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Reversible pressure-induced crystal-amorphous structural transformation in ice Ih
Chemical Physics Letters 609 (2014) 54–58
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Reversible pressure-induced crystal-amorphous structural transformation in ice Ih Niall J. English a,⇑, John S. Tse b,⇑ a The SEC Strategic Research Cluster and the Centre for Synthesis and Chemical Biology, School of Chemical and Bioprocess Engineering, University College Dublin, Belfield, Dublin 4, Ireland b Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5B2, Canada
a r t i c l e
i n f o
Article history: Received 2 March 2014 In final form 16 June 2014 Available online 20 June 2014
a b s t r a c t Molecular dynamics (MD) simulation of depressurised high-density amorphous ice (HDA) at 80 K and at negative pressures has been performed. Over several attempts, HDA recrystallised to a form close to hexagonal ice Ih, albeit with some defects. The results support the hypothesis that compression of ice-Ih to HDA is a reversible first-order phase transition, with a large hysteresis. Therefore, it would appear that LDA is not truly amorphous. The elastic energy estimated from the area of the hysteresis loop is ca. 4.5 kJ/mol, in some way consistent with experimentally-determined accumulated successive heats of transformations from recovered HDA ? ice Ih. Ó 2014 Elsevier B.V. All rights reserved.
Two very early reports on the compression of crystalline ice Ih into a high-density form, i.e., high-density amorphous ice (a-ice, HDA) [1] at low temperature, and the subsequent transformation to another low-density amorphous form (LDA) [2] upon decompression, respectively, may be regarded as important turning points in ice physics. The novel phenomenon of pressure-induced amorphisation (PIA) was conjectured to be a thermodynamic melting process [1]. The apparent first-order-like transition from HDA to LDA has led to the suggestion that these ices are thermodynamically distinctive forms and motivated the proposal of the twoliquid model of water [3]. For instance, HDA has been described as an isotropic glass that may devitrify, with some experimental studies appearing to offer relatively persuasive evidence in this vein [4–6]. In addition, further experimental evidence suggests that the underlying mechanism of PIA changes from mechanical instability at low temperatures to pressure-induced melting at higher temperatures [7]. For its part, it has been suggested from experimental studies that LDA is a distinctive thermodynamic phase, supporting the concept of ice polyamorphism at positive pressure; certainly, LDA has been kept stable at positive pressures over a period of years [3,8,9]. However, there are still many open questions on the nature of these a-ices, and these conclusions inferred from the experimental studies of Refs. [3–9] are certainly not without controversy or criticism (vide infra); therefore, one key, largely unresolved matter relates to their underlying thermodynamic stability. For instance, ⇑ Corresponding authors. E-mail addresses: [email protected] (N.J. English), [email protected] (J.S. Tse). http://dx.doi.org/10.1016/j.cplett.2014.06.026 0009-2614/Ó 2014 Elsevier B.V. All rights reserved.
the findings on the nature of LDA as a distinct phase have been disputed directly [10,11], whilst there is now a body of conclusive theoretical and experimental evidence showing that the mechanism for PIA arises not from melting, but is rather due to mechanical instability of the crystal structure in ice Ih [12–14]. Crystalline-like thermal conductivities [15] and sustained phonon dispersion observed in HDA and LDA ices [16–18] have shown unambiguously the presence of intermediate-range order in the structures not related to an isotropic liquid [10,19]. Experimental investigation of the intermediate-range ordering in these forms of amorphous ices also raises a question on the relationship between HDA and LDA. One suggestion is that HDA ice is a metastable, frustrated structure, arising from a large activation energy barrier due to proton re-orientation necessary for the formation of associated crystalline ice polymorphs [15,20,21]. It was postulated that the compression–decompression of amorphous ices reflects a hysteresis process with a large van der Waals loop [21] and the experimental recovery of LDA at ambient pressure is possible due to a large kinetic barrier. If this hypothesis is correct, ice Ih should be recoverable from HDA at negative pressure and low temperature [15,21]. Our principal goal in the present study is to address whether any such compression–decompression cycle displays large hysteresis at low temperatures, which would be a prerequisite for any (quasi-, or apparent) ‘first-order’ transition from ice Ih to HDA to have any grounding. It should be borne in mind that many of the experiments underlying the conclusions in Refs. [3–9] were carried out above the postulated glass transition temperature (around 130 K, and inferred to exist from an increase in heat capacity rather than via direct viscosity measurements) [7] and, as such, though
N.J. English, J.S. Tse / Chemical Physics Letters 609 (2014) 54–58
certainly interesting in their own right, are less relevant to the low-temperature work in the present study. To test this hypothesis on putative hysteresis in a compression– decompression cycle, molecular dynamics (MD) simulations of depressurisation of HDA at 80 K, at negative pressure, have been performed. An earlier result for such a process is non-conclusive, as it only shows a partially re-formed ice Ih-like framework [21]. This previous work, however, was limited by the size of the system simulated and the length of simulation time [21]. The premise of the present work is to investigate the possibility of ‘spontaneous’ (versus thermally activated) reversibility of PIA without thermal activation (i.e., maintaining the temperature at 80 K). The ‘recrystallisation’ process therefore depends only on stochastic thermal fluctuations. For this purpose, a large ice model with very long (>nanosecond) simulation times are needed. It was found that recrystallisation from the amorphous phase indeed took place to a form close to hexagonal ice (Ih), albeit with some reminiscence of LDA-like defects (vide infra). However, it must be stressed here that another alternative perspective would be to label this defective structure as being closer to LDA in nature, with ice Ih-like characteristics; we show, however, that the former interpretation appears more reasonable. Upon pressurisation of a 23 040-molecule system of ice Ih (cf. Supplementary information [22], using the TIP4P-Ice model [23] in the present study, and shown previously to be appropriate for various ices [24]), densification to a non-crystalline form was observed to take place between 12 and 14 kbar within 10 ns (cf. Figure 1), as judged by consideration of density and examination of the radial distribution functions (RDFs). 10 ns, however, was not entirely sufficient to remove the essential hallmarks of crystal structure at 14 kbar in terms of a low value of the O–O partial RDF in the 3–3.6 Å range; extending the simulation to 30 ns achieved HDA-like RDFs. Similar findings were reported previously [25] on a much smaller system (128 molecules using TIP4P, arguably an inferior model for ices [24]). The density of the resultant HDA was found to be 1.29–1.305 g/cm3 at 14 and 16 kbar, respectively, with a reduction to 1.2 g/cm3 at atmospheric pressure, where is was found to be kinetically stable (vide infra and cf. Figure 1). This latter value is some 2.5% larger than the experimental value at recovered at ambient pressure at 77 K of 1.17 g/cm3 [26], but it should be noted that experimental density estimates for amorphous ices recovered at ambient pressures are
Figure 1. Density–pressure relationship at 80 K, demonstrating the hysteresis of the Ih ? HDA and HDA ? Ih transitions, showing the ‘Ih-like’ density at 5 and 10 kbar for the cases where (partial) recrystallisation was observed; not all simulations at these negative pressures resulted in recrystallisation within 50 ns.
