This work reports on frequency dependent ambient-pressure dielectric measurements of hyperquenched glassy water, ice IV, ice VI, as well as a CO2-filled clathrate hydrate, the latter featuring a chiral water network. The dipolar time scales and the spectral shapes of the loss spectra of these specimens are mapped out and compared with literature data on low-density and high-density amorphous ices as well as on amorphous solid water. There is a trend that the responses of the more highly dense amorphous ices are slightly more dynamically heterogeneous than those of the lower-density amorphous ices. Furthermore, practically all of the amorphous ices, for which broadband dielectric spectra are available, display a curved high-frequency wing. Conversely, the high-frequency flanks of the nominally pure ice crystals including ice V and ice XII can be characterized by an approximate power-law behavior. While the spectral shapes of the nominally pure ices thus yield some hints regarding their amorphicity or crystallinity, a comparison of their time scale appears less distinctive in this respect. In the accessible temperature range, the relaxation times of the crystalline ices are between those of low-density and high-density amorphous ice. Hence, with reference also to previous work, the application of suitable doping currently seems to be the best dielectric spectroscopy approach to distinguish amorphous from crystalline ices.

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