The capacity of clay minerals to store large amounts of water is utilized in a number of industrial and environmental applications on Earth, for example, as components in geosynthetic clay liners in landfills or ingredients in water-based drilling fluids, and could prove important on Mars to identify future human landing sites where water could be harvested. The subzero behavior of water interacting within the interlayer space of clay minerals is of particular interest in most applications but remains poorly understood. To better understand the hydrothermal mechanism by which water ice bonds and separates from clay interlayers, we have utilized neutron spectroscopy, spectral analysis, and phonon band assignment. The inelastic neutron scattering from sodium montmorillonite, hydrated at 24, 73, and 166% water content, as well as an oven-dried sample, were measured to assess the vibrational density of states. The water contents studied provide a range of pore dimensions within clay gels that have varying degrees of confinement. The type of ice formed from water held in larger intraand interparticle pores differs substantially from that confined within the interlayer (pseudo-two-layer hydrate), and the differences vary with hydration level. Spectral subtraction over an energy transfer range 50 < E < 550 cm-1 (8 < E < 70 meV) produces clearly two different forms of ice: hexagonal and cubic in the two wetter samples. A form of interfacial ice, presumably of a lower density, is observed in the vibrational density of states spectrum of the sample hydrated to a pseudo-two-layer hydrate (ie 24% gravimetric water content (GWC), 10 H2O/Na+). No hexagonal or cubic ice is observed in this sample. The four vibrational modes within the translation band of hexagonal ice are apparent within the sample hydrated to 166% gravimetric water content, in which pores greater than 20 nm are largely water-filled. By considering hydrogen bonding of the water to the clay surface, our data indicate an increase in the strength of the H-bond due to a shorter distance to the hydroxyl. We attribute this decrease to the pores in the clay generating a localized negative pressure or "suction" effect, thus attracting the water.