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also quite dependent on synthetic pathways, which makes only approximate estimates possible. This complicates a direct, quantitative comparison with our present results; bearing this in mind, however, our 2.5% density overestimate with TIP4P-ice for HDA appears reasonable. Following this TIP4P-Ice density comparison with experiment, although the thermal volume-expansivity of amorphous ices has not been measured experimentally, it is worth considering the role of temperature ‘undercooling’ vis-à-vis the presently-used 80 K and the ice-Ih melting point for the given potential model (TIP4P-Ice). The (ambient-pressure, ice Ih-liquid) melting point of the TIP4P-Ice model has been estimated to be 270 K (in contrast with 230 K for TIP4P) [27], so this much-better performance of TIP4P-Ice is reassuring. This 190 K ‘drop’ in temperature below the melting point down to 80 K means that the presently studied temperature with TIP4P-Ice is indeed substantially below the postulated glass transition temperature (around 130 K, inferred from heat-capacity increases rather than directly from viscosity measurements) [7]. Five independent constant pressure–constant temperature (NPT) MD simulations of pressure-amorphised HDA ice generated from a 32 768-molecule system were performed at 80 K and for each of 0.001, 5 and 10 kbar (cf. Supplementary information). [22] No hint of ‘recrystallisation’ was found in the simulation at 0.001 kbar (atmospheric pressure). In contrast, MD calculations performed at 5 and 10 kbar show the systems have, in some cases, respectively, recrystallised either partially or almost to an ice Ih-like form, after circa 25–35 ns. Of the five independent runs, one and two out of five recrystallised at 5 and 10 kbar, respectively, indicating the extent of kinetic limitation. In these particular cases, a dramatic volume-expansion took place suddenly, with the density decreasing down to around 0.92 g/cm3, which is close to (1.6% less than) the experimental density of ice Ih at 80 K (0.935 g/cm3) [28]; this agreement with TIP4P-Ice is somewhat reasonable – indeed, we have found in previous work that TIP4P tends to overestimate the ice Ih density vis-à-vis TIP4P-Ice [19], and we have noted above the superior estimation of the melting point of ice-Ih by TIP4P-Ice (270 K versus 230 K for TIP4P, much closer to the experimental value of 273 K) [27]. The elastic energy estimated from the area of the hysteresis loop in Figure 1 is around 4.5 kJ/mol. Careful calorimetry measurements for the combined transitions of recovered HDA ? LDA ? ice Ic ? Ice Ih give an aggregate of 2.1 kJ/mol [29]. This result shows that it is possible that the heat of transformation between HDA and ice Ih could be, in part, recovered from the stored elastic energy. On the other hand, in view of the previous comment that a legitimate alternative view of the nature of the recrystallised form of the ice would be to consider it closer to LDA with ice Ih-like features, then a more appropriate comparison would be with the value for HDA ? LDA, which is around 0.75 kJ/mol [29]. The somewhat closer agreement of the theoretical value here with the experimental estimate of 2.1 kJ/mol rather than 0.75 kJ/mol [29] arguably offers some indirect support towards the view that the recrystallised, defective ice may be closer to ice Ih in nature, but this is admittedly somewhat tentative; the observed value of 4.5 kJ/mol is still around double the corresponding experimental HDA ? Ice Ih estimate. The O–O pair distribution functions (PDFs) are shown in Figure 2a for the recrystallised structures from the 5 and 10 kbar decompression cases shortly after these events, along with those of ‘native’ Ih (270 K and 1 bar) and LDA (at 1 kbar) and HDA (at 8 kbar) structures, both at 80 K, for reference. With decreasing (i.e., more negative) pressure, the structure resembles more closely initial ice Ih, even though the densities of ice Ih and LDA are similar. The negative-pressure ‘driving force’ causes the PDF of the recrystallised sample to exhibit O–O correlation shells similar to that of the initial ice Ih, at least up to 7 Å. The interstitial
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Figure 2. (a) O–O Pair distribution functions at 80 K for HDA and the recrystallised form at the specified pressures and compared with the reference LDA (80 K) and Ih (270 K) structures. The PDFs have been displaced upwards for ease of viewing. (b) Corresponding gOO (r) plots with the same curve styles of Figure 2a.
