Abstract
The theory of lattice vibrations which we discussed in the preceeding chapters has been based on the harmonic approximation which neglects all terms in the expansion of the potential energy (3.6) higher than the second-order terms. The most important consequences of the harmonic approximations are:
-
a)
there is no thermal expansion;
-
b)
the force constants and hence the elastic constants are independent of temperature and pressure;
-
c)
the heat capacity becomes constant at high temperatures;
-
d)
the specific heats measured at constant pressure and constant volume are equal: cP =cV;
-
e)
since there are no collisions between phonons, their mean free paths and lifetimes are infinite;
-
f)
as a consequence of (e), a perfectly harmonic crystal would have an infinite thermal conductivity;
-
g)
the line widths of the infrared absorption peaks and of the Raman, Brillouin and inelastic neutron scattering peaks are zero for perfectly-ordered harmonic crystals.
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Brüesch, P. (1982). Anharmonicity. In: Phonons: Theory and Experiments I. Springer Series in Solid-State Sciences, vol 34. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81781-6_5
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