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Poisson's ratio and modern materials

Nature Materials volume 10, pages 823–837 (2011)Cite this article

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An Author Correction to this article was published on 21 February 2019

A Corrigendum to this article was published on 23 November 2011

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Abstract

In comparing a material's resistance to distort under mechanical load rather than to alter in volume, Poisson's ratio offers the fundamental metric by which to compare the performance of any material when strained elastically. The numerical limits are set by ½ and −1, between which all stable isotropic materials are found. With new experiments, computational methods and routes to materials synthesis, we assess what Poisson's ratio means in the contemporary understanding of the mechanical characteristics of modern materials. Central to these recent advances, we emphasize the significance of relationships outside the elastic limit between Poisson's ratio and densification, connectivity, ductility and the toughness of solids; and their association with the dynamic properties of the liquids from which they were condensed and into which they melt.

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Figure 1: Poisson's ratio: physical significance, materials characteristics and the Milton map.
Figure 2: Varying Poisson's ratio structurally.
Figure 3: Poisson's ratio and atomic packing.
Figure 4: Connectivity in glasses and liquids.
Figure 5: Poisson's ratio and phase transformations.
Figure 6: Indentation of glasses: densification or shear flow.
Figure 7: Poisson's ratio, non-ergodicity and fracture toughness.
Figure 8: Boson peak and melt fragility.

Change history

  • 24 October 2011

    In the print version of this Review, in Box 2, 'an order of magnitude' should read 'orders of magnitude' in the sixth sentence from the end. In the caption for Fig. 1, the credit given for part a actually related to part b. In Fig. 5c, the arrow labels for the inner and outer core are transposed. In the Acknowledgements, C. Kurkjian is spelt incorrectly. The online versions are correct.

References

  1. http://gallica.bnf.fr/.

  2. Poisson, S. D. Traité de Mécanique 2, 476 (1811).

    Google Scholar 

  3. Poisson, S. D. Ann. Chim. Phys. (eds Gay-Lussac, L. J. & Arago, F.) 36, 384–385 (1827).

    Google Scholar 

  4. Cauchy, A. L. Sur les équations qui expriment les conditions d'équilibre, ou les lois du mouvement intérieur d'un corps solide élastique ou non élastique. Exercices de Mathématiques vol. 3 (1828).

  5. Voigt, W. Allgemeine Formeln für die Bestimmung der Elasticitätsconstanten von Krystallen durch die Beobachtung der Biegung und Drillung von Prismen. Ann. Phys. 16, 273–310; 398–415 (1882).

    Article  Google Scholar 

  6. Love, A. E. H. A Treatise on the Mathematical Theory of Elasticity (Dover, 1944).

    Google Scholar 

  7. Haeri, A. Y., Weidner, D. J. & Parise, J. B. Elasticity of α-cristobalite: a silicon dioxide with a negative Poisson's ratio. Science 257, 650–652 (1992).

    Article  Google Scholar 

  8. Evans, K. E., Nkansah, M. A., Hutchinson, I. J. & Rogers, S. C. Molecular network design, Nature 353, 124, (1991). This paper introduces the term auxetic, from the root word for growth, to describe expansion under tension.

    Article  CAS  Google Scholar 

  9. Lakes, R. S. Foam structures with a negative Poisson's ratio. Science 235, 1038–1040 (1987).

    Article  CAS  Google Scholar 

  10. Caddock, B. D. & Evans, K. E. Microporous materials with negative Poisson's ratios. I: Microstructure and mechanical properties. J. Phys. D. 22, 1877–1882 (1989).

    Article  CAS  Google Scholar 

  11. Milton, G. Composite materials with Poisson's ratios close to −1. J. Mech. Phys. Solids 40, 1105–1137 (1992).

    Article  Google Scholar 

  12. Lakes, R. S. Advances in negative Poisson's ratio materials. Adv. Mater. 5, 293–296 (1993).

    Article  CAS  Google Scholar 

  13. Alderson, K. L. & Evans, K. E. The fabrication of microporous polyethylene having negative Poisson's ratio. Polymer, 33, 4435–4438 (1992).