in structure. It can be seen that, especially in the intermediate range beyond the first shell, that the recrystallised forms (especially at 10 kbar) are closer to ice Ih than LDA or HDA. It is also instructive in this regard to consider the ratio of the O–O PDF vis-à-vis that of ice Ih, and this is plotted in Figure 3 for HDA, LDA and the recrystallised form at 10 kbar, with the evolution of the integral of this quantity shown in the inset. It is clear that the recrystallised form has a ratio substantially closer to unity; equally, a better fit (i.e., a ratio closer to unity) would exhibit a straight-line relationship in the running value of its integral, and this is also the case for the recrystallised form (in dashed grey, in the inset of Figure 3). This has the best coefficient of goodnessof-fit (v2-quantity nearest 1) derived from a straight-line leastsquares fit to the running integral. A schematic showing the values of v2 with decreasing pressure is shown in Figure 4. The amorphous ice recovered at 10 kbar shows the highest resemblance to crystalline ice Ih structure; a perfect match would have v2 = 1. The O–O static structure factors are shown in Figure 5 for the same structures at their respective stable pressures, i.e., the same temperature and pressure conditions as in Figure 2. Although Klotz et al. have suggested for HDA structure-determination [30], that there may be some second-order, minor differences in structure factors due to pressure effects, this will not change the complexion of the matter appreciably, and we present the structures at their respective pressures (270 K and 1 bar for Ih, and 80 K for other structures with 8 kbar for HDA, 1 kbar for LDA, and the 5/ 10 kbar recrystallised forms). In Figure 5, it can be seen that the recrystallised forms are closer to Ih than LDA, with the main peaks at 1.67 and 1.66 Å 1 for 5 and 10 kbar, respectively, in increasingly better agreement with that of Ih, as opposed to 1.71 Å 1 for LDA. The secondary peak of Ih at around 2.4 Å 1 is also reproduced by the recrystallised forms. However, the less pronounced LDA secondary peak at 2 Å 1 is echoed by the recrystallised structure from 5 kbar, emphasising the imperfect crystalline nature, and localised instances of near-amorphous structure. This is less prominent in the structure arising from simulation at 10 kbar, indicating a structure almost, but yet not quite perfectly, like ice Ih. The decay to zero of S(k) around the peaks for the
oxygen density between the first and second oxygen coordination shell, i.e., the region between 3.0 and 3.6 Å, is still somewhat apparent in the recrystallised structure. However, this spurious feature is removed when the pressure is further reduced to 10 kbar. The first coordination shell, however, still is not as sharp as ice Ih with a small distribution from 2.7 to 3.2 Å. The slightly broadened O–O first coordination shell may be attributable to the average O–O distance being longer with increasing negative pressure and the distribution of O–O distances not being elastically isotropic. The imperfect crystal structure may also be due to the activation energy required for proton re-orientation into a perfect proton alignment following the Bernal–Fowler rules and with vanishingly-small dipole in the structure. Still, referring to the PDF of LDA, there is considerably less interstitial oxygen density than the HDA amorphous structure. The average configurational energy of the recrystallised system was around 0.4–0.45 kcal/mol lower than that of HDA, but some 1.2–1.4 kcal/mol higher than that of ice Ih, which quantifies the level of distortion in the recrystallised structure, essentially due to strained and imperfect hydrogen bonds. The enthalpy was found to decline by a similar level (0.4–0.5 kcal/mol) vis-à-vis HDA upon ‘recrystallisation’, but yet remain ‘stubbornly’ above that of ice Ih (by circa 1.3 kcal/mol). To probe further, and more directly, the similarity, or otherwise, of the various studied structures to ice Ih (at 270 K and 1 bar) in Figure 2a, particularly beyond the first shell, we have plotted the O–O r g(r) in Figure 2b, which emphasises longer-range differences
Figure 3. Ratio of O–O g(r) to that of ice Ih (with the latter at 270 K and 1 bar), with the running value of the integral of this ratio shown in the inset. These plots are for HDA, LDA and the recrystallised form at 10 kbar (all at 80 K, and at their respective pressures in Figure 2). The same curve styles are adopted as in Figure 2a (specified again in the legend here). Note that effectively identical structures to ice Ih (from an O–O point of view, at least) would have a straight-line relationship, and the recrystallised form (dashed grey) appears the ‘best’ in this regard. Please see the text for further discussion.
Ih, 270 K, 1 bar (a) HDA, 80 K, 8 kbar LDA 80 K LDA, K, 1 kbar 'Recrys.' HDA, 80 K, -5 kbar 'R 'Recrys.' ' HDA, HDA 80 K, K -10 10 kbar kb
12
gOO O (r)
10 8 6 4 2 0 2
3
4
5
6
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8
r (Å) ( )
(b)
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r gOO O (r)
10 8 6 4 2 0 2
3
4
5
6
7
8
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Figure 4. A plot of the goodness of fit (v2) of the O–O radial distribution functions of the relevant forms of amorphous ices with respect to crystalline ice Ih with pressure. A v2 = 1 indicates a perfect match.
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instead of recovered HDA, although this needs to be framed carefully within the broader context of this study; the structure is a hybrid, of sorts. The ‘crux of the matter’, however, appears to be that the ultimate outcome will be conversion to ice Ih, and O–O PDF analysis suggests a closer structural relationship to ice Ih. Bearing these observations of structural characteristics in mind, in relation to the partially recrystallised structures, it befits an examination of stability and the vibrational density of states (VDOS) before, during and immediately following the rapid transition itself, in order to characterise, at least crudely and indirectly, the nature of the energy landscape itself. To this end, we have carried out additional NVT simulations (by necessity) to probe the vibrational density of states (VDOS) of two ‘intermediate’, transient structures encountered during one particular instance of the rapid recrystallisation events (which is representative of the various such sampled events). These were carried out at 80 K and 5 kbar; the constant-volume prevented conversion to the final recrystallised form and ‘wholesale’ volume fluctuation. These inherently unstable intermediate structures were 1.01 and 1.07 g/cm3 in density; these were sufficiently long-lived for velocity autocorrelation function (VACF)-sampling under NVT conditions only. These VDOS are shown in Figure 6, from Fourier transformation of the VACFs of oxygen atoms, for the essentiallyHDA structure just prior to recrystallisation, and for the defective ice Ih structure (or, conversely, LDA-like structure with prominent Ih features) directly afterwards. For frequencies around 120– 145 cm 1, there are much lower values of the VDOS for the intermediate structures, underlying their lack of feature and inherent instability. These findings indeed show that the ‘recrystallised’ structure possesses ‘soft’ modes, indicating that the potential surface is rather flat and the structure is located in a shallow minimum. Although this may suggest, to some extent, that the ‘label’ (i.e., closer to LDA or ice Ih) to describe the structure is arguably semantic, it is closer to ice Ih from a structural point of view (in terms of O–O distribution), albeit with some substantial hydrogen-bond strain.
Figure 5. Static structure factors S(k) for the various structures at the same temperature/pressure conditions in Figure 2, i.e., 270 K and 1 bar for ice Ih, and 80 K for the other structures with 8 kbar for HDA, 1 kbar for LDA, and the 5/ 10 kbar recrystallised forms. The peaks have been normalised to circa 2, and the various S(k) curves have been displaced vertically for ease of viewing.
recrystallised structure is much more reminiscent of crystalline Ih, underlying its essentially crystalline nature, albeit imperfect. Certainly, the recrystallised form from 10 kbar simulation is indeed tantalisingly closer. Running the 5 kbar recrystallised form for around 30 ns at a pressure of 10 kbar led to similar PDF and S(k) results for the 10 kbar-recrystallised case depicted in Figures 2 and 3 with no particular closer ‘fit’ to perfect ice Ih, emphasising again the kinetic limitations of proton rearrangement. Thermal annealing will certainly accelerate the ‘healing’ of the defects. This latter concern, however, is not the intended goal of this study, but rather the demonstration of spontaneous isothermal reversal of the amorphous ? crystalline transformation from stochastic thermal fluctuations. The less pronounced feature in the structure factors at circa 2 Å 1 (declining at 10 kbar) is more reminiscent of LDA; this suggests that another interpretation of the recrystallised structures would be to regard them as closer to LDA, with prominent ice Ih characteristics, although the PDF-based analysis of Figures 2b, 3 and 4 suggests a closer structural relationship to ice Ih. Perhaps a more illuminating approach is to dub the ‘recrystallised’ structures at negative pressure a recovered ice
Figure 6. Vibrational density of states (VDOS) at 80 K and 5 kbar from Fourier transformation of velocity autocorrelation functions (VACFs) of oxygen atoms (sampled, by necessity, under NVT conditions) for the essentially-HDA structure just prior to recrystallisation, and for the imperfect ice structure (with LDA-like features) just afterwards. Also shown are two unstable intermediate structures during the rapid transition (of 1.01 and 1.07 g/cm3), which were sufficiently longlived for VACF-sampling under NVT conditions only. For frequencies around 120– 145 cm 1, there are lower values of the VDOS for the intermediate structures, underlying their lack of stability, which is ‘preserved’ artificially for 20 ps of VACFsampling under constant-volume conditions.
