Abstract
A great success of solid state physics comes from the characterization of crystal structures in the reciprocal (wave vector) space. The power of structural characterization in Fourier space originates from the breakdown of translational and rotational symmetries. However, unlike crystals, liquids and amorphous solids possess continuous translational and rotational symmetries on a macroscopic scale, which makes Fourier space analysis much less effective. Lately, several studies have revealed local breakdown of translational and rotational symmetries even for liquids and glasses. Here, we review several mathematical methods used to characterize local structural features of apparently disordered liquids and glasses in real space. We distinguish two types of local ordering in liquids and glasses: energy-driven and entropy-driven. The former, which is favoured energetically by symmetry-selective directional bonding, is responsible for anomalous behaviours commonly observed in water-type liquids such as water, silicon, germanium and silica. The latter, which is often favoured entropically, shows connections with the heterogeneous, slow dynamics found in hard-sphere-like glass-forming liquids. We also discuss the relationship between such local ordering and crystalline structures and its impact on glass-forming ability.
Key points
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Liquids and glasses possess neither long-range translational nor orientational order but still tend to form local structural order, which is not easily accessed by conventional scattering (wave vector) analysis.
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Local structural analysis in real space — based on modern mathematical descriptions of geometrical structures and topologies — is a powerful tool to characterize the structure and elucidate its link to the physical properties of liquids.
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Local structural ordering lowers the free energy locally and can be driven energetically and entropically.
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Energetically driven ordering — which is commonly seen in liquids with specific directional bonding, such as water and silica — usually leads to the formation of spatially localized structures with translational order.
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Entropically driven ordering — which is often seen in liquids interacting with isotropic potentials, such as hard spheres — usually leads to the formation of spatially extended structures with orientational order.
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The understanding of local structural ordering in liquids brings new physical insights into the role of many-body correlations in many mysterious phenomena of fundamental importance in liquids such as the anomalies of water, liquid–liquid transition, glass transition and crystallization.
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The knowledge of local orders in liquids provides invaluable information on the interpretation of the physical quantities experimentally accessed by scattering and spectroscopic measurements.
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References
Hansen, J.-P. & McDonald, I. R. Theory of simple liquids (Elsevier, 1990).
Finney, J. L. Random packings and the structure of simple liquids. I. The geometry of random close packing. Proc. R. Soc. Lond. A 319, 479–493 (1970).
Snook, I., Van Megen, W. & Pusey, P. Structure of colloidal glasses calculated by the molecular-dynamics method and measured by light scattering. Phys. Rev. A 43, 6900–6907 (1991).
Cargill, G. III Dense random packing of hard spheres as a structural model for noncrystalline metallic solids. J. Appl. Phys. 41, 2248–2250 (1970).
Truskett, T. M., Torquato, S., Sastry, S., Debenedetti, P. G. & Stillinger, F. H. Structural precursor to freezing in the hard-disk and hard-sphere systems. Phys. Rev. E 58, 3083–3088 (1998).
O’Malley, B. & Snook, I. Structure of hard-sphere fluid and precursor structures to crystallization. J. Chem. Phys. 123, 054511 (2005).
Shintani, H. & Tanaka, H. Frustration on the way to crystallization in glass. Nat. Phys. 2, 200–206 (2006).
Russo, J. & Tanaka, H. The microscopic pathway to crystallization in supercooled liquids. Sci. Rep. 2, 505 (2012).
Tanaka, H. Bond orientational order in liquids: towards a unified description of water-like anomalies, liquid-liquid transition, glass transition, and crystallization. Eur. Phys. J. E 35, 113 (2012).
Frank, F. C. Supercooling of liquids. Proc. R. Soc. Lond. A 215, 43–46 (1952).
Tanaka, H. Simple view of waterlike anomalies of atomic liquids with directional bonding. Phys. Rev. B 66, 064202 (2002).
Soper, A. K. & Ricci, M. A. Structures of high-density and low-density water. Phys. Rev. Lett. 84, 2881–2884 (2000).
Yan, Z. et al. Structure of the first-and second-neighbor shells of simulated water: quantitative relation to translational and orientational order. Phys. Rev. E 76, 051201 (2007).
Saika-Voivod, I., Sciortino, F. & Poole, P. H. Computer simulations of liquid silica: equation of state and liquid–liquid phase transition. Phys. Rev. E 63, 011202 (2000).
Cuthbertson, M. J. & Poole, P. H. Mixturelike behavior near a liquid-liquid phase transition in simulations of supercooled water. Phys. Rev. Lett. 106, 115706 (2011).
Russo, J. & Tanaka, H. Understanding water’s anomalies with locally favoured structures. Nat. Commun. 5, 3556 (2014).
Shi, R. & Tanaka, H. Impact of local symmetry breaking on the physical properties of tetrahedral liquids. Proc. Natl Acad. Sci. USA 115, 1980–1985 (2018).