    Article  CAS  Google Scholar 

  14. Baughman, R. H., Shacklette, J-M., Zakhidev, A. A. & Stafström, S. Negative Poisson's ratio as a common feature of cubic metals. Nature 392, 362–365 (1998).

    Article  CAS  Google Scholar 

  15. Sanchez-Valle, C. et al. Negative Poisson's ratios in siliceous zeolite MFI-silicalite. J. Chem. Phys. 128, 184503 (2008).

    Article  CAS  Google Scholar 

  16. Hall, L. J. et al. Sign change of Poisson's ratio for carbon nanotube sheets, Science 320, 504–507 (2008).

    Article  CAS  Google Scholar 

  17. Smith, C. W., Wootton, R. J. & Evans, K. E. Interpretation of experimental data for Poisson's ratio of highly nonlinear materials. Exp. Mech. 39, 356–362 (1999).

    Article  Google Scholar 

  18. Tschoegl, N. W., Knauss, W. J. & Emri, I. Poisson's ratio in linear viscoelasticity, a critical review. Mech. Time-Depend. Mater. 6, 3–51 (2002).

    Article  Google Scholar 

  19. Lakes, R. S. & Wineman, A. On Poisson's ratio in linearly viscoelastic solids. J. Elast. 85, 46–63 (2006).

    Article  Google Scholar 

  20. Lu, H., Zhang, X. & Krauss, W. G. Uniaxial, shear, and Poisson relaxation and their conversion to bulk relaxation: studies on poly(methyl methacrylate). Polym. Eng. Sci. 37, 1053–1064 (1997).

    Article  CAS  Google Scholar 

  21. http://www.youtube.com/watch?v=BN2D5y-AxIY.

  22. Wang, Y. C. & Lakes, R. S. Composites with inclusions of negative bulk modulus: extreme damping and negative Poisson's ratio. J. Comp. Mater. 39, 1645–1657 (2005).

    Article  CAS  Google Scholar 

  23. Smith, C. W., Grima, J. N. & Evans, K. E., A novel mechanism for generating auxetic behaviour in reticulated foams: missing rib foam model. Acta. Mater. 48, 4349–4356 (2000).

    Article  CAS  Google Scholar 

  24. Baughman, R. H. et al. Negative Poisson's ratios for extreme states of matter. Science 288, 2018–2022 (2000).

    Article  CAS  Google Scholar 

  25. Grima, J. N., Jackson, R., Alderson, A. & Evans, K. E. Do zeolites have negative Poisson's ratios? Adv. Mater. B 12, 1912–1918 (2000).

    Article  CAS  Google Scholar 

  26. Poirier, J-P. Introduction to the Physics of the Earth's Interior (Cambridge Univ. Press, 2000).

    Book  Google Scholar 

  27. Cohen, M. L. Calculation of bulk moduli of diamond and zinc–blende solids. Phys. Rev. B 32, 7988–7991 (1985).

    Article  CAS  Google Scholar 

  28. Fukumoto, A. First-principles pseudopotential calculations of the elastic properties of diamond, Si, and Ge. Phys. Rev. B 42, 7462–7469 (1990).

    Article  CAS  Google Scholar 

  29. Perottoni, C. A. & Da Jornada, J. A. H. First-principles calculation of the structure and elastic properties of a 3D-polymerized fullerite. Phys. Rev. B 65, 224208 (2002).

    Article  CAS  Google Scholar 

  30. Cottrell, A. H. in Advances in Physical Metallurgy (eds Charles, J. A. & Smith, G. C.) (Inst. Metals, London, 1990).

    Google Scholar 

  31. Kelly, A., Tyson, W. R. & Cottrell, A. H. Ductile and brittle crystals. Phil. Mag. 15, 567–586 (1967).

    Article  CAS  Google Scholar 

  32. Jiang, M. Q. & Dai, L. H. Short-range-order effects on the intrinsic plasticity of metallic glasses. Phil. Mag. Lett. 90, 269–277 (2010).

