Shock induced phase transition of water: Molecular dynamics investigationAnupam Neogi and Nilanjan Mitra Citation: Physics of Fluids 28, 027104 (2016); doi: 10.1063/1.4941049 View online: http://dx.doi.org/10.1063/1.4941049 View Table of Contents: http://scitation.aip.org/content/aip/journal/pof2/28/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Revisiting dynamics near a liquid-liquid phase transition in Si and Ga: The fragile-to-strongtransition J. Chem. Phys. 139, 224504 (2013); 10.1063/1.4843415 Phase transition and chemical decomposition of shocked CO–N2 mixture J. Chem. Phys. 137, 054504 (2012); 10.1063/1.4734867 Molecular dynamics investigation on liquid–liquid phase change in carbon with empirical bond-orderpotentials J. Chem. Phys. 119, 6053 (2003); 10.1063/1.1601216 Molecular dynamics simulations of structural transitions and phase coexistence in water pentamers J. Chem. Phys. 117, 9286 (2002); 10.1063/1.1515764 Molecular scale precursor of the liquid–liquid phase transition of water J. Chem. Phys. 108, 3264 (1998); 10.1063/1.475723

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PHYSICS OF FLUIDS 28, 027104 (2016)

Shock induced phase transition of water: Moleculardynamics investigation

Anupam Neogi1,a) and Nilanjan Mitra2,b)1Advanced Technology Development Center, Indian Institute of Technology Kharagpur,Kharagpur 721302, India2Department of Civil Engineering, Indian Institute of Technology Kharagpur,Kharagpur 721302, India

(Received 18 July 2015; accepted 19 January 2016; published online 4 February 2016)

Molecular dynamics simulations were carried out using numerous force potentials toinvestigate the shock induced phenomenon of pure bulk liquid water. Partial phasetransition was observed at single shock velocity of 4.0 km/s without requirementof any external nucleators. Change in thermodynamic variables along with radialdistribution function plots and spectral analysis revealed for the first time in theliterature, within the context of molecular dynamic simulations, the thermodynamicpathway leading to formation of ice VII from liquid water on shock loading. Thestudy also revealed information for the first time in the literature about the statisticaltime-frame after passage of shock in which ice VII formation can be observed andvariations in degree of crystallinity of the sample over the entire simulation time of100 ns. C 2016 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4941049]

I. INTRODUCTION

The behaviour of water under extreme pressure and temperature is of profound importance toplanetary science,1 geochemistry,2 and fundamental chemistry.3–6 Apart from diamond anvil cellexperiments,7,8 strong shock-waves6,9,10 (using two stage light gas gun or high intensity laser)are able to simulate situations of extreme conditions of pressure and temperature in a medium.Shock-wave effects on bulk liquid water are typically studied within the context of generation ofplanetary magnetic fields in icy giants such as Neptune and Uranus, presence of high-pressure icepolymorphs in the interior of Galilean satellites such as Ganymed, Europa, and Callisto and Saturn’sTitan due to cataclysmic events, describing effects of high intensity and/or near field explosionin water, explaining different petrological process in the lower crust and upper mantle regions ofthe earth apart from fundamental studies in chemistry. Even though there exists numerous shockcompression experiments on bulk water,11–17 there appears to be a lacuna in fundamental under-standing of the thermodynamic pathway during the process of phase transition of shocked liquidwater to ice VII.

Some previous shock experiments on water11–15 comment on the phase of the water basedon final temperature and pressure data. It should be noted that pressure and molar volume deter-mination in those experiments were done using Rankine-Hugoniot relations whereas temperaturewas estimated from theoretical equations of state. It is quite well known that no single theoreticalequation of state is able to predict a wide range of temperatures.18 Typically the recent experimentsdeduce phase change based on changes in refractive index of the sample.16,17,19 One of the maincontroversial questions for these experiments (refer the literature Ref. 19) on shock induced phasetransformation of water is the purity of the sample and the presence of trace impurities whichmay act as nucleators/inhibitors for phase transition. It has been pointed out that no purificationtechnique can completely remove all bulk contamination.20 Another controversial issue in these

a)Electronic mail: anupamneogi@atdc.iitkgp.ernet.inb)Electronic mail: nilanjan@civil.iitkgp.ernet.in

1070-6631/2016/28(2)/027104/15/$30.00 28, 027104-1 ©2016 AIP Publishing LLC

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sets of experiments16,17 is presence of external nucleators such as quartz plate which may facilitatephase transition. The manuscript strives to answer many unanswered questions and controversialremarks through molecular dynamic (MD) investigations (as suggested in the literature Ref. 19).The questions that would be answered as part of this investigation are as follows.

• What is the approximate statistical time-frame after the passage of shock in which nucleationof ice VII formation can be observed in pure bulk liquid water at ambient conditions?

• Is there a complete or partial nucleation of ice VII in a single shocked bulk liquid waterinitially at ambient temperature and pressure?

• What is the percentage of crystallinity of the nucleated ice VII? Does the percentage ofcrystallinity of the shock induced water sample evolve along with time?

• Is this process of phase transition of pure bulk liquid water to ice VII possible at any shockspeeds?

It should be noted that there exists MD studies which demonstrate formation of ice VII fromliquid water at an elevated pressure21 without consideration of shock wave effects (which includesboth elevated pressure and temperature) which is the main highlight of this manuscript. Apart fromexplanation of the physics involved in the thermodynamic trajectory of shocked liquid water toice VII through MD simulations; it is expected that the study presented in this manuscript wouldbenefit future experimental investigations to be carried out in this domain as well as answer severalfundamental questions in astrophysics, geophysics and planetary science.

Ab initio MD studies are also present in the existing literature Refs. 22 and 23 which exploresthe ionization of water when subjected to shock velocities of 5 km/s and above. The electricalconductivity of shock compressed water was observed to increase until it reaches a plateau of30 GPa;24 the authors contribute the plateau region formation to ionization of water. Similar conclu-sions were also put forward by Hamann25 in which the author predicted ionization at 15–20 GPapressure at 1000 ◦C temperature. Thereby taking into consideration the conclusions of these pre-vious studies, this manuscript has been restricted to shock velocities which does not result inpressures above 12 GPa. It is thereby assumed that structural reorientation of the molecule willpreclude ionization under 12 GPa pressures. It is quite well known that conventional MD simu-lations are not appropriate for study of ionization events, one should consider DFT simulationsor use MD with polarizable/reactive potentials beyond 5 km/s shock velocities in water whereionization of water has been reported by previous researchers.22 Using reactive ReaxFF potentialbased non-equilibrium MD simulation26 researchers have reported ice VII phase transition motifat a pico-second time scale when liquid water was subjected to shock loading and suggested thatproper ice VII formation may be observed in the nano-second range of simulation at shock ve-locity of 3.625 km/s (particle velocity of 1.5 km/s). In this manuscript, the details of the physicsinvolved in the process of phase transition at a nano-second time scale along with study of the radialdistribution function, dynamics of hydrogen bond network, static structure factor of the obtainedice VII, amount of crystallinity in terms of intensity of the Bragg reflection, vibrational spectra ofO–H bond are presented when bulk liquid water is subjected to shock compression. Observationsof the time-evolution upto 100 ns are made to identify formation of metastable states (if any) andstructural reorientation during this thermodynamic pathway.

