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Searching for Crystal-Ice Domains in Amorphous Ices

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Searching for Crystal-Ice Domains in Amorphous Ices PHYSICAL REVIEW MATERIALS 2, 075601 (2018) Searching for crystal-ice domains in amorphous ices Fausto Martelli,1,2,* Nicolas Giovambattista,3,4 Salvatore Torquato,2 and Roberto Car2 1IBM Research, Hartree Centre, Daresbury WA4 4AD, United Kingdom 2Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA 3Department of Physics, Brooklyn College of the City University of New York, Brooklyn, New York 11210, USA 4The Graduate Center of the City University of New York, New York, New York 10016, USA (Received 7 May 2018; published 2 July 2018) Weemploy classical molecular dynamics simulations to investigate the molecular-level structure of water during the isothermal compression of hexagonal ice (Ih) and low-density amorphous (LDA) ice at low temperatures. In both cases, the system transforms to high-density amorphous ice (HDA) via a first-order-like phase transition. We employ a sensitive local order metric (LOM) [F. Martelli et al., Phys. Rev. B 97, 064105 (2018)] that can discriminate among different crystalline and noncrystalline ice structures and is based on the positions of the oxygen atoms in the first- and/or second-hydration shell. Our results confirm that LDA and HDA are indeed amorphous, i.e., they lack polydispersed ice domains. Interestingly, HDA contains a small number of domains that are reminiscent of the unit cell of ice IV,although the hydrogen-bond network (HBN) of these domains differs from the HBN of ice IV. The presence of ice-IV-like domains provides some support to the hypothesis that HDA could be the result of a detour on the HBN rearrangement along the Ih-to-ice-IV pressure-induced transformation. Both nonequilibrium LDA-to-HDA and Ih-to-HDA transformations are two-step processes where a small distortion of the HBN first occurs at low pressures and then, a sudden, extensive rearrangement of hydrogen bonds at the corresponding transformation pressure follows. Interestingly, the Ih-to-HDA and LDA-to-HDA transformations occur when LDA and Ih have similar local order, as quantified by the site-averaged LOMs. Since Ih has a perfect tetrahedral HBN while LDA does not, it follows that higher pressures are needed to transform Ih into HDA than that for the conversion of LDA to HDA. In correspondence with both first-order-like phase transitions, the samples are composed of a large HDA cluster that percolates within the Ih/LDA samples. Our results shed light on the debated structural properties of amorphous ices and indicate that the kinetics of the Ih-to-HDA and LDA-to-HDA transformations require an in-depth inspection of the underlying HBN. Such investigation is currently ongoing. DOI: 10.1103/PhysRevMaterials.2.075601 I. INTRODUCTION for the case of HDA [5,6,20,21]. However, this distinction is less clear in computer simulations and, therefore, we refer to At deeply supercooled conditions, water exhibits polyamor- glassy water as either LDA or HDA. phism, i.e., it exists in more than one amorphous solid state. At small length scales, LDA and HDA are structurally very The most common forms of glassy water are the low-density different. LDA has well-separated first- and second-hydration amorphous (LDA) and the high-density amorphous (HDA) shells, with nearest neighbors arranged in a tetrahedral-like ice [1–6]. LDA is likely the most abundant form of ice in local structure. In this regard, the structure of LDA is rem- the universe and can be produced, for example, by rapid iniscent of the local structure of Ih. By contrast, HDA has quenching of liquid water at atmospheric pressure [7]. The interstitial molecules populating the space between the first- LDA that is thought to exist in space forms by condensa- tion of water from the gas phase onto cold surfaces [8,9]. and the second-hydration shells, thus acquiring distorted local HDA can be produced, for example, by pressure-induced configurations similar to liquid-water configurations at ambi- amorphization (PIA) of hexagonal ice (Ih) or by isothermal ent conditions [16,22–26]. LDA and HDA also differ in terms compression of LDA [10–13]. Remarkably, LDA and HDA can of the hydrogen-bond network (HBN). The HBN of LDA is be interconverted by isothermal compression/decompression dominated by five-, six-, and sevenfold rings, in contrast to at T = 130 − 140 K [10,14,15] and by isobaric heating at HDA whose HBN includes a significant fraction of longer different pressures [14,16,17]. A third form of glassy water, a member rings to accommodate the larger density of the system ∼ − very high-density amorphous (VHDA) ice, has been identified ( 20 25% larger than LDA) [27]. Despite these local at very high pressures [18]. We note that experiments