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In conclusion, it has been shown that HDA can be recrystallised to a form close to hexagonal ice (Ih) with relatively small defects, or, conversely and more tentatively, to an LDA-like structure with prominent ice Ih features, as determined from consideration of structure factors and radial distribution functions. Given that the simulations were not run for more than 50 ns and it appears that ice Ih is the final ‘outcome’, in that one and two out of five recrystallised at 5 and 10 kbar, respectively, this suggests a kinetically-limited process. Although these results may appear to suggest that the formation of LDA may be controlled kinetically, it is difficult to conclude this with any level of confidence; the central goal of this study has not been to investigate if LDA is a ‘kinetic product’, but rather the extent of hysteresis in the HDA/ice Ih compression–decompression cycle. In any event, perhaps timescales of microseconds or milliseconds may be required for deterministic MD to recover an essentially perfect crystal structure. This hysteresis was demonstrated by the densification of Ih to a non-crystalline form, redolent of HDA. The area enclosed by the hysteresis loop is the elastic energy stored in HDA and from Figure 1 it is estimated to be ca. 4.5 kJ mol 1. The conversion of HDA to LDA or ice Ih is highly exothermic and very rapid, thus giving, arguably, a quasi-first-order-like transition [20,31]. It is noteworthy that under hydrostatic conditions, the prototypical pressure-induced amorphisation transformations previously reported, i.e., a-quartz [32] and berlinite [33], were no longer observed; instead, the respective systems were observed to transform into new crystalline structures [34,35]. We conjecture that PIA in ice is no different in this respect. The authors wish to thank an anonymous reviewer for very useful comments and suggestions on improving the comparison of the different ice structures.
1. Author contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. N.J. English and J.S. Tse contributed equally.
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.cplett.2014. 06.026. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30]
2. Funding sources
[31] [32]
The authors thank the Ireland Canada University Foundation and the Royal Irish Academy.
[33] [34] [35]
O. Mishima, L.D. Calvert, E. Whalley, Nature 310 (1984) 393. O. Mishima, L.D. Calvert, E. Whalley, Nature 314 (1985) 76. O. Mishima, H.E. Stanley, Nature 392 (1998) 164. O. Mishima, J. Chem. Phys. 121 (2004) 3161. O. Andersson, Proc. Nat. Acad. Sci. 108 (2011) 11013. M. Seidl, M.S. Elsaesser, K. Winkel, G. Zifferer, E. Mayer, T. Loerting, Phys. Rev. B 83 (2011) 100201. O. Mishima, Nature 384 (1996) 546. R.J. Nelmes, J.S. Loveday, T. Strässle, C.L. Bull, M. Guthrie, G. Hamel, S. Klotz, Nature Phys. 2 (2006) 414. S. Klotz et al., Phys. Rev. Lett. 94 (2005) 025506. C.A. Tulk, C.J. Benmore, D.D. Klug, J. Neuefeind, Phys. Rev. Lett. 96 (2006) 149601. S. Klotz et al., Phys. Rev. Lett. 96 (2006) 149602. J.S. Tse, J. Chem. Phys 96 (1992) 5482. J.S. Tse et al., Nature 400 (1999) 647. Th. Strässle, A.M. Saitta, S. Klotz, M. Braden, Phys. Rev. Lett. 93 (2004) 225901. J.S. Tse, D.D. Klug, Phys. Chem. Chem. Phys. 14 (2012) 8255. O. Andersson, H. Suga, Phys. Rev. B 65 (2002) 140201. H. Schober, M.M. Koza, A. Tölle, C.C. Masciovecchio, F. Sette, F. Fujara, Phys. Rev. Lett. 85 (2000) 4100. M.M. Koza, B. Geil, M. Scheuermann, H. Schober, G. Monaco, H. Requardt, Phys. Rev. B 78 (2008) 224301. N.J. English, J.S. Tse, R. Gallagher, Phys. Rev. B 82 (2010) 092201; N.J. English, J.S. Tse, Phys. Rev. B 83 (2011) 184114. C.A. Tulk, C.J. Benmore, J. Urquidi, D.D. Klug, J. Neufeind, B. Tomberli, P.A. Egelstaff, Science 297 (2002) 1320. J.S. Tse, D.D. Klug, M. Guthrie, C.A. Tulk, C.J. Benmore, J. Urquidi, Phys. Rev. B 71 (2005) 214107. Supplementary information (to follow within this document file). Details on molecular dynamics calculations. J.L.F. Abascal, E. Sanz, R. Garcia, J. Chem. Phys. 122 (2005) 234511. C. Vega, J.L.F. Abascal, Phys. Chem. Chem. Phys. 13 (2011) 19663. J.S. Tse, M.L. Klein, Phys. Rev. Lett. 58 (1987) 1672. T. Loerting, W. Schustereder, K. Winkel, C.G. Salzmann, I. Kohl, E. Mayer, Phys. Rev. Lett. 96 (2006) 025702. R.G. Fernández, J.L.F. Abascal, C. Vega, J. Chem. Phys. 124 (2006) 144506. D. Eisenberg, W. Kauzmann, The Structure and Properties of Water, Oxford University Press, Oxford, 1969. Y.P. Handa, O. Mishima, E. Whalley, J. Chem. Phys. 84 (1986) 2766. S. Klotz, G. Hamel, J.S. Loveday, R.J. Nelmes, M. Guthrie, Phys. Rev. Lett. 89 (2002) 285502. O. Mishima, J. Chem. Phys. 100 (1994) 5910. R.J. Hemley, A.P. Jephcoat, H.K. Mao, L.C. Ming, M.H. Manghnani, Nature 334 (1988) 52. M.B. Kruger, R. Jeanloz, Science 249 (1990) 648. J. Haines, J.M. Léger, F. Gorelli, M. Hanfland, Phys. Rev. Lett. 87 (2001) 155503. S.M. Sharma, N. Garg, S.K. Sikka, J. Phys.: Condens. Matter 12 (2000) 6683.
