Downloaded by guest on September 27, 2021 www.pnas.org/cgi/doi/10.1073/pnas.1817135116 a Fitzner Martin supercooled of regions liquid low-mobility in born is in way heterogeneities dynamical the of pave nucleation. role solution-based will the and heterogeneous of findings examination our the and that dynamics for between anticipate connection We clear a nucleation. establish molecules. we water this of surrounding (iii With in mobility and dynamics (ii the ordering, arrested ice-like cause which liquid, clusters any in the before period drops of incubation molecules (i the regions dynamical that a low-mobility reveal is in we which there Here occurs simulations level. computer nucleation molecular ice via the ice of at issue nucleation directly this the unraveled tackle and be water to of yet has DH microscopic the the relatively between Strikingly, of coexist. connection particles domains immobile separated and mobile spatially lat- where (DH), phenomenon the heterogeneity a dynamical to notably on paid most behavior, focused complex attention dynamical and on fascinating has less exhibits research water general) with supercooled However, Most ter. in former positions. the crystallization lattice understanding (and their nucleation adopt changes key ice they two water, as liquid 2018) drops from 4, October born review for is (i (received occur: crystal 2018 4, ice December an approved and When NJ, Princeton, University, Princeton Debenedetti, G. 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G.C.S., research; M.F., designed research; A.M. formed and S.J.C., G.C.S., M.F., contributions: Author ice-like (iii) molecules. and water of surrounding ordering, in mobility dynamics ice-like arrested the cause before (ii) which clusters in drops liquid, period the molecules incubation of the dynamical regions a (i) low-mobility is that in there show occurs which nucleation nucleation other ice ice any and water indeed liquid or supercooled water for preference date any to is established liquid. there not supercooled is whether all preferential But argu- at being nucleation. find regions for mobile can readily and domains immobile one more both to Overall, for ability ments self-assembly. the explo- therefore collective effective and more perform space a phase for Mobile of potential barrier. ration the nucleation have the would of view molecules reduction traditional heterogeneous the a than explain of can rather nanowires that crystallization of (24) surface surface-induced liquids the metallic immobile near for mobility strongly enhanced argued in the been has rota- hindered it be neces- that Indeed, could regions. rearrangements found crystallization the (23) for of and sary motions al. water, transformative in et the correlate Mazza thus, heterogeneities regions hand, translational these and other in tional preferred the be On will (22). nucleation that indication an of picture two-state a (21). by regions described disordered be and ordered can DH of emergence the owo orsodnesol eadesd mi:[email protected] Email: addressed. be should correspondence CB2 whom Cambridge To Cambridge, of University Kingdom. y Chemistry, United 1EW, of Department address: Present et ra nefcsvaudrtnigterefcso liquid on effects their dynamics. understanding via confine- interfaces in at understand solution, or ment, in to nucleation ways heterogeneous nucleation open control of and and topics heterogeneity the dynamical link we and hetero- this from With emerge dynamics. that geneous regions liquid water immobile supercooled at in in predict happens nucleation process homogeneous cannot techniques that nucleation we computational show Using we and ice occur. will elusive know the nucleation remains we where of scale as comprehension life molecular shapes the full crystal- and A the ubiquitous formation, is it. water cloud of to lization freezing intracellular From Significance ee efilti a ypromn optrsmltosof simulations computer performing by gap this fill we Here, as seen be could domains mobile less in preordering The e etefrSinicCmuig nvriyo Warwick, of University Computing, Scientific for Centre y PNAS | eray5 2019 5, February b hmsYugCnr,Uiest College University Centre, Young Thomas a,b,c,2 . y raieCmosAttribution-NonCommercial- Commons Creative | o.116 vol. www.pnas.org/lookup/suppl/doi:10. | o 6 no. | 2009–2014

