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Part B: Condensed Matter Physics

A one parameter fit for glassy dynamics as a quantum corollary of the liquid to solid transition

Pages 1509-1566 | Received 04 May 2016, Accepted 11 Dec 2016, Published online: 28 Feb 2017

References

  • P.W. Anderson, Through the glass lightly, Science 267 (1995), p. 1615–1616.
  • S.A. Kivelson and G. Tarjus, In search of a theory of supercooled liquids, Nat. Mater. 7 (2008), pp. 831–833.
  • C.A. Angell, Formation of glasses from liquids and biopolymers, Science 267 (1995), pp. 1924–1935.
  • R. Busch, The thermophysical properties of bulk metallic glass-forming liquids, J. Minerals Metals Mater. Soc. 52 (2000), pp. 39–42.
  • G. Adam and J.H. Gibbs, On the temperature dependence of cooperative relaxation properties in glass-forming liquids, J. Chem. Phys. 43 (1965), pp. 139–146.
  • T.R. Kirkpatrick, D. Thirumalai, and P.G. Wolynes, Scaling concepts for the dynamics of viscous liquids near an ideal glassy state, Phys. Rev. A 40 (1989), pp. 1045–1054.
  • G. Parisi and M. Mezard, A first-principle computation of the thermodynamics of glasses, J. Chem. Phys. 111 (1999), pp. 1076–1095.
  • X. Xia and P.G. Wolynes, Fragilities of liquids predicted from the random first order transition theory of glasses, Proc. Nat. Acad. Sci. USA 97 (2000), pp. 2990–2994.
  • M.H. Cohen and G.S. Grest, Liquid--glass transition, a free-volume approach, Phys. Rev. B 20 (1979), pp. 1077–1098; G.S. Grest and M.H. Cohen, Liquid--glass transition: Dependence of the glass transition on heating and cooling rates, Phys. Rev. B 21 (1980), pp. 4113–4117; G.S. Grest and M.H. Cohen, Liquids, glasses, and the glass transition: A free-volume approach, Adv. Chem. Phys. 48 (1981), pp. 455–525; M.H. Cohen and G.S. Grest, The nature of the glass transition, J. Non-Crystaline Solids 61/62 (1984), pp. 749–759.
  • V. Lubchenko and P.G. Wolynes, Theory of structural glasses and supercooled liquids, Annu. Rev. Phys. Chem. 58 (2007), pp. 235–266.
  • F. Stillinger and P.G. Debenedetti, Glass transition thermodynamics and Kinetics, Annu. Rev. Condensed Matter Phys. 4 (2013), pp. 263–285.
  • J.S. Langer, Theories of glass formation and the glass transition, Rep. Progress Phys. 77 (2014), p. 042501. (12 pages).
  • G. Tarjus, preprint (2010). Available at arXiv:1010.2938.
  • L. Berthier and G. Biroli, Theoretical perspective on the glass transition and amorphous materials, Rev. Modern Phys. 83 (2011), pp. 587–645.
  • S. Sastry, P.G. Debenedetti, and F.H. Stillinger, Signatures of distinct dynamical regimes in the energy landscape of a glass-forming liquid, Nature 393 (1998), pp. 554–557.
  • W. Gotze, Aspects of structural glass transitions, in Liquids, Freezing and the Glass Transition, J.P. Hansen, D. Levesque, and J. Zinn-Justin, eds., North-Holland, Amsterderm, 1991, pp. 287–503.
  • S.P. Das, Mode-coupling theory and the glass transition in supercooled liquids, Rev. Modern Phys. 76 (2004), pp. 785–851.
  • Y.S. Elmatad, R.L. Jack, D. Chandler, and J.P. Garrahan, Finite-temperature critical point of a glass transition, Proc. Nat. Acad. Sci. USA 107 (2010), pp. 12793–12798.
  • Y.S. Elmatad, D. Chandler, and J.P. Garrahan, Corresponding states of structural glass formers, J. Phys. Chem. B 113 (2009), pp. 5563–5567; Y.S. Elmatad, D. Chandler, and J.P. Garrahan, Corresponding states of structural glass formers. II, J. Phys. Chem. B 114 (2010), pp. 17113–17119.