Shi, R. & Tanaka, H. Microscopic structural descriptor of liquid water. J. Chem. Phys. 148, 124503 (2018).
Shi, R., Russo, J. & Tanaka, H. Origin of the emergent fragile-to-strong transition in supercooled water. Proc. Natl Acad. Sci. USA 115, 9444–9449 (2018).
Shi, R., Russo, J. & Tanaka, H. Common microscopic structural origin for water’s thermodynamic and dynamic anomalies. J. Chem. Phys. 149, 224502 (2018).
Shiratani, E. & Sasai, M. Molecular scale precursor of the liquid–liquid phase transition of water. J. Chem. Phys. 108, 3264–3276 (1998).
Appignanesi, G. A., Fris, J. R. & Sciortino, F. Evidence of a two-state picture for supercooled water and its connections with glassy dynamics. Eur. Phys. J E 29, 305–310 (2009).
Accordino, S., Fris, J. R., Sciortino, F. & Appignanesi, G. Quantitative investigation of the two-state picture for water in the normal liquid and the supercooled regime. Eur. Phys. J E 34, 48 (2011).
Singh, R. S., Biddle, J. W., Debenedetti, P. G. & Anisimov, M. A. Two-state thermodynamics and the possibility of a liquid-liquid phase transition in supercooled TIP4P/2005 water. J. Chem. Phys. 144, 144504 (2016).
Wikfeldt, K., Nilsson, A. & Pettersson, L. G. Spatially inhomogeneous bimodal inherent structure of simulated liquid water. Phys. Chem. Chem. Phys. 13, 19918–19924 (2011).
de Oca, J. M. M., Fris, J. A. R., Accordino, S. R., Malaspina, D. C. & Appignanesi, G. A. Structure and dynamics of high-and low-density water molecules in the liquid and supercooled regimes. Eur. Phys. J. E 39, 124 (2016).
Altabet, Y. E., Singh, R. S., Stillinger, F. H. & Debenedetti, P. G. Thermodynamic anomalies in stretched water. Langmuir 33, 11771–11778 (2017).
Chau, P.-L. & Hardwick, A. J. A new order parameter for tetrahedral configurations. Mol. Phys. 93, 511–518 (1998).
Errington, J. R. & Debenedetti, P. G. Relationship between structural order and the anomalies of liquid water. Nature 409, 318–321 (2001).
Xu, L. et al. Appearance of a fractional stokes–einstein relation in water and a structural interpretation of its onset. Nat. Phys. 5, 565–569 (2009).
Kumar, P., Buldyrev, S. V. & Stanley, H. E. A tetrahedral entropy for water. Proc. Natl Acad. Sci. USA 106, 22130–22134 (2009).
Overduin, S. & Patey, G. Understanding the structure factor and isothermal compressibility of ambient water in terms of local structural environments. J. Phys. Chem. B 116, 12014–12020 (2012).
Overduin, S. & Patey, G. An analysis of fluctuations in supercooled tip4p/2005 water. J. Chem. Phys. 138, 184502 (2013).
Overduin, S. & Patey, G. Fluctuations and local ice structure in model supercooled water. J. Chem. Phys. 143, 094504 (2015).
Sellberg, J. A. et al. Ultrafast x-ray probing of water structure below the homogeneous ice nucleation temperature. Nature 510, 381–384 (2014).
Ni, Y. & Skinner, J. Evidence for a liquid-liquid critical point in supercooled water within the E3B3 model and a possible interpretation of the kink in the homogeneous nucleation line. J. Chem. Phys. 144, 214501 (2016).
Ni, Y. & Skinner, J. IR spectra of water droplets in no man’s land and the location of the liquid-liquid critical point. J. Chem. Phys. 145, 124509 (2016).
Pathak, H. et al. The structural validity of various thermodynamical models of supercooled water. J. Chem. Phys. 145, 134507 (2016).
Luzar, A. et al. Hydrogen-bond kinetics in liquid water. Nature 379, 55–57 (1996).
Luzar, A. & Chandler, D. Effect of environment on hydrogen bond dynamics in liquid water. Phys. Rev. Lett. 76, 928–931 (1996).
Shi, R. & Tanaka, H. Distinct signature of local tetrahedral ordering in the scattering function of covalent liquids and glasses. Sci. Adv. 5, eaav3194 (2019).
Sharma, R., Chakraborty, S. N. & Chakravarty, C. Entropy, diffusivity, and structural order in liquids with waterlike anomalies. J. Chem. Phys. 125, 204501 (2006).
Nayar, D. & Chakravarty, C. Water and water-like liquids: relationships between structure, entropy and mobility. Phys. Chem. Chem. Phys. 15, 14162–14177 (2013).
Ghrist, R. Barcodes: the persistent topology of data. Bull. Amer. Math. Soc. 45, 61–75 (2008).
Bauer, U., Kerber, M. & Reininghaus, J. PHAT (persistent homology algorithm toolbox), v1.5. Bitbucket https://bitbucket.org/phat-code/phat (2018).
