By John R. Hardy, Arnold M. Karo (auth.)

Lattice dynamics is a vintage a part of good nation physics and the alkali halide crystals are vintage fabrics. approximately each new method in many-body idea has first been utilized to lattice-dynamical prob lems, and masses of our current realizing of the physics of genuine crystals has its origins in pioneering paintings, either experimental and theoretical, performed among 1920 and 1950 on alkali halide structures. the item of the current textual content is to provide a unified assurance of that a part of physics the place those components overlap and to increase this insurance a little bit with a purpose to contain now not only the dynamical habit of alkali halides but additionally their static habit. particularly, we speak about the way during which those fabrics reply to the presence of aspect imperfections. the reason for this extension is straightforward: mechanics contains either dynamics and statics and a textual content which discusses the previous must also talk about the latter. different unifying issues also are current; the knowledge offered are principally the results of our lengthy collaboration during this region, and the paintings is a partial heritage of the impression of electronic pcs on lattice dynamics, an effect which parallels their impression most of the time of reliable country physics. when you consider that this paintings is essentially an account of version calculations, now we have under pressure using the easiest attainable version at every one point of class and its uniform program to the crystals discussed.

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**Extra info for The Lattice Dynamics and Static of Alkali Halide Crystals**

**Example text**

26) Chap. III 40 • Dipolar Models 2 Hence, using Eq. (44) Note that b l2 has been eliminated during this argument and that this result for b ll stands on its own. Agreement between {3 calculated using Eq. , anharmonic) data with equations derived from a harmonic theory, whereas we should really be using "mechanical equilibrium" data, as defined by Hardy and Karo in a recent paper;(45) that is, data reduced to the case of a lattice in mechanical equilibrium at OOK (no zero-point motion). However, the errors are not large for the alkali halides, and we shall ignore them.

However, these parameters are always uniquely determined by the instantaneous nuclear configuration, as required by the adiabatic approximation. The situation in metals is somewhat different since the criteria demanded in the preceding section for the validity of the Born-Oppenheimer approximation are not obviously satisfied. Nonetheless, the adiabatic approximation has been used extensively in treatments of the lattice dynamics of metals. In fact, the criteria that we have given previously are excessively stringent, but they are certainly satisfied by the alkali halide crystals.

The situation in metals is somewhat different since the criteria demanded in the preceding section for the validity of the Born-Oppenheimer approximation are not obviously satisfied. Nonetheless, the adiabatic approximation has been used extensively in treatments of the lattice dynamics of metals. In fact, the criteria that we have given previously are excessively stringent, but they are certainly satisfied by the alkali halide crystals. The only novel effect in the dynamics of metals is the existence in the dispersion curves of Kohn anomaiies,(52) which have their origin in a sudden change in the effective screening of the interionic potential.