  • C.S. O’Hern, S.A. Langer, A.J. Liu, and S.R. Nagel, Force distributions near jamming and glass transitions, Phys. Rev. Lett. 86 (2001), pp. 111–114; G. Parisi and F. Zamponi, Mean-field theory of hard sphere glasses and jamming, Rev. Modern Phys. 82 (2010), pp. 789–845; P. Charbonneau, J. Kurchan, G. Parisi, P. Urbani, and F. Zamponi, Fractal free energy landscapes in structural glasses, Nat. Commun. 5 (2014), p. 3725 (6 pages).
  • P. Charbonneau, J. Kurchan, G. Parisi, P. Urbani, F. Zamponi, P. Charbonneau, J. Kurchan, G. Parisi, P. Urbani, and F. Zamponi, Glass and jamming transitions: From exact results to finite-dimensional descriptions, Annu. Rev. Condensed Matter Phys. 8, in press (2017). Available at arXiv: 1605.03008.
  • M.A. Moore and J. Yeo, Thermodynamic glass transition in finite dimensions, Phys. Rev. Lett. 96 (2006), p. 095701 (4 pages).
  • J.C. Mauro, Y. Yue, A.J. Ellison, P.K. Gupta, and D.C. Allan, Viscosity of glass-forming liquids, Proc. Nat. Acad. Sci. USA 106 (2009), pp. 19780–19784.
  • M.D. Demetriou, J.S. Harmon, M. Tao, G. Duan, K. Samwer, and W.L. Johnson, Cooperative shear model for the rheology of glass-forming metallic liquids, Phys. Rev. Lett. 97 (2006), p. 065502 (4 pages).
  • D. Kivelson, S.A. Kivelson, X. Zhao, Z. Nussinov, and G. Tarjus, A thermodynamic theory of supercooled liquids, Physica A 219 (1995), pp. 27–38.
  • Z. Nussinov, Avoided phase transitions and glassy dynamics in geometrically frustrated systems and non-Abelian theories, Phys. Rev. B 69 (2004), p. 014208 (25 pages).
  • G. Tarjus, S.A. Kivelson, Z. Nussinov, and P. Viot, The frustration-based approach of supercooled liquids and the glass transition: A review and critical assessment, J. Phys. Condensed Matter 17 (2005), pp. R1143–R1182.
  • H. Vogel, The temperature dependence law of the viscosity of fluids, Physikalische Zeitscrift 22(645) (1921), pp. 645–646; G.S. Fulcher, Analysis of recent measurements of the viscosity of glasses, J. Amer. Ceramic Soc. 8 (1925), pp. 339–355; G. Tammann and W.Z. Hesse, The dependancy of viscosity on temperature in hypothermic liquids, Z. Anorganische Allgemeine Chem. 156 (1926), p. 245.
  • J. Rault, Origin of the Vogel--Fulcher--Tammann law in glass-forming materials: The alpha--beta bifurcation, J. Non-Crystalline Solids 271 (2000), pp. 177–217.
  • W.M. Saslow, Scenario for the Vogel--Fulcher “law”, Phys. Rev. B 37 (1988), pp. 676(R)–678(R).
  • L.S. Garca-Colin, L.F. del Castillo, and P. Goldstein, Theoretical basis for the Vogel--Fulcher--Tammann equation, Phys. Rev. B 40 (1989), pp. 7040–7044.
  • S.R. Nagel and P.K. Dixon, Relation between stretched-exponential relaxation and Vogel-Fulcher behavior above the glass transition, J. Chem. Phys. 90 (1989), pp. 3885–3886.
  • J. Zhao, S.L. Simon, and G.B. McKenna, Using 20-million-year-old amber to test the super-Arrhenius behaviour of glass-forming systems, Nat. Commun. 4 (2013), p. 1783 (6 pages).
  • K. Huang, Statistical Mechanics, John Wiley & Sons, New York 1987. ISBN: 0471815187.
  • K. Binder and A.P. Young, Spin glasses: Experimental facts, theoretical concepts, and open questions, Rev. Modern Phys. 58 (1986), pp. 801–976.
  • M. Mezard, G. Parisi, and M.A. Virasoro, Spin glass theory and beyond, World Scientific, Singapore, 1987.
  • J.M. Deutsch, Quantum statistical mechanics in a closed system, Phys. Rev. A 43 (1991), pp. 2046–2049.