Nakamura, T., Hiraoka, Y., Hirata, A., Escolar, E. G. & Nishiura, Y. Persistent homology and many-body atomic structure for medium-range order in the glass. Nanotechnology 26, 304001 (2015).
Hiraoka, Y. et al. Hierarchical structures of amorphous solids characterized by persistent homology. Proc. Natl Acad. Sci. USA 113, 7035–7040 (2016).
Gallet, G. A. & Pietrucci, F. Structural cluster analysis of chemical reactions in solution. J. Chem. Phys. 139, 074101 (2013).
Pipolo, S. et al. Navigating at will on the water phase diagram. Phys. Rev. Lett. 119, 245701 (2017).
Steinhardt, P. J., Nelson, D. R. & Ronchetti, M. Bond-orientational order in liquids and glasses. Phys. Rev. B 28, 784–805 (1983).
Lechner, W. & Dellago, C. Accurate determination of crystal structures based on averaged local bond order parameters. J. Chem. Phys. 129, 114707 (2008).
Martelli, F., Ko, H.-Y., Oğuz, E. C. & Car, R. Local-order metric for condensed-phase environments. Phys. Rev. B 97, 064105 (2018).
Martelli, F., Giovambattista, N., Torquato, S. & Car, R. Searching for crystal-ice domains in amorphous ices. Phys. Rev. Mater. 2, 075601 (2018).
Larsen, P. M., Schmidt, S. & Schiøtz, J. Robust structural identification via polyhedral template matching. Model. Simul. Mater. Sci. Eng 24, 055007 (2016).
Salzmann, C. G., Kohl, I., Loerting, T., Mayer, E. & Hallbrucker, A. Pure ices IV and XII from high-density amorphous ice. Can. J. Phys. 81, 25–32 (2003).
Salzmann, C. G., Mayer, E. & Hallbrucker, A. Effect of heating rate and pressure on the crystallization kinetics of high-density amorphous ice on isobaric heating between 0.2 and 1.9 GPa. Phys. Chem. Chem. Phys. 6, 5156–5165 (2004).
Fang, X. et al. Spatially resolved distribution function and the medium-range order in metallic liquid and glass. Sci. Rep. 1, 194 (2011).
Behler, J. & Parrinello, M. Generalized neural-network representation of high-dimensional potential-energy surfaces. Phys. Rev. Lett. 98, 146401 (2007).
Geiger, P. & Dellago, C. Neural networks for local structure detection in polymorphic systems. J. Chem. Phys. 139, 164105 (2013).
Reinhart, W. F., Long, A. W., Howard, M. P., Ferguson, A. L. & Panagiotopoulos, A. Z. Machine learning for autonomous crystal structure identification. Soft Matter 13, 4733–4745 (2017).
Reinhart, W. F. & Panagiotopoulos, A. Z. Automated crystal characterization with a fast neighborhood graph analysis method. Soft matter 14, 6083–6089 (2018).
Spellings, M. & Glotzer, S. C. Machine learning for crystal identification and discovery. AIChE J. 64, 2198–2206 (2018).
Engel, E. A., Anelli, A., Ceriotti, M., Pickard, C. J. & Needs, R. J. Mapping uncharted territory in ice from zeolite networks to ice structures. Nat. Commun. 9, 2173 (2018).
Tanaka, H. Simple physical model of liquid water. J. Chem. Phys. 112, 799–809 (2000).
Gallo, P. et al. Water: a tale of two liquids. Chem. Rev. 116, 7463–7500 (2016).
Tanaka, H. Two-order-parameter description of liquids: critical phenomena and phase separation of supercooled liquids. J. Phys. Condens. Matter 11, L159–L168 (1999).
Tanaka, H. General view of a liquid-liquid phase transition. Physi Rev. E 62, 6968–6976 (2000).
Tanaka, H. Simple physical explanation of the unusual thermodynamic behavior of liquid water. Phys. Rev. Lett. 80, 5750–5753 (1998).
Tanaka, H. A new scenario of the apparent fragile-to-strong transition in tetrahedral liquids: water as an example. J. Phys. Condens. Matter 15, L703–L711 (2003).
Palmer, J. C., Poole, P. H., Sciortino, F. & Debenedetti, P. G. Advances in computational studies of the liquid–liquid transition in water and water-like models. Chem. Rev. 118, 9129–9151 (2018).
Okabe, A. Spatial Tessellations — Concepts and Applications of Voronoi Diagrams (John Wiley & Sons, 1992).
Sheng, H. W., Luo, W. K., Alamgir, F. M., Bai, J. M. & Ma, E. Atomic packing and short-to-medium-range order in metallic glasses. Nature 439, 419–425 (2006).
Rycroft, C. H. Voro++: a three-dimensional Voronoi cell library in C++. Chaos 19, 041111 (2009).
