High-resolution thermal expansion and dielectric relaxation measurements on H 2O and D 2O ice Ih
Buckingham, David Tracy Willis
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Ice Ih, formed by freezing liquid water below 273 K at atmospheric pressure, is well known and highly-studied, but some of its fundamental physical properties have mystified scientists since the early twentieth century. The thermal expansion is one of those properties; the low relative-resolution of past measurements has left questions regarding the structural isotropy and negative thermal expansion (NTE). Furthermore, the existence of relaxation phenomena near 100 K, related to the residual entropy at 0 K, may reveal itself through subtle features in the thermal expansion and, thus, warrants further investigation. Here we measure the thermal expansion of ultra-pure single crystal ice from 5-265 K with 10 6 times higher relative resolution than has previously been made. The data reveal a distinct crossover to NTE below 62 K, and a third-order transition along the crystallographic c-axis near 100 K, as evident by an unambiguous relaxational decrease in the thermal expansion coefficient on cooling. To further understand the nature of the transition, isotopic substitution and dielectric measurements were performed. Three properties of the dielectric relaxation in ice were probed at temperatures between 80-250 K; the thermally stimulated depolarization (TSD) current, static electrical conductivity, and dielectric relaxation time. The dielectric data agree with relaxation-based models and provide for the determination of activation energies which identify the dielectric relaxation in ice as being dominated by Bjerrum defects below 140 K. An anisotropy was also found in the data which revealed that molecular reorientations, in the form of propagating Bjerrum point defects, are energetically favored along the c-axis between 80-140 K. Furthermore, a similar relaxational effect to that observed in the thermal expansion was observed in the TSD current along c, which provides a strong correlation between dielectric relaxation and inherent thermodynamic relaxation in ice. Finally, isotopic substitution in both measurement sets indicates the transition is related the movements of hydrogen nuclei, not those of the whole molecule, and provides details about the low temperature phonon modes. These findings paint a picture of ice as a proton-disordered crystal which undergoes a partial ordering on cooling near 100 K but, before an ordered equilibrium state is realized, the exponentially increasing relaxation time rapidly slows the ordering and ultimately freezes-in the residual entropy, causing a continuous decrease in the thermal expansion coefficient.