II. SIMULATION METHODOLOGY

It is well known that results obtained from MD simulations depends upon the force poten-tial used. Till date many different models have been proposed for MD study of water, e.g., rigidfixed-point charge model such as SPC,27 TIP3P,28 TIP4P,29 TIP5P,30 TIP4P/2005,31 SPC/E;32 polar-izable/reactive models such as ReaxFF,33 SPC-FQ,34 SPC/P,35 TIP4P/P;35 and flexible fixed-pointcharge models such as TIP4P/2005f,36 RWK2,37 SPC-mTR,38 TIP3P-mTR,38 SPC-TR,39 and modi-fied SPC/E by Zhang et al.40 Obviously the list is not exhaustive and many models have beenmissed; however, it should be noted that the objective of this manuscript is to demonstrate thethermodynamic pathway from bulk liquid water to ice VII on shock loading by choosing a propermodel of water which can be used in both ambient and high temperature and pressure regions (as

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observed in shock simulation study). Since we are interested in the real dynamics of the event, rigidfixed-point models can be eliminated.41 Moreover it has also been reported that ionization occursat very high shock speeds (at and above 5 km/s shock speeds);22 thereby consideration of polariz-able/reactive models can also be eliminated from the list of suitable models for this study. Therebywe are left with more commonly utilized flexible variations of the SPC and TIP4P models. Hydro-static compression of liquid water to ice VII has been reported21 using TIP4P flexible potential inwhich at ambient temperature the pressure was increased to achieve phase transition. The applica-bility of rigid TIP4P potential has been extended to that of 2500 K temperature and 35 GPa pressureby Brodholt et al.42 Since the difference between flexible and rigid versions of TIP4P potential isprimarily based on addition of anharmonic potential to represent flexibility of the OH bond stretch-ing and harmonic potential to represent flexibility of HOH angle bending,36 it is quite expected thatflexible version of TIP4P can also be utilized for high temperature and pressure as that observed inshock studies. Thereby flexible TIP4P/2005 model has been chosen as one of the models for thissimulation study.36 Even though TIP4P type models have been used for representation of water inmany literatures, SPC type models have also been used extensively. Thereby when demonstratingnew physics of water subjected to shock loads it is absolutely essential to highlight if similar type ofbehaviors are obtained by using different types of potentials. Thereby a recent SPC type of model40

(being referred to as SPC/E/z) demonstrating excellent correlation with experimental investigations(not only at ambient temperature and pressure conditions but also at high temperature and pressureconditions) [refer Table 3 in the literature Ref. 40] was also chosen for this study. In addition to thetwo flexible models considered in this manuscript, behavioral observations were also done using therigid versions of TIP4P/2005 and SPC/E models and similar behavior was obtained. The results ofthese rigid models are only presented in Figs. 1 and 2.

In this regard, the main differences between SPC and TIP4P type of models have been elabo-rated in Table I. Typically the HOH bond angle is equal to the ideal tetrahedral angle of 109.47◦ inSPC type models which is not the case for TIP4P type models. In TIP4P type of models, thecharge of the O atom (qO) is placed along the HOH bisector at a specified distance from the Oatom position (referred to as dOM). As can be observed from the Table I, the charge of the Hatom (qH) is located either on the H atom position (being represented as r0 = 1) as in SPC/E orat certain specified distance along the OH bond (being measured from the O atom position). Theinteratomic potentials for both the SPC and TIP4P type models shown in here are based on the12–6 LJ potential, where ϵ determines the depth of the potential well and σ the finite distance atwhich the inter-particle potential is zero. An interesting feature of the SPC/E/z model is consider-ation of finite depth of the potential well and finite distance at which the inter-particle potential iszero for H atom in comparison to other models (presented in Table I). Apart from that, distanceat which the inter-particle potential is zero for O atom is also reduced in SPC/E/z in comparison

FIG. 1. Shock velocity-particle velocity (US−up) Hugoniot plots of water for different shock intensities.

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FIG. 2. Shock compressed Hugoniot plots of water: (a) temperature vs mean stress; the red colored arrows indicate theHugoniot points corresponding to shock velocity of 4 km/s at which nucleation of ice VII have been identified later in thismanuscript. (b) Density vs mean stress.

to other models. It should also be noted from the table that out of 5 forcefield model parameterspresented, only SPC/E/z and TIP4P/2005f represent flexible models whereas others represent rigidmodels. Thereby in addition to the forcefield parameters presented in the table, these two modelsalso has function definitions to represent flexibility of OH bond stretching and HOH bond anglevibration. TIP4P/2005f uses an anharmonic Morse type function for representing OH bond stretch-ing flexibility and harmonic function for the HOH bond and vibration flexibility;36 whereas theSPC/E/z model uses harmonic functions for representing both OH bond stretching and HOH bondangle vibration flexibilities.40 Apart from this, since the value of water dielectric constant decreasesquickly as temperature increases and increases little as pressure increases,43 the values of atomiccharges on O and H are changed at different temperatures and ambient pressure [refer Table 2 in theliterature Ref. 40] for the SPC/E/z model.

A box with a dimension of 41.5 Å × 22 Å × 22 Å, containing 560 water molecules is equil-ibrated by employing time-reversible measure-preventing integrator44 on Nose-Hoover style non-Hamiltonian equation of motion (EOM), sampled by isotropic isothermal-isobaric (NPT) ensemblewith time step of 0.25 fs until it reaches the desired ambient temperature and pressure. After theNPT equilibration run for several hundred picoseconds, the initially chosen sample attains a densityof 0.998 gm/cc while the dimension of the sample changed to 41.9006 Å × 20.0125 Å × 20.0125 Åat ambient temperature and pressure. Note a multiple of 8 was chosen for simulation purpose sinceit is being commensurate with the unit cell of ice VII which is composed of two interpenetratingcubic lattices. Approximately 120 simulations (with different initial structure and different forcepotentials for water) were carried out to determine statistically significant values of shock-inducednucleation time of ice VII from bulk liquid water at shock velocity of 4 km/s.

From equilibration to the production run, periodic boundary conditions are utilized in threeorthogonal directions. The L-J interactions are truncated at 10 Å. For the long-range columbic

TABLE I. Forcefield parameters of water models.