Faken, D. & Jónsson, H. Systematic analysis of local atomic structure combined with 3d computer graphics. Comput. Mater. Sci. 2, 279–286 (1994).
Honeycutt, J. D. & Andersen, H. C. Molecular dynamics study of melting and freezing of small lennard-jones clusters. J. Phys. Chem. 91, 4950–4963 (1987).
Williams, S. R. Topological classification of clusters in condensed phases. Preprint at arXiv https://arxiv.org/abs/0705.0203?context=cond-mat (2007).
Wales, D. J. & Doye, J. P. Global optimization by basin-hopping and the lowest energy structures of lennard-jones clusters containing up to 110 atoms. J. Phys. Chem. A 101, 5111–5116 (1997).
Wales, D. J. GMIN a program for finding global minima and calculating thermodynamic properties from basin-sampling. GMIN http://www-wales.ch.cam.ac.uk/GMIN/ (2018).
Malins, A., Williams, S. R., Eggers, J. & Royall, C. P. Identification of structure in condensed matter with the topological cluster classification. J. Chem. Phys. 139, 234506 (2013).
Malins, A., Williams, S. R., Eggers, J. & Royall, C. P. Identification of structure in condensed matter with the topological cluster classification. J. Chem. Phys. 139, 234506 (2013).
Hallett, J. E., Turci, F. & Royall, C. P. Local structure in deeply supercooled liquids exhibits growing lengthscales and dynamical correlations. Nat. Commun. 9, 3272 (2018).
Kawasaki, T., Araki, T. & Tanaka, H. Correlation between dynamic heterogeneity and medium-range order in two-dimensional glass-forming liquids. Phys. Rev. Lett. 99, 215701 (2007).
Tanaka, H., Kawasaki, T., Shintani, H. & Watanabe, K. Critical-like behaviour of glass-forming liquids. Nat. Mater. 9, 324–331 (2010).
Kawasaki, T. & Tanaka, H. Structural origin of dynamic heterogeneity in three-dimensional colloidal glass formers and its link to crystal nucleation. J. Phys. Condens. Matter 22, 232102 (2010).
Kawasaki, T. & Tanaka, H. Structural evolution in the aging process of supercooled colloidal liquids. Phys. Rev. E 89, 062315 (2014).
Schröder-Turk, G. E. et al. Disordered spherical bead packs are anisotropic. EPL 90, 34001 (2010).
Kapfer, S. C., Mickel, W., Mecke, K. & Schröder-Turk, G. E. Jammed spheres: minkowski tensors reveal onset of local crystallinity. Phys. Rev. E 85, 030301 (2012).
Mickel, W., Kapfer, S. C., Schröder-Turk, G. E. & Mecke, K. Shortcomings of the bond orientational order parameters for the analysis of disordered particulate matter. J. Chem. Phys. 138, 044501 (2013).
Arai, S. & Tanaka, H. Surface-assisted single-crystal formation of charged colloids. Nat. Phys. 13, 503–509 (2017).
Tong, H. & Tanaka, H. Revealing hidden structural order controlling both fast and slow glassy dynamics in supercooled liquids. Phys. Rev. X 8, 011041 (2018).
Nelson, D. R. Defects and Geometry in Condensed Matter Physics (Cambridge Univ. Press, 2002).
Gellatly, B. J. & Finney, J. L. Characterisation of models of multicomponent amorphous metals: the radical alternative to the voronoi polyhedron. J. Non-Cryst. Solids 50, 313–329 (1982).
Anikeenko, A. V. & Medvedev, N. N. Polytetrahedral nature of the dense disordered packings of hard spheres. Phys. Rev. Lett. 98, 235504 (2007).
Xia, C. et al. The structural origin of the hard-sphere glass transition in granular packing. Nat. Commun. 6, 8409 (2015).
Nelson, D. R. & Spaepen, F. in Solid State Physics, vol. 42, 1–90 (Elsevier, 1989).
Cao, Y. et al. Structural and topological nature of plasticity in sheared granular materials. Nat. Commun. 9, 2911 (2018).
Reichert, H. et al. Observation of five-fold local symmetry in liquid lead. Nature 408, 839–841 (2000).
Goldstein, M. Viscous liquids and the glass transition: a potential energy barrier picture. J. Chem. Phys. 51, 3728–3739 (1969).
Stillinger, F. H. A topographic view of supercooled liquids and glass formation. Science 267, 1935–1939 (1995).
Debenedetti, P. G. & Stillinger, F. H. Supercooled liquids and the glass transition. Nature 410, 259–267 (2001).
Sastry, S. The relationship between fragility, configurational entropy and the potential energy landscape of glass-forming liquids. Nature 409, 164–167 (2001).
Kauzmann, W. The nature of the glassy state and the behavior of liquids at low temperatures. Chem. Rev. 43, 219–256 (1948).
Adam, G. & Gibbs, J. H. On the temperature dependence of cooperative relaxation properties in glass-forming liquids. J. Chem. Phys. 43, 139–146 (1965).
