  Nanoscale particles embedded in a metallic matrix are of considerable
interest as a route towards identifying and tailoring material properties. We
present a detailed investigation of the electronic structure, and in particular
the Fermi surface, of a nanoscale phase ($L1_2$ Al$_3$Li) that has so far been
inaccessible with conventional techniques, despite playing a key role in
determining the favorable material properties of the alloy (Al\nobreakdash-9
at. %\nobreakdash-Li). The ordered precipitates only form within the
stabilizing Al matrix and do not exist in the bulk; here, we take advantage of
the strong positron affinity of Li to directly probe the Fermi surface of
Al$_3$Li. Through comparison with band structure calculations, we demonstrate
that the positron uniquely probes these precipitates, and present a 'tuned'
Fermi surface for this elusive phase.
