Work hardening in colloidal crystals.

Publisher: Nature Publishing Group Country of Publication: England NLM ID: 0410462 Publication Model: Print-Electronic Cited Medium: Internet ISSN: 1476-4687 (Electronic) Linking ISSN: 00280836 NLM ISO Abbreviation: Nature Subsets: MEDLINE

Publication: Basingstoke : Nature Publishing Group
Original Publication: London, Macmillan Journals ltd.

Colloids*/chemistry ; Crystallization*; Microscopy, Confocal ; Shear Strength ; Hardness ; Elasticity

Colloidal crystals exhibit interesting properties ^1-4 that are in many ways analogous to their atomic counterparts. They have the same crystal structures ^2,5-7 , undergo the same phase transitions ^8-10 , and possess the same crystallographic defects ^11-14 . In contrast to these structural properties, the mechanical properties of colloidal crystals are quite different from those of atomic systems. For example, unlike in atomic systems, the elasticity of hard-sphere colloidal crystals is purely entropic ¹⁵ ; as a result, they are so soft that they can be melted just by stirring ^16,17 . Moreover, crystalline materials deform plastically when subjected to increasing shear and become stronger because of the ubiquitous process of work hardening ¹⁸ ; but this has so far never been observed in colloidal crystals, to our knowledge. Here we show that hard-sphere colloidal crystals exhibit work hardening. Moreover, despite their softness, the shear strength of colloidal crystals can increase and approach the theoretical limit for crystals, a value reached in very few other materials so far. We use confocal microscopy to show that the strength of colloidal crystals increases with dislocation density, and ultimately reaches the classic Taylor scaling behaviour for atomic materials ^19-21 , although hard-sphere interactions lack the complexity of atomic interactions. We demonstrate that Taylor hardening arises through the formation of dislocation junctions ²² . The Taylor hardening regime, however, is established only after a transient phase, and it ceases when the colloidal crystals become so hard that the strain is localized within a thin boundary layer in which slip results from an unconventional motion of dislocations. The striking resemblance between colloidal and atomic crystals, despite the many orders of magnitude difference in particle size and shear modulus, demonstrates the universality of work hardening.
(© 2024. The Author(s).)