    Article  CAS  Google Scholar 

  33. McQueen, R. G., Hopson, J. W. & Fritz, J. N. Optical technique for determining rarefaction wave velocities at very high pressures. Rev. Sci. Instrum. 53, 245–250 (1982).

    Article  Google Scholar 

  34. Santamaría-Pérez, D. et al. X-ray diffraction measurements of Mo melting at 119 GPa and the high pressure phase diagram. J. Chem. Phys. 130, 124509 (2009).

    Article  CAS  Google Scholar 

  35. Hixson, R. S., Boness, D. A. & Shaner, J. W., Acoustic velocities and phase transitions in molybdenum under strong shock compression. Phys. Rev. Lett. 62, 637–640 (1989).

    Article  CAS  Google Scholar 

  36. Nguyen, J. H. & Holmes, N. C. Melting of iron at the physical conditions of the Earth's core. Nature 427, 339–342 (2004).

    Article  CAS  Google Scholar 

  37. Jensen, B. J., Cherne, F. J. & Cooley, J. C. Shock melting of cerium. Phys. Rev. B 81, 214109 (2010).

    Article  CAS  Google Scholar 

  38. Greaves, G. N. et al. Zeolite collapse and polyamorphism. J. Phys. Cond. Mat. 19, 415102 (2007).

    Article  CAS  Google Scholar 

  39. Zha, C-S., Hemley, R. J., Mao, H-K., Duffy, T. S. & Meade, C. Acoustic velocities and refractive index of SiO2 glass to 57.5 GPa by Brillouin scattering. Phys. Rev. B 50, 13105–13112 (1994).

    Article  CAS  Google Scholar 

  40. Zeng, Z-Y., Hu, C-E., Cai L-C., Chen, X-R. & Jing, F-Q. Lattice dynamics and thermodynamics of molybdenum from first-principles calculations. J. Phys. Chem. B 114, 298–310 (2010).

    Article  CAS  Google Scholar 

  41. Davies, R. A. et al. Geometric, electronic and elastic properties of dental silver amalgam γ-(Ag3Sn), γ1-(Ag2Hg3), γ2-(Sn8Hg) phases, comparison of experiment and theory. Intermetallics 18, 756–760 (2010).

    Article  CAS  Google Scholar 

  42. Rouxel, T. Elastic properties and short-to-medium range order in glasses. J. Am. Ceram. Soc. 90, 3019–3039 (2007).

    Article  CAS  Google Scholar 

  43. Makishima, A. & Mackenzie, J. D. Calculation of bulk modulus, shear modulus and Poisson's ratio of glass. J. Non-Cryst. Sol. 17, 147–157 (1975).

    Article  CAS  Google Scholar 

  44. Antao, S. M. et al. Network rigidity in GeSe2 glass at high pressure. Phys. Rev. Lett. 100, 115501 (2008).

    Article  CAS  Google Scholar 

  45. Nicholas, J., Sinogeikin, S., Kieffer, J. & Bass J. A high pressure Brillouin scattering study of vitreous boron oxide up to 57 GPa. J. Non-Cryst. Sol. 349, 30–34 (2004).

    Article  CAS  Google Scholar 

  46. Rouxel, T., Ji, H., Guin, J. P., Augereau, F. & Rufflé, B. Indentation deformation mechanism in glass: densification versus shear flow. J. Appl. Phys. 107, 094903 (2010).

    Article  CAS  Google Scholar 

  47. Rouxel, T., Ji, H., Hammouda, T. & Moreac, A. Poisson's ratio and the densification of glass under high pressure. Phys. Rev. Lett. 100, 225501 (2008).

    Article  CAS  Google Scholar 

  48. Das, B. M. Advanced Soil Mechanics 2nd edn (Spon, 2002).

    Google Scholar 

  49. Ji, H., Robin, E. & Rouxel, T. Physics and mechanics of the deformation of plasticine: macroscopic indentation behaviour for temperature between 103–293 K. J. Mech. Mat. 41, 199–209 (2009).