PHYSICS SEE COMMENTARY Uncovering DH between DH and ice nucleation, we focus on precritical clusters, We begin by characterizing the extent of DH in supercooled i.e., the ice-like clusters that form via frequent thermal fluctua- liquid water represented by the atomistic Transferable Inter- tions and thus are readily probed by unbiased MD (29). The key molecular Potential, 4-point, Ice (TIP4P/Ice) (25) model. To results of our simulations with the TIP4P/Ice model are reported this end we perform molecular dynamics (MD) simulations in a in Fig. 2, where we find a strong tendency for the precritical homogeneous water system in the temperature range 230–273 K, ice nuclei to form within MI domains, rather than within MM using iso-configurational analysis (ISOCA) (26, 27). This tech- domains. To quantify their preference to form in the immobile nique allows us to obtain spatially resolved maps of DH. We regions we have split the whole range of (sorted) DP values quantify the tendency of each molecule to move with a dynamical into 20 equal sections (i.e., each corresponding to 5% of the propensity (DP), whole range). This means that the molecules in the first (last) DP section are the same molecules as the ones in the MI (MM)  kr (t ) − r (0)k2  region. In Fig. 2B we plot the average overlap of molecules in DP = i 0 i , [1] i MSD the biggest ice-like cluster with these DP sections. The expected ISO overlap in the absence of any correlation with the DP would be 5%. We clearly see that there is a strong preference for precrit- where ri (t) is the position vector of molecule i at time t, t0 is the time of maximum heterogeneity (definition in Materials and ical ice clusters to belong to the lower DP sections (i.e., more Methods), and MSD is the mean-square displacement of all oxy- immobile molecules). In addition, we find that the formation gen atoms. In this approach we average the outcome over many of precritical clusters is suppressed in the MM domains as the trajectories that start from the same initial configuration but with overlap values there are below the baseline of 5%. Consider- a different set of random velocities, indicated by the notation ing the fact that nucleation is stochastic in nature, this is strong evidence for the connection between immobile and ice-forming h. . . iISO. By doing this we are able to evaluate the effect of struc- ture alone on DH. In Fig. 1A we show two snapshots of initial regions. configurations used for the ISOCA at 230 K and 273 K, where Having shown that precritical ice clusters strongly overlap with each oxygen atom is colored according to its DP. This choice the immobile regions from their early stages we now study the of temperatures is to illustrate the maximum difference in the temporal connection between immobility and clusters before extent of DH as well as the relevance of strong their first time of assembly. In Fig. 2C we show the average value like 230 K in homogeneous nucleation of ice (11, 12, 28). It can of the DP and the crystallinity parameter lq6 (9) of molecules be seen that spatially localized domains of relatively immobile that belong to a cluster at its first time of assembly (taken to be (blue) and mobile (red) particles emerge and that the spatial at t = 0). It can be seen that the mobility drops at ∼ −1,000 ps, aggregation of the domains differs drastically. As reported in which is significant compared with the structural relaxation time Fig. 1B, the probability density distribution of the DP at 230 K is of the liquid: τliq ≈ 68 ps at 240 K (Materials and Methods). In rather broad with a factor of 30 between the mobilities of parti- addition, this drop occurs earlier and is much less abrupt than cles at opposite tails. From the distribution of the DP we select the change in structure, which can be associated with the rise the top and bottom 5% and label the corresponding molecules as of the lq6 order parameter at about 400 ps before the assembly. most mobile (MM) and most immobile (MI) regions for further This finding is crucial and it confirms that immobility on aver- analysis. We show in SI Appendix that the choice of this threshold age precedes ice-cluster formation by a significant timespan. This has no major influence on our results. can be thought of as a dynamical incubation period in which the dynamics of the molecules change before the structural change Dynamics of Precritical Fluctuations toward ice. While this mechanism is not necessarily orthogonal to the commonly applied reasoning of purely structural order- The simulation of nucleation with atomistic water models cur- ing, our results suggest that arguing in terms of a process that rently remains a challenge, coming at enormous computational involves distinct dynamical and subsequent structural steps is a cost (11). Hence, as a first step to understand the connection viable route for a better description of nucleation. Connection Between Nucleation and Dynamics The results reported above point strongly toward an interplay between structural motifs pertinent to nucleation and the dynam- ics of the system. Unbiased MD simulations, however, cannot directly sample nucleation events, except under extreme con- ditions close to the homogeneous nucleation temperature (8). In this section, we report results from transition path sampling (TPS) (30) simulations that allow us to sample many nucleation events at reasonably high