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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Reversible pressure-induced crystal-amorphous structural transformation in ice Ih Niall J. English a,⇑, John S. Tse b,⇑ a The SEC Strategic Research Cluster and the Centre for Synthesis and Chemical Biology, School of Chemical and Bioprocess Engineering, University College Dublin, Belfield, Dublin 4, Ireland b Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5B2, Canada
a r t i c l e
i n f o
Article history: Received 2 March 2014 In final form 16 June 2014 Available online 20 June 2014
a b s t r a c t Molecular dynamics (MD) simulation of depressurised high-density amorphous ice (HDA) at 80 K and at negative pressures has been performed. Over several attempts, HDA recrystallised to a form close to hexagonal ice Ih, albeit with some defects. The results support the hypothesis that compression of ice-Ih to HDA is a reversible first-order phase transition, with a large hysteresis. Therefore, it would appear that LDA is not truly amorphous. The elastic energy estimated from the area of the hysteresis loop is ca. 4.5 kJ/mol, in some way consistent with experimentally-determined accumulated successive heats of transformations from recovered HDA ? ice Ih. Ó 2014 Elsevier B.V. All rights reserved.
Two very early reports on the compression of crystalline ice Ih into a high-density form, i.e., high-density amorphous ice (a-ice, HDA) [1] at low temperature, and the subsequent transformation to another low-density amorphous form (LDA) [2] upon decompression, respectively, may be regarded as important turning points in ice physics. The novel phenomenon of pressure-induced amorphisation (PIA) was conjectured to be a thermodynamic melting process [1]. The apparent first-order-like transition from HDA to LDA has led to the suggestion that these ices are thermodynamically distinctive forms and motivated the proposal of the twoliquid model of water [3]. For instance, HDA has been described as an isotropic glass that may devitrify, with some experimental studies appearing to offer relatively persuasive evidence in this vein [4–6]. In addition, further experimental evidence suggests that the underlying mechanism of PIA changes from mechanical instability at low temperatures to pressure-induced melting at higher temperatures [7]. For its part, it has been suggested from experimental studies that LDA is a distinctive thermodynamic phase, supporting the concept of ice polyamorphism at positive pressure; certainly, LDA has been kept stable at positive pressures over a period of years [3,8,9]. However, there are still many open questions on the nature of these a-ices, and these conclusions inferred from the experimental studies of Refs. [3–9] are certainly not without controversy or criticism (vide infra); therefore, one key, largely unresolved matter relates to their underlying thermodynamic stability. For instance, ⇑ Corresponding authors. E-mail addresses: [email protected] (N.J. English), [email protected] (J.S. Tse). http://dx.doi.org/10.1016/j.cplett.2014.06.026 0009-2614/Ó 2014 Elsevier B.V. All rights reserved.
the findings on the nature of LDA as a distinct phase have been disputed directly [10,11], whilst there is now a body of conclusive theoretical and experimental evidence showing that the mechanism for PIA arises not from melting, but is rather due to mechanical instability of the crystal structure in ice Ih [12–14]. Crystalline-like thermal conductivities [15] and sustained phonon dispersion observed in HDA and LDA ices [16–18] have shown unambiguously the presence of intermediate-range order in the structures not related to an isotropic liquid [10,19]. Experimental investigation of the intermediate-range ordering in these forms of amorphous ices also raises a question on the relationship between HDA and LDA. One suggestion is that HDA ice is a metastable, frustrated structure, arising from a large activation energy barrier due to proton re-orientation necessary for the formation of associated crystalline ice polymorphs [15,20,21]. It was postulated that the compression–decompression of amorphous ices reflects a hysteresis process with a large van der Waals loop [21] and the experimental recovery of LDA at ambient pressure is possible due to a large kinetic barrier. If this hypothesis is correct, ice Ih should be recoverable from HDA at negative pressure and low temperature [15,21]. Our principal goal in the present study is to address whether any such compression–decompression cycle displays large hysteresis at low temperatures, which would be a prerequisite for any (quasi-, or apparent) ‘first-order’ transition from ice Ih to HDA to have any grounding. It should be borne in mind that many of the experiments underlying the conclusions in Refs. [3–9] were carried out above the postulated glass transition temperature (around 130 K, and inferred to exist from an increase in heat capacity rather than via direct viscosity measurements) [7] and, as such, though
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certainly interesting in their own right, are less relevant to the low-temperature work in the present study. To test this hypothesis on putative hysteresis in a compression– decompression cycle, molecular dynamics (MD) simulations of depressurisation of HDA at 80 K, at negative pressure, have been performed. An earlier result for such a process is non-conclusive, as it only shows a partially re-formed ice Ih-like framework [21]. This previous work, however, was limited by the size of the system simulated and the length of simulation time [21]. The premise of the present work is to investigate the possibility of ‘spontaneous’ (versus thermally activated) reversibility of PIA without thermal activation (i.e., maintaining the temperature at 80 K). The ‘recrystallisation’ process therefore depends only on stochastic thermal fluctuations. For this purpose, a large ice model with very long (>nanosecond) simulation times are needed. It was found that recrystallisation from the amorphous phase indeed took place to a form close to hexagonal ice (Ih), albeit with some reminiscence of LDA-like defects (vide infra). However, it must be stressed here that another alternative perspective would be to label this defective structure as being closer to LDA in nature, with ice Ih-like characteristics; we show, however, that the former interpretation appears more reasonable. Upon pressurisation of a 23 040-molecule system of ice Ih (cf. Supplementary information [22], using the TIP4P-Ice model [23] in the present study, and shown previously to be appropriate for various ices [24]), densification to a non-crystalline form was observed to take place between 12 and 14 kbar within 10 ns (cf. Figure 1), as judged by consideration of density and examination of the radial distribution functions (RDFs). 10 ns, however, was not entirely sufficient to remove the essential hallmarks of crystal structure at 14 kbar in terms of a low value of the O–O partial RDF in the 3–3.6 Å range; extending the simulation to 30 ns achieved HDA-like RDFs. Similar findings were reported previously [25] on a much smaller system (128 molecules using TIP4P, arguably an inferior model for ices [24]). The density of the resultant HDA was found to be 1.29–1.305 g/cm3 at 14 and 16 kbar, respectively, with a reduction to 1.2 g/cm3 at atmospheric pressure, where is was found to be kinetically stable (vide infra and cf. Figure 1). This latter value is some 2.5% larger than the experimental value at recovered at ambient pressure at 77 K of 1.17 g/cm3 [26], but it should be noted that experimental density estimates for amorphous ices recovered at ambient pressures are
Figure 1. Density–pressure relationship at 80 K, demonstrating the hysteresis of the Ih ? HDA and HDA ? Ih transitions, showing the ‘Ih-like’ density at 5 and 10 kbar for the cases where (partial) recrystallisation was observed; not all simulations at these negative pressures resulted in recrystallisation within 50 ns.
