Experimental evidence for the existence of a second partially-ordered phase of ice VI

Crystal structure and spectroscopic determination of the phase transitions in methylammonium- and formamidinium bismuth iodide perovskites

Understanding of the structural properties of hybrid organic-inorganic perovskites (HOIPs) and their behavior is crucial for their use as photovoltaics and for the design and assembly of solar cells. As part of this work, a detailed study was conducted to further understand bismuth iodide perovskites, with a specific focus on the phase transitions of methylammonium and formamidinium analogs. A detailed analysis of the temperature-dependent IR spectra was also performed in order to analyze the structural changes that occur. The presence of five phases in the methylammonium bismuth iodide (MABiI) and four phases in formamidinium bismuth iodide (FABiI) were determined. An additional confirmation of the reported results was obtained from the differential scanning calorimetry. The ambiguities concerning the crystal structure of FABiI were resolved based on the results by X-ray powder diffraction (XRPD).

Kinetic isotope effects on hydrogen/deuterium disordering and ordering in ice crystals: A Raman and dielectric study of ice VI, XV, and XIX

Ice XIX and ice XV are both partly hydrogen-ordered counterparts to disordered ice VI. The ice XIX → XV transition represents the only order-to-order transition in ice physics. Using Raman and dielectric spectroscopies, we investigate the ambient-pressure kinetics of the two individual steps in this transition in real time (of hours), that is, ice XIX → transient ice VI (the latter called VI‡) and ice VI‡ → ice XV. Hydrogen-disordered ice VI‡ appears intermittent between 101 and 120 K, as inferred from the appearance and subsequent disappearance of the ice VI Raman marker bands. A comparison of the rate constants for the H2O ices reported here with those from D2O samples [Thoeny et al., J. Chem. Phys. 156, 154507 (2022)] reveals a large kinetic isotope effect for the ice XIX decay, but a much smaller one for the ice XV buildup. An enhancement of the classical overbarrier rate through quantum tunneling for the former can provide a possible explanation for this finding. The activation barriers for both transitions are in the 18-24 kJ/mol range, which corresponds to the energy required to break a single hydrogen bond. These barriers do not show an H/D isotope effect and are the same, no matter whether they are derived from Raman scattering or from dielectric spectroscopy. These findings favor the notion that a dipolar reorientation, involving the breakage of a hydrogen bond, is the rate determining step at the order-to-order transition.

Configurational entropy of ice XIX and its isotope effect

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.

Revealing isochoric water nucleation: a visual study

The phenomena of water freezing at constant volume, or isochoric, is becoming more and more fascinating. However, because the system is subjected to extremely high pressures, it is exceedingly challenging to investigate it visually. Fewer properties have been found visually up till now, but many have been found through other means. Nevertheless, we were able to design a reactor so that it could be observed through a microscope as water was frozen and thawed at constant volume, reaching temperatures as low as - 12 °C and pressures up to 129 MPa. In this study, we observed critical characteristics visually, focusing on the location of the ice nucleus, its shape, and dynamics. Phase transitions from liquid to solid state are essential mechanisms in the physical sciences. The creation of ice stands as the quintessential and pervasive example of nucleation, playing a central role in diverse disciplines such as geology, biology, aviation, and climate research.

High-dimensional order parameters and neural network classifiers applied to amorphous ices

Amorphous ice phases are key constituents of water's complex structural landscape. This study investigates the polyamorphic nature of water, focusing on the complexities within low-density amorphous ice (LDA), high-density amorphous ice, and the recently discovered medium-density amorphous ice (MDA). We use rotationally invariant, high-dimensional order parameters to capture a wide spectrum of local symmetries for the characterization of local oxygen environments. We train a neural network to classify these local environments and investigate the distinctiveness of MDA within the structural landscape of amorphous ice. Our results highlight the difficulty in accurately differentiating MDA from LDA due to structural similarities. Beyond water, our methodology can be applied to investigate the structural properties and phases of disordered materials.

Thermodynamically Stable Intermediate in the Course of Hydrogen Ordering from Ice V to Ice XIII

Even though many partially ordered ices are known, it remains elusive to understand and categorize them. In this study, we study the ordering from ice V to XIII using calorimetry at ambient pressure and discover that the transition takes place via an intermediate that is thermodynamically stable at 113-120 K. Our isothermal ordering approach allows us to highlight the distinction of this intermediate from ice V and XIII, where there are clear differences both in terms of enthalpy and ordering kinetics. We suggest that the approach developed in the present work can also reveal the nature of partially ordered forms in the hydrogen order-disorder series of other ice phases.

