  LiNb$_{1-x}$Ta$_x$O$_3$ solid solutions are investigated from first
principles and by optical spectroscopy. The ground- and excited-state
properties of the solid solutions are modelled within density functional theory
as a function of the Ta concentration using special quasirandom structures
spanning the entire composition range between LiNbO$_3$ and LiTaO$_3$.
Deviations from a Vegard behavior are predicted for the lattice parameters, the
heat capacity, the electronic bandgap, and consequently the absorption edge.
The latter is measured for crystals of different composition by low temperature
optical spectroscopy, qualitatively confirming the theoretical predictions. The
LiNb$_{0.11}$Ta$_{0.89}$O$_3$ composition is found to be a highly unusual
crystal with a permanent macroscopic electric polarization and nonetheless zero
birefringence.
