Structural aspects of amorphization in a cluster model of a disordered phase are presented. Molecular dynamics simulations were done within a "mobile cluster static boundary" model, in which static, disordered particles at the boundary of the simulation cell cause particles within the cell to adjust themselves structurally. With sufficient boundary disorder, both the radial distribution function and the orientational order parameter show onset of amorphization behavior. For Lennard-Jones particles, which are not good glass formers, the amorphization occurs only within a certain healing distance of the disordered boundary. With increasing boundary disorder, the orientational correlation function and the radial distribution function indeed show orientational phase scrambling, disappearance of long-range order, and the onset of glass-like amorphized structure.