Neutrons meet ice polymorphs

Abstract

The current epoch can be described as the ‘age of ice-rush’, as the rate of discovery of ice polymorphs, of which there are currently 20 known, has accelerated, particularly since the end of the last century. This is largely owing to advances in neutron diffraction under pressure. Neutrons can interact with light elements such as hydrogen as well as heavy elements, making neutron diffraction essential for full structural analyses of newly discovered ice polymorphs. It is especially useful for detecting crystallographic symmetry breaking due to hydrogen ordering. This review will go over the most recent technical advances in neutron-diffraction experiments and how they contribute to our understanding of ice polymorphs.

KEYWORDS:

• Ice polymorphs
• neutron diffraction
• high pressure

Subject index

DAC, 229, 233, 234, 235, 236, 271, 276

electron diffraction, 226

gas-cell, 228

graph, 246, 249

HDA, 228, 230, 261

hydrogen-bond symmetrization, 226, 277

LDA, 228, 277

Mito system, 228, 229, 230

nano-polycrystalline diamond, 229, 278

partially ordered, 226, 240, 256, 258

Paris–Edinburgh press, 284

PEARL, 229, 230, 231, 269

piston-cylinder, 225, 228, 268

PLANET, 229, 256

Single-crystal neutron-diffraction, 235

SNAP, 229, 230, 231, 233

superionic, 245, 278, 282

VHDA, 228

Acknowledgments

I would like to thank all of the people who helped me with the research described in this paper. I appreciated two anonymous reviewers and Mr. Hiroki Kobayashi for reading through the manuscript and provide useful comments. My career in studying ice polymorphs using neutron-diffraction methods began while I was a postdoc at the University of Edinburgh, so I’d like to thank all of my ex-colleagues at that time. Most of the crystal structures in this manuscript were drawn with VESTA [306].

Disclosure statement

No potential conflict of interest was reported by the author(s ).

Notes

1 Strictly speaking, these initially reported ‘ice I_c’ should be denoted as ice I_sd (stacking disordered ice I) according to current knowledge, as mentioned in chapter 4.1.2.

2 The occupancy of hydrogen is 0 or 1 for a fully ordered state and 0.5 for a completely disordered state, but many ice polymorphs exist in between these two states (partial order). The fully ordered state of ice I_h, for example, has yet to be discovered, and ice XI should be regarded as a partially ordered phase.

3 Surprisingly, this fcc structure also appeared as a hypothetical structure in a paper by Kamb and Davis [18] more than half a century ago.

4 Roman numeral, ice XIX, was first appeared in Prakapenka et al. [28] in their arXiv preprint for superionic bcc structure of ice, but it is not designated in their final published paper in Nature Physics [29]. This is probably because the thermodynamic and crystallographic difference between the superionic bcc ice and ice VII/X is still controversial. A new Roman numeral, ice XX, may be deposited [1] for the superionic bcc ice if their crystallographic difference is proven.

5 For more information on the history of high-P neutron diffraction, see a review by J.B. Parise [48].

6 Note that the specific feature of the Paris-Edinburgh press is not the toroidal profile of anvils, but the high load-capability compared to its size, though it is often misunderstood.

7 Due to space constraints, the 1st stage and liquid nitrogen paths cannot connect to the binding rings simultaneously. In a strict sense, the system without the liquid nitrogen path is no longer regarded as a modification of the Mito system, rather a combination of a cryostat and a high-P press.

8 In March 2021, B. Haberl and R. Boehler announced through the ORNL web site (https://www.ornl.gov/news/neutrons-hard-diamonds-high-pressures) that they reached above 120 GPa, but the results may have not been published yet and the details of the cell design and samples are not shown.

9 In Prakapenka et al., the Simon–Glatzel equation is introduced as P = P₀+ a(T/T₀)ⁿ, but it should be a typo. The Simon–Glatzel equation is basically identical to the Equation $\left(3\right)$, but use both forms for correspondence to previous literature.

10 Note here that a common difficulty to analyze the crystal structures of ices, in particular for in-situ high-P diffraction studies, is to obtain a good single crystal or randomly oriented powder, since ice crystals are generally coarse and textured.

11 This equation is corresponding to Equation (5) in [160]. Note that there is a typo in the Equation (5), the upper bound of the integral is not X, but T as shown in Equation (6).

12 Fortes, A.D., private communication.

13 In the neutron diffraction experiments, heavy water (D₂O) and magnesium deuteride were used to avoid strong incoherent scattering from light hydrogen.

14 Even in this ‘pure’ ice I_c, some amount of stacking faults which could not be detected by neutron diffraction may exist, as is found in ‘pure’ ice I_h (e.g. [193]). Note here that the terms ‘stacking fault (or stacking defect)’ and ‘stacking disorder’ should be distinguished (though not that clear in many literatures); ‘Stacking fault (defect)’ stands for each mistake in a periodic stacking sequence, whereas I suggest ‘stacking disorder’ should be used for a state that there are so many mistakes that can be clearly observable by diffraction measurements.

15 They refer it as ‘without stacking defects,’ but it should be termed as ‘without stacking disorder’ as explained above.

16 The space group Cmc2₁ for an ordered form of ice I_h was first suggested by Kamb [103].

17 The highest mass fraction of ice XI up to date (f = 0.59) was achieved when 0.001 M KOH-doped ice was annealed at 70 K for 135.30 h [198].

18 They refer it as ice I_c, but it should be ice I_sd, assigned from current understandings.

19 30 min of irradiation by 30 W of D₂ lamp, corresponding to the UV fluence of ∼4 × 10¹⁶ photons cm⁻² according to Kouchi et al. [203].

20 Lobban mentioned that the temperature sensors located on the outside of the cell, so that the sample temperature may have some lag from the monitored temperature.

21 This term ‘intra-penetrated’ may be more appropriate rather than ‘inter-penetrated’ to describe the self-penetrated structure of ice IV.

22 In their original paper [20] and also in other papers [228–230], a space group Cc, which is transformed from Pc via a transformation of a' = a + b, b' = − a + b, c' = c, was used. But this transformation makes no physical sense, so the space group Pc should be used.

23 This value is not for the $\sqrt{2}\times \sqrt{2}\times 1$ unit cell of ice XIX, but is for the reduced $1\times 1\times 1$ unit cell for the comparison to ice XV.

24 Lobban et al. also reported five-membered (or 5-fold) rings, but there are no such rings, strictly speaking. In fact, five molecules make a pentagon, but these five molecules do not close to make a ring, but make a helix by shifting along c-axis.

Additional information

Funding

This work was supported by JSPS [grant number 21K18154, 18H05224, 18H01936].

Notes on contributors

Kazuki Komatsu

Kazuki Komatsu is a high-pressure crystallographer based at the University of Tokyo. He started studying the high-temperature and high-pressure behaviour of hydrous minerals at the mineralogy group in Tohoku University. After receiving his PhD in 2006, he moved to the University of Edinburgh as a visiting scientist and started studies for ice polymorphs using high-pressure neutron diffraction techniques. In 2009, he obtained a position at Geochemical Research Center (GCRC), Graduate School of Science, the University of Tokyo, and joined a project to construct a high-pressure beamline, called ‘PLANET’ in J-PARC. He has been an associate professor at GCRC since 2012, and has contributed to crystallographic studies of ice polymorphs with developing various devices for high-pressure x-ray and neutron diffraction such as the pressure-temperature variable ‘Mito system’.