    Article  Google Scholar 

  50. Lewandowski, J. J., Wang, W. H. & Greer, A. L. Intrinsic plasticity or brittleness of metallic glasses. Phil. Mag. Lett 85, 77–87 (2005).

    Article  CAS  Google Scholar 

  51. Lewandowski, J. J. & Greer, A. L., Temperature rise at shear bands in metallic glasses. Nature Mater. 5, 15–18 (2006).

    Article  CAS  Google Scholar 

  52. Bridge, B. & Higazy, A. A. A model of the compositional dependence of the elastic moduli of multicomponent oxide glasses. Phys. Chem. Glasses 27, 1–14 (1986).

    CAS  Google Scholar 

  53. Sreeram, A. N., Varshneya, A. K. & Swiler, D. R. Molar volume and elastic properties of multicomponent chalcogenide glasses. J. Non-Cryst. Sol. 128, 294–309 (1991).

    Article  CAS  Google Scholar 

  54. Moysan, C., Riedel, R., Harshe, R., Rouxel, T. & Augereau, F. Mechanical characterization of a polysiloxane-derived SiOC glass, J. Europ. Ceram. Soc. 27 397–403 (2007).

    Article  CAS  Google Scholar 

  55. Miracle, D. B. A structural model for metallic glasses. Nature Mater. 3, 697–701 (2004).

    Article  CAS  Google Scholar 

  56. Sheng, H. W., Luo, W. K., Alamgir, F. M., Bai, J. M. & Ma, E. Atomic packing density and short-to-medium range order in metallic glasses. Nature 439, 419–425 (2006).

    Article  CAS  Google Scholar 

  57. Hessinger, J., White, B. E. & Pohl, R. O. Elastic properties of amorphous and crystalline ice films. Planet. Space Sci. 44, 937–944 (1996).

    Article  CAS  Google Scholar 

  58. Loerting, T. & Giovambattista, N., Amorphous ices: experiments and numerical simulations, J. Phys. Cond. Mat. 18, R919–R977 (2006).

    Article  CAS  Google Scholar 

  59. Mishima, O., Calvert, L. D. & Whalley, E. 'Melting ice' I at 77 K and 10 kbar: a new method of making amorphous materials. Nature 310, 393–395 (1984).

    Article  CAS  Google Scholar 

  60. Gibson, L. J. & Ashby, M. F. Cellular Solids 2nd edn (Cambridge Univ. Press, 1997).

    Book  Google Scholar 

  61. Beer, F. P. & Johnston, E. R. Mechanics of Materials (McGraw Hill, 1981); 2nd edn (1992).

    Google Scholar 

  62. Lakes, R. S. Negative Poisson's ratio materials. Science 238, 551 (1987).

    Article  CAS  Google Scholar 

  63. Wojciechowski, K. W. Two-dimensional isotropic system with a negative Poisson ratio. Phys. Lett. A 137, 60–64 (1989).

    Article  Google Scholar 

  64. Grima, J. N., Alderson, A. & Evans, K. E. Auxetic behaviour from rotating rigid units. Phys. Stat. Solidi B 242, 561–75 (2005).

    Article  CAS  Google Scholar 

  65. Rothenburg, L., Berlin, A. A. & Bathurst, R. J. Microstructure of isotropic materials with negative Poisson's ratio. Nature 354, 470–472 (1991).

    Article  Google Scholar 

  66. Silva, S. P. et al. Cork: properties, capabilities and applications. Int. Mater. Rev. 50, 345–365 (2005).

    Article  CAS  Google Scholar 

  67. Grima, J. N. et al. Hexagonal honeycombs with zero Poisson's ratios and enhanced stiffness. Adv. Eng. Mater. 12, 855–862 (2010).

    Article  Google Scholar 

  68. Barré de Saint-Venant, Resumé des Leçons sur l'application de la mécanique à l'établissement des constructions et des machines. Première section. De la Résistance des corps solides par Navier. 3ème édition avec des notes et des Appendices (Paris, 1848).

