  The investigation of the structural phase transition in the vicinity of the
Curie temperature $T_c$ of LiNb$_{1-x}$Ta$_x$O$_3$ crystals is motivated by the
expected combination of advantageous high-temperature properties of LiNbO$_3$
and LiTaO$_3$, including high piezoelectric modules and remarkable
high-temperature stability, respectively. $T_c$ marks the ultimate limit for
exploiting the piezoelectric properties, however transition related structural
modifications might impact this and other properties even below $T_c$.
Remarkably, the phase transition from the ferroelectric to the paraelectric
phase, whose temperature strongly depends on the composition $x$, shows a
significant drop in the activation energy of the electrical conductivity. The
magnitude, temperature dependence and underlying mechanisms of this drop are
discussed from a microscopic perspective. Molecular dynamics calculations in
the framework of the density functional theory show that substantial
displacements of the cations occur below $T_c$ for both the end compounds
LiNbO$_3$ and LiTaO$_3$, and might thus affect the electrical conductivity.
Above $T_c$, the migration of lithium ions is presumably facilitated by a
shortened diffusion path for the most favorable jump of the lithium ions.
Electronic contributions to the conductivity, which become important above 900
K, are explained within the polaronic picture by the formation and migration of
free small polarons.