  • M. Srednicki, Chaos and quantum thermalization, Phys. Rev. E 50 (1994), pp. 888–901.
  • M. Rigol, V. Dunjko, and M. Olshanii, Thermalization and its mechanism for generic isolated quantum systems, Nature 452 (2008), pp. 854–858.
  • M. Rigol, Breakdown of thermalization in finite one-dimensional systems, Phys. Rev. Lett. 103 (2009), p. 100403 (4 pages).
  • A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalattore, Colloquium: Nonequilibrium dynamics of closed interacting quantum systems, Rev. Modern Phys. 83 (2011), pp. 863–883.
  • L.F. Santos, A. Polkovnikov, and M. Rigol, Entropy of isolated quantum systems after a quench, Phys. Rev. Lett. 107 (2011), p. 040601. (4 pages).
  • L. D’Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics, Adv. Phys. 65 (2016), pp. 239–362.
  • J. von Neumann, Proof of the Ergodic theorem and the H-Theorem in the new Mechanics, Z. Phys. 57 (1929), pp. 30–70; English translation by R. Tumulka, J. Eur. Phys. H 35 (2010), pp. 201–237; P. Reimann, Generalization of von Neumann’s approach to thermalization, Phys. Rev. Lett. 115 (2015), p. 010403 (5 pages).
  • D. Basko, I. Aleiner, and B. Altshuler, Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states, Ann. Phys. 321 (2006), pp. 1126–1205; D. Basko, I. Aleiner, and B. Altshuler, Possible experimental manifestations of the many-body localization, Phys. Rev. B 76 (2007), p. 052203 (4 pages).
  • V. Oganesyan and D.A. Huse, Localization of interacting fermions at high temperature, Phys. Rev. B 75 (2007), p. 155111 (5 pages).
  • R. Vosk and E. Altman, Many-body localization in one dimension as a dynamical renormalization group fixed point, Phys. Rev. Lett. 110 (2013), p. 067204 (5 pages). E. Altman and R. Vosk, Universal dynamics and renormalization in many-body-localized systems, Annu. Rev. Condensed Matter Phys. 6 (2015), pp. 383–409.
  • J.Z. Imbrie, On many-body localization for quantum spin chains, J. Stat. Phys. 163 (2016), pp. 998–1048.
  • R. Nandkishore and D.A. Huse, Many-body localization and thermalization in quantum statistical mechanics, Annu. Rev. Condensed Matter Phys. 6 (2015), pp. 15–38.
  • M. Schreiber, S.S. Hodgman, P. Bordia, H.P. Luschen, M.H. Fischer, R. Vosk, E. Altman, U. Schneider, and I. Bloch, Observation of many-body localization of interacting fermions in a quasirandom optical lattice, Science 349 (2015), pp. 842–845.
  • E. Rossler and H. Sillescu, Organic glasses and polymers, in Materials Science and Technology, Wiley Online Library, 2006. doi:10.1002/9783527603978.mst0100, ISBN: 3527313958.
  • R. Soklaski, V. Tran, Z. Nussinov, K.F. Kelton, and L. Yang, A locally preferred structure characterises all dynamical regimes of a supercooled liquid, Philos. Mag. 96 (2016), pp. 1212–1227.
  • A. Jaiswal, T. Egami, and Y. Zhang, Atomic-scale dynamics of a model glass-forming metallic liquid: Dynamical crossover, dynamical decoupling, and dynamical clustering, Phys. Rev. B 91 (2015), p. 134204 (14 pages).
  • A.O. Caldeira and A.J. Leggett, Quantum tunneling in a dissipative system, Ann. Phys. 149 (1983), pp. 374–456; A.O. Caldeira and A.J. Leggett, Influence of dissipation on quantum tunneling in macroscopic systems, Phys. Rev. Lett. 46 (1981), pp. 211–214; A.O. Caldeira and A.J. Leggett, Path integral approach to quantum Brownian motion, Physica A 121 (1983), pp. 587–616.
  • I. M. Hodge, Physical Aging in Polymer Glasses, Science 267 (1995), pp. 1945–1947.
