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.


Fitting the ice XIX diffraction data with the P42/nmc ice VI crystallographic model: Supplementary
Figure 1(left) shows the Rietveld fit of the low-temperature ice XIX diffraction data using the ice VI crystallographic model. Most of the Bragg peaks are fitted quite well. However, the ice VI model does not allow the two additional Bragg peaks at ~2.14 and ~2.21 Å, and the intensity of the Bragg peak at ~1.77 Å is too low. Due to a combination of the symmetry of P42/nmc and the constraints imposed by the ice rules, the ice VI model does not allow any deviation of the fractional occupancies of the hydrogen sites from ½ which can therefore not be refined. The structure of ice VI obtained from the Rietveld fit displays realistic bond distances and angles as shown in Supplementary Figure 1( These results indicate that the crystal structures of ices VI and XIX are not fundamentally different.
However, the inability of the ice VI model to reproduce the additional Bragg peaks at ~2.14 and ~2.21 Å shows that a new crystallographic model is needed for ice XIX.
Supplementary Figure 1(left) also shows the expected peak positions for a corresponding P1 unit cell with the same lattice constants as ice VI which also does not permit the additional Bragg peaks. This therefore indicates that the size of the unit cell needs to be increased. Indexing the Bragg peaks with the dicvol06 software 1 suggests a √2×√2×1 supercell of the ice VI unit cell. According to this, the new peaks are indexed as 231 and 321 for the ~2.14 Å feature and 212 for the ~2.21 Å peak. As shown in the next section, this specific increase in the size of the unit cell arises frequently as the symmetry of the P42/nmc space group is reduced to its various crystallographic subgroups. resulting structures were then analysed with respect to two criteria: (1) If they allow the new Bragg peaks, which is not the case for all √2×√2×1 unit cells, and (2) if the two hydrogen-bonded networks contain the same number of atom sites. As shown in Table S1, this analysis leads to six possible candidate space groups (P42nm, P42cm, Pcnb, Pcca, Pnna and Pncb). Please note that Pcnb found here and the Pbcn setting in the main article are only different settings of space group 60 and hence describe the same structure.

Supplementary
The only immediate subgroup of P42/nmc that yields a √2×√2×1 supercell is Ccca. However, this space group does not permit the additional Bragg peaks. The other subgroups of P42/nmc retain the same size unit cell as ice VI and therefore also do not permit the additional Bragg peaks. This means that the symmetry needs to be reduced further to the subgroups of the subgroups of P42/nmc. It is worth stressing that all candidate space groups shown in Figure 3, which were derived based on crystal-chemical reasoning in the main article, appear in our systematic subgroup analysis here and are highlighted by asterisks in Table S1.
The P2/a structure identified here is a different setting describing the same structure as the structure with the conventional P2/c setting used in the main article. As mentioned earlier, the same applies to the Pcnb setting Since the neighbouring hexameric units have identical structures in ice VI, it seems likely that they will retain at least some symmetry relationship between them in ice XIX which is in contraction with the Pncb model. Despite the symmetry concerns, all six candidate structures were fitted against the experimental diffraction data in a next step together with the Ccca structure which seems to be an important first-level subgroup of P42/nmc.

Supplementary note 3
Tests of the subgroup candidate structures: Supplementary Figure 3 shows the  2 values, which reflect the goodness of fit, obtained upon fitting the ice VI P42/nmc crystallographic model (see chapter 1), the firstlevel subgroup Ccca structure and the six second-level subgroup structures to the experimental ice XIX diffraction data. All structures were fully hydrogen disordered which is strictly required from a combination of symmetry and the ice rules for P42/nmc and Ccca. Despite being unable to reproduce the additional Bragg peaks (see Table S1), the Ccca model could already fit the intensity of the Bragg peak at ~1.77 Å well which led to an overall better fit compared to the P42/nmc model. The Pcnb model (which is equivalent to the Pbcn model discussed in the main article) gave the best fit to the data out of all the candidate structures. This means that both the crystal-chemical considerations presented in the main article as well as the systematic group-subgroup investigations carried out here point towards this crystallographic model. Despite the symmetry concerns raised earlier, the second best fit is provided by the P42nm model. absolute deviation from ½ was found to be 0.032 in this case. Based on this analysis, it can be concluded that the amount of hydrogen order in ice XIX is very small if it is present at all. An upper limit for the average absolute deviation can be estimated as 0.052 -0.032 = 0.020. Ice XIX is certainly far from being more ordered than ice XV as it has been claimed. 4 For ice XV, the average deviation of the occupancies from ½ was found to be 0.275. 5 It is emphasised that these conclusions were also reached based on spectroscopic data in ref. 6. Weak hydrogen ordering is compatible and even required by our deep-glassy ice scenario. 6,7 Regarding the question of hydrogen ordering, it is interesting to point out that the Ccca subgroup of