*3.2.2 Hydrogen-ordered cubic ice*

Although the existence of hydrogen-ordered cubic ice (ice XIc) has been discussed theoretically [18, 19, 37–39], there has been no experimental evidence for this crystal structure. Raza et al. [18] and Geiger et al. [19] suggested 11 and 4 different structures, respectively, for ice XIc. We observed the annealing of ice Ic deposited on an a-SiN thin film by TEM and found that several polymorphs of ice were formed at temperatures between 100 and 130 K without doping [40]. **Figure 4** represents the TEM images and corresponding electron diffraction patterns of the ice XIc formed by the annealing of a-H2O and ice Ic, showing the formation of ice XIc. However, we could not determine which structures were formed in terms of the different structures proposed by Raza et al. [18] and Geiger et al. [19]. However, because five-twelfths of the proposed structures were chiral (space group: *P*41212, *P*21212, *P*21, and *P*41), some chiral crystals might be included not only in our samples but also in H2O ice crystals in

#### **Figure 4.**

*Transmission electron microscopy images and corresponding electron diffraction patterns of hydrogen-ordered cubic ice (ice XIc) formed by (A) the annealing of amorphous H2O at 130 K and (B) the annealing of ice Ic at 130 K. The blue and yellow arrowheads indicate the diffraction spots of* d *= 4.50 Å and* d *= 6.41 Å, respectively, originating from ice XIc. The white and yellow scale bars are 500 nm and 2 nm<sup>1</sup> , respectively.*

space. Furthermore, the calculation of the infrared spectra of ice XIc, as demonstrated by Geiger et al. [19], will help identify ice XIc in space.

#### *3.2.3 Hydrogen-ordered hexagonal ice*

As mentioned in Section 3.2.1, the thermodynamically stable phase of hydrogenordered hexagonal ice is ice XI. However, Raza et al. [18] proposed 15 different structures of hydrogen-ordered hexagonal ice (XIh) as metastable phases, and sevenfifteenths of the proposed structures are chiral (space group: *P*212121, *P*21, and *P*1). Although there has been no experimental investigation of this, we should consider the occurrence of these polymorphs, as demonstrated in the Section 3.2.2.

#### *3.2.4 Ice III*

Here, it is worthwhile commenting on the structure of ice III, although ice III is stable only at higher pressures between 210 and 344 MPa and higher temperatures between 238 and 256 K [33]. The space group of ice III is *P*41212, meaning that the arrangement of the oxygen atoms is ordered and chiral. Conversely, the arrangement of the hydrogen atoms is disordered [20]. Therefore, we concluded that the surface of ice III does not behave as an asymmetric catalyst on which asymmetric adsorption and/or asymmetric synthesis can proceed.
