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Configurational entropy of ice XIX and its isotope effect - PubMed

  • ️Mon Jan 01 2024

Configurational entropy of ice XIX and its isotope effect

Tobias M Gasser et al. Sci Rep. 2024.

Abstract

Ice XIX is a partly hydrogen-ordered polymorph related to disordered ice VI, similar to ice XV. We here investigate the order-order-disorder sequence ice XIX→ice XV→ice VI based on calorimetry at ambient pressure both for D2O and H2O-ice XIX. From these data we extract configurational entropy differences between ice XIX, ice XV and ice VI. This task is complex because, unlike for all other ices, the order-disorder transition from ice XIX to ice VI takes place in two steps via ice XV. Even more challenging, these two steps take place in an overlapping manner, so that careful separation of slow kinetics is necessary. This is evidenced best by changing the heating rate in calorimetry experiments: For fast heating experiments the second step, disordering of ice XV, is suppressed because the first step, formation of ice XV from ice XIX, is too slow. The transient state ice VI‡ that is initially produced upon ice XIX decay then does not have enough time to convert to ice XV, but remains disordered all along. In order to tackle the challenge to determine the entropy difference between ice XIX and VI as well as the entropy difference between ice XV and VI we employ two different approaches that allow assessing the impact of kinetics on the entropy change. "Single peak integration" defines a kinetically limited result, but "combined peak integration" allows estimation of the true thermodynamic values. Our best estimate for the true value shows ice XIX to be much more ordered than ice XV (25 ± 3% vs 9 ± 4% of the Pauling entropy). For D2Oice XIX samples we obtain 28% of order, but only when a small number of fast H-isotope defects are used. In the second part we use these results to estimate the location of the ice XIX phase boundary both for protiated and deuterated ice XIX. The initial Clapeyron slope at ambient pressure is determined from the combination of neutron powder diffraction volume differences and calorimetry entropy differences data to be 21 K GPa-1 with an order-disorder transition temperature To-d(0.0 GPa) = 103 ± 1 K. An in situ bracketing experiment at 1.8 GPa yields To-d(1.8 GPa) = 116 ± 3 K, i.e., the phase boundary slope flattens at higher pressures. These data allow us to determine the region of thermodynamic stability of ice XIX in the phase diagram and to explain the surprising isotope shift reversal at 1.6 GPa compared to 0.0 GPa, i.e., why D2O-ice XIX disorders at lower temperatures than H2O-ice XIX at 1.6 GPa, but at higher temperatures at ambient pressures.

© 2024. The Author(s).

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Conflict of interest statement

The authors declare no competing interests.

Figures

Figure 1
Figure 1

Kinetic effect of heating rates on enthalpies of transition sequence Ice XIX → Ice VI‡ → Ice XV → Ice VI. (a) Calorigrams recorded at 5 (black trace), 10 (red trace), 30 (blue trace) and 50 (green trace) K min−1 scan rate. The grey dashed line represents the baseline, the grey shaded areas illustrate the calculation of the peak enthalpies. (b) Peak enthalpies and (c) peak ratios (grey dots) of disordering transitions XIX → VI‡ (black dots) and XV → VI (red dots) at different heating rates. Lines in (b) and (c) are guides to the eyes. Pure H2O ice XIX samples prepared at 1.8 GPa were used for the experiments. Endothermic peaks are pointing upwards.

Figure 2
Figure 2

Impact of H/D isotope substitution on calorimetry scans for (a) ice XV prepared at 1.0 GPa and (b) ice XIX prepared at 1.8 GPa. All scans were recorded at 10 K min−1. The grey dashed line represents the baseline. D2O and D2O + 5% H2O samples were cooled at 0.5 K min−1, whereas H2O and H2O + 5% D2O were cooled faster (3 K min−1 for ice XIX, and > 40 K min−1 for ice XV).

Figure 3
Figure 3

Volume per water molecule for ice XIX and ice VI as deduced from HRPD measurements, where the volume of the unit cell was divided by 10 molecules/unit cell for ice VI; and divided by 20 molecules/unit cell for ice XIX.

Figure 4
Figure 4

Estimate for the location of the H2O ice XIX phase boundary (blue dashed and full line) and the thermodynamic stability range of ice XIX (yellow area) and ice XV (light blue area). This estimate is based on (i) the calorimetric order–disorder temperature at 0.0 GPa (green square), (ii) the Clapeyron slope at ambient pressure (green line) and (iii) the high-pressure experiment at 1.8 GPa outlined in Fig. 5 (blue square). The ice XV and ice XIX phase boundaries estimated by Yamane et al. in ref. from in situ dielectric experiments are shown as black lines. The calorimetric order–disorder temperature and Clapeyron slope for D2O ice XIX are shown as red square and red line, respectively, where the intersection near 1.2 GPa explains the reversal of the isotope effect at 1.6 GPa.

Figure 5
Figure 5

Bracketing experiment to obtain the location of the ice XIX phase boundary at 1.8 GPa using a 95% H2O and 5% D2O sample. (a) Schematic representation of experimental paths starting from ice VI at 1.8 GPa and 255 K. Cooling rates are 3 K min−1 at 1.8 GPa and ≈60 ± 10 K min−1 at 1.0 GPa. The rate of decompression is − 0.1 GPa min−1. (b) Calorimetry traces recorded upon heating recovered samples at 10 K min−1 at ambient pressure. The dashed grey line represents the baseline. Endothermic peaks are pointing upwards. (c) Transformation enthalpies for the ice XIX endotherm (blue), ice VI‡ exotherm (orange) and ice XV endotherm (purple). (d) Ratio of the areas for the ice XIX and ice XV endotherms. Lines in (b) and (c) are guides to the eye. In (c) and (d) the light blue and grey lines are used to estimate the upper and lower limit for To-d(XIX, 1.8 GPa).These estimates are marked with light blue and grey dashed arrows. We regard the upper limit as the most likely value because this leads to a more natural, smooth curve.

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