  In this paper we present a first-principles study of the high-pressure
superconducting phase diagram of calcium alanates (Ca-Al-H), based on ab-initio
crystal structure prediction and anisotropic Migdal-Eliashberg Theory. Calcium
alanates have been intensively studied at ambient pressure for their
hydrogen-storage properties, but their high-pressure behavior is largely
unknown. By performing a full scan of the ternary convex hull at several
pressures between 0 and 300 GPa, we identify several new structural motifs,
characterized by a high Al-H coordination, where Al--$d$ orbitals participate
in the bonding. Among all new phases thus identified, we focus in particular on
a phase with CaAlH$_7$ composition, which lies on the convex hull at 300 GPa,
and remains dynamically stable down to 50 GPa, with a predicted superconducting
T$_c$ of 82 K, which likely represents a new promising template to achieve
increase chemical precompression in ternary hydrides. Our findings reveal
important insights into the structure-property relationships of calcium
alanates under high pressure, and highlight a possible strategy to achieve
conventional superconductivity at low pressures.
