Is High-density Amorphous Ice Simply a 'Derailed' State along the Ice I to Ice IV Pathway?

The structural nature of high-density amorphous ice (HDA), which forms through low-temperature pressure-induced amorphization of the 'ordinary' ice I, is heavily debated. Clarifying this question is not only important for understanding the complex condensed states of H$_2$O but also in the wider context of pressure-induced amorphization processes, which are encountered across the entire materials spectrum. We first show that ammonium fluoride (NH$_4$F), which has a similar hydrogen-bonded network to ice I, also undergoes a pressure collapse upon compression at 77 K. However, the product material is not amorphous but NH$_4$F II, a high-pressure phase isostructural with ice IV. This collapse can be rationalized in terms of a highly effective mechanism. In the case of ice I, the orientational disorder of the water molecules leads to a deviation from this mechanism and we therefore classify HDA as a 'derailed' state along the ice I to ice IV pathway.

4 compared to the corresponding members of the ice I family. From this, we then aim to gain new insights into the origin of the pressure collapse of ice upon low-temperature compression and to propose a structural mechanism for the PIA of ice I which we also test with density functional theory (DFT) calculations.
Ice I and NH4F I are similar materials from the structural point of view. Figure 1a shows the isostructural hydrogen-bonded networks of the hexagonal ice Ih and NH4F Ih materials which are the stable phases at ambient conditions. The hydrogen bonds in NH4F Ih are less than 2% shorter than in ice Ih. 26 A metastable variant of ice Ih exists which contains interlaced sequences of cubic and hexagonal stacking, generally known as stacking disordered ice (ice Isd). [27][28][29][30] The most cubic ice Isd prepared so far, which will be used in the following, was obtained by slowly heating the ice II high-pressure phase at ambient pressure. 30 The material obtained by heating the NH4F II high-pressure phase at ambient pressure has been labelled as NH4F V. 31 Yet, as we will show, this material is, in analogy with the situation for ice, best described as stacking-disordered ammonium fluoride I (NH4F Isd).   6 ice I samples. The X-ray diffraction patterns of the starting materials are shown in Figure 1c.
Using our MCDIFFaX software, 30, 32 the ice Isd and NH4F Isd samples were shown to contain 67.8% and 76.6% cubic stacking, respectively. Figure 1d shows that the diffraction patterns obtained after the compression of the ice materials are consistent with HDA in line with previous studies. 1,33 On the basis of the similar pressure collapses, we initially assumed that the NH4F samples had also undergone transitions to high-density amorphous materials in analogy to what has been observed for ice. Surprisingly, the diffraction patterns of the NH4F materials after compression shown in Figure 1d revealed that they actually consist of crystalline mixtures of ~90% NH4F II and ~10% NH4F I. Upon comparison of the crystal structure of NH4F II 34 with the known phases of ice it was realized that NH4F II is isostructrual with the metastable ice IV. 35 Although NH4F II is the first high-pressure phase to form upon compression of NH4F Ih at room temperature, it is probably not the stable phase at 77 K and ~1 GPa due to the pronounced slope of the NH4F II / III phase boundary. 36 This suggests that the NH4F II, which results from the low-temperature compression, is a kinetic product that forms as a consequence of a favorable mechanistic pathway.
The transformation of NH4F I to NH4F II can be understood on the basis of a remarkable mechanism that achieves a 37% increase in density while only breaking one in four hydrogen bonds. This collapse was first described by Engelhardt and Kamb for the transition from the hypothetical fully cubic ice I (ice Ic) to ice IV. 35 The corresponding collapse starting from the hexagonal starting material was later described in the NH4F literature. 34 The mechanistic details of this collapse, which we refer to as the Engelhard-Kamb collapse (EKC), are shown in Figure   2. The ice Ic/Ih networks contain identical layers consisting of puckered six-membered rings in 7 the armchair conformation. These networks are shown in Figure 2a with the network nodes of the individual layers highlighted in different colors. The transition from the ice Ic to the ice IV network requires breaking of the inter-layer hydrogen bonds followed by flattening and ultimately a complete 're-buckling' of the layers. 35 The last step is the formation of hydrogen bonds right through the center of the six-membered This 'threading-through' is the hallmark structural feature of the ice IV network which 'pulls' the layers closer together and thereby achieves the increase in density (inset in Figure 2a).
Starting off from the ice Ih network, the 're-buckling' of layers is not required. Instead, the individual layers need to shift or rotate with respect to one another to achieve the 'threadingthrough' of the six-membered rings. Since both the ice Ic and Ih networks can undergo the EKC, it is of course also possible to start from stacking disordered starting materials.
The effect of the ice IV network formation on an individual layer is shown in Figure 2b. The six-membered rings labelled with '1' are the ones that experience 'threading-through' with hydrogen bonds during the transition to the ice IV network. This leads to a flatting of these rings, a slight increase in diameter and rotation. These changes in the '1' rings distort the rings labelled with '2' which either raises or lowers the nodes which are not members of the '1' rings so that they can form the hydrogen bonds with two layers above or below.
A remarkable feature of the EKC is that the density increase is highly anisotropic and achieved almost exclusively by contraction along [001]. 34 It is difficult to imagine that there is another mechanism that achieves a similar increase in density while breaking fewer hydrogen bonds. So, the EKC seems to be a particularly important mechanism for densification under kinetically controlled low-temperature conditions.
