Shrinking water's no man's land by lifting its low-temperature boundary

Markus Seidl, Alice Fayter, Josef N. Stern, Gerhard Zifferer, and Thomas Loerting

Phys. Rev. B 91, 144201 – Published 15 April 2015

Abstract

Investigation of the properties and phase behavior of noncrystalline water is hampered by rapid crystallization in the so-called “no man's land.” We here show that it is possible to shrink the no man's land by lifting its low-temperature boundary, i.e., the pressure-dependent crystallization temperature $T_{x} (p)$ . In particular, we investigate two types of high-density amorphous ice (HDA) in the pressure range of $0.10 - 0.50 GPa$ and show that the commonly studied unannealed state, uHDA, is up to 11 K less stable against crystallization than a pressure-annealed state called eHDA. We interpret this finding based on our previously established microscopic picture of uHDA and eHDA, respectively [M. Seidl et al., Phys. Rev. B 88, 174105 (2013)]. In this picture the glassy uHDA matrix contains ice $I_{h}$ -like nanocrystals, which simply grow upon heating uHDA at pressures $\leq 0.20 GPa$ . By contrast, they experience a polymorphic phase transition followed by subsequent crystal growth at higher pressures. In comparison, upon heating purely glassy eHDA, ice nuclei of a critical size have to form in the first step of crystallization, resulting in a lifted $T_{x} (p)$ . Accordingly, utilizing eHDA enables the study of amorphous ice at significantly higher temperatures at which we regard it to be in the ultraviscous liquid state. This will boost experiments aiming at investigating the proposed liquid-liquid phase transition.

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Received 14 February 2015

DOI:https://doi.org/10.1103/PhysRevB.91.144201

Authors & Affiliations

Markus Seidl¹, Alice Fayter¹, Josef N. Stern¹, Gerhard Zifferer², and Thomas Loerting^1,*

¹Institute of Physical Chemistry, Universität Innsbruck, Innrain 80–82, 6020 Innsbruck, Austria
²Department of Physical Chemistry, Universität Wien, Währinger Straße 42, 1090 Wien, Austria

^*Corresponding author: thomas.loerting@uibk.ac.at

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Vol. 91, Iss. 14 — 1 April 2015