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also quite dependent on synthetic pathways, which makes only approximate estimates possible. This complicates a direct, quantitative comparison with our present results; bearing this in mind, however, our 2.5% density overestimate with TIP4P-ice for HDA appears reasonable. Following this TIP4P-Ice density comparison with experiment, although the thermal volume-expansivity of amorphous ices has not been measured experimentally, it is worth considering the role of temperature ‘undercooling’ vis-à-vis the presently-used 80 K and the ice-Ih melting point for the given potential model (TIP4P-Ice). The (ambient-pressure, ice Ih-liquid) melting point of the TIP4P-Ice model has been estimated to be 270 K (in contrast with 230 K for TIP4P) [27], so this much-better performance of TIP4P-Ice is reassuring. This 190 K ‘drop’ in temperature below the melting point down to 80 K means that the presently studied temperature with TIP4P-Ice is indeed substantially below the postulated glass transition temperature (around 130 K, inferred from heat-capacity increases rather than directly from viscosity measurements) [7]. Five independent constant pressure–constant temperature (NPT) MD simulations of pressure-amorphised HDA ice generated from a 32 768-molecule system were performed at 80 K and for each of 0.001, 5 and 10 kbar (cf. Supplementary information). [22] No hint of ‘recrystallisation’ was found in the simulation at 0.001 kbar (atmospheric pressure). In contrast, MD calculations performed at 5 and 10 kbar show the systems have, in some cases, respectively, recrystallised either partially or almost to an ice Ih-like form, after circa 25–35 ns. Of the five independent runs, one and two out of five recrystallised at 5 and 10 kbar, respectively, indicating the extent of kinetic limitation. In these particular cases, a dramatic volume-expansion took place suddenly, with the density decreasing down to around 0.92 g/cm3, which is close to (1.6% less than) the experimental density of ice Ih at 80 K (0.935 g/cm3) [28]; this agreement with TIP4P-Ice is somewhat reasonable – indeed, we have found in previous work that TIP4P tends to overestimate the ice Ih density vis-à-vis TIP4P-Ice [19], and we have noted above the superior estimation of the melting point of ice-Ih by TIP4P-Ice (270 K versus 230 K for TIP4P, much closer to the experimental value of 273 K) [27]. The elastic energy estimated from the area of the hysteresis loop in Figure 1 is around 4.5 kJ/mol. Careful calorimetry measurements for the combined transitions of recovered HDA ? LDA ? ice Ic ? Ice Ih give an aggregate of 2.1 kJ/mol [29]. This result shows that it is possible that the heat of transformation between HDA and ice Ih could be, in part, recovered from the stored elastic energy. On the other hand, in view of the previous comment that a legitimate alternative view of the nature of the recrystallised form of the ice would be to consider it closer to LDA with ice Ih-like features, then a more appropriate comparison would be with the value for HDA ? LDA, which is around 0.75 kJ/mol [29]. The somewhat closer agreement of the theoretical value here with the experimental estimate of 2.1 kJ/mol rather than 0.75 kJ/mol [29] arguably offers some indirect support towards the view that the recrystallised, defective ice may be closer to ice Ih in nature, but this is admittedly somewhat tentative; the observed value of 4.5 kJ/mol is still around double the corresponding experimental HDA ? Ice Ih estimate. The O–O pair distribution functions (PDFs) are shown in Figure 2a for the recrystallised structures from the 5 and 10 kbar decompression cases shortly after these events, along with those of ‘native’ Ih (270 K and 1 bar) and LDA (at 1 kbar) and HDA (at 8 kbar) structures, both at 80 K, for reference. With decreasing (i.e., more negative) pressure, the structure resembles more closely initial ice Ih, even though the densities of ice Ih and LDA are similar. The negative-pressure ‘driving force’ causes the PDF of the recrystallised sample to exhibit O–O correlation shells similar to that of the initial ice Ih, at least up to 7 Å. The interstitial
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Figure 2. (a) O–O Pair distribution functions at 80 K for HDA and the recrystallised form at the specified pressures and compared with the reference LDA (80 K) and Ih (270 K) structures. The PDFs have been displaced upwards for ease of viewing. (b) Corresponding gOO (r) plots with the same curve styles of Figure 2a.
in structure. It can be seen that, especially in the intermediate range beyond the first shell, that the recrystallised forms (especially at 10 kbar) are closer to ice Ih than LDA or HDA. It is also instructive in this regard to consider the ratio of the O–O PDF vis-à-vis that of ice Ih, and this is plotted in Figure 3 for HDA, LDA and the recrystallised form at 10 kbar, with the evolution of the integral of this quantity shown in the inset. It is clear that the recrystallised form has a ratio substantially closer to unity; equally, a better fit (i.e., a ratio closer to unity) would exhibit a straight-line relationship in the running value of its integral, and this is also the case for the recrystallised form (in dashed grey, in the inset of Figure 3). This has the best coefficient of goodnessof-fit (v2-quantity nearest 1) derived from a straight-line leastsquares fit to the running integral. A schematic showing the values of v2 with decreasing pressure is shown in Figure 4. The amorphous ice recovered at 10 kbar shows the highest resemblance to crystalline ice Ih structure; a perfect match would have v2 = 1. The O–O static structure factors are shown in Figure 5 for the same structures at their respective stable pressures, i.e., the same temperature and pressure conditions as in Figure 2. Although Klotz et al. have suggested for HDA structure-determination [30], that there may be some second-order, minor differences in structure factors due to pressure effects, this will not change the complexion of the matter appreciably, and we present the structures at their respective pressures (270 K and 1 bar for Ih, and 80 K for other structures with 8 kbar for HDA, 1 kbar for LDA, and the 5/ 10 kbar recrystallised forms). In Figure 5, it can be seen that the recrystallised forms are closer to Ih than LDA, with the main peaks at 1.67 and 1.66 Å 1 for 5 and 10 kbar, respectively, in increasingly better agreement with that of Ih, as opposed to 1.71 Å 1 for LDA. The secondary peak of Ih at around 2.4 Å 1 is also reproduced by the recrystallised forms. However, the less pronounced LDA secondary peak at 2 Å 1 is echoed by the recrystallised structure from 5 kbar, emphasising the imperfect crystalline nature, and localised instances of near-amorphous structure. This is less prominent in the structure arising from simulation at 10 kbar, indicating a structure almost, but yet not quite perfectly, like ice Ih. The decay to zero of S(k) around the peaks for the
