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DOS & Thermodynamics.

Density of States & Thermodynamics. PhononA computes the anharmonic phonon density of states (DOS) by probing the reciprocal space over the anharmonic peaks. Since anharmonic bands could depend on temperature, this temperature dependence could be reflected in the shape of DOS functions. Such a behaviour is demonstrated on an example for lead (Pb). Notice that the evolution of spectra is confined to V=const. With some small additional computational efford similar results can be derived for P=const.

Anharmonic density of states for Pb1
Anharmonic density of states for Pb2

FIGURE.3. (Up) Plot of anharmonic phonon density of states for Pb at V=const conditions.

Thermodynamics. The thermodynamical functions, E - internal energy, S - entropy, F - free energy cv - heat capacity, and mean square displacements for all μ atoms <U2μ> can be handled with the anharmonic DOS functions corresponding to a given temperature.

Thermal conductivity. Knowing the width of all phonon peaks, hence the phonon lifetime, computing the phonon frequencies and group phonon velocities it is strainghforward to find the temperature behaviour of the thermal conductivity κ at V=const. The mentioned behaviour of κ is shown on FIGURE. 4 and 5 for lead Pb and lead tellurate PbTe, respectively.

Thermal conductivity of Pb

FIGURE.4. Plot of thermal lattice conductivity κ of Pb crystal. The electron conductivity is not included into κ.

Thermal conductivity of PbTe

FIGURE.5. Plot of lattice thermal conductivity of stoichiometric PbTe crystal.

Last update: September 20, 2017