SPC/E SPC/E/z TIP4P TIP4P/2005 TIP4P/2005f

θHOH (deg) 109.47 109.47 104.52 104.52 107.4qH (e) 0.4238 0.4238 0.52 0.5564 0.5564qO (e) −0.8476 −0.8476 −1.04 −1.1128 −1.1128dOM (Å) 0.15 0.1546 0.1546ϵO (Kcal/mol) 0.1553 0.1503 0.155 0.1852 0.1852ϵH (Kcal/mol) 0 0.0077 0 0 0σO (Å) 3.166 3.1169 3.1536 3.1589 3.1644σH (Å) 0 0.98 0 0 0r0 (Å) 1 0.9611 0.9572 0.9572 0.9419

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electrostatics interactions, particle-particle particle-mesh (PPPM)45 solver (which maps atomicpoint charges to a 3d grid and computes electrostatic energy with sufficient accuracy) is used.

The equilibrated bulk “pure” water sample is subjected to a series of shock velocities rangingfrom 2.5–5 km/s (where the maximum pressure is limited within 12 GPa) upto 100 ns time scale.A simulation methodology based on the Navier-Stokes equations for compressible flow which isable to simulate shock wave for small system sizes but for long time, MSST46 implemented underLAMMPS47 framework is utilized for this shock simulation study. Instead of simulating a shockwave within a large computational cell with many atoms,48 the MSST computational cell followsa Lagrangian point through the shock wave which is accomplished by time evolving equations ofmotion for the atoms as well as volume of the computational cell to constrain the stress in the propa-gation direction to the Rayleigh line and the energy of the system to the Hugoniot energy condition.For a given shock speed, these two relations describe a steady planar shock wave within continuumtheory. Incorporation of these constraints results in additional terms to the Lagrangian for an MSSTmethodology—one of which is the mass-like parameter Q which controls the degree of couplingbetween the atomic and volume degrees of freedom or the rate of decay of volume oscillations(for further details one is referred to the manuscript of MSST methodology46). For shock velocitiesof 2.5–4.0 km/s, the Q parameter has been estimated as 30; for 4.5–5.0 km/s the value has beenestimated as 35. On the other hand, the “tscale” value, i.e., the value which determines the amountof thermal kinetic energy converted to compressive strain at the beginning of the simulation hasbeen estimated as 0.02 for the shock velocity of 2.5–5.0 km/s. During the long time scale integrationprocess of 100 ns, it was ensured that no significant drift was observed in the energy values atany time instant with the chosen values of Q and “tscale” for a specific shock speed. It should benoted here that any choice of “tscale” and Q values typically does not affect the obtained resultsfrom simulation since the choice of higher or lower values of these parameters yields a sloweror faster freezing in pico-second time scale, whereas the observations of phase transition obtainedfrom simulations in this study (as shown later) are in nano-second time scale. During shock simu-lations, standard Verlet-velocity integration scheme was chosen with time step of 0.25 fs for shockintensities (US = 2.5–4.5 km/s) and 0.1 fs for stronger intensities (US = 5.0 km/s). Computationalcell size for simulation was so chosen such that stress, density, and energy density do not varyappreciably along the length of the computational domain (as requirement for MSST in whichthe stress and energy of a molecular dynamic simulation are constrained to obey the momentumand energy Hugoniot relations such that the simulation proceeds through the same thermodynamicstates as would occur in a steady shock46) as well as not too small such that boundary effects plays arole in the simulation. It should be noted in this regard that similar simulations were performed with250 and 432 water molecules and same trend of results was obtained as observed for simulationspresented in this manuscript with 560 water molecules.

III. RESULTS AND DISCUSSIONS

A. Hugoniot plots

In a MSST simulation, the Hamiltonian for the molecular dynamic simulation is modified toinclude degree of freedom associated with changes in volume.46 Within few femto-second timescale there occurs an irreversible flow of energy from the volume degrees of freedom to the atomicdegrees of freedom resulting in development of an shock equilibrium state. Hugoniot plots indifferent planes are obtained after sample achieves a shock equilibrium state. The shock-particlevelocity plot obtained from simulation shows good correlation with experimental investigations(refer Fig. 1)11,15,49,50 thereby endorsing the validity of the simulation protocol.

Differences are observed between the simulated results and experimental investigations forplots in other Hugoniot planes (mean stress–temperature and density–mean stress) (refer Fig. 2).In fact a lot of scatter can also be observed within the experimental investigation results carriedout by different groups11,12,15,49,50 and the simulated results are observed to be within the scatter.This scatter in experimental investigations with regards to temperature is primarily due to extremelylarge uncertainties of the pyrometric measurements or use of theoretical equation of state.

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The density plots (refer Fig. 2(b) obtained from SPC/E/z model40 matches closely with thoseof the experimental values by Rice and Walsh.11 Whereas density plots obtained from TIP4P/2005rigid, flexible, and SPC/E rigid matches with another sets of experiments.49,50 Given the experi-mental variations between different sets of data, the densities evaluated by different potentials usedin this study give a good correlation with experimental observations. A comparison of the densitiesbetween different force potentials used in this study reveals that SPC/E/z gives the highest densities.It should be noted that the oxygen σ parameter for the SPC/E/z model is a bit lower than thosefrom the others, indicating a less hard or repulsive oxygen-oxygen potential. Since O atoms are theheavier atoms and they can possibly come nearer to each other than other atoms in compression, thedensity predicted by the SPC/E/z model provides the highest values of densities obtained. Results ofDFT simulations22 give the lowest values of density for the models used in this study.

Temperature plots (refer Fig. 2(a)) obtained using SPC/E/z model40 matches closely withexperimental results by Cowperthwaite and Shaw12 whereas the TIP4P/2005f model matchestemperature observations by Rybakov.15 Since temperature in these experiments is calculated usingequation of states, comments cannot be made with regards to quantitative validation of temperaturesobtained from simulation and that of the experiments. It should also be pointed out that variationscan also be observed in the experimental phase diagrams of water at the junction of liquid waterand ice VII [refer Fig. 4 in Lin et al.51]. Apart from that, differences can also be observed in phasediagrams between experiment and computer simulations [refer Fig. 1 in the literature Ref. 52 inwhich phase diagram of TIP4P and SPC/E was compared with that of one experimental phasediagram]. Thereby obtaining a P-T point from simulation and placing the point on a phase diagram,one cannot definitively conclude about the phase of the sample and one need to do an extensiveradial distribution function check along with the check of spectral signature before commentingon the phase of the sample obtained. Inspite of that, experimental phase diagram of water (referthe literature Ref. 51) has been overlaid on Fig. 2(a) so as to provide a context for the reader tounderstand where the simulation occurs with respect to the equilibrium melt line. The region belowthe equilibrium melt line represents ice VII region whereas above the line represents liquid waterregion.