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Figure 1
“Phase diagram” of disordered forms of water. $T_{m}$ is the melting temperature and $T_{h}$ is the homogeneous nucleation temperature. Both lines are redrawn from Fig. 6 in Ref. [4] and adapted originally from Ref. [80]. The $T_{h}$ line is obtained upon isobaric cooling of emulsified liquid water droplets with ∼3 K/min [80]. Lines denoted $T_{x}$ are determined in the present study upon isobaric heating with 2 K/min (cf. Fig. 8) and represent the crystallization temperatures of two types of high-density amorphous ice (uHDA and eHDA, respectively). In the no man's land disordered forms of water crystallize extremely fast. If uHDA is considered (light-gray background), the no man's land is larger than in the case of eHDA (dark-gray background).
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Figure 2
Proposed scenario for the relation between the time scales of structural relaxation and crystallization of water. The dashed line indicates the melting temperature $T_{m}$ . $τ_{α}$ is the structural relaxation time, $τ_{cn}$ is the characteristic time of crystal nucleation, and $τ_{cg}$ is the characteristic time of crystal growth. That is, the red curve marked $τ_{cg}$ illustrates the crystallization time scale as observed in seeded samples (crystal growth only), while the green curve marked $τ_{cn} + τ_{cg}$ illustrates the crystallization time scale for initially completely noncrystalline samples (crystal nucleation followed by crystal growth). Both curves provide the characteristic time the system takes to form a certain amount (e.g., experimentally detectable fraction) of crystalline material. Each of the two crystallization curves intersects the blue relaxation curve at the temperatures $T_{1}$ and $T_{2}$ . Thus, these temperatures represent the approximate limits between which water crystallizes faster than it relaxes. For times exceeding $τ_{cg}$ (crystal growth only, light-gray background) or $τ_{cn} + τ_{cg}$ (crystal nucleation followed by crystal growth, dark-gray background), the sample contains at least a certain fraction of crystalline material. The orange arrow illustrates the time scale of the isobaric heating experiments (given by the heating rate of 2 K/min) reported in the present study. The crystallization temperature $T_{x}$ obtained in these experiments is then given by the intersection of the arrow with the curve marked $τ_{cg}$ (crystal growth only) or $τ_{cn} + τ_{cg}$ (crystal nucleation followed by crystal growth).
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Figure 3
Sketch of the transformations taking place upon isobaric heating of starting materials uHDA (red) and eHDA (green) at 0.20 GPa (a) and 0.30 GPa (b), respectively. Amorphous material, i.e., HDA, is represented by ellipses. In uHDA nanocrystals of ice $I_{h}$ are present (hexagonal prisms). These nanocrystals grow upon heating at pressures $\leq 0.20 GPa$ (a), but upon heating at $0.30 - 0.50 GPa$ they first transform from ice $I_{h}$ to ice IX nanocrystals (rhomboidal prisms) and start to grow subsequently (b). At pressures $\leq 0.20 GPa$ uHDA transforms to a mixture of ice I and ice IX, while eHDA transforms to ice IX only (a). In contrast, at pressures $0.30 - 0.50 GPa$ a mixture of ice polymorphs (namely, ice IX and ice V) may be obtained from both uHDA and eHDA (b).
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Figure 4
Phase diagram of the stable phases of water, including metastable ice IX. Solid and dot-dashed lines indicate measured phase boundaries between stable and metastable phases, respectively. Dashed and dotted lines indicate extrapolated or estimated phase boundaries between stable and metastable phases, respectively. Gray arrows indicate the path of the isobaric heating experiments in the present study. Figure adapted from Ref. [81]; phase boundaries of ice XV as provided in Ref. [82].
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Figure 5
Density or volume change associated with crystallization upon isobaric heating of HDA. Panel (a) provides the pressure-dependent density ρ( $p$ ) of uHDA, ice IX, and ice V, respectively; the figure is a cut-out of Fig. 2 in Ref. [26] (adopted with changes). In panel (b) the evolution of volume change $Δ V (T)$ upon crystallization of starting material uHDA is illustrated schematically. The arrow (labeled “exp.”) close to the ordinate indicates the direction of expansion. The figures in the upper row show the volume increase upon slow (curve 1) and fast crystallization of ice IX (curve 2) as well as volume decrease upon fast crystallization of ice V (curve 3). The figures in the lower row illustrate a more complex crystallization behavior caused by parallel crystallization kinetics. Labels refer to the curves shown in the upper row and indicate the distinct crystallization processes taking place in one and the same sample. Straight lines illustrate how the onset and end point of crystallization are defined (for details see Sec. 2 in the main text).
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Figure 6
Volume change $Δ V$ and pressure evolution while isobarically heating (2 K/min) high-density amorphous ices at 0.30, 0.40, and 0.50 GPa, respectively. Data for starting material uHDA are shown in the first row while data for starting material eHDA are shown in the second row. Colors refer to the maximum temperature $T_{\max}$ reached in the respective experiment; $T_{\max}$ is 148 K (orange), 153 K (red), 156 K (pink), 160 K (green), or 170 K (blue). Circles (uHDA) and triangles (eHDA) mark the end points of the curves at $T_{\max}$ . The $Δ V (T)$ curves are corrected for the apparatus behavior (see Sec. 2 in the main text) and vertically shifted to match at 110 K. The dotted horizontal line helps one recognize the positive or negative slope of the $Δ V (T)$ curves. In each panel the solid vertical line indicates the crystallization temperature $T_{x}$ as plotted in Fig. 8, considering either the onset point or the position of the sudden volume jump.
