Ice rules

Abstract: Common water ice (ice I-h) is an unusual solid-the oxygen atoms form a periodic structure but the hydrogen atoms are highly disordered due to there being two inequivalent O-H bond lengths'. Pauling showed that the presence of these two bond lengths leads to a macroscopic degeneracy of possible ground states(2,3), such that the system has finite entropy as the temperature tends towards zero. The dynamics associated with this degeneracy are experimentally inaccessible, however, as ice melts and the hydrogen dynamics cannot be studied independently of oxygen motion(4). An analogous system(5) in which this degeneracy can be studied is a magnet with the pyrochlore structure-termed 'spin ice'-where spin orientation plays a similar role to that of the hydrogen position in ice I-h. Here we present specific-heat data for one such system, Dy2Ti2O7, from which we infer a total spin entropy of 0.67Rln2. This is similar to the value, 0.71Rln2, determined for ice I-h, SO confirming the validity of the correspondence. We also find, through application of a magnetic field, behaviour not accessible in water ice-restoration of much of the ground-state entropy and new transitions involving transverse spin degrees of freedom.

Abstract: The lattice statistical problem of calculating the residual entropy of ice has been considered in some detail for the hexagonal and cubic ice lattices as well as for a two‐dimensional icelike lattice. Even for the two‐dimensional lattice, this problem appears to be intractable using exact methods, so an approximation method is in order. The series method of DiMarzio and Stillinger has been developed so that the series is completely characterized by the numbers of various kinds of cycles on the lattice. The first five terms of the series have been evaluated and used to extrapolate values of the residual entropy S(0) within rather narrow limits for all practical purposes. The result for hexagonal ice and cubic ice is S(0) = .8145 ± .0002 cal/deg/mole which agrees with experiment even better than Pauling's original approximation. Some other methods are also discussed, and their results tend to confirm the series results.

Abstract: Using the Deep Potential methodology, we construct a model that reproduces accurately the potential energy surface of the SCAN approximation of density functional theory for water, from low temperature and pressure to about 2400 K and 50 GPa, excluding the vapor stability region The computational efficiency of the model makes it possible to predict its phase diagram using molecular dynamics Satisfactory overall agreement with experimental results is obtained The fluid phases, molecular and ionic, and all the stable ice polymorphs, ordered and disordered, are predicted correctly, with the exception of ice III and XV that are stable in experiments, but metastable in the model The evolution of the atomic dynamics upon heating, as ice VII transforms first into ice VII^{''} and then into an ionic fluid, reveals that molecular dissociation and breaking of the ice rules coexist with strong covalent fluctuations, explaining why only partial ionization was inferred in experiments