Strong off-stoichiometry and large Gr\"{u}neisen parameter in AgSbTe$_2$: a first principles study

We use first-principles density-functional theory calculations to study the dynamical and compositional instabilities in AgSbTe$_2$, and compare the theoretical predictions to the results of an experimental investigation. For pure AgSbTe$_2$, some native defects, particularly Ag vacancies, have negative formation energies for a wide range of experimental conditions, thus forming in high concentrations even at low $T$. This leads to large deviations from the formal stoichiometry, in agreement with experimental results. Substantial deviations of the AgSbTe$_2$ phase field away from the isoplethal Ag$_2$Te-Sb$_2$Te$_3$ section may be expected, potentially explaining the contradictions in the low-temperature regions of the previously published phase diagrams. We estimate the defect concentrations and the resulting intrinsic doping levels under various experimental conditions. Finally, we demonstrate that the stoichiometric AgSbTe$_2$ is at the verge of a dynamical instability: the energies of acoustic phonons near the L point depend strongly on volume, changing sign at nearly the experimental volume. This leads to an unusually large value of the Gr\"{u}neisen parameter, in agreement with experiment.