oxygen density between the first and second oxygen coordination shell, i.e., the region between 3.0 and 3.6 Å, is still somewhat apparent in the recrystallised structure. However, this spurious feature is removed when the pressure is further reduced to 10 kbar. The first coordination shell, however, still is not as sharp as ice Ih with a small distribution from 2.7 to 3.2 Å. The slightly broadened O–O first coordination shell may be attributable to the average O–O distance being longer with increasing negative pressure and the distribution of O–O distances not being elastically isotropic. The imperfect crystal structure may also be due to the activation energy required for proton re-orientation into a perfect proton alignment following the Bernal–Fowler rules and with vanishingly-small dipole in the structure. Still, referring to the PDF of LDA, there is considerably less interstitial oxygen density than the HDA amorphous structure. The average configurational energy of the recrystallised system was around 0.4–0.45 kcal/mol lower than that of HDA, but some 1.2–1.4 kcal/mol higher than that of ice Ih, which quantifies the level of distortion in the recrystallised structure, essentially due to strained and imperfect hydrogen bonds. The enthalpy was found to decline by a similar level (0.4–0.5 kcal/mol) vis-à-vis HDA upon ‘recrystallisation’, but yet remain ‘stubbornly’ above that of ice Ih (by circa 1.3 kcal/mol). To probe further, and more directly, the similarity, or otherwise, of the various studied structures to ice Ih (at 270 K and 1 bar) in Figure 2a, particularly beyond the first shell, we have plotted the O–O r g(r) in Figure 2b, which emphasises longer-range differences
Figure 3. Ratio of O–O g(r) to that of ice Ih (with the latter at 270 K and 1 bar), with the running value of the integral of this ratio shown in the inset. These plots are for HDA, LDA and the recrystallised form at 10 kbar (all at 80 K, and at their respective pressures in Figure 2). The same curve styles are adopted as in Figure 2a (specified again in the legend here). Note that effectively identical structures to ice Ih (from an O–O point of view, at least) would have a straight-line relationship, and the recrystallised form (dashed grey) appears the ‘best’ in this regard. Please see the text for further discussion.
Ih, 270 K, 1 bar (a) HDA, 80 K, 8 kbar LDA 80 K LDA, K, 1 kbar 'Recrys.' HDA, 80 K, -5 kbar 'R 'Recrys.' ' HDA, HDA 80 K, K -10 10 kbar kb
12
gOO O (r)
10 8 6 4 2 0 2
3
4
5
6
7
8
r (Å) ( )
(b)
12
r gOO O (r)
10 8 6 4 2 0 2
3
4
5
6
7
8
r (Å)
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Figure 4. A plot of the goodness of fit (v2) of the O–O radial distribution functions of the relevant forms of amorphous ices with respect to crystalline ice Ih with pressure. A v2 = 1 indicates a perfect match.
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instead of recovered HDA, although this needs to be framed carefully within the broader context of this study; the structure is a hybrid, of sorts. The ‘crux of the matter’, however, appears to be that the ultimate outcome will be conversion to ice Ih, and O–O PDF analysis suggests a closer structural relationship to ice Ih. Bearing these observations of structural characteristics in mind, in relation to the partially recrystallised structures, it befits an examination of stability and the vibrational density of states (VDOS) before, during and immediately following the rapid transition itself, in order to characterise, at least crudely and indirectly, the nature of the energy landscape itself. To this end, we have carried out additional NVT simulations (by necessity) to probe the vibrational density of states (VDOS) of two ‘intermediate’, transient structures encountered during one particular instance of the rapid recrystallisation events (which is representative of the various such sampled events). These were carried out at 80 K and 5 kbar; the constant-volume prevented conversion to the final recrystallised form and ‘wholesale’ volume fluctuation. These inherently unstable intermediate structures were 1.01 and 1.07 g/cm3 in density; these were sufficiently long-lived for velocity autocorrelation function (VACF)-sampling under NVT conditions only. These VDOS are shown in Figure 6, from Fourier transformation of the VACFs of oxygen atoms, for the essentiallyHDA structure just prior to recrystallisation, and for the defective ice Ih structure (or, conversely, LDA-like structure with prominent Ih features) directly afterwards. For frequencies around 120– 145 cm 1, there are much lower values of the VDOS for the intermediate structures, underlying their lack of feature and inherent instability. These findings indeed show that the ‘recrystallised’ structure possesses ‘soft’ modes, indicating that the potential surface is rather flat and the structure is located in a shallow minimum. Although this may suggest, to some extent, that the ‘label’ (i.e., closer to LDA or ice Ih) to describe the structure is arguably semantic, it is closer to ice Ih from a structural point of view (in terms of O–O distribution), albeit with some substantial hydrogen-bond strain.
Figure 5. Static structure factors S(k) for the various structures at the same temperature/pressure conditions in Figure 2, i.e., 270 K and 1 bar for ice Ih, and 80 K for the other structures with 8 kbar for HDA, 1 kbar for LDA, and the 5/ 10 kbar recrystallised forms. The peaks have been normalised to circa 2, and the various S(k) curves have been displaced vertically for ease of viewing.
recrystallised structure is much more reminiscent of crystalline Ih, underlying its essentially crystalline nature, albeit imperfect. Certainly, the recrystallised form from 10 kbar simulation is indeed tantalisingly closer. Running the 5 kbar recrystallised form for around 30 ns at a pressure of 10 kbar led to similar PDF and S(k) results for the 10 kbar-recrystallised case depicted in Figures 2 and 3 with no particular closer ‘fit’ to perfect ice Ih, emphasising again the kinetic limitations of proton rearrangement. Thermal annealing will certainly accelerate the ‘healing’ of the defects. This latter concern, however, is not the intended goal of this study, but rather the demonstration of spontaneous isothermal reversal of the amorphous ? crystalline transformation from stochastic thermal fluctuations. The less pronounced feature in the structure factors at circa 2 Å 1 (declining at 10 kbar) is more reminiscent of LDA; this suggests that another interpretation of the recrystallised structures would be to regard them as closer to LDA, with prominent ice Ih characteristics, although the PDF-based analysis of Figures 2b, 3 and 4 suggests a closer structural relationship to ice Ih. Perhaps a more illuminating approach is to dub the ‘recrystallised’ structures at negative pressure a recovered ice
Figure 6. Vibrational density of states (VDOS) at 80 K and 5 kbar from Fourier transformation of velocity autocorrelation functions (VACFs) of oxygen atoms (sampled, by necessity, under NVT conditions) for the essentially-HDA structure just prior to recrystallisation, and for the imperfect ice structure (with LDA-like features) just afterwards. Also shown are two unstable intermediate structures during the rapid transition (of 1.01 and 1.07 g/cm3), which were sufficiently longlived for VACF-sampling under NVT conditions only. For frequencies around 120– 145 cm 1, there are lower values of the VDOS for the intermediate structures, underlying their lack of stability, which is ‘preserved’ artificially for 20 ps of VACFsampling under constant-volume conditions.