  • A. Mashur, T. A. Waniuk, R. Busch, and W. L. Johnson, Time scales for Viscous Flow, Atomic Transport, and Crystallization in the Liquid and Supercooled Liquid States of Zr41:2Ti13:8Cu12:5Ni10:0Be22:5, Phys. Rev. Lett. 82 (1999), pp. 2290 (4 pages); A. L. Greer, New horizons forglass formation and stability, Nat. Mater. 14 (2015), pp. 542--546.
  • N.B. Weingartner, R. Soklaski, K.F. Kelton, and Z. Nussinov, Dramatically growing shear rigidity length scale in the supercooled glass former NiZr2, Phys. Rev. B 93 (2016), p. 214201.
  • N.B. Weingartner and Z. Nussinov, Probing local structure in glass by the application of shear, J. Stat. Mech. (2016), p. 094001.
  • N.B. Weingartner and Z. Nussinov, in preparation.
  • M. Born and V.A. Fock, Proof of Adiabatic law, Z. Phys. A 51 (1928), pp. 165–180; T. Kato, On the adiabatic theorem of quantum mechanics, J. Phys. Soc. Japan 5 (1950), pp. 435–439; J.E. Avron and A. Elgart, Adiabatic theorem without a gap condition, Commun. Math. Phys. 203 (1999), pp. 445–463; G. Rigolin and G. Ortiz, Proof of Adiabatic law, Phys. Rev. A 85 (2012), p. 062111 (4 pages).
  • N. Goldenfeld, Lectures on phase transitions and the renormalization group, Frontiers in Physics (book 85), Westview Press, Boulder (1992), ISBN: 0-201-55408-9.
  • N. Weingartner, C. Pueblo, F.S. Nogueira, K.F. Kelton, and Z. Nussinov, preprint (2015), Available at arXiv:1512.04565.
  • N. Weingartner, C. Pueblo, F.S. Nogueira, K. F. Kelton, and Z. Nussinov, preprint (2016). Available at arXiv: 1607.08625.
  • Z. Nussinov, F.S. Nogueira, M. Blodgett, and K.F. Kelton, preprint (2014). Available at arXiv:1409.1915.
  • N. Weingartner, C. Pueblo, F. S. Nogueira, K. F. Kelton, and Z. Nussinov, A phase space approach to supercooled liquids and a universal collapse of their viscosity, Front. Mater. 3 (2016), 50 (12 pages).
  • D.W. Davidson and R.H. Cole, Dielectric relaxation in glycerine, J. Chem. Phys. 18 (1950), p. 1417–1418; D.W. Davidson and R.H. Cole, Dielectric relaxation in glycerol, propylene glycol, and n-propanol, J. Chem. Phys. 19 (1951), p. 1484–1490.
  • N.W. Aschcroft and N.D. Mermin, Solid State Physics, Harcourt College Publishers, Fort Worth, 1976.
  • M. Blodgett, T. Egami, Z. Nussinov, and K.F. Kelton, Proposal for universality in the viscosity of metallic liquids, Sci. Rep. 5 (2015), p. 13837 (8 pages).
  • J.F. Stebbins, I.S.E. Carmichael, and D.E. Weill, The high-temperature liquid and glass heat contents and the heats of fusion of diopside, albite, sanidine, and nepheline, Amer. Mineralogist 68 (1983), pp. 717–730.
  • C. Austin Angell, Heat capacity and entropy functions in strong and Fragile glass-formers, relative to those of disordering crystalline materials, in Glassy, Amorphous and Nano-crystalline Materials: Thermal Physics, Analysis, Structure and Properties, Chapter 2, Vol. 8, Hot topics in thermal analysis and calorimetry, J. Sesták, J.J. Mare, and P. Hubk, eds., Springer, Dordrecht, London, 2011.
  • V. Paulauskas and A. Rackauskas, Approximation Theory in the Central Limit Theorem: Exact Results in Banach Spaces, Kluwer Academic Publishers, Dordrecht, 2012.
  • Z. Nussinov, preprint (2015). Available at arXiv:1510.03875.
  • E.T. Jaynes, Information theory and statistical mechanics, Phys. Rev. 106 (1957), pp. 620–630; E.T. Jaynes, Information theory and statistical mechanics 2, Phys. Rev. 108 (1957), pp. 171–190.
  • S. Sastry, Inherent structure approach to the study of glass-forming liquids, Phase Transitions 75 (2002), pp. 507–517.
  • N. Weingartner, F.S. Nogueira, and Z. Nussinov, in preparation.
