  The search for high-temperature superconductors in hydrides under high
pressure has always been a research hotspot. Hydrogen-based superconductors
offer an avenue to achieve the long-sought goal of superconductivity at room
temperature. We systematically explore the high-pressure phase diagram,
electronic properties, lattice dynamics and superconductivity of the ternary
Ca-Al-H system using ab initio methods. We found two stable ternary hydrides at
50 GPa: Cmcm-CaAlH5 and Pnnm-CaAl2H8, which both are semiconductors. At 200
GPa, a new phase of P21/m-CaAlH5, P4/mmm-CaAlH7 and a metastable compound
Immm-Ca2AlH12 were found. Furthermore, P4/mmm-CaAlH7 has obvious phonon
softening of high frequency vibrations along the Z-A direction, point A and
point X, which improves the strength of electron-phonon coupling. Therefore, a
superconducting transition temperature Tc of 71 K is generated at 50 GPa. In
addition, the thermodynamic metastable Immm-Ca2AlH12 exhibits a superconducting
transition temperature of 118 K at 250 GPa. These results are very useful for
the experimental searching of new high-Tc superconductors in ternary hydrides.