Pieranski, P. Colloidal crystals. Contemp. Phys. 24, 25–73 (1983). (PMID: 10.1080/00107518308227471)
Pusey, P. N. & van Megen, W. Phase behaviour of concentrated suspensions of nearly hard colloidal spheres. Nature 320, 340–342 (1986). (PMID: 10.1038/320340a0)
Poon, W. Colloids as big atoms. Science 304, 830–831 (2004). (PMID: 10.1126/science.109796415131294)
Manoharan, V. N. Colloidal matter: packing, geometry, and entropy. Science 349, 1253751 (2015). (PMID: 10.1126/science.125375126315444)
Leunissen, M. E. et al. Ionic colloidal crystals of oppositely charged particles. Nature 437, 235–240 (2005). (PMID: 10.1038/nature0394616148929)
Pusey, P. N. et al. Structure of crystals of hard colloidal spheres. Phys. Rev. Lett. 63, 2753–2756 (1989). (PMID: 10.1103/PhysRevLett.63.275310040981)
He, M. et al. Colloidal diamond. Nature 585, 524–529 (2020). (PMID: 10.1038/s41586-020-2718-632968261)
Gasser, U., Weeks, E. R., Schofield, A., Pusey, P. N. & Weitz, D. A. Real-space imaging of nucleation and growth in colloidal crystallization. Science 292, 258–262 (2001). (PMID: 10.1126/science.105845711303095)
Alsayed, A. M., Islam, M. F., Zhang, J., Collings, P. J. & Yodh, A. G. Premelting at defects within bulk colloidal crystals. Science 309, 1207–1210 (2005). (PMID: 10.1126/science.111239915994377)
Li, B., Zhou, D. & Han, Y. Assembly and phase transitions of colloidal crystals. Nat. Rev. Mater. 1, 15011 (2016). (PMID: 10.1038/natrevmats.2015.11)
Schall, P., Cohen, I., Weitz, D. A. & Spaepen, F. Visualization of dislocation dynamics in colloidal crystals. Science 305, 1944–1948 (2004). (PMID: 10.1126/science.110218615448265)
Schall, P., Cohen, I., Weitz, D. A. & Spaepen, F. Visualizing dislocation nucleation by indenting colloidal crystals. Nature 440, 319–323 (2006). (PMID: 10.1038/nature0455716541069)
Lin, N. Y. C., Bierbaum, M., Schall, P., Sethna, J. P. & Cohen, I. Measuring nonlinear stresses generated by defects in 3D colloidal crystals. Nat. Mater. 15, 1172–1176 (2016). (PMID: 10.1038/nmat471527479210)
Irvine, W. T. M., Hollingsworth, A. D., Grier, D. G. & Chaikin, P. M. Dislocation reactions, grain boundaries, and irreversibility in two-dimensional lattices using topological tweezers. Proc. Natl Acad. Sci. USA 110, 15544–15548 (2013). (PMID: 10.1073/pnas.1300787110240093413785718)
Frenkel, D. & Ladd, A. J. C. Elastic constants of hard-sphere crystals. Phys. Rev. Lett. 59, 1169–1169 (1987). (PMID: 10.1103/PhysRevLett.59.116910035159)
Ackerson, B. J. & Clark, N. A. Shear-induced melting. Phys. Rev. Lett. 46, 123–126 (1981). (PMID: 10.1103/PhysRevLett.46.123)
Wu, Y. L., Derks, D., van Blaaderen, A. & Imhof, A. Melting and crystallization of colloidal hard-sphere suspensions under shear. Proc. Natl Acad. Sci. USA 106, 10564–10569 (2009). (PMID: 10.1073/pnas.0812519106195416432705612)
Cottrell, A. H. Dislocations and Plastic Flow in Crystals 2nd edn (Clarendon Press, 1953).
Taylor, G. I. The mechanism of plastic deformation of crystals. Part I.—Theoretical. Proc. R. Soc. A 145, 362–387 (1934).
Basinski, S. J. & Basinski, Z. S. in Dislocations in Solids Vol. 4, Dislocations in Metallurgy (ed. Nabarro, F. R. N.) 261–362 (North-Holland, 1979).
Hansen, N. & Huang, X. Microstructure and flow stress of polycrystals and single crystals. Acta Mater. 46, 1827–1836 (1998). (PMID: 10.1016/S1359-6454(97)00365-0)
Saada, G. Sur le durcissement dû à la recombinaison des dislocations. Acta Metall. 8, 841–847 (1960). (PMID: 10.1016/0001-6160(60)90150-4)
Anderson, P. M., Hirth, J. P. & Lothe, J. Theory of Dislocations 3rd edn (Cambridge Univ. Press, 2017).
Seeger, A., Mader, S. & Kronmüller, H. in Electron Microscopy and Strength of Crystals (eds. Thomas, G. & Washburn, J.) 665–712 (Interscience, 1963).
Hirsch, P. B. The Physics of Metals Vol. 2, Defects (ed. P. B. Hirsch) 189–246 (Cambridge Univ. Press, 1975).
Zepeda-Ruiz, L. A. et al. Atomistic insights into metal hardening. Nat. Mater. 20, 315–320 (2021). (PMID: 10.1038/s41563-020-00815-133020613)
Liao, M., Xiao, X., Chui, S. T. & Han, Y. Grain-boundary roughening in colloidal crystals. Phys. Rev. X 8, 021045 (2018).
Dinsmore, A. D., Weeks, E. R., Prasad, V., Levitt, A. C. & Weitz, D. A. Three-dimensional confocal microscopy of colloids. Appl. Opt. 40, 4152–4159 (2001). (PMID: 10.1364/AO.40.00415218360451)
Dullens, R. P. A. & Bechinger, C. Shear thinning and local melting of colloidal crystals. Phys. Rev. Lett. 107, 138301 (2011). (PMID: 10.1103/PhysRevLett.107.13830122026907)
van Blaaderen, A., Ruel, R. & Wiltzius, P. Template-directed colloidal crystallization. Nature 385, 321–324 (1997). (PMID: 10.1038/385321a0)
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). (PMID: 10.1021/j100303a014)