Kirkpatrick, T., Thirumalai, D. & Wolynes, P. G. Scaling concepts for the dynamics of viscous liquids near an ideal glassy state. Phys. Rev. A 40, 1045–1054 (1989).
Sciortino, F., Kob, W. & Tartaglia, P. Inherent structure entropy of supercooled liquids. Phys. Rev. Lett. 83, 3214–3217 (1999).
Berthier, L. et al. Configurational entropy measurements in extremely supercooled liquids that break the glass ceiling. Proc. Natl Acad. Sci. USA 114, 11356–11361 (2017).
Berthier, L. & Biroli, G. Theoretical perspective on the glass transition and amorphous materials. Rev. Mod. Phys. 83, 587–645 (2011).
Nettleton, R. & Green, M. Expression in terms of molecular distribution functions for the entropy density in an infinite system. J. Chem. Phys. 29, 1365–1370 (1958).
Baranyai, A. & Evans, D. J. Direct entropy calculation from computer simulation of liquids. Phys. Rev. A 40, 3817–3822 (1989).
Mountain, R. D. & Raveché, H. J. Entropy and molecular correlation functions in open systems. ii two-and three-body correlations. J. Chem. Phys. 55, 2250–2255 (1971).
Banerjee, A., Sengupta, S., Sastry, S. & Bhattacharyya, S. M. Role of structure and entropy in determining differences in dynamics for glass formers with different interaction potentials. Phys. Rev. Lett. 113, 225701 (2014).
Raveché, H. J. Entropy and molecular correlation functions in open systems. I. Derivation. J. Chem. Phys. 55, 2242–2250 (1971).
Leocmach, M., Russo, J. & Tanaka, H. Importance of many-body correlations in glass transition: an example from polydisperse hard spheres. J. Chem. Phys. 138, 12A536 (2013).
Piaggi, P. M. & Parrinello, M. Entropy based fingerprint for local crystalline order. J. Chem. Phys. 147, 114112 (2017).
Tong, H. & Xu, N. Order parameter for structural heterogeneity in disordered solids. Phys. Rev. E 90, 010401 (2014).
Yang, X., Liu, R., Yang, M., Wang, W.-H. & Chen, K. Structures of local rearrangements in soft colloidal glasses. Phys. Rev. Lett. 116, 238003 (2016).
Zheng, Z. et al. Structural signatures of dynamic heterogeneities in monolayers of colloidal ellipsoids. Nat. Commun. 5, 3829 (2014).
Lubchenko, V. & Wolynes, P. G. Theory of structural glasses and supercooled liquids. Annu. Rev. Phys. Chem. 58, 235–266 (2007).
Kirkpatrick, T. & Thirumalai, D. Colloquium: random first order transition theory concepts in biology and physics. Rev. Mod. Phys. 87, 183–209 (2015).
Bouchaud, J.-P. & Biroli, G. On the adam-gibbs-kirkpatrick-thirumalai-wolynes scenario for the viscosity increase in glasses. J. Chem. Phys. 121, 7347–7354 (2004).
Montanari, A. & Semerjian, G. Rigorous inequalities between length and time scales in glassy systems. J. Stat. Phys. 125, 23–54 (2006).
Franz, S. & Montanari, A. Analytic determination of dynamical and mosaic length scales in a kac glass model. J. Phys. A Math. Theor. 40, F251 (2007).
Cavagna, A., Grigera, T. S. & Verrocchio, P. Mosaic multistate scenario versus one-state description of supercooled liquids. Phys. Rev. Lett. 98, 187801 (2007).
Biroli, G., Bouchaud, J. P., Cavagna, A., Grigera, T. S. & Verrocchio, P. Thermodynamic signature of growing amorphous order in glass-forming liquids. Nat. Phys. 4, 771–775 (2008).
Grigera, T. S. & Parisi, G. Fast monte carlo algorithm for supercooled soft spheres. Phys. Rev. E 63, 045102 (2001).
Hocky, G. M., Markland, T. E. & Reichman, D. R. Growing point-to-set length scale correlates with growing relaxation times in model supercooled liquids. Phys. Rev. Lett. 108, 225506 (2012).
Ozawa, M., Kob, W., Ikeda, A. & Miyazaki, K. Equilibrium phase diagram of a randomly pinned glass-former. Proc. Natl Acad. Sci. USA 112, 6914–6919 (2015).
Kob, W., Roldán-Vargas, S. & Berthier, L. Non-monotonic temperature evolution of dynamic correlations in glass-forming liquids. Nat. Phys. 8, 164–167 (2012).
Berthier, L. & Kob, W. Static point-to-set correlations in glass-forming liquids. Phys. Rev. E 85, 011102 (2012).
Kim, K. Effects of pinned particles on the structural relaxation of supercooled liquids. EPL 61, 790–795 (2003).