Close-Packed Ices in Nanopores

Water molecules in any of the ice polymorphs organize themselves into a perfect four-coordinated hydrogen-bond network at the expense of dense packing. Even at high pressures, there seems to be no way to reconcile the ice rules with the close packing. Here, we report several close-packed ice phases in carbon nanotubes obtained from molecular dynamics simulations of two different water models. Typically they are in plastic states at high temperatures and are transformed into the hydrogen-ordered ice, keeping their close-packed structures at lower temperatures. The close-packed structures of water molecules in carbon nanotubes are identified with those of spheres in a cylinder. We present design principles of hydrogen-ordered, close-packed structures of ice in nanotubes, which suggest many possible dense ice forms with or without nonzero polarization. In fact, some of the simulated ices are found to exhibit ferroelectric ordering upon cooling.

Slightly Hydrogen-Ordered State of Ice IV Evidenced by In Situ Neutron Diffraction

Ice IV is a metastable high-pressure phase of ice in which the water molecules exhibit orientational disorder. Although orientational ordering is commonly observed for other ice phases, it has not been reported for ice IV. We conducted in situ powder neutron diffraction experiments for DCl-doped D2O ice IV to investigate its hydrogen ordering. We found abrupt changes in the temperature derivative of unit-cell volume, dV/dT, at ∼120 K, and revealed a slightly ordered structure at low temperatures based on the Rietveld method. The occupancy of the D1 site deviates from 0.5 in particular; it increased when samples were cooled at higher pressures and reached 0.174(14) at 2.38 GPa, 58 K. Our results evidence the presence of a low-symmetry hydrogen-ordered state corresponding to ice IV. It seems, however, difficult to experimentally access the completely ordered phase corresponding to ice IV by slow cooling at high pressure.

Simultaneous measurements of volume, pressure, optical images, and crystal structure with a dynamic diamond anvil cell: A real-time event monitoring system

The dynamic diamond anvil cell (dDAC) technique has attracted great interest because it possibly provides a bridge between static and dynamic compression studies with fast, repeatable, and controllable compression rates. The dDAC can be a particularly useful tool to study the pathways and kinetics of phase transitions under dynamic pressurization if simultaneous measurements of physical quantities are possible as a function of time. We here report the development of a real-time event monitoring (RTEM) system with dDAC, which can simultaneously record the volume, pressure, optical image, and structure of materials during dynamic compression runs. In particular, the volume measurement using both Fabry-Pérot interferogram and optical images facilitates the construction of an equation of state (EoS) using the dDAC in a home-laboratory. We also developed an in-line ruby pressure measurement (IRPM) system to be deployed at a synchrotron x-ray facility. This system provides simultaneous measurements of pressure and x-ray diffraction in low and narrow pressure ranges. The EoSs of ice VI obtained from the RTEM and the x-ray diffraction data with the IRPM are consistent with each other. The complementarity of both RTEM and IRPM systems will provide a great opportunity to scrutinize the detailed kinetic pathways of phase transitions using dDAC.

The hydrogen-bond network in sodium chloride tridecahydrate: analogy with ice VI

The structure of a recently found hyperhydrated form of sodium chloride (NaCl·13H2O and NaCl·13D2O) has been determined by in situ single-crystal neutron diffraction at 1.7 GPa and 298 K. It has large hydrogen-bond networks and some water molecules have distorted bonding features such as bifurcated hydrogen bonds and five-coordinated water molecules. The hydrogen-bond network has similarities to ice VI in terms of network topology and disordered hydrogen bonds. Assuming the equivalence of network components connected by pseudo-symmetries, the overall network structure of this hydrate can be expressed by breaking it down into smaller structural units which correspond to the ice VI network structure. This hydrogen-bond network contains orientational disorder of water molecules in contrast to the known salt hydrates. An example is presented here for further insights into a hydrogen-bond network containing ionic species.

Medium-density amorphous ice

Amorphous ices govern a range of cosmological processes and are potentially key materials for explaining the anomalies of liquid water. A substantial density gap between low-density and high-density amorphous ice with liquid water in the middle is a cornerstone of our current understanding of water. However, we show that ball milling "ordinary" ice Ih at low temperature gives a structurally distinct medium-density amorphous ice (MDA) within this density gap. These results raise the possibility that MDA is the true glassy state of liquid water or alternatively a heavily sheared crystalline state. Notably, the compression of MDA at low temperature leads to a sharp increase of its recrystallization enthalpy, highlighting that H₂O can be a high-energy geophysical material.