Stukowski, A., Bulatov, V. V. & Arsenlis, A. Automated identification and indexing of dislocations in crystal interfaces. Model. Simul. Mater. Sci. Eng. 20, 085007 (2012). (PMID: 10.1088/0965-0393/20/8/085007)
Falk, M. L. & Langer, J. S. Dynamics of viscoplastic deformation in amorphous solids. Phys. Rev. E 57, 7192–7205 (1998). (PMID: 10.1103/PhysRevE.57.7192)
VanSaders, B., Dshemuchadse, J. & Glotzer, S. C. Strain fields in repulsive colloidal crystals. Phys. Rev. Mater. 2, 063604 (2018). (PMID: 10.1103/PhysRevMaterials.2.063604)
Madec, R., Devincre, B. & Kubin, L. P. From dislocation junctions to forest hardening. Phys. Rev. Lett. 89, 255508 (2002). (PMID: 10.1103/PhysRevLett.89.25550812484901)
Hull, D. & Bacon, D. J. Introduction to Dislocations 5th edn (Elsevier, 2011).
Svetlizky, I., Kim, S., Weitz, D. A. & Spaepen, F. Dislocation interactions during plastic relaxation of epitaxial colloidal crystals. Nat. Commun. 14, 5760 (2023). (PMID: 10.1038/s41467-023-41430-33771704410505195)
Caillard, D. & Martin, J.-L. Glide of dislocations in non-octahedral planes of fcc metals: a review. Int. J. Mater. Res. 100, 1403–1410 (2009). (PMID: 10.3139/146.110190)
Karnthaler, H. P. The study of glide on {001} planes in f.c.c. metals deformed at room temperature. Phil. Mag. A 38, 141–156 (1978). (PMID: 10.1080/01418617808239225)
Abu-Odeh, A., Allaparti, T. & Asta, M. Structure and glide of Lomer and Lomer-Cottrell dislocations: atomistic simulations for model concentrated alloy solid solutions. Phys. Rev. Mater. 6, 103603 (2022). (PMID: 10.1103/PhysRevMaterials.6.103603)
Essmann, U. & Mughrabi, H. Annihilation of dislocations during tensile and cyclic deformation and limits of dislocation densities. Phil. Mag. A 40, 731–756 (1979). (PMID: 10.1080/01418617908234871)
Devincre, B., Hoc, T. & Kubin, L. Dislocation mean free paths and strain hardening of crystals. Science 320, 1745–1748 (2008). (PMID: 10.1126/science.115610118583605)
Caillard, D. & Martin, J. Thermally Activated Mechanisms in Crystal Plasticity (Pergamon, 2003).
Kocks, U. & Mecking, H. Physics and phenomenology of strain hardening: the FCC case. Prog. Mater Sci. 48, 206 (2003). (PMID: 10.1016/S0079-6425(02)00003-8)
Sills, R. B., Bertin, N., Aghaei, A. & Cai, W. Dislocation networks and the microstructural origin of strain hardening. Phys. Rev. Lett. 121, 085501 (2018). (PMID: 10.1103/PhysRevLett.121.08550130192605)
Shenoy, V. B., Kukta, R. V. & Phillips, R. Mesoscopic analysis of structure and strength of dislocation junctions in fcc metals. Phys. Rev. Lett. 84, 1491–1494 (2000). (PMID: 10.1103/PhysRevLett.84.149111017550)
Franciosi, P., Berveiller, M. & Zaoui, A. Latent hardening in copper and aluminium single crystals. Acta Metall. 28, 273–283 (1980). (PMID: 10.1016/0001-6160(80)90162-5)
Sethna, J. P. et al. Deformation of crystals: connections with statistical physics. Annu. Rev. Mater. Res. 47, 217–246 (2017). (PMID: 10.1146/annurev-matsci-070115-032036)
Yamakov, V., Wolf, D., Phillpot, S. R., Mukherjee, A. K. & Gleiter, H. Deformation-mechanism map for nanocrystalline metals by molecular-dynamics simulation. Nat. Mater. 3, 43–47 (2004). (PMID: 10.1038/nmat103514704784)
Jensen, K. E., Pennachio, D., Recht, D., Weitz, D. A. & Spaepen, F. Rapid growth of large, defect-free colloidal crystals. Soft Matter 9, 320–328 (2013). (PMID: 10.1039/C2SM26792F)
Crocker, J. C. & Grier, D. G. Methods of digital video microscopy for colloidal studies. J. Colloid Interface Sci. 179, 298–310 (1996). (PMID: 10.1006/jcis.1996.0217)
Pronk, S. & Frenkel, D. Can stacking faults in hard-sphere crystals anneal out spontaneously? J. Chem. Phys. 110, 4589–4592 (1999). (PMID: 10.1063/1.478339)
Marechal, M., Hermes, M. & Dijkstra, M. Stacking in sediments of colloidal hard spheres. J. Chem. Phys. 135, 034510 (2011). (PMID: 10.1063/1.360910321787016)
Zepeda-Ruiz, L. A., Stukowski, A., Oppelstrup, T. & Bulatov, V. V. Probing the limits of metal plasticity with molecular dynamics simulations. Nature 550, 492–495 (2017). (PMID: 10.1038/nature2347228953878)
Frenkel, J. Zur Theorie der elastizitätsgrenze und der festigkeit kristallinischer körper. Z. Phys. 37, 572–609 (1926). (PMID: 10.1007/BF01397292)
Kelly, A. & Macmillan, N. H. Strong Solids 3rd edn (Clarendon Press, 1986).
Schoeck, G. & Frydman, R. The Contribution of the Dislocation Forest to the Flow Stress. Phys. Stat. Solidi B Basic Solid State Phys. 53, 661–673 (1972). (PMID: 10.1002/pssb.2220530227)
Devincre, B., Kubin, L. & Hoc, T. Physical analyses of crystal plasticity by DD simulations. Scr. Mater. 54, 741–746 (2006). (PMID: 10.1016/j.scriptamat.2005.10.066)

0 (Colloids)

Date Created: 20240529 Date Completed: 20240619 Latest Revision: 20240622

20240623

PMC11186786

10.1038/s41586-024-07453-6

38811735