A study of the temperature dependence of the far-infrared reflectance of the fast-ion conductors ${\mathrm{Ag}}_{2}$${\mathrm{HgI}}_{4}$ and ${\mathrm{Cu}}_{2}$${\mathrm{HgI}}_{4}$ has been completed. These materials are unusual in that the transition into the fast-ion conducting state is first order with a disordering of several cation species, but no reconstitution or symmetry change of the ``rigid'' anion sublattice. By examining the temperature dependence of the phonon lifetimes, we find that the phase transition into the fast-ion state occurs more rapidly than in typical fast-ion materials such as AgI. In addition, the low-frequency modes are strongly anharmonic and tightly coupled to the mobile ions. We conclude that the existence of three disordering ion species (monovalent silver or copper ions, divalent mercury ions, and vacancies) leads to a two-component disordering, where the mercury ions act to block the monovalent cation and vacancy disordering.
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