Nanoporous ices: an emerging class in the water/ice family

The history of scientific research on diverse ice structures dates back to more than a century. To date, 20 three-dimensional crystalline ice phases (ice I-ice XX) have been identified in the laboratory, among which ice XVI and ice XVII belong to a class of low-density nanoporous ices. Nanoporous ices can also be viewed as a special class of porous materials or water ice, as they possess a relatively high fraction of nano-cavities and/or nano-channels built into the hydrogen-bonded water framework. As such, like the prototypical class of porous materials (e.g., MOFs and COFs), nanoporous ices can be named as water oxygen-vertex frameworks (WOFs). Because of their large surface-to-volume ratio, WOFs may be potential media for gas storage, gas purification and separation. They may be applied to the biomedical field owing to their excellent biocompatibility. The field of porous ices is still emerging, as many porous ice structures that are predicted to be stable by computer simulations require future experimental confirmation. For future theoretical/computational studies, as the machine-learning method becomes an increasingly popular research tool in the material science and chemical science fields, more reliable porous ice structures and phase diagrams will be predicted with the development of more accurate machine-learning force fields.

Accurate crystal structure of ice VI from X-ray diffraction with Hirshfeld atom refinement

Water is an essential chemical compound for living organisms, and twenty of its different crystal solid forms (ices) are known. Still, there are many fundamental problems with these structures such as establishing the correct positions and thermal motions of hydrogen atoms. The list of ice structures is not yet complete as DFT calculations have suggested the existence of additional and - to date - unknown phases. In many ice structures, neither neutron diffraction nor DFT calculations nor X-ray diffraction methods can easily solve the problem of hydrogen atom disorder or accurately determine their anisotropic displacement parameters (ADPs). Here, accurate crystal structures of H2O, D2O and mixed (50%H2O/50%D2O) ice VI obtained by Hirshfeld atom refinement (HAR) of high-pressure single-crystal synchrotron and laboratory X-ray diffraction data are presented. It was possible to obtain O-H/D bond lengths and ADPs for disordered hydrogen atoms which are in good agreement with the corresponding single-crystal neutron diffraction data. These results show that HAR combined with X-ray diffraction can compete with neutron diffraction in detailed studies of polymorphic forms of ice and crystals of other hydrogen-rich compounds. As neutron diffraction is relatively expensive, requires larger crystals which can be difficult to obtain and access to neutron facilities is restricted, cheaper and more accessible X-ray measurements combined with HAR can facilitate the verification of the existing ice polymorphs and the quest for new ones.

Comparative Analysis of the Hydrogen Bond Vibrations of Ice XII

It is difficult to theoretically study the vibrational spectrum of hydrogen-disordered ice XII compared with its hydrogen-ordered counterpart, ice XIV. We constructed a 24-molecule supercell of ice XII to mimic its real structure. We focused on hydrogen bond (HB) vibrational modes in the translation band using first-principles density functional theory (DFT). Our simulated results were in good agreement with inelastic neutron scattering experiments. We found that the optical vibrational modes of HBs are composed of three main components. These are cluster vibrations in the lowest-frequency region, four-bond HB vibrations in the highest-frequency region, and two-bond modes in between. Although the experimentally recorded curve of ice XII is smooth in the translation region, our results support the proposal that two types of intrinsic HB vibrational modes are common in the ice family.

Capturing Individual Hydrogen Bond Strengths in Ices via Periodic Local Vibrational Mode Theory: Beyond the Lattice Energy Picture

Local stretching force constants derived from periodic local vibrational modes at the vdW-DF2 density functional level have been employed to quantify the intrinsic hydrogen bond strength of 16 ice polymorphs, ices Ih, II, III, IV, V, VI, VII, VIII, IX, XI, XII, XIII, XIV, XV, XVII, and XIX, that are stable under ambient to elevated pressures. Based on this characterization on 1820 hydrogen bonds, relationships between local stretching force constants and structural parameters such as hydrogen bond length and angle were identified. Moreover, different bond strength distributions, from uniform to inhomogeneous, were observed for the 16 ices and could be explained in relation to different local structural elements within ices, that is, rings, that consist of different hydrogen bond types. In addition, criteria for the classification of hydrogen bonds as strong, intermediate, and weak were introduced. The latter was used to explore a different dimension of the water-ice phase diagram. These findings will provide important guidelines for assessing the credibility of new ice structures.

