physics, low-temperature physics) of a number of the actual principles and methods built within the path, a previous wisdom of solid-siaie physics used to be now not considered as a sine qua non. consequently, either bankruptcy 2 on phono ns and bankruptcy three on electrons comprise a specific amount of fabric that's frequently integrated in an introductory solid-state physics path.
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Extra resources for Elementary Excitations In Solids: Lectures on Protons, Electrons, and Plasmons
Solutions of the Phonon Dispersion Relation for Metals The phonon dispersion relation, (2-39) or (2-54), is in general quite difficult to solve even for metals where the forces between the ions are primarily central in character. The required algebraic computations are far from trivial; still more important, one does not, in general, have a knowledge, based on first principles, of the relevant interatomic force constants. One possible approach is essentially phenomenological in nature. It is to assume that the only forces of importance a r e those between nearest neighbors, or nearest neighbors plus next neighbors.
There are N permissible and meaningful different values of k. Instead of integrating over the basic cell in the reciprocal lattice, Debye defined an equivalent sphere in k space such that the sphere contains the correct number of degrees of freedom. Thus kD, defined by 34 ELEMENTARY 3 _ (2g) kD EXCITATIONS IN 3N _ 6TT2N SOLIDS . (2 76) ' THT'IX is taken as the upper limit of integration with respect to k. It is convenient to express s by the relation hwD = nsk D = K9Z> (2-77) where 0D is defined as the Debye temperature.
2° are shown. One sees that such an experiment provides a detailed survey of the phonon spectra, one which goes far beyond the information hitherto available on the long-wavelength dispersion relation. As we have mentioned earlier, one may use the data to learn something of the interatomic forces for the solid in question. To do this, one begins with the basic phonon dispersion relation, (2-39). ,)] n=l (2-127) where qij is half the distance to the nearest reciprocal lattice point in the direction of the phonon wave vector q, while $ n corresponds to a force constant for the planes of atoms normal to q and n atoms away.