By R. E. Peierls
This publication develops the topic from the elemental rules of quantum mechanics. The emphasis is on a unmarried assertion of the information underlying a few of the approximations that experience for use and care is taken to split sound arguments from conjecture. This e-book is written for the coed of theoretical physics who desires to paintings within the box of solids and for the experimenter with an information of quantum idea who's now not content material to take different people's arguments without any consideration. The therapy covers the electron concept of metals in addition to the dynamics of crystals, together with the author's paintings at the thermal conductivity of crystals which has been formerly released in English.
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Extra info for Quantum Theory of Solids (Oxford Classic Texts in the Physical Sciences)
Sample text
The third term, which vanishes at infinite T, and which measures the deviation from the classical result, is seen to be of the second order in the quantum constant h. This is a very common feature of quantum statistics. For estimating this term one must know something of the vibration spectrum. 25) for this purpose, since the sum of the squares of the frequencies can be obtained directly in terms of the coefficients of the equation. > indicates the diagonal sum or 'trace' of the tensor. The last sum has a fairly direct interpretation: it represents the sum of the potential energies obtained by displacing in turn each atom of the crystal in each coordinate direction by an infinitesimal amount, dividing by the square of the displacement and half the mass of the atom.
They are the only ones with f = 0 if we have a simple lattice with r = 1. Otherwise there are still 3r—3 other solutions of higher frequency. These represent vibrations in which the displacement of corresponding atoms in different unit cells is the same, but the atoms in the same cell move relatively to each other. g. the alkali halides) the two atoms in a unit cell must move in opposite directions. Now consider the case of a small, but finite, f. The solutions will now lie close to those for f = 0,f in other words, there are always three modes of vibration in which the frequency is small; though for r > 1 there are also 3r—3 modes of high frequency.
20). 20), and the result sorted according to powers of the u'. The terms independent of u' represent the equilibrium energy of the new lattice. 57) and contained in the F2 term of (2. 17). Similarly, the 'B' terms contribute a term proportional to e3, which we may neglect. The terms linear in the u' must vanish, since we know the atoms are in equilibrium when u' = 0. 2 CRYSTAL LATTICES. APPLICATIONS 33 where the cubic term is still negligible, but the coefficients of the quadratic term are modified: The occurrence of an.