Effects of Ge replacement in GeTe by Ag or Sb on the Seebeck coefficient and carrier concentration modified by local electron imbalance

XRD, SEM, EDS, $^{125}$Te NMR, Seebeck coefficient, and electrical resistivity of Ag$_{x}$Ge$_{50-x}$Te$_{50}$ and Sb$_{x}$Ge$_{50-x}$Te$_{50}$ alloys have been studied. Replacement of Ge in GeTe by Sb significantly increases the Seebeck coefficient, while replacement by Ag decreases it. These effects can be attributed to a change in carrier concentration observed via $^{125}$Te NMR spin-lattice relaxation measurements and NMR signal position, which mostly depends on the Knight shift. Variation in carrier concentration in Ag$_{x}$Ge$_{50-x}$Te$_{50}$ and Sb$_{x}$Ge$_{50-x}$Te$_{50}$ can be attributed to different electron configurations of valence electrons of Ag (4$d^{10}$5$s^{1})$ and Sb (5$s^{2}$5$p^{3})$ compared to that of Ge (4$s^{2}$4$p^{2})$ resulting in local electron imbalances and changing the concentration of charge carrier (holes) generated by Ge vacancies. In contrast, our $^{125}$Te NMR and Seebeck coefficient data for Ag$_{2}$Sb$_{2}$Ge$_{46}$Te$_{50}$ are similar to those observed for GeTe. This shows that effects from Ag and Sb compensate each other and indicates the existence of [Ag$+$Sb] pairs. The effects of Ge replacement in GeTe by Ag, Sb, or [Ag$+$Sb] on rhombohedral lattice distortion also have been analyzed. Interplay between the Seebeck coefficient and electrical resistivity in these alloys results in variation of power factor; the value of 45 mW/cm K$^{2}$, the highest among known tellurides, was found for Sb$_{2}$Ge$_{48}$Te$_{50}$.