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Figure 7
X-ray diffraction patterns of states obtained by isobaric heating of high-density amorphous ices at 0.30, 0.40, and 0.50 GPa, respectively (see Fig. 6), recorded after samples’ recovery to ∼80 K and (sub)ambient pressure. Curves are offset for clarity. Data for uHDA are shown in the first row while data for eHDA are shown in the second row. Temperature labels providing the maximum temperature reached in the respective experiment (as well as use of the same color code as in Fig. 6) allow assignment of the individual diffractograms to the samples’ volumetric curves in Fig. 6. The number of heating/cooling cycles (for details, see Sec. 2 in the main text) are stated in brackets. In each panel the diffractogram labeled 80 K (turquoise curve) refers to the starting material, i.e., uHDA or eHDA. In the case of starting material uHDA (first row) the pattern shows a broad halo peak with a maximum at ∼30.1°, while in the case of starting material eHDA (second row) the halo peak maximum occurs at ∼31.4°. At the bottom of each set of diffractograms the Bragg peak positions of ice IX and ice V as well as those of the sample holder are indicated by tics (only peaks with a theoretical intensity of >2% of the most intense peak's intensity are considered). The Bragg peak positions of ice IX are also marked in the diffraction pattern at the very top of each set. Vertical lines indicate the position of the most intense Bragg peak of ice IX and ice V, respectively. The intensities of the peaks found at these positions are used to estimate the phase composition of fully crystallized samples (see Table 1).
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Figure 8
In panel (a) and panel (b) the crystallization temperature $T_{x}$ of uHDA (circles) and eHDA (triangles), respectively, is plotted as a function of pressure. Open symbols correspond to the onset point of crystallization and full symbols to the sudden volume jump [cf. Fig. 5]. The data are obtained from the $Δ V (T)$ curves shown in Fig. 6 of the present paper, Figs. 2(d)–2(f) and Fig. SM3(d)–3(f) in Ref. [23], and similar curves of additional experiments (not shown). All data points at pressures 0.10–0.30 GPa represent mean values of two to five independent experiments, except the data point of uHDA obtained from a sudden volume jump at 0.30 GPa. This one as well as all data points at 0.40 and 0.50 GPa are based on only one experiment, where the respective $Δ V (T)$ curve is shown in Fig. 6. The size of the symbols is equal to or larger than twice the standard deviation. In particular, panel (a) provides a comparison of our result for $T_{x} (p)$ of starting material uHDA with earlier results on the same material, while panel (b) provides a comparison of our result for both starting material uHDA and eHDA, respectively. Crosses and the plus correspond to the end FIG. 8. (Continued) point of crystallization of starting material uHDA and eHDA, respectively [cf. Fig. 5]. The dashed lines are linear fits to the onset point of crystallization of starting material uHDA at pressures $\leq 0.20 GPa$ and $0.30 - 0.50 GPa$ , respectively. The dotted line is a linear fit to the end point of crystallization of starting material uHDA in the whole pressure range. The solid line is a quadratic fit to the temperature where a sudden volume jump occurred upon heating eHDA, again considering the whole pressure range. Panels (c) and panel (d) show the differences between several specific crystallization temperatures as a function of pressure. In panel (c), crosses and pluses depict the crystallization width $Δ T_{x}$ for uHDA and eHDA, respectively. In both cases, a sudden volume jump has a pressure-independent width of ∼0.1 K (data points below the thin horizontal line). In experiments where no such volume jump occurred (data points above the horizontal line), the difference between the onset and end temperature of crystallization is at least ∼2 K; lines fitting the data of uHDA are analogously obtained from the respective fits plotted in panel (b). In panel (d), full pentagons depict the difference between the crystallization temperature of eHDA defined by the sudden volume jump and the crystallization temperature of uHDA as obtained from evaluation of the onset point; empty pentagons depict the difference between the crystallization temperature of eHDA and uHDA, respectively, both as obtained from evaluation of the onset point. The lines are analogously obtained from the respective fits plotted in panel (b).
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Figure 9
Simplified schematic representation of the changes in the free energy surface upon changing pressure. The order of stability of crystalline and amorphous phases reflects experimental findings for bulk ices. Temperature labels indicate transition temperatures for bulk ices ( $IX \to II$ and $VHDA \to IV$ ) or nanocrystalline ices embedded in a HDA matrix ( $I_{h} \to IX$ and $I_{h} \to VHDA$ ). In each panel, crystalline and amorphous polymorphs that are irrelevant for the present discussion are omitted for clarity.
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