    Google Scholar 

  69. Lempriere, B. M. Poisson's ratio in orthotropic materials. AIAA J. 6, 2226–2227 (1968).

    Article  Google Scholar 

  70. Gunton, D. J. & Saunders, G. A. The Young's modulus and Poisson's ratio of arsenic, antimony, and bismuth. J. Mater. Sci. 7, 1061–1068 (1972).

    Article  CAS  Google Scholar 

  71. Kimizuka, H., Kaburaki, H. & Kogure, Y. Mechanism for negative Poisson ratios over the α-β transition of cristobalite, SiO2: a molecular-dynamics study. Phys. Rev. Lett. 84, 5548–5551 (2000).

    Article  CAS  Google Scholar 

  72. Williams, J. J., Smith, C. W. & Evans, K. E. Off-axis elastic properties and the effect of extraframework species on structural flexibility of the NAT-type zeolites: simulations of structure and elastic properties, Chem. Mater. 19, 2423–2434 (2007).

    Article  CAS  Google Scholar 

  73. Lee, Y., Vogt, T., Hriljac, J. A., Parise, J. B. & Artioli, G. J. Am. Chem. Soc. 124, 5466–5475 (2002).

    Article  CAS  Google Scholar 

  74. Lethbridge, Z. A. D., Walton R. I., Marmier, A. S. H., Smith, C. & Evans, K. E. Elastic anisotropy and extreme Poisson's ratios in single crystals. Acta Mater. 58, 6444–6451 (2010).

    Article  CAS  Google Scholar 

  75. Goodwin, A. L., Keen, D. A. & Tucker, G. Large negative linear compressibility of Ag3[Co(CN)6], Proc. Natl Acad. Sci. USA 105, 18708–18713 (2008).

    Article  CAS  Google Scholar 

  76. Goodwin, A. L. et al. Colossal positive and negative thermal expansion in the framework material Ag3[Co(CN)6]. Science 319, 794 (2008).

    Article  CAS  Google Scholar 

  77. Mary, T. A., Evans, J. S. O., Vogt, T. & Sleight, A. W. Negative thermal expansion from 0.3 K to 1050 K in ZrW2O8 . Science 272, 90–92 (1996).

    Article  CAS  Google Scholar 

  78. Bridgman, P. W. The Physics of High Pressure (Bell, 1949).

    Google Scholar 

  79. Greaves, G. N. & Sen, S. Inorganic glasses, glass-forming liquids and amorphising solids. Adv. Phys. 56, 1–166 (2007).

    Article  CAS  Google Scholar 

  80. Poole, P. H., Grande, T., Angell, C. A. & McMillan, P. F. Science 275, 322 (1997).

    Article  CAS  Google Scholar 

  81. Greaves, G. N. et al. Detection of first order liquid–liquid phase transitions in yttrium oxide–aluminium oxide melts. Science 322, 566–570 (2008).

    Article  CAS  Google Scholar 

  82. Hirotsu, S. Elastic anomaly near the critical point of volume phase transition in polymer gels. Macromolecules 23, 903–905 (1990).

    Article  CAS  Google Scholar 

  83. Lakshtanov, D. L., Sinogeikin, S. V. & Bass, J. D. High-temperature phase transitions and elasticity of silica polymorphs. Phys. Chem. Miner. 34, 11–22 (2007).

    Article  CAS  Google Scholar 

  84. McKnight, R. E. A. et al. Grain size dependence of elastic anomalies accompanying the alpha-beta phase transition in polycrystalline quartz. J. Phys. Cond. Mat. 20, 075229 (2008).

    Article  CAS  Google Scholar 

  85. Li, C., Hu, Z. & Li, Y. Poisson's ratio in polymer gels near the phase-transition point. Phys. Rev. E 48, 603–606 (1993).

    Article  CAS  Google Scholar 

  86. Dong, L. Stone, D. S. & Lakes, R. S. Softening of bulk modulus and negative Poisson's ratio in barium titanate ceramic near the Curie point. Phil. Mag. Lett. 90, 23–33 (2010).