It should also be mentioned in here that SPC/E/z model specifies lowering the dielectric prop-erties of water above 675 K and ambient pressure; the simulations that have been performed inthis manuscript do not approach that specified temperature and the states are also at much higherpressures (it is known that increasing pressure increases the dielectric properties of water). Therebyno change in atomic charges has been done during the course of the simulation for the simulationscontaining SPC/E/z model for water. It should be reminded that the major aim of this manuscriptis to demonstrate the thermodynamic pathway of phase transition within a MD framework withoutloss of essential generality of the physics involved in the process. The samples corresponding to4 km/s shock speed (in which phase change was demonstrated later in the manuscript) are alsomarked in Fig. 2 by an arrow. Highest values of temperature were observed using the SPC/E/zmodel whereas the TIP4P/2005f model gives the lowest values of temperature. Only one pointfrom DFT simulations22 was available within the range of pressure-temperature selected for thisstudy and it provides significant differences from the experimental observations as well as MDsimulations which may be because of quantum nuclear vibrational effects23,53 (which are due topresence of covalent bonds in water). MD simulations (applicable only for reactive force fields) alsounderestimate degree of ionization in comparison to that of DFT simulations. It has been reported(refer Fig. 6 in the literature Ref. 22) that degree of ionization is small for shock velocities of 5 km/s(resulting in pressure of 8 GPa) which somewhat justifies the use of MD simulations in this manu-script for shock velocities below 5 km/s. However, in order to answer the question as to whetherionization precedes or happens at the same time as that of phase transition, one needs to do a fullDFT study which is beyond the scope of this manuscript. It should be reminded to the reader thatthe main objective is to find evidence of phase transition of water under shock compression and alsoto validate claims of experimental observance of phase transition of water under shock loading.19

Determination of exact temperatures using quantum nuclear vibrational corrections would havebeen good for drawing proper phase diagram of water using classical force fields but it should bereminded to the reader that it is also outside the scope of work of this manuscript.

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B. Discontinuities in thermodynamic variables

As evident from the Fig. 3, discontinuities in thermodynamic parameters are observed forshock velocities of 4 km/s which are not observed for other shock velocities (within 2.5–5 km/srange); suggesting possibilities of phase transition of the bulk liquid water (similar studies exist incooling of liquid water to ice Ih54). These results correspond to the SPC/E/z potential for water.40

The increase in density from 1.60 to 1.66 gm/cc for 4 km/s shock speed indicates attainment ofan energetically favourable configuration of 8 nearest neighbours (a phenomenon which has beendescribed in details with radial distribution function plots and spectral analysis later in the manu-script). It should be noted that results presented here are for one simulation in which the nucleationwas observed to start at 1.4 ns; however, similar behavior is observed for almost all the 120 simu-lations carried out as part of this work at 4 km/s shock velocity. In this context, it should also bementioned that no such sharp discontinuities in thermodynamic variables could be observed whenusing other potentials for water such as TIP4P/2005f, even though the timeframe of nucleation ofphase change could be observed from changes in the radial distribution functions (as discussed laterin the manuscript).

Out of the 60 simulations carried out as part of this work using the SPC/E/z potential at a shockvelocity of 4 km/s, 5 samples did not demonstrate nucleation to solid phase. The mean obtainedfrom rest of the samples gave a nucleation time of 1.52 ns with a 95% confidence interval of1.15–1.87 ns. Since the thermodynamic variables are related to each other, an increase in densitywill obviously indicate an increase in temperature. The rate of increase in density over time isobserved as approximately 0.07 (gm/cc)/ns for 4 km/s shock speed. This observed rate of nucleationin the process of shock induced phase transition of water is significantly fast in comparison toisothermal freezing of water to ice Ih (refer Fig. 1 in Ref. 54). Similarly 60 more simulations at4 km/s were carried out using TIP4P/2005f water molecules and the nucleation time was measuredas 1.96 ns with a 95% confidence interval of 1.32–2.01 ns. Thereby based on above simulations, itcan be stated with certainty that at 4 km/s shock speed nucleation can be observed approximatelyaround 1.5–2 ns time scale after passage of shock. The pressures measured at this shock speed are6.25 GPa and 5.09 GPa, respectively, using SPC/E/z and TIP4P/2005f force potential for water;whereas the temperature measurements are 556.25 K and 443.46 K for SPC/E/z and TIP4P/2005f,respectively. In fact these simulation observation matches closely to that of observations by Dolanet al.,19 who prescribed ice VII transition at around 6.5 GPa pressure. However it should also be

FIG. 3. Discontinuity of (a) temperature, (b) pressure, (c) density, and (d) particle velocity for 4 km/s shock speed along withsimulation time.

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mentioned that there exists differences between Dolan’s experimental work19 and this work sinceDolan achieved ice VII transition at around 4 ns by double shock technique whereas single shocktechnique has been utilized here. The reason for this difference might be pure water used for simu-lation may not be entirely pure as pointed out by Dolan in conclusion.19 The requirement for doubleshock instead of single shock may also be due to typical lower experimental rise time of shockpressure in comparison to computationally simulated rise times.55 Experimental shock pressurerise times similar to computational rise times can be achieved if one uses laser ablation techniqueinstead of shock gun technique;55 and in fact for water, shock wave generated by laser ablation didresult in phase transition.56 Although the atomistic study reveals that shock induced phase transitionis possible without the use of an external nucleator (similar observations being made in the previousliterature Ref. 19); yet, the presence of an external nucleator may also influence the phase transitionin shocked liquid water (as reported in the literature Ref. 17).

For details regarding stages of nucleation of phase transition at 4 km/s, one is refereed to the setof snapshots in Fig. 4 which shows temporal evolution of oxygen atom patterns (with blue one indi-cating bcc lattice structure and white indicating disordered pattern of bulk liquid water as observedfrom adaptive common neighbor analysis (CNA)57). Prior to the nucleation of phase transition, thehydrogen bond network in liquid water primarily contains five-, six-, and seven- membered ringscomposed of water molecules. Although individual rings are destroyed and reformed continuously,the overall fraction of water molecules contained in different ring types remains almost unchanged.After the nucleation of phase transition has occurred, a stable “stacked honeycomb structure” isestablished which indicates phase transition of liquid water to that of a solid phase.

Typically fixed cutoff based common neighbor filtering method is an efficient and convenienttechnique to determine the crystal structure in atomistic simulation, such as MD study. But thesensitivity of structure recognition through this filtering method might be hampered due to theperturbations to the particle positions at high temperature and/or large deformation situation (partic-ularly, if the resulting structure leads to coexistence of multiphase) because of the difficulty ofchoosing accurate cutoff distance for neighbor based filtering. In case of multiphase system toassign a local crystal structure to an atom, three characteristic numbers are computed for each N

FIG. 4. Atomic configuration of oxygen sites at different time instances for the shock velocity of 4 km/s.

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neighbor bonds of the central atom. Those characteristic numbers are (i) the number of neighboratoms, the central atom and its bonded neighbor have in common, ncn, (ii) total number of bondsbetween these common neighbors, nb and (iii) the number of bonds in the longest chain of bondsconnecting the common neighbors, n1cb. Then the computed N triplets (ncn, nb, n1cb) will becompared with a set of reference signatures to assign local crystal structure. These modificationsover the neighbor based filtering method (CNA analyses) are being referred as adaptive CNAmethod.57 Even though adaptive CNA technique based on nearest neighbour algorithms performsbetter than standard CNA analysis, but typically it gives a preliminary estimate of the nearest neigh-bours and thereby this method should not be used for conclusive proof of phase change in materials.Thereby, a detailed identification of the solid phase obtained as a result of shock induced phasetransition of liquid water is presented next in the manuscript through radial distribution functionplots, spectral investigations, static structure factor, and Bragg reflection intensity.