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In conclusion, it has been shown that HDA can be recrystallised to a form close to hexagonal ice (Ih) with relatively small defects, or, conversely and more tentatively, to an LDA-like structure with prominent ice Ih features, as determined from consideration of structure factors and radial distribution functions. Given that the simulations were not run for more than 50 ns and it appears that ice Ih is the final ‘outcome’, in that one and two out of five recrystallised at 5 and 10 kbar, respectively, this suggests a kinetically-limited process. Although these results may appear to suggest that the formation of LDA may be controlled kinetically, it is difficult to conclude this with any level of confidence; the central goal of this study has not been to investigate if LDA is a ‘kinetic product’, but rather the extent of hysteresis in the HDA/ice Ih compression–decompression cycle. In any event, perhaps timescales of microseconds or milliseconds may be required for deterministic MD to recover an essentially perfect crystal structure. This hysteresis was demonstrated by the densification of Ih to a non-crystalline form, redolent of HDA. The area enclosed by the hysteresis loop is the elastic energy stored in HDA and from Figure 1 it is estimated to be ca. 4.5 kJ mol 1. The conversion of HDA to LDA or ice Ih is highly exothermic and very rapid, thus giving, arguably, a quasi-first-order-like transition [20,31]. It is noteworthy that under hydrostatic conditions, the prototypical pressure-induced amorphisation transformations previously reported, i.e., a-quartz [32] and berlinite [33], were no longer observed; instead, the respective systems were observed to transform into new crystalline structures [34,35]. We conjecture that PIA in ice is no different in this respect. The authors wish to thank an anonymous reviewer for very useful comments and suggestions on improving the comparison of the different ice structures.
1. Author contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. N.J. English and J.S. Tse contributed equally.
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.cplett.2014. 06.026. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30]
2. Funding sources
[31] [32]
The authors thank the Ireland Canada University Foundation and the Royal Irish Academy.
[33] [34] [35]
O. Mishima, L.D. Calvert, E. Whalley, Nature 310 (1984) 393. O. Mishima, L.D. Calvert, E. Whalley, Nature 314 (1985) 76. O. Mishima, H.E. Stanley, Nature 392 (1998) 164. O. Mishima, J. Chem. Phys. 121 (2004) 3161. O. Andersson, Proc. Nat. Acad. Sci. 108 (2011) 11013. M. Seidl, M.S. Elsaesser, K. Winkel, G. Zifferer, E. Mayer, T. Loerting, Phys. Rev. B 83 (2011) 100201. O. Mishima, Nature 384 (1996) 546. R.J. Nelmes, J.S. Loveday, T. Strässle, C.L. Bull, M. Guthrie, G. Hamel, S. Klotz, Nature Phys. 2 (2006) 414. S. Klotz et al., Phys. Rev. Lett. 94 (2005) 025506. C.A. Tulk, C.J. Benmore, D.D. Klug, J. Neuefeind, Phys. Rev. Lett. 96 (2006) 149601. S. Klotz et al., Phys. Rev. Lett. 96 (2006) 149602. J.S. Tse, J. Chem. Phys 96 (1992) 5482. J.S. Tse et al., Nature 400 (1999) 647. Th. Strässle, A.M. Saitta, S. Klotz, M. Braden, Phys. Rev. Lett. 93 (2004) 225901. J.S. Tse, D.D. Klug, Phys. Chem. Chem. Phys. 14 (2012) 8255. O. Andersson, H. Suga, Phys. Rev. B 65 (2002) 140201. H. Schober, M.M. Koza, A. Tölle, C.C. Masciovecchio, F. Sette, F. Fujara, Phys. Rev. Lett. 85 (2000) 4100. M.M. Koza, B. Geil, M. Scheuermann, H. Schober, G. Monaco, H. Requardt, Phys. Rev. B 78 (2008) 224301. N.J. English, J.S. Tse, R. Gallagher, Phys. Rev. B 82 (2010) 092201; N.J. English, J.S. Tse, Phys. Rev. B 83 (2011) 184114. C.A. Tulk, C.J. Benmore, J. Urquidi, D.D. Klug, J. Neufeind, B. Tomberli, P.A. Egelstaff, Science 297 (2002) 1320. J.S. Tse, D.D. Klug, M. Guthrie, C.A. Tulk, C.J. Benmore, J. Urquidi, Phys. Rev. B 71 (2005) 214107. Supplementary information (to follow within this document file). Details on molecular dynamics calculations. J.L.F. Abascal, E. Sanz, R. Garcia, J. Chem. Phys. 122 (2005) 234511. C. Vega, J.L.F. Abascal, Phys. Chem. Chem. Phys. 13 (2011) 19663. J.S. Tse, M.L. Klein, Phys. Rev. Lett. 58 (1987) 1672. T. Loerting, W. Schustereder, K. Winkel, C.G. Salzmann, I. Kohl, E. Mayer, Phys. Rev. Lett. 96 (2006) 025702. R.G. Fernández, J.L.F. Abascal, C. Vega, J. Chem. Phys. 124 (2006) 144506. D. Eisenberg, W. Kauzmann, The Structure and Properties of Water, Oxford University Press, Oxford, 1969. Y.P. Handa, O. Mishima, E. Whalley, J. Chem. Phys. 84 (1986) 2766. S. Klotz, G. Hamel, J.S. Loveday, R.J. Nelmes, M. Guthrie, Phys. Rev. Lett. 89 (2002) 285502. O. Mishima, J. Chem. Phys. 100 (1994) 5910. R.J. Hemley, A.P. Jephcoat, H.K. Mao, L.C. Ming, M.H. Manghnani, Nature 334 (1988) 52. M.B. Kruger, R. Jeanloz, Science 249 (1990) 648. J. Haines, J.M. Léger, F. Gorelli, M. Hanfland, Phys. Rev. Lett. 87 (2001) 155503. S.M. Sharma, N. Garg, S.K. Sikka, J. Phys.: Condens. Matter 12 (2000) 6683.