Calorimetric Investigation of Hydrogen-Atom Sublattice Transitions in the Ice VI/XV/XIX Trio

Ice XIX represents the latest discovery of ice polymorphs and exists in the medium pressure range near 1–2 GPa. Ice XIX is a partially hydrogen-ordered phase, by contrast to its disordered mother phase ice VI, which shares the same oxygen-atom network with ice XIX. Ice XIX differs in terms of the ordering of the hydrogen-atom sublattice, and hence the space group, from its hydrogen-ordered sibling ice XV, which also features the same type of oxygen network. Together, ice VI, XV, and XIX form the only known trio of ice polymorphs, where polymorphic transformations from order to order, order to disorder, and disorder to order are possible, which also compete with each other depending on the thermodynamic path taken and the cooling/heating rates employed. These transitions in the H-sublattice have barely been investigated, so we study here the unique triangular relation in the ice VI/XV/XIX trio based on calorimetry experiments. We reveal the following key features for H-sublattice transitions: (i) upon cooling ice VI, domains of ice XV and XIX develop simultaneously, where pure ice XV forms at ≤0.85 GPa and pure ice XIX forms at ≥1.60 GPa, (ii) ice XIX transforms into ice XV via a transient disordered state, (iii) ice XV recooled at ambient pressure features a complex domain structure, possibly containing an unknown H-ordered polymorph, (iv) recooled ice XV partly transforms back into ice XIX at 1.80 GPa, and (v) partial deuteration slows down domain reordering strongly. These findings not only are of interest in understanding possible hydrogen-ordering and -disordering processes in the interior of icy moons and planets but, more importantly, also provide a challenging benchmark for our understanding and parameterizing many-body interactions in H-bonded networks.

Metastability of Liquid Water Freezing into Ice VII under Dynamic Compression

The ubiquitous nature and unusual properties of water have motivated many studies on its metastability under temperature- or pressure-induced phase transformations. Here, nanosecond compression by a high-power laser is used to create the nonequilibrium conditions where liquid water persists well into the stable region of ice VII. Through our experiments, as well as a complementary theoretical-computational analysis based on classical nucleation theory, we report that the metastability limit of liquid water under nearly isentropic compression from ambient conditions is at least 8 GPa, higher than the 7 GPa previously reported for lower loading rates.

The everlasting hunt for new ice phases

Water ice exists in hugely different environments, artificially or naturally occurring ones across the universe. The phase diagram of crystalline phases of ice is still under construction: a high-pressure phase, ice XIX, has just been reported but its structure remains ambiguous.

Structure and nature of ice XIX

Ice is a material of fundamental importance for a wide range of scientific disciplines including physics, chemistry, and biology, as well as space and materials science. A well-known feature of its phase diagram is that high-temperature phases of ice with orientational disorder of the hydrogen-bonded water molecules undergo phase transitions to their ordered counterparts upon cooling. Here, we present an example where this trend is broken. Instead, hydrochloric-acid-doped ice VI undergoes an alternative type of phase transition upon cooling at high pressure as the orientationally disordered ice remains disordered but undergoes structural distortions. As seen with in-situ neutron diffraction, the resulting phase of ice, ice XIX, forms through a Pbcn-type distortion which includes the tilting and squishing of hexameric clusters. This type of phase transition may provide an explanation for previously observed ferroelectric signatures in dielectric spectroscopy of ice VI and could be relevant for other icy materials.

Structural characterization of ice XIX as the second polymorph related to ice VI

Ice polymorphs usually appear as hydrogen disorder-order pairs. Ice VI has a wide range of thermodynamic stability and exists in the interior of Earth and icy moons. Our previous work suggested ice β-XV as a second polymorph deriving from disordered ice VI, in addition to ice XV. Here we report thermal and structural characterization of the previously inaccessible deuterated polymorph using ex situ calorimetry and high-resolution neutron powder diffraction. Ice β-XV, now called ice XIX, is shown to be partially antiferroelectrically ordered and crystallising in a √2×√2×1 supercell. Our powder data recorded at subambient pressure fit best to the structural model in space group [Formula: see text]. Key to the synthesis of deuterated ice XIX is the use of a DCl-doped D₂O/H₂O mixture, where the small H₂O fraction enhances ice XIX nucleation kinetics. In addition, we observe the transition from ice XIX to its sibling ice XV upon heating, which proceeds via a transition state (ice VI^‡) containing a disordered H-sublattice. To the best of our knowledge this represents the first order-order transition known in ice physics.