Extensive molecular dynamics simulations have been applied to investigate the solidification process of atomic fluid confined in a hollow spherical shell for the inertial-confinement-fusion cryotarget. Supercooling is demonstrated to be induced by an ultrarapid cooling due to the formation of the critical nucleus with delays in temperature. Solidification out of the liquid phase is revealed to start at the core/shell interface in the local hexagonal close-packed form. Slow cooling is favourable to improve the inner surface shape, structure, and roughness of the resultant solid inside the shell.