Charbonneau, B., Charbonneau, P. & Tarjus, G. Geometrical frustration and static correlations in a simple glass former. Phys. Rev. Lett. 108, 035701 (2012).
Charbonneau, P. & Tarjus, G. Decorrelation of the static and dynamic length scales in hard-sphere glass formers. Phys. Rev. E 87, 042305 (2013).
Cammarota, C., Gradenigo, G. & Biroli, G. Confinement as a tool to probe amorphous order. Phys. Rev. Lett. 111, 107801 (2013).
Russo, J. & Tanaka, H. Assessing the role of static length scales behind glassy dynamics in polydisperse hard disks. Proc. Natl Acad. Sci. USA 112, 6920–6924 (2015).
Yaida, S., Berthier, L., Charbonneau, P. & Tarjus, G. Point-to-set lengths, local structure, and glassiness. Phys. Rev. E 94, 032605 (2016).
Tah, I., Sengupta, S., Sastry, S., Dasgupta, C. & Karmakar, S. Glass transition in supercooled liquids with medium-range crystalline order. Phys. Rev. Lett. 121, 085703 (2018).
Karmakar, S., Dasgupta, C. & Sastry, S. Length scales in glass-forming liquids and related systems: a review. Rep. Prog. Phys. 79, 016601 (2015).
Royall, C. P. & Williams, S. R. The role of local structure in dynamical arrest. Phys. Rep. 560, 1–75 (2015).
Royall, C. P., Turci, F., Tatsumi, S., Russo, J. & Robinson, J. The race to the bottom: approaching the ideal glass? J. Phys. Condens. Matter 30, 363001 (2018).
Kurchan, J. & Levine, D. Order in glassy systems. J. Phys. A Math. Theor. 44, 035001 (2010).
Sausset, F. & Levine, D. Characterizing order in amorphous systems. Phys. Rev. Lett. 107, 045501 (2011).
Dunleavy, A. J., Wiesner, K. & Royall, C. P. Using mutual information to measure order in model glass formers. Phys. Rev. E 86, 041505 (2012).
Jack, R. L., Dunleavy, A. J. & Royall, C. P. Information-theoretic measurements of coupling between structure and dynamics in glass formers. Phys. Rev. Lett. 113, 095703 (2014).
Widmer-Cooper, A., Perry, H., Harrowell, P. & Reichman, D. R. Irreversible reorganization in a supercooled liquid originates from localized soft modes. Nat. Phys. 4, 711–715 (2008).
Manning, M. L. & Liu, A. J. Vibrational modes identify soft spots in a sheared disordered packing. Phys. Rev. Lett. 107, 108302 (2011).
Chen, K. et al. Measurement of correlations between low-frequency vibrational modes and particle rearrangements in quasi-two-dimensional colloidal glasses. Phys. Rev. Lett. 107, 108301 (2011).
Ghosh, A., Chikkadi, V., Schall, P. & Bonn, D. Connecting structural relaxation with the low frequency modes in a hard-sphere colloidal glass. Phys. Rev. Lett. 107, 188303 (2011).
Brito, C. & Wyart, M. Heterogeneous dynamics, marginal stability and soft modes in hard sphere glasses. J. Stat. Mech. Theory Exp. 2007, L08003 (2007).
Schoenholz, S. S., Liu, A. J., Riggleman, R. A. & Rottler, J. Understanding plastic deformation in thermal glasses from single-soft-spot dynamics. Phys. Rev. X 4, 031014 (2014).
Liu, A. J. & Nagel, S. R. The jamming transition and the marginally jammed solid. Annu. Rev. Condens. Matter Phys. 1, 347–369 (2010).
Xu, N., Vitelli, V., Liu, A. J. & Nagel, S. R. Anharmonic and quasi-localized vibrations in jammed solids–modes for mechanical failure. EPL 90, 56001 (2010).
Henkes, S., Brito, C. & Dauchot, O. Extracting vibrational modes from fluctuations: a pedagogical discussion. Soft Matter 8, 6092–6109 (2012).
Yang, X., Tong, H., Wang, W.-H. & Chen, K. Emergence and percolation of rigid domains during colloidal glass transition. Preprint at arXiv https://arxiv.org/abs/1710.08154 (2019).
Cubuk, E. D. et al. Identifying structural flow defects in disordered solids using machine-learning methods. Phys. Rev. Lett. 114, 108001 (2015).
Cubuk, E. et al. Structure-property relationships from universal signatures of plasticity in disordered solids. Science 358, 1033–1037 (2017).
Schoenholz, S. S., Cubuk, E. D., Sussman, D. M., Kaxiras, E. & Liu, A. J. A structural approach to relaxation in glassy liquids. Nat. Phys. 12, 469–471 (2016).
Schoenholz, S. S., Cubuk, E. D., Kaxiras, E. & Liu, A. J. Relationship between local structure and relaxation in out-of-equilibrium glassy systems. Proc. Natl Acad. Sci. USA 114, 263–267 (2017).