C. Radial distribution functions

To obtain structural information of the observed solid phase during shock induced transforma-tion, radial distribution function (RDF) was calculated. Discussion is presented in this section on theshort range ordering or local molecular packing by using the radial distribution function plots whichprovides the probability of finding a particle a particular distance away from another particle.

Fig. 5(b) shows RDF of oxygen-oxygen (at different time instances averaged over 100 ps) asobtained from this study (using SPC/E/z potential for water) compared against the perfect ice VIIcrystal modelled with this same force-field40 at a temperature of 300 K and pressure of 10 GPaand also bulk liquid water at 300 K and 1 atm pressure (shown as 0 ns in Fig. 5(b)). Since thetemperature and pressure of shocked water (obtained in this study corresponding to the shockvelocity of 4.0 km/s is 556.25 K, 6.25 GPa) significantly differ from the temperature and pressureof the constructed perfect ice VII crystal model at its ambient temperature and pressure, it canbe well expected that the RDF’s would not show a close match. The slight shoulder inflammation(portion zoomed in Fig. 5(b)) definitively suggests formation of interpenetrated bcc lattice structureof oxygen sites (a characteristic observed in ice VII and ice VIII). In fact this “shoulder region” (orsometimes a “kink region”) is a typical characteristic of bcc type crystal structure which is formedas the second coordination shell peak coalesce with the first coordination shell peak. In this regard,it should be noted that motif of formation of ice VII (by visualizing the eight nearest neighbourmolecules for each water molecule in a body-centered-cubic configuration) was demonstrated in

FIG. 5. (a) Radial distribution function of hydrogen-hydrogen for shock velocity of 4.0 km/s. In inset the molecularconfiguration of nucleated ice VII is shown, where red and white colours indicate oxygen and hydrogen atoms, respectively.(b) Radial distribution function of oxygen-oxygen for shock velocity of 4.0 km/s at different time instances after propagationof shock front using SPC/E/z water model. In the inset, the shoulder portion has been zoomed and the red arrows indicatesthe shoulder.

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027104-10 A. Neogi and N. Mitra Phys. Fluids 28, 027104 (2016)

earlier study26 in which non-equilibrium molecular dynamics simulations were done in pico-secondrange.

The interpenetrated simple-cubic lattices are inter-connected in case of ice VIII, but in ice VII,those sub-lattices are unconnected. Fig. 5(a) shows the RDF of hydrogen-hydrogen atoms for shockvelocity of 4 km/s. Absence of any major or minor peak depicts the proton disorderedness of thenucleated ice structure. Proton disorder typically means random orientation of the hydrogen atomswhich is depicted in the inset of the figure. The red particles indicates oxygen whereas the whiteparticles are the hydrogen atoms. This substantial amount of proton disorderedness occurs due tothe residual entropy of the shock compressed water and by virtue of the lower mass and muchhigher kinetic energy of hydrogen atoms. Typically in an ice VII structure, two simple cubic (sc)lattices are interpenetrated, but unconnected to form a bcc lattice where the corner site of one ofthe sc lattice serves as the centre of an unit bcc lattice. The distance between the first peak and thesecond minor peak (shoulder inflammation) of the radial distribution function of O–O atoms is theinterpenetration distance of the cubic lattices to form the bcc lattice. It can be observed from simu-lation study that maximum interpenetration distance is around 0.332 Å for 4.0 km/s shock speed incomparison to 0.392 Å interpenetration distance observed for ice VII at ambient temperature fromperfect ice VII model using the SPC/E/z force potential for water.

For shock velocity of 4 km/s, the first peak position (along the x-axis at around 2.74 Å),corresponding to the first coordination shell (representing the lattice vector), shows very closeagreement with the calculated RDF of oxygen-oxygen of perfect ice VII. This close match of thepeak position suggests that hydrogen bonds are still preserved at shock conditions thereby main-taining short range ordering. Apart from first coordination shell peak, no peaks are observed at0 ns thereby representing absence of any coordination of the molecule. With time evolution forthe shocked sample, other peaks starts forming thereby representing increase in coordination ofthe molecule. It should be noted that a distinctive “shoulder region” is formed for perfect ice VIIcrystal at 300 K and 10 GPa pressure. However this “shoulder region,” even though observed forthe shocked sample at other time instants (such as 1, 15, and 100 ns) is not that distinct. The reasonfor this is thermal broadening of the curves associated with increase in temperature of the system(approximately around 500-600 K obtained from shock study in comparison to ambient temperatureof 300 K; whereas the pressure is lower by around 3.75 GPa from the pressure of 10 GPa at whichideal ice VII crystal was modeled). Even though the position of the first coordination shell is almostunchanged for shock induced phase transitions, but the second next nearest neighbour distanceincrease significantly. Similar observations have been made by earlier research works.58,59 This shiftof second, third, and fourth peak positions (located at 4.89 Å, 5.48 Å, and 7.20 Å along the rangeof O–O RDF curve) of the obtained RDF of shocked water supports the fact of thermal broadeningin the shocked sample. The tendency of splitting of those peaks at time scale of 100 ns is observedwhich hints that percentage of transformation to ice VII in shocked liquid water may increase as theshock front moves. So future study should be made to investigate the phenomena for micro-secondtime scale. It should be noted that the position obtained from the shock simulation study closelymatches the position of the minima as obtained for ice VII at ambient temperature and pressure of10 GPa. It should be noted that the RDF presented above was obtained using the SPC/E/z forcepotential for water which claims to give better correlation with experimental observations speciallyat high temperatures and pressures.

In this manuscript, studies were also carried out using the TIP4P/2005f potential and similarbehavioural observations could be obtained at 4 km/s shock speed. Fig. 6 shows RDF plots ofpure ice VII at 10 GPa and 300 K and ice VII obtained from simulation for different shock speedsat 20 ns. Interestingly, even though there exists significant differences in the two force potentialsused in this manuscript along with its associated phase diagrams, phase transition characterized by“shoulder inflammation region” could be obtained at 4 km/s shock speed corresponding to 5.09 GPaof pressure and temperature of 443.46 K using TIP4P/2005f potential. Changes in the RDF withregards to formation of peaks at higher pair distances could be observed for 3 km/s and 5 km/sshock speeds; however, formation of “shoulder region” is unclear for these two velocities.

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027104-11 A. Neogi and N. Mitra Phys. Fluids 28, 027104 (2016)

FIG. 6. Comparison of radial distribution functions of oxygen-oxygen atoms for TIP4P/2005f water model at 20 ns for shockvelocities of 3.0, 4.0, and 5.0 km/s with perfect ice VII at 300 K and 10 GPa. Observed shoulder portion of the first peak hasbeen zoomed in the inset where the orange and dark cyan colored arrows typically indicates the shoulder at shock velocity5 and 4 km/s, respectively.