The similar onset-pressures and volume changes of the low-temperatures collapses of ice I and NH4F I suggest that both materials suffer from a similar mechanical instability that marks the onset of the EKC. However, in both cases, the EKC is not followed through entirely at 77 K. In the case of NH4F I, the conversion to NH4F II is ~90 w% leaving ~10 w% of NH4F I unconverted. The incomplete conversion is attributed to the build-up of macroscopic strain environments which arise from the highly anisotropic nature of the EKC.
In the case of ice, it is important to recall that the ice I materials are hydrogen-disordered which means that they display disorder with respect to the orientations of the hydrogen-bonded molecules ( Figure 1a). As mentioned earlier, during the EKC, the interlayer hydrogen bonds are broken and reformed with water molecules one and two layers above or below. The chances of successfully connecting a broken hydrogen bond to another water molecule are 50% since water molecules can be either hydrogen-bond donors or acceptors. This implies, that in case of ice I, not all broken hydrogen bonds will necessarily thread-through the six-membered rings in the final stage of the EKC but form hydrogen-bonds with other close water molecules instead that fulfil the donor / acceptor conditions. The resulting material is HDA which displays a lack of long-range order and a density somewhat lower than ice IV. Accordingly, HDA can be classified as a 'derailed' state along the EKC and we provide further arguments for this in the following.
The hydrogen-bond donor / acceptor mismatch in ice could in principle be resolved with molecular reorientations. These are known to be very slow at 77 K, 37 but have been shown to 'unfreeze' during the glass transition of HDA at higher temperatures. 38 When HDA is heated at around its 'natural' pressure of 1 GPa, the amorphous sample becomes denser at first followed by crystallization. [39][40] The crystallization to ice IV has been shown to have the lowest activation energy out of all the possible crystallization pathways around 1 GPa. [41][42][43] This means that the 'derailed' state of HDA can be brought 'back on track' with respect to the EKC by thermal annealing under pressure as dynamic molecular reorientations resolve the problem of the hydrogen-bond donor / acceptor mismatches. The similar structures of pressure-annealed HDA and ice IV are also evident from their Raman spectra. 40,44 Furthermore, the first strong diffraction peak of pressure-annealed HDA, which reflects the intermediate range structural order, is in the same position as the strongest Bragg peaks of ice IV. [39][40][41] An interesting question now arises if the 'derailment' upon low-temperature compression of ice I could be prevented by using hydrogen-ordered starting materials. The hydrogen-ordered ice Ic (ice XIc) 45 is a promising starting material since the EKC from a cubic starting material does not require the translational movement of layers. All inter-layer hydrogen bonds point in the same direction in ice XIc which means that the problem of the hydrogen-bond donor / acceptor mismatches does not apply. Unfortunately, ice Ic has not been prepared so far, 30 and consequently it is unknown if and how ice XIc can be prepared. Also, the fact that ice Ih becomes only partially hydrogen-ordered upon doping with potassium hydroxide below 77 K [46][47][48] illustrates how much of a challenge the low-temperature compression of ice XIc would be.
To investigate the feasibility of the ice XIc to ice IV pathway, we therefore performed a transition-state search using the solid-state nudged-elastic-band (NEB) method 49 at the dispersion-corrected DFT level. The solid-state NEB method couples the atomic and lattice degrees of freedom of a crystal structure, and it requires a reasonable initial guess of the transition pathway from XIc to ice IV. A minimum-energy contiguous path was obtained after optimization, and the energy profile and cell volumes of all frames on the transition path are shown in Figure 3. The activation energy for the phase transition is found to be 11 kJ/mol, about twice as large as the enthalpy difference between ice IV and XIc. The initial configurations are associated with the formation of point defects that resemble interstitials. The volume changed slowly during the first stages of the transition but close to and after the transition state, there was a marked drop. The largest change in volume at the very end of the transition is clearly 11 associated with the formation of hydrogen bonds passing through the six-membered rings ( Figure 2). We note that our estimated activation energy is about an order of magnitude higher than what is expected for a purely enthalpy-motivated transition at 77 K. Several factors could contribute to this overestimation. First, we started from a perfect lattice of ice XIc. In ice, nonnegligible concentrations of kinetically trapped point and line defects will be present, which, together with grain-boundary effects, may act as the seeds for the transition to ice IV, effectively lowering the transition barrier. Second, our predicted transition mechanism only represents one of the possible transition pathways; lower-energy transition mechanisms may exist for larger simulation cells, where the point defects, that facilitate the transition, are more spatially separated, allowing for greater lattice relaxation. Third, overestimation of the activation barrier may also be enhanced from the DFT method we use (PBE+D3) which 'overbinds' the ice phases. 50 Nevertheless, overall it seems very plausible that ice XIc is likely to undergo the EKC upon low-temperature compression and to avoid the 'derailment' to HDA.  CryojetHT.
The solid-state NEB calculations were performed using the atomic simulation environment 52 and the TSASE code. 49 Thirteen frames of the 2x2x3 supercells from ice XIc to ice IV were considered on the transition path. The transition-state search was considered converged if the maximum atomic force falls below 0.1 eV/Å. The energies, forces and stress tensors were calculated using the CP2K code, which uses a mixed Gaussian/planewave basis set. [53][54] We employed double-ζ polarization quality Gaussian basis sets and a 600 Ry plane-wave cutoff for the auxiliary grid, in conjunction with the Goedecker-Teter-Hutter pseudopotentials. [55][56] All calculations were performed using the popular pairwise-additive descriptions of the dispersion interactions, i.e. the D3 method with the Axilrod-Teller-Muto three-body terms, 57 in combination with the PBE functional. 58 ASSOCIATED CONTENT