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We report an {\sl ab initio} study of pressure-induced amorphization (PIA) in zeolites, which are model systems for this phenomenon. We confirm the occurrence of low-density amorphous phases like the one reported by Greaves {\sl et al.} [Science {\bf 308}, 1299 (2005)], which preserves the crystalline topology and might constitute a new type of glass. The role of the zeolite composition regarding PIA is explained. Our results support the correctness of existing models for the basic PIA mechanim, but suggest that energetic, rather than kinetic, factors determine the irreversibility of the transition.

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