temperature. Specifically, we study a system of water molecules represented by the coarse-grained monoatomic water (mW) model (31) at 235 K. In the case of the brute force simulations, we used an ISOCA to quantify mobil- ity. However, in the case of TPS we harvest many more (7,500) reactive trajectories, making ISOCA for each frame of each trajectory impractical. To fully exploit the statistical sampling provided by TPS, we therefore use the enduring displacement (32, 33) formalism, which permits on-the-fly calculation of each particle’s mobility. Using this approach has the added benefit of allowing us to validate the robustness of our previous results Fig. 1. Dynamical heterogeneity in supercooled liquid water with the (we show that there exists a correspondence between quantifying TIP4P/Ice model. (A) Spatial distribution of the dynamical propensity (DP) at 230 K and 273 K. Molecules (only oxygens shown) are colored according the mobility with enduring displacements and the DP method in to the scale at Left.(B) Probability density distribution of the DP at 230 K. SI Appendix). Blue and red shaded regions highlight the 5% of water molecules labeled To identify regions of space as either ice-like or liquid-like as most immobile (MI) and most mobile (MM). and either immobile or mobile (and the boundaries separating

2010 | www.pnas.org/cgi/doi/10.1073/pnas.1817135116 Fitzner et al. Downloaded by guest on September 27, 2021 Downloaded by guest on September 27, 2021 ihna moiedmi.I diint hstaetr,we trajectory, ensem- this whole to the addition characterizing quantities In forms statistical nucleus domain. calculated ice immobile the find- that an clear our is within with it nuclei, consistent precritical and the for Crucially, the ings nucleation. in of domains onset immobile the large 3 see Fig. liquid. do supercooled we ice-like, regions no as are there identified While TPS. from harvested trajectory typical regions [only negative a ation with particles mobile and Gaussian simi- Gaussian. positive a a In with fluctuations. understanding, fashion, small intuitive lar our neglecting with simultaneously consistent while are that ice-like as with surfaces that and show by ice-like we are Appendix, defined separating nega- that are Boundaries the regions regions water. to liquid-like in liquid close of values whereas density take ice, tive will of it density liquid-like, the predominantly ice-like, Gaus- to predominantly negative close are a values that with regions molecule In normalized liquid-like sian. positive, each a and with position Gaussian molecule’s ice-like each field ing crystallinity field coarse-grained immobility the and introduce we them), K. 240 at model water ize tal. et Fitzner (B order. snapshots crystalline in of cluster absence an and domains crystallinity and silver) 3. Fig. (C line). the dashed to the corresponds by bar largest (indicated (last) first the 5% the be in i.e., would molecules values; DP DP the the lq (sorted) between with of and overlap uncorrelated fraction DP (lq were 5% Average crystallinity a clusters (B) and to if representation). (DP) corresponds overlap bar surface mobility expected Each blue The range. (transparent region. DP (MM) relative region the MI MI in the molecules and in cluster immersed ice-like spheres) and bonds (red 2. Fig. nFg 3A Fig. In c ulainocr nrltvl moiedmiso uecoe ae.Soni ieeouino h oregandimmobility coarse-grained the of evolution time is Shown water. supercooled of domains immobile relatively in occurs nucleation Ice ersnaiesaso fasotnosyfre cluster formed spontaneously a of snapshot Representative (A) model. TIP4P/Ice the in formation cluster precritical and DH between Connection 6 fteliquid. the of I eso nphtof snapshot a show we (r) B sotie ysern moieparticles immobile smearing by obtained is and eoenceto eselreimmobile large see we nucleation Before (A) model. mW the with TPS by harvested trajectory a from fields, blue) (opaque Q(r) Q(r) I τ liq C nbrief, In (r). Q(r) opie 3ad26mlcls epciey h imtro h c-iergo in region ice-like the of diameter The respectively. molecules, 296 and 83 comprises stesrcua eaaintm.Sae ein niae9%cndneitras l aawr bandwt h TIP4P/Ice the with obtained were data All intervals. confidence 95% indicate regions Shaded time. relaxation structural the is > B 6 0 and o oeue nacutrbfr t rttm fasml tknt be to (taken assembly of time first its before cluster a in molecules for ) efrswl tietfigregions identifying at well performs and C hw iia npht after snapshots similar shows I Q(r) Q(r) (r) > and and sotie ysmear- by obtained is 0 r hw]fo a from shown] are C I n rw (C grows and (B) forms nucleus ice the nucleation, During ) (r) In 0. = Q(r) Q(r) eoenucle- before iltake will Q(r) SI enanme fwrsarayhglgtn ifrn id of kinds different highlighting already works of have number there a Introduction, between the been in differences mentioned structural