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I n this paper a method is described for the numerical evaluation of phonon widths and shifts due to three-phonon processes in an anharmonic crystal. With this method thed-function and principal value restrictions on the frequencies of the phonons participating in the three-phonon processes do not have to be taken into account explicitly. The method is based on a dispersion relation satisfied by the width and shift, and on their expansion in Legendre functions of the first and second kinds, respectively. It is illustrated by a numerical example. Es wird eine Methode beschrieben zur numerischen Berechnung vonPhononenbreiten und Phononenverschiebungen bei Drei-Phononenprozessen in einem anharmonischen Kristall. Bei dieser Methode ist eine explizite Berucksichtigung der &Funktion und der Hauptwertbedingungen fur die Frequenzen der an diesen Prozessen beteiligten Phononen nicht notwendig. Die Methode beruht auf einer Dispersionsrelation fur Breite und Verschiebung sowie auf deren Entwicklung in Legendrefunktionen erster bzw. zweiter Art. Das geschilderte Verfahren wird durch ein numerisches Beispiel illustriert.

The directions of particle motion associated with acoustic waves have been computed and are displayed graphically, for each of the three waves, as a function of propagation direction. The numerical example used is cubic nickel and the maximum polarization angle found is 11½ degrees.

The thermoelectric figure of merit Tz of a semiconductor is calculated as a function of the width of the conduction band. It is found that Tz approaches zero as the bandwidth goes to zero. The existence of an optimum bandwidth is established; however, the magnitude cannot be ascertained on the basis of the simple model used here.