B1 : anharmonic effects
B1 : anharmonic effects
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 approximation. The higher order tcrms of the expansion give rise to anharmonic effects. For not too high te...
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Personal Name(s):  Leibfried, G. (Corresponding author) 

Contributing Institute: 
Publikationen vor 2000; PRE2000; Retrocat 
Imprint: 
Jülich
Kernforschungsanlage Jülich, Verlag
1964

Physical Description: 
p. 23745 
Document Type: 
Report Book 
Research Program: 
Addenda 
Series Title: 
Berichte der Kernforschungsanlage Jülich
318 
Link: 
OpenAccess OpenAccess 
Publikationsportal JuSER 
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 approximation. The higher order tcrms of the expansion give rise to anharmonic effects. For not too high temperature the 3rd and 4th order terms determine the anharmonic behaviour. In a theory with general expansion parameters one has restrictions due to crystal symmetry and equilibrium 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 approximation, the lattice frequences now depending on the shape of the crystal. The calculations are all straightforward 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 most reasonable procedure to investigate the potential which is the basis of the whole theory. The most detailed knowledge about the microscopic behaviour is obtained by analyzing Xray and neutron scattering data. Anharmonicity leads to temperature dependent dispersion curves. Again one can obtain by extrapolation the harmonic behaviour and from there the harmonic spectrum. 