D. Spectral analysis

The vibrational spectrum envelope is calculated by a Fourier transform of the velocity auto-correlation function. Typically the vibrational spectra of bulk water displays three characteristicbands - stretching of OH bond, bending of HOH bond and librational (rotational around differentaxis) motion of water molecules.

Since it has been reported in the previous literature that librational and bending motions are notpredominantly affected in the process of phase transition from liquid water to ice VII;51 vibrationalspectra of OH stretching mode of shocked water are determined in this manuscript (refer Fig. 7) forthe entire range of shock intensities to explore the combined effect of temperature and pressure onthe dynamics of the water molecules (by relative absorbance). The OH vibrational spectra of shockcompressed water using TIP4P/2005f model are presented in Fig. 7(b). Thermal Doppler broaden-ing is observed for the peaks along with decrease in consecutive intensity as the shock velocitiesare increased. A blue shift in peak frequencies could be observed as the shock velocity is increasedfrom 2.5 to 3.5 km/s (3379.6 cm−1 to 3457.3 cm−1) whereas a red shift could be observed forshock velocity of 4 km/s (3452.4 cm−1). Similar shifts in peak frequencies are observed using the

FIG. 7. Power spectrum of O–H stretching mode the shock velocity ranging from 2.5–4.5 km/s for (a) SPC/E/z and (b) forTIP4P/2005f water model.

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027104-12 A. Neogi and N. Mitra Phys. Fluids 28, 027104 (2016)

SPC/E/z model for water in Fig. 7(a)—for 2.5–3.5 km/s blue shift in frequencies can be observedfrom 3425 to 3439 cm−1 which can be attributed primarily due to thermal agitation and not due topressure followed by red shift in frequencies from 3439 to 3423 cm−1 at 4 and 4.5 km/s shock speed.Although the temperature is high enough, i.e., 556.25 K and 637.5 K in case of the solid phases(corresponding to shock velocities 4 and 4.5 km/s, respectively) but the pressure in those states, i.e.,6.25 GPa and 8.65 GPa are enough to negate the temperature effect by setting up the thermodynam-ically stable atomic configuration eventually preventing thermal broadening. The relatively narrowspectra at 8.65 GPa in comparison to 6.25 GPa can be explained by the effect of temperature whichrises by about 81.25 K. One major difference between the spectral observations of the two potentialsis the presence of peak splitting (identified as A1g and B1g) when using SPC/E/z potential comparedto no such distinction when using TIP4P/2005f potential. Typical Raman scattering experiments ofliquid water at ambient temperature and pressure do not show presence of peak splitting60 whereaspeak splitting could be observed for water at high pressure and temperature.51 The peak splittingcan be simulated by use of computationally inexpensive harmonic functions (as used in SPC/E/z)for the OH bond stretching flexibility31 whereas anharmonic functions (as used in TIP4P/2005f) donot result in peak splitting. Using SPC/E/z potential at 2.5 km/s shock velocity, the anti-symmetricstretch (B1g) is observed to be dominant (showing higher peak values) in comparison to the sym-metric stretch (A1g) thereby demonstrating existence of liquid water phase; whereas A1g peak showshigher peak value at shock velocities of 4 and 4.5 km/s demonstrating presence of solid ice VIIphase.51

E. Static structure factor and Bragg reflection intensity

In this subsection, extended RDF between oxygen oxygen sites for 20 Å along with the calcu-lated static structure factor, S(q) are illustrated to obtain more intuitive information regarding thelong range ordering of large scale molecular arrangements. Percentage of crystallinity based onprogression of Bragg reflection intensity was also investigated in this subsection.

Pair distribution functions were calculated for an extended inter-atomic potential cutoff dis-tance of 20 Å for simulations using SPC/E/z potential for water. Fig. 8 shows long range order-ing patterns for instantaneous oxygen-oxygen RDF’s at different time frame for a shock speedof 4 km/s. The first curve, (a) shows the extended O–O RDF for initial liquid water at ambienttemperature and pressure before shock loading with the density of 0.998 gm/cc. The curve at (b)shows a step prior to the onset of nucleation of the solid ice VII phase. The curve at (c) showsthe step at onset of nucleation whereas curves (d) and (e) shows some intermediate steps in thesimulation. Curve at (f) demonstrates the pattern at end of simulation or 100 ns. No significantalteration in pattern of the peaks in the figures could be observed between figures (c)–(f) whichsuggests that the phase transformation is homogeneous in nature (at least upto the period of study of

FIG. 8. Extended radial distribution function of oxygen atoms at different time instances for the shock velocity of 4 km/s.All the RDFs were obtained from the instantaneous trajectory of the system (no time averaging has been done).

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027104-13 A. Neogi and N. Mitra Phys. Fluids 28, 027104 (2016)

FIG. 9. Comparison between static structure factor of oxygen-oxygen for shock velocity of 4.0 km/s (T = 552 K andP = 6.5 GPa) and that of ideal unit cell of ice VII (T = 300 K and P = 10 GPa).

100 ns). A closer observation would reveal that in between (c) and (f), there is an improvement inthe local molecular packing by a continuous change in the sharpness and intensity of the peaks andtroughs towards the ideal ice VII structure. It should be mentioned in here that the peaks that arosebeyond 10 Å (sharp peaks at 12.30, 14.63, 16.67, 17.49 followed by two minor peaks at 18.47 and19.34) during the phase of nucleation and after its completion exhibits a clear case of long rangecorrelation of the O–O atoms in the nucleated ice VII.

Static structure factor or atomic structure factor was evaluated for the shock induced structureand as well as for the perfect ice VII structure using the SPC/E/z potential for water. As in caseof water in extreme condition, within the momentum space (q space), the O–H and H–H partialstructure factors are very small, accounting for only 5% of the total X-ray scattering intensity.Thereby only oxygen-oxygen atoms are considered in the following structure factor calculationsin this manuscript. At temperature of 300 K and pressure 10 GPa, the evaluated S(q) of per-fect ice VII crystal shows four primary peaks for wave vectors(q) of 27.51, 40.63, 48.98, and57.69 nm−1. Those peaks were characterized by comparing with the previous X-ray diffractiondata61 and can be assigned for the crystal planes of (110), (200), (211), and (220). In case ofshock loading at a speed of 4.0 km/s, temperature was quite higher than 300 K, so it is ex-pected that at that elevated temperature the diffraction pattern from different crystal plans wouldbe poorly identified; in spite of that those four identified primary peaks of ice VII were pres-ent for the shock induced structure, although the peaks were less intense and were broadened(Fig. 9).

The temporal change in crystallinity of the sample upto 100 ns time scale was monitoredby following the progression of the intensity of the Bragg reflection from the hkl planes ofthe crystal structure (similar to a study62). Only oxygen atoms were considered for the struc-ture factor calculation and atomic scattering factor for oxygen was set to 1.62 The most intenseline corresponding to (110) plane was only considered for the determination of crystallinity ofthe sample in Table II (which also contains data of ice VII at 300 K and 10 GPa pressure forcomparison).

