  Ternary compounds of Transition Metal Dichalcogenides are emerging as an
interesting class of crystals with tunable electronic properties, which make
them attractive for nano-electronic and optoelectronic applications. Among
them, Mo$_x$W$_{1-x}$S$_2$ is one of the most studied alloys, due to the
well-known, remarkable features of its binary constituents, MoS$_2$ and WS$_2$.
The band-gap of this compound can be modelled varying Mo and W percentages in
the sample, and its vibrational modes result from a combination of MoS$_2$ and
WS$_2$ phonons. In this work, we report transmission measurements on a
Mo$_{0:5}$W$_{0:5}$S$_2$ single crystal in the far-infrared range. Absorbance
spectra collected at ambient conditions enabled, for the first time, a
classification of the infrared-active phonons, complementary to Raman studies.
High-pressure measurements allowed to study the evolution of both the lattice
dynamics and the free carrier density up to 31 GPa, indicating the occurrence
of an isostructural semiconductor-to-metal transition above 18 GPa.