Cortes, C. & Vapnik, V. Support-vector networks. Mach. Learn 20, 273–297 (1995).
Starr, F. W., Sastry, S., Douglas, J. F. & Glotzer, S. C. What do we learn from the local geometry of glass-forming liquids? Phys. Rev. Lett. 89, 125501 (2002).
Cohen, M. H. & Grest, G. S. Liquid-glass transition, a free-volume approach. Phys. Rev. B 20, 1077–1098 (1979).
Yoshimoto, K., Jain, T. S., Van Workum, K., Nealey, P. F. & de Pablo, J. J. Mechanical heterogeneities in model polymer glasses at small length scales. Phys. Rev. Lett. 93, 175501 (2004).
Mizuno, H., Mossa, S. & Barrat, J.-L. Measuring spatial distribution of the local elastic modulus in glasses. Phys. Rev. E 87, 042306 (2013).
Matharoo, G. S., Razul, M. S. G. & Poole, P. H. Structural and dynamical heterogeneity in a glass-forming liquid. Phys. Rev. E 74, 050502 (2006).
La Nave, E., Sastry, S. & Sciortino, F. Relation between local diffusivity and local inherent structures in the kob-andersen lennard-jones model. Phys. Rev. E 74, 050501 (2006).
Zylberg, J., Lerner, E., Bar-Sinai, Y. & Bouchbinder, E. Local thermal energy as a structural indicator in glasses. Proc. Natl Acad. Sci. USA 114, 7289–7294 (2017).
Peng, H., Li, M. & Wang, W. Structural signature of plastic deformation in metallic glasses. Phys. Rev. Lett. 106, 135503 (2011).
Hu, Y., Li, F., Li, M., Bai, H. & Wang, W. Five-fold symmetry as indicator of dynamic arrest in metallic glass-forming liquids. Nat. Commun. 6, 8310 (2015).
Sciortino, F. & Kob, W. Debye-waller factor of liquid silica: theory and simulation. Phys. Rev. Lett. 86, 648–651 (2001).
Widmer-Cooper, A. & Harrowell, P. Predicting the long-time dynamic heterogeneity in a supercooled liquid on the basis of short-time heterogeneities. Phys. Rev. Lett. 96, 185701 (2006).
Mosayebi, M., Ilg, P., Widmer-Cooper, A. & Del Gado, E. Soft modes and nonaffine rearrangements in the inherent structures of supercooled liquids. Phys. Rev. Lett. 112, 105503 (2014).
Karmakar, S., Dasgupta, C. & Sastry, S. Growing length and time scales in glass-forming liquids. Proc. Natl Acad. Sci. USA 106, 3675–3679 (2009).
Hu, Y.-C. et al. Configuration correlation governs slow dynamics of supercooled metallic liquids. Proc. Natl Acad. Sci. USA 115, 6375–6380 (2018).
Tsuzuki, H., Branicio, P. S. & Rino, J. P. Structural characterization of deformed crystals by analysis of common atomic neighborhood. Comput. Phys. Commun. 177, 518–523 (2007).
Tong, H., Tan, P. & Xu, N. From crystals to disordered crystals: a hidden order-disorder transition. Sci. Rep. 5, 15378 (2015).
Milkus, R. & Zaccone, A. Local inversion-symmetry breaking controls the boson peak in glasses and crystals. Phys. Rev. B 93, 094204 (2016).
Leocmach, M. & Tanaka, H. Roles of icosahedral and crystal-like order in the hard spheres glass transition. Nat. Commun. 3, 974 (2012).
Ganapathi, D., Nagamanasa, H. H., Sood, A. K. & Ganapathi, R. Measurement of growing surface tension of amorphous-amorphous interfaces on approaching the colloidal glass transition. Nat. Commun. 9, 397 (2018).
Ghosh, A., Chikkadi, V. K., Schall, P., Kurchan, J. & Bonn, D. Density of states of colloidal glasses. Phys. Rev. Lett. 104, 248305 (2010).
Ediger, M. & Harrowell, P. Perspective: supercooled liquids and glasses. J. Chem. Phys. 137, 080901 (2012).
Biroli, G., Karmakar, S. & Procaccia, I. Comparison of static length scales characterizing the glass transition. Phys. Rev. Lett. 111, 165701 (2013).
Watanabe, K., Kawasaki, T. & Tanaka, H. Structural origin of enhanced slow dynamics near a wall in glass-forming systems. Nat. Mater. 10, 512–520 (2011).
Kawasaki, T. & Tanaka, H. Formation of a crystal nucleus from liquid. Proc. Natl Acad. Sci. USA 107, 14036–14041 (2010).
Tan, P., Xu, N. & Xu, L. Visualizing kinetic pathways of homogeneous nucleation in colloidal crystallization. Nat. Phys. 10, 73–79 (2014).
Russo, J. & Tanaka, H. Crystal nucleation as the ordering of multiple order parameters. J. Chem. Phys. 145, 211801 (2016).