TABLE II. Temporal evolution of intensity of Bragg reflection.

0 ns 1.42 ns 1.45 1.5 100 ns Perfect ice VII

0.00 0.615 0.678 0.732 0.740 0.942

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027104-14 A. Neogi and N. Mitra Phys. Fluids 28, 027104 (2016)

IV. CONCLUSIONS

The manuscript presents MD investigations for the first time which reveals convincingly(through radial distribution plots, vibrational spectral analysis and structure factor evaluations) thata single shock velocity of 4 km/s is able to produce partial phase transition in bulk “pure” liquid wa-ter to that of ice VII without the need of any nucleators. It has been demonstrated statistically in thisstudy that ice VII structure is formed within few nanoseconds after the shock wave passes throughthe bulk liquid water medium and is stable upto 100 ns time scale. Static structure factor and Braggreflection intensity calculations demonstrate convincingly the temporal evolution of crystallinity inthe sample. More detailed study with regards to sample ionization which may happen along withphase transition can be undertaken by performing DFT simulations.

ACKNOWLEDGMENTS

This work was supported by Naval Research Board, India under Award No. NRB-226/HYD/10-11. Any opinions, findings, and conclusions or recommendations expressed in this manuscript arethose of the writers and do not necessarily reflect those of the Naval Research Board, India.

1 L. K. M. Kanani, L. R. Benedetti, R. Jeanloz, P. M. Celliers, J. H. Eggert, D. G. Hicks, S. J. Moon et al., “Laser-drivenshock experiments on precompressed water: Implications for icy giant planets,” J. Chem. Phys. 125(1), 014701 (2006).

2 B. R. Simoneit, “Aqueous high-temperature and high-pressure organic geochemistry of hydrothermal vent systems,”Geochim. Cosmochim. Acta 57, 3231 (1993).

3 A. Polian and M. Grimsditch, “New high-pressure phase of H2O: Ice X,” Phys. Rev. Lett. 52, 1312 (1984).4 N. Holmes, W. Nellis, W. Graham, and G. Walrafen, “Spontaneous Raman scattering from shocked water,” Phys. Rev. Lett.

55, 2433 (1985).5 G. Walrafen, M. Hokmabadi, W. Yang, and G. Piermarini, “High-temperature high-pressure Raman spectra from liquid

water,” J. Phys. Chem. 92, 4540 (1988).6 Z. Men, W. Fang, D. Li, Z. Li, and C. Sun, “Raman spectra from symmetric hydrogen bonds in water by high-intensity

laser-induced breakdown,” Sci. Rep. 4, 4606 (2014).7 R. Hemley, A. Jephcoat, H. Mao, C. Zha, L. Finger, and D. Cox, “Static compression of H2O-ice to 128 GPa (1.28 Mbar),”

Nature 330, 737 (1987).8 A. Goncharov, V. Struzhkin, M. Somayazulu, R. Hemley, and H. Mao, “Compression of ice to 210 gigapascals: Infrared

evidence for a symmetric hydrogen-bonded phase,” Science 273(5272), 218 (1996).9 W. J. Evans, C.-S. Yoo, G. W. Lee, H. Cynn, M. J. Lipp, and K. Visbeck, “Dynamic diamond anvil cell (dDAC): A novel

device for studying the dynamic-pressure properties of materials,” Rev. Sci. Instrum. 78, 073904 (2007).10 C. G. Salzmann, P. G. Radaelli, A. Hallbrucker, E. Mayer, and J. L. Finney, “The preparation and structures of hydrogen

ordered phases of ice,” Science 311, 1758 (2006).11 M. H. Rice and J. M. Walsh, “Equation of state of water to 250 kilobars,” J. Chem. Phys. 26, 824 (1957).12 M. Cowperthwaite and R. Shaw, “Cupsilo (T) equation of state for liquids. Calculation of the shock temperature of carbon

tetrachloride, nitromethane, and water in the 100-kbar region,” J. Chem. Phys. 53, 555 (1970).13 G. Lyzenga, T. J. Ahrens, W. Nellis, and A. Mitchell, “The temperature of shock-compressed water,” J. Chem. Phys. 76,

6282 (1982).14 G. Bogdanov and A. Rybakov, “Anomalies of the shock compressibility of water,” J. Appl. Mech. Tech. Phys. 33, 162

(1992).15 A. Rybakov, “Phase transformation of water under shock compression,” J. Appl. Mech. Tech. Phys. 37, 629 (1996).16 D. Dolan and Y. M. Gupta, “Nanosecond freezing of water under multiple shock wave compression: Optical transmission

and imaging measurements,” J. Chem. Phys. 121, 9050 (2004).17 D. Dolan, J. Johnson, and Y. M. Gupta, “Nanosecond freezing of water under multiple shock wave compression: Continuum

modeling and wave profile measurements,” J. Chem. Phys. 123, 064702 (2005).18 T. J. Ahrens and J. D. O’Keefe, in Shock Vaporization and the Accretion of the Icy Satellites of Jupiter and Saturn, edited

by J. Klinger et al. (D. Reidel, Norwell, Mass, 1985), p. 631.19 D. H. Dolan, M. D. Knudson, C. A. Hall, and C. Deeney, “A metastable limit for compressed liquid water,” Nat. Phys. 3(5),

339 (2007).20 V. Smith, Ultrapurity: Methods and Techniques (Marcel Dekker, New York, 1972).21 J. Aragones, M. Conde, E. Noya, and C. Vega, “The phase diagram of water at high pressures as obtained by computer

simulations of the TIP4P/2005 model: The appearance of a plastic crystal phase,” Phys. Chem. Chem. Phys. 11, 543 (2009).22 N. Goldman, E. J. Reed, I.-F. W. Kuo, L. E. Fried, C. J. Mundy, and A. Curioni, “Ab initio simulation of the equation of

state and kinetics of shocked water,” J. Chem. Phys. 130, 124517 (2009).23 N. Goldman, E. J. Reed, and L. E. Fried, “Quantum mechanical corrections to simulated shock Hugoniot temperatures,” J.

Chem. Phys. 131, 204103 (2009).24 A. C. Mitchell and W. J. Nellis, “Equation of state and electrical conductivity of water and ammonia shocked to the 100

GPa (1 Mbar) pressure range,” J. Chem. Phys. 76(12), 6273 (1982).25 S. D. Hamann, “Properties of electrolyte solutions at high pressures and temperatures,” Phys. Chem. Earth 13, 89 (1981).26 M. Vedadi, A. Choubey, K. Nomura, R. K. Kalia, A. Nakano, P. Vashishta, and A. C. T. van Duin, “Structure and dynamics

of shock-induced nanobubble collapse in water,” Phys. Rev. Lett. 105, 014503 (2010).

Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP:

203.110.242.22 On: Mon, 04 Apr 2016 10:12:31

027104-15 A. Neogi and N. Mitra Phys. Fluids 28, 027104 (2016)

27 H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, and J. Hermans, in Intermolecular Forces, edited by B.Pullman (Reidel, Dordrecht, 1981), p. 331.

28 W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein, “Comparison of simple potential functionsfor simulating liquid water,” J. Chem. Phys. 79, 926 (1983).

29 W. L. Jorgensen, “Revised TIPS for simulations of liquid water and aqueous solutions,” J. Chem. Phys. 77, 4156 (1982).30 M. W. Mahoney and W. L. Jorgensen, “A five-site model for liquid water and the reproduction of the density anomaly by

rigid, nonpolarizable potential functions,” J. Chem. Phys. 112, 8910 (2000).31 J. L. Abascal and C. Vega, “A general purpose model for the condensed phases of water: TIP4P/2005,” J. Chem. Phys.

123(23), 234505 (2005).32 H. Berendsen, J. Grigera, and T. Straatsma, “The missing term in effective pair potentials,” J. Phys. Chem. 91, 6269 (1987).33 M. Aryanpour, A. C. T. van Duin, and J. D. Kubicki, “Development of a reactive force field for iron-oxyhydroxide systems,”

J. Phys. Chem. A 114, 6298 (2010).34 B. Chen, J. J. Potoff, and J. I. Siepmann, “Adiabatic nuclear and electronic sampling Monte Carlo simulations in the Gibbs

ensemble: Application to polarizable force fields for water,” J. Phys. Chem. B 104, 2378 (2000).35 K. E. G. K. Kiyohara and A. Z. Panagiotopoulos, “Phase coexistence properties of polarizable water models,” Mol. Phys.

94, 803 (1998).36 M. A. González and J. L. Abascal, “A flexible model for water based on TIP4P/2005,” J. Chem. Phys. 135, 224516 (2011).37 Z. Duan, N. Møller, and J. H. Weare, “Gibbs ensemble simulations of vapor/liquid equilibrium using the flexible RWK2

water potential,” J. Phys. Chem. B 108, 20303 (2004).38 C. C. Liew, H. Inomata, and K. Arai, “Flexible molecular models for molecular dynamics study of near and supercritical

water,” Fluid Phase Equilib. 144, 287 (1998).39 K. Toukan and A. Rahman, “Molecular-dynamics study of atomic motions in water,” Phys. Rev. B 31, 2643 (1985).40 X. B. Zhang, Q. L. Liu, and A. M. Zhu, “An improved fully flexible fixed-point charges model for water from ambient to

supercritical condition,” Fluid Phase Equilib. 262, 210 (2007).41 T. I. Mizan, P. E. Savage, and R. M. Ziff, “Comparison of rigid and flexible simple point charge water models at supercritical

conditions,” J. Comput. Chem. 17, 1757 (1996).42 J. Brodholt and W. Bernard, “Simulations of the structure and thermodynamic properties of water at high pressures and

temperatures,” J. Geophys. Res.: Solid Earth 98(B1), 519, doi:10.1029/92jb01407 (1993).43 ASME, Steam Tables, 6th ed. (The American Society of Mechanical Engineers, New York, NY, 1992).44 M. E. Tuckerman, J. Alejandre, R. López-Rendón, A. L. Jochim, and G. J. Martyna, “A Liouville-operator derived measure-

preserving integrator for molecular dynamics simulations in the isothermal-isobaric ensemble,” J. Phys. A: Math. Gen. 39,5629 (2006).

45 R. W. Hockney and J. W. Eastwood, Computer Simulation Using Particles (CRC Press, 1988).46 E. J. Reed, L. E. Fried, and J. Joannopoulos, “A method for tractable dynamical studies of single and double shock compres-

sion,” Phys. Rev. Lett. 90, 235503 (2003).47 S. Plimpton, “Fast parallel algorithms for short-range molecular dynamics,” J. Comput. Phys. 117, 1 (1995).48 A. Neogi and N. Mitra, “On shock response of nano-void closed/open cell copper material: Non-equilibrium molecular

dynamic simulations,” J. Appl. Phys. 115, 013504 (2014).49 J. M. Walsh and M. H. Rice, “Dynamic compression of liquids from measurements on strong shock waves,” J. Chem. Phys.

26, 815 (1957).50 S. P. Marsh, LASL Shock Hugoniot Data (University of California Press, 1980), Vol. 5.51 J.-F. Lin, B. Militzer, V. V. Struzhkin, E. Gregoryanz, R. J. Hemley, and H.-K. Mao, “High pressure-temperature Raman

measurements of H2O melting to 22 GPa and 900 K,” J. Chem. Phys. 121(17), 8423 (2004).52 E. Sanz, C. Vega, J. L. F. Abascal, and L. G. MacDowell, “Phase diagram of water from computer simulation,” Phys. Rev.

Lett. 92(25), 255701 (2004).53 F. Martin and R. Redmer, “Estimating the quantum effects from molecular vibrations of water under high pressures and

temperatures,” J. Phys.: Condens. Matter 21(37), 375101 (2009).54 C. Lobban, J. L. Finney, and W. F. Kuhs, “The structure of a new phase of ice,” Nature 391, 268 (1998).55 B. Cao, E. M. Bringa, and M. A. Meyers, “Shock compression of monocrystalline copper: Atomistic simulations,” Metall.

Mater. Trans. A 38(11), 2681 (2007).56 V. R. Kumar and P. P. Kiran, “Onset of ice VII phase of liquid water: Role of filamentation in stimulated Raman scattering,”

Opt. Lett. 40(12), 2802 (2015).57 A. Stukowski, “Structure identification methods for atomistic simulations of crystalline materials,” Modell. Simul. Mater.

Sci. Eng. 20, 045021 (2012).58 C. Vega, C. McBride, E. Sanz, and J. L. Abascal, “Radial distribution functions and densities for the SPC/E, TIP4P and

TIP5P models for liquid water and ices Ih, Ic, II, III, IV, V, VI, VII, VIII, IX, XI and XII,” Phys. Chem. Chem. Phys. 7,1450 (2005).

59 J. D. Madura, B. M. Pettitt, and D. F. Calef, “Water under high pressure,” Mol. Phys. 64, 325 (1988).60 J. J. Max and C. Chapados, “Isotope effects in liquid water by infrared spectroscopy. III. H2O and D2O spectra from 6000

to 0 cm−1,” J. Chem. Phys. 131(18), 184505 (2009).61 B. Kamb and B. L. Davis, “Ice VII, the densest form of ice,” Proc. Natl. Acad. Sci. U. S. A. 52, 1433 (1964).62 M. Carl, C. Vega, E. Sanz, and J. L. Abascal, “Formation of high density amorphous ice by decompression of ice VII and

ice VIII at 135 K,” J. Chem. Phys. 121(23), 11907 (2004).

Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP:

203.110.242.22 On: Mon, 04 Apr 2016 10:12:31