As nucleation domains. the two investigate ice these ones, to mobile that in interesting than is shows rather it regions that immobile relatively evidence in occurs presented the Given Regions Nucleating in of Hallmarks those Structural than mobile less significantly are molecules bulk. vicinity the liquid the direct as the to modeling relevant in is theoretical molecules This and bulk. water growth the in find crystal that than lower also substantially Appendix) are we values (SI Indeed, model surroundings. within atomistic ice-clusters their the that suggests down for which slow 3 region, Fig. ice-like further In the than immobility. larger classifying of iii) ( and method and trajectories, different nucleation clus- of larger a ensemble for with large (i) a insight for have (ii) also strengthen ters, now and we since simulations conclusion unbiased our the from observations our all for typical indeed is 3 Fig. trajectories. in nucleation in identified discussed behavior are the that These show trajectories. TPS of ble vrl,terslsotie rmTSspotadextend and support TPS from obtained results the Overall, C tcnas ese httesronigimbl einis region immobile surrounding the that seen be also can it . yrto hlshv retddnmc sterDP their as dynamics arrested have shells hydration ∼2.5 PNAS t | = ) ahdlnsidct h envle of values mean the indicate lines Dashed 0). eray5 2019 5, February C is ihnteimbl oan h ice The domain. immobile the within ) . nm. ∼3.4 | vrg vlto fthe of evolution Average ) o.116 vol. IAppendix SI I | (translucent (r) o 6 no. | 2011 and B

PHYSICS SEE COMMENTARY preordering, i.e., regarding tetrahedrality (14, 19) or coordina- Discussion and Conclusions tion number (8, 14). We add to this by analyzing the distribution Our results have established a clear link between DH and ice of primitive rings (i.e., not divisible into smaller ones) in the nucleation, suggesting that the complex nature of dynamics regions of extreme mobilities (MM and MI as defined in Fig. 1B) should not be overlooked in theoretical descriptions of nucle- for the atomistic water model. As can be seen from Fig. 4 the ation. We have shown that liquid molecules in the vicinity of a MI regions have a rings distribution strongly peaked around nucleus are slowed down significantly, which implies that their 6 ± 1 members while the distribution for the MM domains is diffusivity (connected to the attachment rate) is reduced com- very broad. Moreover, the amount of entirely H-bonded rings pared with bulk molecules, an aspect neglected by classical is substantially higher in the MI region. Indeed, if we were to nucleation theory. regard hydrogen bonds between members as a necessary crite- We verified that our results on the rings distribution also hold rion for being a ring [as is done in other literature (11, 34)], for the coarse-grained mW model (31) even though for mW the the MM region would be almost free of rings. In particular, an extent of DH is much smaller (SI Appendix). This means that the abundance of 6 ±1-membered hydrogen-bonded rings can be characteristic features identified in our study are not sensitive to regarded as the key structural characteristic of the MI domains in the specific hydrogen bond parameterization, but rather caused the liquid. by the tetrahedral order inherent in the modeled material. Thus, These results add to the findings of Haji-Akbari and our findings may be of relevance not just to water but to a Debenedetti (11), who showed that the nucleating ice nucleus much broader range of materials, evidently ones with tetrahe- exhibits a similar rings distribution, and Pirzadeh et al. (34), who dral order (such as group IV elements and silica). More broadly, highlight the presence of 6 ± 1-membered rings near growing ice it remains to be seen whether the immobility of precrystalline surfaces. We stress here, however, that in the liquid snapshots structures is connected to nucleation in nontetrahedral liquids in we investigated for the rings analysis, we find only negligible the same manner since the population of, e.g., rings is material amounts of actual ice (according to different criteria; for details specific. However, based on our findings we can suggest that it is see SI Appendix). Since the majority of 6-membered rings in the correspondence between immobile and crystalline topologi- the MI domains can be seen as ice-like if regarded in isola- cal features (such as rings) that connects immobile regions with tion, this means that it is the relative orientation between rings nucleation. that is different from the crystal and thus the missing ingredi- The connection of DH and nucleation in water could be ent in forming ice. Because this happens in the MI region, which probed experimentally by investigating heavier water molecules has a reduced diffusivity compared with other regions, we can as their mobility might be