Bi. ANHARMONIC EFFECTS

Abstract—This paper reviews the theory of anharmonic effects in crystals. The expansion of the potential between the nuclei of the lattice is discussed. The second order terms alone define the harmonic approx imation. The higher order terms of the expansion give rie i11ätmohic ctFor no!!öã Tãgli temperature the 3rd and 4th order terms determine the anharmonic behaviour. In a theory with general expansion parameters one has restrië!toi due Fo crys1aI symmetry and equiltbrium conditions. The thermodynamical properties can be determined from the free energy. In the harmonic approximation the free energy is separated into an elastic and caloric part, the first part determining essentially the elastic behaviour, being independent of temperature, and the second determining the specific heat, not depending on deformation. The anharmonic free energy can be obtained by pertubation theory. Elastic and caloric behaviour are now related. For the purely elastic behaviour one can employ a quasiharmonic approxim ation, the lattice frequences now depending on the shape of the crystal. The calculations are all straight forward in principle, the difficulties lying in the evaluation of complicated lattice sums. Some examples will be discussed. By extrapolation of the high temperature results to zero temperature one can remove the influence of the zero point motion thus obtaining the true data of the harmonic theory. The differences from the harmonic values give information about the higher order terms. This seems to be the mos