Russo, J., Romano, F. & Tanaka, H. Glass forming ability in systems with competing orderings. Phys. Rev. X 8, 021040 (2018).
Charbonneau, P., Kurchan, J., Parisi, G., Urbani, P. & Zamponi, F. Glass and jamming transitions: from exact results to finite-dimensional descriptions. Ann. Rev. Condens. Matter Phys. 8, 265–288 (2017).
Raiteri, P., Laio, A. & Parrinello, M. Correlations among hydrogen bonds in liquid water. Phys. Rev. Lett. 93, 087801 (2004).
Sharma, M., Resta, R. & Car, R. Intermolecular dynamical charge fluctuations in water: a signature of the h-bond network. Phys. Rev. Lett. 95, 187401 (2005).
Matsumoto, M. Relevance of hydrogen bond definitions in liquid water. J. Chem. Phys. 126, 054503 (2007).
Kumar, R., Schmidt, J. & Skinner, J. Hydrogen bonding definitions and dynamics in liquid water. J. Chem. Phys. 126, 05B611 (2007).
Stillinger, F. H. & Rahman, A. Improved simulation of liquid water by molecular dynamics. J. Chem. Phys. 60, 1545–1557 (1974).
Stillinger, F. H. Water revisited. Science 209, 451–457 (1980).
Jorgensen, W. L., Chandrasekhar, J., Madura, J. D., Impey, R. W. & Klein, M. L. Comparison of simple potential functions for simulating liquid water. J. Chem. Phys. 79, 926–935 (1983).
Sciortino, F. & Fornili, S. Hydrogen bond cooperativity in simulated water: time dependence analysis of pair interactions. J. Chem. Phys. 90, 2786–2792 (1989).
Hsu, C. & Rahman, A. Interaction potentials and their effect on crystal nucleation and symmetry. J. Chem. Phys. 71, 4974–4986 (1979).
Swope, W. C. & Andersen, H. C. 106-particle molecular-dynamics study of homogeneous nucleation of crystals in a supercooled atomic liquid. Phys. Rev. B 41, 7042–7054 (1990).
Stukowski, A. Structure identification methods for atomistic simulations of crystalline materials. Model. Simul. Mater. Sci. Eng. 20, 045021 (2012).
Brostow, W., Dussault, J.-P. & Fox, B. L. Construction of voronoi polyhedra. J. Comput. Phys. 29, 81–92 (1978).
Lazar, E. A., Han, J. & Srolovitz, D. J. Topological framework for local structure analysis in condensed matter. Proc. Natl Acad. Sci. USA 112, E5769–E5776 (2015).
van Meel, J. A., Filion, L., Valeriani, C. & Frenkel, D. A parameter-free, solid-angle based, nearest-neighbor algorithm. J. Chem. Phys. 136, 234107 (2012).
Acknowledgements
This study was partially supported by Grants-in-Aid for Specially Promoted Research (grant no. JP25000002) and Scientific Research (A) (18H03675) from the Japan Society for the Promotion of Science (JSPS). J.R. acknowledges support from the European Research Council Grant DLV-759187 and the Royal Society University Research Fellowship.
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Glossary
- Structure factor
-
The two-point correlation function of the Fourier component of the microscopic density.
- Radial distribution function
-
The two-point correlation function of variation of density as a function of distance from a reference particle.
- Directional bondings
-
The bondings between atoms with preferred symmetry and directions.
- Second coordination shell
-
The spherical shell formed by neighbours at a distance between the first and second minima of the radial distribution function from the central molecule, ion or atom.
- Rosenfeld relation
-
The scaling relation between diffusion constant and excess entropy presented by Yaakov Rosenfeld in 1977.
- Disclinations
-
In the description of the melting of 2D crystals, disclinations are elemental topological defects (particles with five or seven neighbours).
- Dislocations
-
Topological defects that consist of pairs of disclinations.
- Kauzmann temperature
-
The temperature at which the extrapolated entropy of the glass becomes smaller than that of the crystal and therefore an ideal glass transition is hypothesized; originated by Walter Kauzmann in 1948.
- Extensive
-
Refers to the relation that a quantity scales proportional to the system size.
- Subextensive
-
Refers to the relation that a quantity scales slower than the system size.
- Isoconfigurational ensemble
-
An ensemble of trajectories that are run from an identical configuration of particles with random initial momenta sampled from the equilibrium Boltzmann distribution.
- Dynamic propensity
-
The mean displacement of individual particles averaged over the isoconfigurational ensemble at the structural relaxation time, describing the tendency of particles’ movement.
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Tanaka, H., Tong, H., Shi, R. et al. Revealing key structural features hidden in liquids and glasses. Nat Rev Phys 1, 333–348 (2019). https://doi.org/10.1038/s42254-019-0053-3
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DOI: https://doi.org/10.1038/s42254-019-0053-3
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