  Functional materials design normally focuses on structurally-ordered systems
because disorder is considered detrimental to many important physical
properties. Here we challenge this paradigm by showing that particular types of
strongly-correlated disorder can give rise to useful characteristics that are
inaccessible to ordered states. A judicious combination of low-symmetry
building unit and high-symmetry topological template leads to aperiodic
"procrystalline" solids that harbour this type of topological disorder. We
identify key classes of procrystalline states together with their
characteristic diffraction behaviour, and establish a variety of mappings onto
known and target materials. Crucially, the strongly-correlated disorder we
consider is associated with specific sets of modulation periodicities
distributed throughout the Brillouin zone. Lattice dynamical calculations
reveal selective disorder-phonon coupling to lattice vibrations characterised
by these same periodicities. The principal effect on the phonon spectrum is to
bring about dispersion in energy rather than wave-vector, as in the
poorly-understood "waterfall" effect observed in relaxor ferroelectrics. This
property of procrystalline solids suggests a mechanism by which
strongly-correlated topological disorder might allow new and useful
functionalities, including independently-optimised thermal and electronic
transport behaviour as required for high-performance thermoelectrics.