different. It is for instance estab- speculate that the mechanism giving rise to the initial formation lished that liquid D2O has a higher nucleation rate than H2O of ice-like clusters in the liquid is collective in nature [a simi- (35). However, this cannot be taken as direct evidence in sup- lar argument based on density changes was made by Errington port of our observation as the change in the hydrogen bonding et al. (18)]. This would be consistent with a picture of reorient- induced by nuclear quantum effects (36) potentially influences ing rings rather than a picture of single-particle attachments via the nucleation rate too. A more rigorous experimental valida- diffusive motion. tion of our findings would be the nucleation rate comparison for 18 H2 O and ordinary water, which to the best of our knowledge has not been achieved. If one of the two liquids is more (less) mobile (diffusive), our results suggest a decreased (enhanced) nucleation rate. Our findings are likely of relevance to heterogeneous nucle- ation and nucleation from solution. Generally, previous work has focused on investigating the structural or templating role of nucleating agents (37–40). However, an impurity or substrate is bound to impact the dynamics of the supercooled liquid in its vicinity, possibly leading to a novel mechanism of heterogeneous nucleation. For the example of water freezing, ice nucleation on hydrophobic surfaces (basically incapable of structuring the water network to a major extent) has been reported (37, 38) as well as intriguing alternating hydrophilic–hydrophobic patterns in the prominent ice-nucleating bacteria (41) and a nucleation enhancement by soluble molecules (42) that could be connected to the liquid dynamics. Moreover, for nucleation from solution it is well known that different solutes change the nucleation mechanisms, i.e., in the case of urea (43). Understanding how solutes change the dynamics and impact the formation of amorphous precursors could shed light on this issue. As such, we hope that this work will push the community to take into account the role of dynamics and particularly of DH in connection with crystal nucleation and growth. In conclusion, we have shown that ice nuclei originate within immobile regions of the supercooled liquid and that there is a dynamical incubation period in which the mobility of particles drops before any structural change. Additionally, the presence Structural differences in regions of adverse mobility in TIP4/Ice Fig. 4. of an ice crystallite causes arrested dynamics in water molecules water. Shown is the number of n-membered primitive rings within the respective domain at 230 K. The dashed portions of the bars represent the that surround it and the distribution of rings can be seen as the fraction of those rings fully connected by H bonds. Top Insets show an exam- structural hallmarks of DH in water. This connection between ple of a fully and nonfully H-bonded 5-membered ring, where lines dynamics and structure provides another perspective on the between oxygens are a guide to the eye and do not imply H bonds. physics of nucleation.

2012 | www.pnas.org/cgi/doi/10.1073/pnas.1817135116 Fitzner et al. Downloaded by guest on September 27, 2021 Downloaded by guest on September 27, 2021 h eutn ausfor values resulting The uniy23K20K20K20K20K20K20K 210 K 220 K 230 K 240 K 250 K 260 K 273 Quantity model TIP4P/Ice the with time temperatures relaxation structural (q and length DH of characterize Overview 1. Table 48). (47, (PLUMED2) molecule 2 each metadynamics for for (lq compute plugin we parameter in First implemented order as Dynamics. (9) an and al. using et Structure detected Water were Between molecules Connection the Analyzing time relaxation structural the as the with together 1 Table iii and nucleation between in connection provided is the which of TPS DH the (vii) impression and (vi) visual clusters, water, ice a of around model dynamics arrested mW (vii) coarse-grained simulations, the in DH parameters, order (v) different with characterization displacements, domain structure the cor- (iv) inherent the iii) ( and domains, DP the between for choice respondence threshold DP the (ii) DP, the ize tal. et Fitzner study. the of rest the for τ t q is which chosen, be to have procedure: following scales the time by achieved and Dynamics. length Liquid appropriate the dynamics Characterize to ISOCA. Flow each the Work for for save use snapshots to we five ns K 1 draw least 210 as at and apart well K, are as that 220 volume temperature properties of K, equilibrium number dynamical at 230 constant ensemble calculate K, the (NVT) to 240 in temperature K, ns and 250 10 volume, K, for particles, propagated 260 are K, Those 273 configurations. At the ps). in ramp 2 Nos cooling of 0.5-K/ns (10-fold a ensemble temperature) (after melting NPT performed at we generat- equilibration upon