Elastic moduli, drag coefficients, and Keating's parameters in germanium

Abstract

It is well known that phonon-phonon interactions produce a drag on moving dislocations in a solid. In the present work, the temperature dependence of the drag coefficients for edge and screw dislocations in germanium has been estimated at 800 and 1000 K. The Keating's-theory parameters have been evaluated as functions of temperature so as to explain the temperature dependence of third-order elastic moduli. The four parameters $\ensuremath{\gamma}$, $\ensuremath{\delta}$, $\ensuremath{\epsilon}$, and $\ensuremath{\zeta}$ have been estimated from the elastic constants ${c}_{11}$, ${c}_{12}$, ${c}_{111}$, ${c}_{112}$, and ${c}_{123}$ and the rest of the third-order elastic moduli have been predicted using the calculated temperature dependence of $\ensuremath{\gamma}$, $\ensuremath{\delta}$, $\ensuremath{\epsilon}$, and $\ensuremath{\zeta}$. Agreement with experimental results is satisfactory.