  • Y.H. Liu, D. Wang, K. Nakajima, W. Zhang, A. Hirata, T. Nishi, A. Inoue, and M.W. Chen, Characterization of nanoscale mechanical heterogeneity in a metallic glass by dynamic force microscopy, Phys. Rev. Lett. 106 (2011), p. 125504.
  • N.F. Mott, Absence of diffusion in certain random lattices, Phys. Rev. 109 (1958), pp. 1492–1505; P.W. Anderson, Absence of diffusion in certain random lattices, Adv. Phys. 16 (1967), pp. 49–144.
  • H. Sillescu, Heterogeneity at the glass transition: A review, J. Non-Crystalline. Solids 243 (1999), pp. 81–108; M.D. Ediger, Spatially heterogeneous dynamics in supercooled liquids, Annu. Rev. Phys. Chem. 51 (2000), pp. 99–128; R. Richert, Heterogeneous dynamics in liquids: Fluctuations in space and time, J. Phys.: Condensed Matter 14 (2002), pp. R703–R703; W. Kob, C. Donati, S.J. Plimpton, P.H. Poole, and S.C. Glotzer, Dynamical heterogeneities in a supercooled Lennard--Jones liquid, Phys. Rev. Lett. 79 (1997), pp. 2827–2830; C. Donati, J.F. Douglas, W. Kob, S.J. Plimpton, P.H. Poole, and S.C. Glotzer, Stringlike cooperative motion in a supercooled liquid, Phys. Rev. Lett. 80 (1998), pp. 2338–2341; S.C. Glotzer, Spatially heterogeneous dynamics in liquids: Insights from simulation, J. Non-Crystalline Solids 274 (2000), pp. 342–355; Y. Gebremichael, T.B. Schroder, F.W. Starr, and S.C. Glotzer, Spatially correlated dynamics in a simulated glass-forming polymer melt: Analysis of clustering phenomena, Phys. Rev. E 64 (2001), pp. 051503 (13 pages).
  • A. Aharony and A.B. Harris, Absence of self-averaging and universal fluctuations in random systems near critical points, Phys. Rev. Lett. 77 (1996), pp. 3700–3703.
  • P.H. Lundow and I.A. Campbell, Non-self-averaging in Ising spin glasses and hyperuniversality, Phys. Rev. E. 93 (2016), p. 012118 (10 pages).
  • K.F. Kelton, G.W. Lee, A.K. Gangopadhyay, R.W. Hyers, T.J. Rathz, J.R. Rogers, M.B. Robinson, and D.S. Robinson, First X-ray scattering studies on electrostatically levitated metallic liquids: Demonstrated influence of local icosahedral order on the nucleation barrier, Phys. Rev. Lett. 90 (2003), p. 195504 (4 pages); T. Schenk, D. Holland-Moritz, V. Simonet, R. Bellissent, and D.M. Herlach, Icosahedral shortrange order in deeply undercooled metallic melts, Phys. Rev. Lett. 89 (2002), p. 075507 (4 pages); F.C. Frank, Supercooling of liquids, Proc. Roy. Soc. A 215 (1952), pp. 43–46.
  • J.F. Sadoc and R. Mosseri, Geometric Frustration, Cambridge University Press, Cambridge, 1999; D.R. Nelson, Defects and Geometry, Cambridge University Press, Cambridge, 2002; F.C. Frank and J.S. Kasper, Complex alloy structures regarded as sphere packings. I. Definitions and basic principles, Acta Crystallogr. 11 (1958), p. 184–190; F.C. Frank and J.S. Kasper, Complex alloy structures regarded as sphere packings. II. Analysis and classification of representative structures, Acta Crystallogr. 12 (1959), pp. 483–499; D.R. Nelson and J.S. Kasper, Order, frustration, and defects in liquids and glasses, Phys. Rev. B 28 (1983), pp. 5515–5535; J.F. Sadoc, Periodic networks of disclination lines -- Applications to metal structures, J. Phys. 44 (1983), pp. L707–L715; J.F. Sadoc, Frustration, curvature, and defect lines in metallic glasses and the cholesteric blue phase, Phys. Rev. B 31 (1985), pp. 6278–6297; J.F. Sadoc and J. Charvolin, Frustration in bilayers and topologies of liquid crystals of amphiphilic molecules, J. Phys. 47 (1986), pp. 683–691; S. Sachdev and D.R. Nelson, Statistical mechanics of pentagonal and icosahedral order in dense liquids, Phys. Rev. B 32 (1985), pp. 1480–1502; D.R. Nelson and M. Widom, Symmetry, Landau theory and polytope models of glass, Nuclear Phys. B 240 (1984), p. 113–139.