    Article  CAS  Google Scholar 

  87. Alefeld, G., Volkl, J. & Schaumann, G. Elastic diffusion relaxation. Phys. Status Solidi 37, 337–351 (1970).

    Article  CAS  Google Scholar 

  88. Boehler, R. & Ross, M. Melting curve of aluminum in a diamond cell to 0.8 Mbar: implications for iron. Earth Planet. Sci. Lett. 153, 223 (1997).

    Article  CAS  Google Scholar 

  89. McMillan, P. F. et al. Polyamorphism and liquid–liquid phase transitions: challenges for experiment and theory. J. Phys. Cond. Mat. 19, 415101 (2007).

    Article  CAS  Google Scholar 

  90. Greaves, G. N. et al. Composition and polyamorphism in supercooled yttria–alumina melts. J. Non-Cryst. Solids 357, 435–441 (2011).

    Article  CAS  Google Scholar 

  91. Inamura, Y., Katyama, Y., Ursumi, W. & Funakoshi, K. I. Transformations in the intermediate-range structure of SiO2 glass under high pressure and temperature. Phys. Rev. Lett. 93, 015501 (2004).

    Article  CAS  Google Scholar 

  92. Richet, P. & Gillet, P. Pressure-induced amorphisation of minerals: a review. Eur. J. Mineral 9, 589–600 (1997).

    Article  Google Scholar 

  93. Greaves, G.N. et al. Rheology of collapsing zeolites amorphised by temperature and pressure. Nature Mater. 2, 622–629 (2003).

    Article  CAS  Google Scholar 

  94. Greaves, G. N., Meneau, F., Majérus, O., Jones, D. & Taylor, J. Identifying the vibrations that destabilise crystals and which characterise the glassy state. Science 308, 1299–1302 (2005).

    Article  CAS  Google Scholar 

  95. Haines, J. et al. Topologically ordered amorphous silica obtained from the collapsed siliceous zeolite, silicalite-1-F: a step toward “perfect” glasses. J. Am. Chem. Soc. 131, 12333–12338 (2009).

    Article  CAS  Google Scholar 

  96. Keen, D. A. et al. Structural description of pressure-induced amorphisation in ZrW2O8 . Phys. Rev. Lett. 98, 225501 (2007).

    Article  CAS  Google Scholar 

  97. Bennett, T. D. et al. Structure and properties of an amorphous metal–organic framework. Phys. Rev. Lett. 104, 115503 (2010).

    Article  CAS  Google Scholar 

  98. Lethbridge, Z. A. D., Walton, R. I., Bosak, A. & Krisch, M. Single-crystal elastic constants of the zeolite analcime measured by inelastic X-ray scattering. Chem. Phys. Lett. 471 286–289 (2009).

    Article  CAS  Google Scholar 

  99. Peral, I. & Iniguez, J. Amorphization induced by pressure: results for zeolites and general implications. Phys. Rev. Lett. 97, 225502 (2006).

    Article  CAS  Google Scholar 

  100. Novikov, V. N. & Sokolov, A. P. Poisson's ratio and the fragility of glass-forming liquids. Nature 431, 961–963 (2004).

    Article  CAS  Google Scholar 

  101. Novikov, V. N., Ding, Y. & Sokolov, A. P. Correlation of fragility of supercooled liquids with elastic properties of glasses. Phys. Rev. E 71, 061501 (2005).

    Article  CAS  Google Scholar 

  102. Jiang, M. & Dai, L. Intrinsic correlation between fragility and bulk modulus in metallic glasses. Phys. Rev B 76, 054204 (2007).

    Article  CAS  Google Scholar 

  103. Shintani, H. & Tanaka, H. Universal link between the boson peak and transverse phonons in glass. Nature Mater. 7, 870–877 (2008).

    Article  CAS  Google Scholar 

  104. Yannopoulos, S. N. & Johari, G. P. Poisson's ratio and liquid's fragility. Nature 442, E7–E8 (2006).

    Article  CAS  Google Scholar 

  105. Scopigno, T., Ruocco, G., Sette, F. & Monaco, G. Is the fragility of a liquid embedded in the properties of its glass? Science 302, 849–852 (2003).