temperatures ns effects different 10 quenching at avoid configurations cubic To starting (46). a ing algorithm use SHAKE We the temperature. vol- with approximate control 68 and to of conditions boundary fs ume periodic 200 3D Nos with of 10-fold box a time simulation using relaxation and step a time with 2-fs equations a atomic/molecular the with integrating large-scale motion (44), of the code (LAMMPS) with simulator performed parallel massively are All (25). simulations model TIP4P/Ice MD the our by represented molecules, water 10,000 taining Simulations. Dynamics Molecular Methods and Materials in terial Appendix (SI Information Supporting iv ii v 0 liq i 0 h ieo aiu heterogeneity maximum of time The ) Via ) factor structure isotropic the calculate We ) o this For ) rmteNTsmlto ftesse with system the of simulation NVT the From ) s51 71560—— — 620 115 27 11 5 ps , , eas ftecmuainlcs eddntcnie 2 n 1 K 210 and K 220 consider not did we cost computational the of Because s261 836—— — 356 68 14 6 2 ps , A egbrrneaems heterogeneous. most are range neighbor χ evaluated. needn ietosacrigto according directions independent N with peak, r F r frames. trajectory all over is average the and density, consider distribu- sums radial oxygen–oxygen the function obtain tion we temperature target the ˚ j (q, (0)] 4 −1 sin(rq) hD (q rlxto au from value α-relaxation t 0 |Φ(q, ). Φ ) , IAppendix SI = t (q, a t aiu,ie,weetemvmnsa h nearest- the at movements the where i.e., maximum, its has ) ×68 hΦ q [ g .119 .118 .017 1.76 1.77 1.80 1.84 1.91 1.96 2.01 t 0 t eoti h efitreit cteigfunction scattering self-intermediate the obtain we ) OO )| q (q, ecluaetequantity the calculate we 2 en eircllength. reciprocal a being (r E g t N ) 68 )i OO hΦ − − xgnaosadterpositions their and atoms oxygen (r A 1] ˚ ) n h yaia susceptibility dynamical the and 3 (q, = n define and h oeo ttsisi calculating in statistics of role the (i) about ttcbnsadage aebe constrained been have angles and bonds Static . q D 0 t –ovrcanbrsa ihrlxto time relaxation with barostat chain e–Hoover ´ )i 2π and oi S1 Movie 2 r i F 1 2 stoi vrgstknoe 200 over taken averages Isotropic . (q, N emil td h Ho ytmcon- system a of DH the study mainly We ρ t 0 t P ). i 0 q o l eprtrscnb on in found be can temperatures all for h quantity the n ie(t time and ) 0 i N =1 stevlewhere value the as . ). P Φ t epoieadtoa ma- additional provide We j N 0 >i (q, F stkna h iewhere time the as taken is (q δ t ocaatrz h liquid the characterize To ) 0 r = , N t kr − 0 ) = N clsue to used scales ) 1 τ = τ S liq P (q) 000mlclsat molecules 10,000 liq hF -ovrcan(45) chain e-Hoover i ´ r − htwsobtained was that 6 i j N (q, /j =1 codn oLi to according ) tdifferent at = r , S j 1 k a t first its has (q) t exp(i ρ )i  + E steliquid the is kq= 4πρ hr the where q χ q 4 · Ice-like (q, [r R 0 0 j ∞ (t t are ) ) dr − = hr h u usoe l oeue,and molecules, all over runs sum the where as algorithm defined ( then (FIRE) immobility are engine coarse-grained The relaxation (50). inertial used fast was the positions, structure ent molecule where such parameters order code common of simulations distributions using as computing as generated well networks as of (49)], investigation rigorous by primitive the established of respective then the number are the in regions the label values these calculating DP to of of properties used 5% structural then (bottom) The top is snapshot. the latter as molecules The MI DP. and the MM calculating when produc- only these time oxygens the of choose length we As runs velocities. tion randomized with starting ensemble, (Eq. DP the culate grouped then 3.4 clusters. are ice-like within molecules entities are Ice-like they liquid. if as otherwise together and ice-like as 0.5 of choice particular the For lq values dnie ihtepsto vector position the with identified (32) formalism displacement enduring as performed one- were the moves was TPS of move 7,500 run. use shifting further production made a a a equilibration We of this length moves. 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PHYSICS SEE COMMENTARY Code Availability. European Union’s Seventh Framework Program (FP/2007-2013)/ERC Grant Agreement 616121 (HeteroIce project). A.M.’s initial work on this project Our custom TPS code is available from the corresponding author was supported by the Miller Foundation at University of California, Berkeley. upon request. We acknowledge the use of the University College London Grace and Legion facilities; the ARCHER UK National Supercomputing Service through the ACKNOWLEDGMENTS. We thank L. Joly, A. Zen, B. Slater, C. G. Salzmann, Materials Chemistry Consortium through Engineering & Physical Sciences D. Limmer, and D. Chandler for stimulating discussions and suggestions. This Research Council (EPSRC) (UK) Grant EP/L000202; and the UK Materials and work was supported by the European Research Council (ERC) un