  • Y. Kohsaka, C. Taylor, K. Fujita, A. Schmidt, C. Lupien, T. Hanaguri, M. Azuma, M. Takano, H. Eisaki, H. Takagi, S. Uchida, and J.C. Davis, An intrinsic bond-centered electronic glass with unidirectional domains in underdoped cuprates, Science 315 (2007), pp. 1380–1385.
  • D. Coslovich, Locally preferred structures and many-body static correlations in viscous liquids, Phys. Rev. E 83 (2011), Article ID: 051505.
  • A. Malins, J. Eggers, S.R. Williams, C.P. Royall, and H. Tanaka, Identification of long-lived clusters and their link toslow dynamics in a model glass, J. Chem. Phys. 138 (2013), Article ID: 12A535.
  • C.A. Angell, Entropy and fragility in supercooling liquids, J. Res. Nat. Inst. Standards Technol. 102 (1997), pp. 171–185; R. Richert and C.A. Angell, Dynamics of glass-forming liquids. V. On the link between molecular dynamics and configurational entropy, J. Chem. Phys. 108 (1998), pp. 9016–9026.
  • A. Agrawal, R. Mishra, K.M. Flores, and W. Windl, Structure evolution of Cu--Zr--Ti metallic glasses, Bulk Metallic Glasses XI, St. Louis, June 2016.
  • W.A. Phillips, Rep. Progress Phys. 50 (1987), p. 1657–1708.
  • P.W. Anderson, B.I. Halperin, and C.M. Varma, Anomalous low-temperature thermal properties of glasses and spin glasses, Philos. Mag. 25 (1972), pp. 1–9.
  • A. Gaita-Arino and M. Schechter, Identification of strong and weak interacting two-level systems in KBr:CN, Phys. Rev. Lett. 107 (2011), p. 105504 (5 pages).
  • D.C. Vural and A.J. Leggett, Universal sound absorption in amorphous solids: A theory of elastically coupled generic blocks, J. Non-Crystalline Solids 357 (2011), pp. 3528–3537.
  • S. Sastry and C.A. Angell, Liquid-liquid phase transition in supercooled silicon, Nat. Mater. 2 (2003), pp. 739–743.
  • H.G.E. Hentschel, S. Karmakar, I. Procaccia, and J. Zylberg, Relaxation mechanisms in glassy dynamics: The Arrhenius and fragile regimes, Phys. Rev. E 85 (2012), p. 061501 (8 pages).
  • S. Horvat, E. Czabarka, and Z. Toroczkai, Reducing degeneracy in maximum entropy models of networks, Phys. Rev. Lett. 114 (2015), p. 158701 (5 pages).
  • F. Sausset, G. Biroli, and J. Kurchan, Do solids flow? J. Stat. Phys. 140 (2010), pp. 718–727.
  • F. Leyvraz and S. Ruffo, Ensemble inequivalence in systems with long-range interactions, J. Phys. A -- Math. Gen. 35 (2002), pp. 285–294.
  • J. Barre, D. Mukamel, and S. Ruffo, Inequivalence of ensembles in a system with long-range Interactions, Phys. Rev. Lett. 87 (2001), p. 030601.
  • A. Campa, T. Dauxois, and S. Ruffo, Statistical mechanics and dynamics of solvable models with long-range interactions, Phys. Rep. 480 (2009), pp. 57–159 (4 pages).
  • Y. Murata and H. Nishimori, Ensemble inequivalence in the spherical spin glass model with nonlinear interactions, J. Phys. Soc. Japan 81 (2012), p. 114008 (7 pages).
  • S.F. Swallen, K.L. Kearns, M.K. Mapes, Y.S. Kim, R.J. McMahon, M.D. Ediger, T. Wu, L. Yu, and S. Satija, Organic glasses with exceptional thermodynamic and kinetic stability, Science 315 (2007), pp. 353–356.

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