    Article  CAS  Google Scholar 

  106. Scopigno, T., Cangialosi, D. & Ruocco, G. Universal relation between viscous flow and fast dynamics in glass-forming materials. Phys. Rev. B 81, 100202(R) (2010).

    Article  CAS  Google Scholar 

  107. Debenedetti, P. G. & Stillinger, F. H. Supercooled liquids and the glass transition. Nature 410, 259–267 (2001).

    Article  CAS  Google Scholar 

  108. Angell, C. A. Structural instability and relaxation in liquid and glassy phases near the fragile liquid limit. J. Non-Cryst. Solids 102, 205–221 (1988).

    Article  CAS  Google Scholar 

  109. Dyre, J. C. Colloquium: The glass transition and elastic models of glass-forming liquids. Rev. Mod. Phys. 78, 953–972 (2006).

    Article  CAS  Google Scholar 

  110. Dyre, J. C. Glasses: Heirs of liquid treasures. Nature Mater. 3, 749–750 (2004).

    Article  CAS  Google Scholar 

  111. Johari, G. P. On Poisson's ratio of glass and liquid vitrification characteristics. Phil. Mag. 86, 1567–1579 (2006).

    Article  CAS  Google Scholar 

  112. Nemilov, S. V. Structural aspect of possible interrelation between fragility (length) of glass forming melts and Poisson's ratio of glasses. J. Non-Cryst. Solids 353, 4613–4632 (2007).

    Article  CAS  Google Scholar 

  113. Krisch, M. & Sette, F. in Light Scattering in Solids: Novel Materials and Techniques (eds Cardona, M & Merlin, R.) (Springer, 2007).

    Google Scholar 

  114. Xi, X. L. et al. Fracture of brittle metallic glasses: brittleness or plasticity. Phys. Rev. Lett. 94, 125510 (2005).

    Article  CAS  Google Scholar 

  115. Pugh, S. F., Relations between the elastic moduli and the plastic properties of polycrystalline pure metals, Phil. Mag. 45, 823–843 (1954).

    Article  CAS  Google Scholar 

  116. Rosenhain, W. & Ewen, D. The intercrystalline cohesion of metals. J. Inst. Met. 10, 119–149 (1913).

    Google Scholar 

  117. Zhang, H., Srolovitz, D. J., Douglas, J. F & Warren, J. A. Grain boundaries exhibit the dynamics of glass-forming liquids. Proc. Natl Acad. Sci. USA 106, 7735–7740 (2009).

    Article  CAS  Google Scholar 

  118. Greer, A. L. Metallic glasses. Science 267, 1947–1953 (1995).

    Article  CAS  Google Scholar 

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Acknowledgements

We acknowledge support from the Higher Education Funding Coucil for Wales, the Engineering and Physical Sciences Research Council (UK), the Natural Environment Research Council (UK), the National Science Foundation (USA), and the Ministry of Research and Higher Education in France. We are also indebted to J. Grima, T. Kelly, C. Kurkjian, J. Orava, R. Reis and R. Walton for discussions in the preparation of this Review.

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Authors and Affiliations

  1. Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge, CB2 3QZ, UK

    G. N. Greaves & A. L. Greer

  2. Institute of Mathematics and Physics, Aberystwyth University, Aberystwyth, SY23 3BZ, UK

    G. N. Greaves

  3. Department of Engineering Physics, Department of Materials Science, University of Wisconsin-Madison, Wisconsin, 53706-1687, USA

    R. S. Lakes

  4. Applied Mechanics Laboratory, LARMAUR ERL-CNRS 6274, Université Rennes 1, Rennes cedex, 35042, France

    T. Rouxel

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Greaves, G., Greer, A., Lakes, R. et al. Poisson's ratio and modern materials. Nature Mater 10, 823–837 (2011). https://doi.org/10.1038/nmat3134

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