Systematic studies of pressure-induced amorphization of natrolites (PIA) containing monovalent extra-framework cations (EFC) Li+, Na+, K+, Rb+, Cs+ allow us to assess the role of two different EFC-H2O configurations within the pores of a zeolite: one arrangement has H2O molecules (NATI) and the other the EFC (NATII) in closer proximity to the aluminosilicate framework. We show that NATI materials have a lower onset pressure of PIA than the NATII materials containing Rb and Cs as EFC. The onset pressure of amorphization (PA) of NATII materials increases linearly with the size of the EFC, whereas their initial bulk moduli (P1 phase) decrease linearly. Only Cs- and Rb-NAT reveal a phase separation into a dense form (P2 phase) under pressure. High-Angle Annular Dark Field Scanning Transmission Electron Microscopy (HAADF-STEM) imaging shows that after recovery from pressures near 25 and 20 GPa long-range ordered Rb-Rb and Cs-Cs correlations continue to be present over length scales up to 100 nm while short-range ordering of the aluminosilicate framework is significantly reduced—this opens a new way to form anti-glass structures.