show structural differences, at large length scales the two glass forms that LDA and HDA can be separated into subfamilies of are nearly hyperuniform, i.e., they possess a similar degree of suppression of large-scale density fluctuations, indicating amorphous structures, e.g., LDAI and LDAII for LDA [19], and unannealed HDA (uHDA) and expanded HDA (eHDA) that they should possess similar large-scale structures and large-scale translational order [28]. LDA and HDA were discovered more than 30 years ago [1]. Yet, the nature of LDA and HDA, and the associated LDA-to- *Corresponding author: [email protected] HDA first-order-like phase transition, remain highly debated. It 2475-9953/2018/2(7)/075601(10) 075601-1 ©2018 American Physical Society MARTELLI, GIOVAMBATTISTA, TORQUATO, AND CAR PHYSICAL REVIEW MATERIALS 2, 075601 (2018) has been suggested that LDA and HDA are thermodynamically that both LDA-to-HDA and Ih-to-HDA transformations are connected with the liquid, e.g., by isobaric cooling/heating reminiscent of spinodal decompositions, without nucleation [10]. Elsewhere, HDA was interpreted to be a collapsed HBN and growth of HDA within LDA/Ih. of water molecules, unrelated to the liquid state [29–31]. It has The article is organized as follows. In Sec. II, we provide also been suggested that HDA may contain nanometer-scale a brief definition of the LOM employed in this work. In Secs. ice domains. After all, HDA transforms to ice IV at very high III A and III B, we discuss the short- and intermediate-range pressure [32,33] and it can be formed by compression of Ih. order, respectively, in both LDA and HDA. In Sec. III C,we Unfortunately, experimental studies that focus on the structure discuss the spatial aggregation (clusters) of LDA-, HDA-, and of LDA and HDA at intermediate length scales are challenging Ih-like molecules during the LDA-to-HDA and Ih-to-HDA [6]. Computer-simulation studies that describe the structure of transformations. Conclusions and final remarks are presented LDA and HDA, especially the search for the presence of icelike in Sec. IV. domains, are rare. In this article, we perform out-of-equilibrium classical II. THE LOCAL ORDER METRIC molecular dynamics (MD) simulations to study the structural order during the Ih-to-HDA and LDA-to-HDA transforma- In this section, we briefly describe the local order metric tions; in particular, we look for traces of crystalline domains employed in this work. The details of the numerical algorithm during these process. We will refer to the HDA produced upon can be found in Ref. [34]. The local environment of an atomic site j in a snapshot of a molecular dynamics or Monte Carlo compression of Ih as HDAIh, and to the HDA obtained upon simulation defines a local pattern formed by M neighboring compression of LDA as HDALDA. We probe the short- and intermediate-range order during these transformations using sites. Typically these include the first and/or second neighbors a recently developed local order metric (LOM). The LOM of the site j. There are N local patterns, one for each atomic measures the degree of order present in the neighborhood of site j in the system. The local reference structure is the set of an atomic or molecular site in a condensed medium [34]. The the same M neighboring sites in an ideal lattice of choice, the LOM is endowed with a high-resolving power [34–36] and spatial scale of which is fixed by setting its nearest-neighbor allows one to look for specific ordered domains defined by distance equal to d, the average equilibrium value in the system the location of selected atoms (e.g., water oxygens) in a given of interest. For a given orientation of the reference structure P reference structure. Typically, the reference structure is taken and a given permutation of the pattern indices, we define to be the local structure of a perfect crystalline phase. the LOM S(j) as the maximum overlap between pattern and We have looked for signatures of ices Ih, cubic (Ic), II, III, reference structure in the j neighborhood by ⎧ ⎛ ⎞⎫ IV,V,VI, and VII, in LDA and HDA. According to our analysis, ⎪ 2 ⎪ ⎨M j − j j ⎬ both amorphous ices lack polydispersed ordered crystalline ⎜ PiP A Ri ⎟ S(j) = max exp ⎝− ⎠ , (1) domains. However, we find that the oxygens of a few water θ,φ,ψ;P ⎩⎪ 2σ 2M ⎭⎪ molecules in HDA are arranged as in the unit cell of ice IV. i=1 This observation provides support to the picture proposed in j j Ref. [37], where the collapse of the HBN of Ih occurring upon where θ,φ, and ψ are Euler angles, PiP and Ri are the pattern and the reference position vectors in the laboratory frame of isothermal compression does not lead to ice IV, but to HDA, j and is hence considered a “derailed” state along the Ih-to- the M neighbors of site j, respectively, and A is an arbitrary ice-IV pathway.
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