Abstract
The mechanical, structural and functional properties of crystals are determined by their defects1,2,3,4, and the distribution of stresses surrounding these defects has broad implications for the understanding of transport phenomena. When the defect density rises to levels routinely found in real-world materials, transport is governed by local stresses that are predominantly nonlinear1,5,6,7,8. Such stress fields however, cannot be measured using conventional bulk and local measurement techniques. Here, we report direct and spatially resolved experimental measurements of the nonlinear stresses surrounding colloidal crystalline defect cores, and show that the stresses at vacancy cores generate attractive interactions between them. We also directly visualize the softening of crystalline regions surrounding dislocation cores, and find that stress fluctuations in quiescent polycrystals are uniformly distributed rather than localized at grain boundaries, as is the case in strained atomic polycrystals. Nonlinear stress measurements have important implications for strain hardening9, yield1,5 and fatigue10.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Schiøtz, J., Di Tolla, F. D. & Jacobsen, K. W. Softening of nanocrystalline metals at very small grain sizes. Nature 391, 561–563 (1998).
Peng, Y., Wang, Z., Alsayed, A. M., Yodh, A. G. & Han, Y. Melting of colloidal crystal films. Phys. Rev. Lett. 104, 205703 (2010).
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).
Hull, D. & Bacon, D. J. Introduction to Dislocations Vol. 257 (Pergamon Press, 1984).
Schiøtz, J. & Jacobsen, K. W. A maximum in the strength of nanocrystalline copper. Science 301, 1357–1359 (2003).
Li, J., Van Vliet, K. J., Zhu, T., Yip, S. & Suresh, S. Atomistic mechanisms governing elastic limit and incipient plasticity in crystals. Nature 418, 307–310 (2002).
Cai, W., Arsenlis, A., Weinberger, C. R. & Bulatov, V. V. A non-singular continuum theory of dislocations. J. Mech. Phys. Solids 54, 561–587 (2006).
Lechner, W. & Dellago, C. Defect interactions in two-dimensional colloidal crystals: vacancy and interstitial strings. Soft Matter 5, 2752–2758 (2009).
Bulatov, V. V. et al. Dislocation multi-junctions and strain hardening. Nature 440, 1174–1178 (2006).
Stephens, R. I., Fatemi, A., Stephens, R. R. & Fuchs, H. O. Metal Fatigue in Engineering (John Wiley & Sons, 2000).
Huang, P. Y. et al. Imaging atomic rearrangements in two-dimensional silica glass: watching silica’s dance. Science 342, 224–227 (2013).
Schall, P., Cohen, I., Weitz, D. A. & Spaepen, F. Visualizing dislocation nucleation by indenting colloidal crystals. Nature 440, 319–323 (2006).
Bausch, A. R. et al. Grain boundary scars and spherical crystallography. Science 299, 1716–1718 (2003).
Irvine, W. T. M., Vitelli, V. & Chaikin, P. M. Pleats in crystals on curved surfaces. Nature 468, 947–951 (2010).
King, A., Johnson, G., Engelberg, D., Ludwig, W. & Marrow, J. Observations of intergranular stress corrosion cracking in a grain-mapped polycrystal. Science 321, 382–385 (2008).
Levine, L. E. et al. X-ray microbeam measurements of individual dislocation cell elastic strains in deformed single-crystal copper. Nature Mater. 5, 619–622 (2006).
Van Blaaderen, A., Ruel, R. & Wiltzius, P. Template-directed colloidal crystallization. Nature 385, 321–324 (1997).
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).
Crocker, J. C. & Grier, D. G. Methods of digital video microscopy for colloidal studies. J. Colloid Interface Sci. 179, 298–310 (1996).
Bi, D., Zhang, J., Chakraborty, B. & Behringer, R. P. Jamming by shear. Nature 480, 355–358 (2011).
Alder, B. J., Hoover, W. G. & Young, D. A. Studies in molecular dynamics. v. high-density equation of state and entropy for hard disks and spheres. J. Chem. Phys. 49, 3688–3696 (1968).
Pronk, S. & Frenkel, D. Large difference in the elastic properties of fcc and hcp hard-sphere crystals. Phys. Rev. Lett. 90, 255501 (2003).
Bennett, C. H. & Alder, B. J. Studies in molecular dynamics. IX. Vacancies in hard sphere crystals. J. Chem. Phys. 54, 4796–4808 (1971).
DaSilva, L. C., Cândido, L., da F Costa, L. & Oliveira, O. N. Jr Formation energy and interaction of point defects in two-dimensional colloidal crystals. Phys. Rev. B 76, 035441 (2007).
Gracie, R., Oswald, J. & Belytschko, T. On a new extended finite element method for dislocations: core enrichment and nonlinear formulation. J. Mech. Phys. Solids 56, 200–214 (2008).
Friesen, C. & Thompson, C. V. Reversible stress relaxation during precoalescence interruptions of Volmer-Weber thin film growth. Phys. Rev. Lett. 89, 126103 (2002).
Gokhale, S., Nagamanasa, H. K., Santhosh, V., Sood, A. K. & Ganapathy, R. Directional grain growth from anisotropic kinetic roughening of grain boundaries in sheared colloidal crystals. Proc. Natl Acad. Sci. USA 109, 20314–20319 (2012).
Robinson, I. & Harder, R. Coherent X-ray diffraction imaging of strain at the nanoscale. Nature Mater. 8, 291–298 (2009).
Acknowledgements
The authors thank F. Spaepen, J. Schiøtz, T. Lubensky and the Cohen laboratory for useful discussions. J.P.S. and M.B. acknowledge funding from Department of Energy DOE-BES DE-FG02-07ER46393. P.S. acknowledges support by a VICI grant from the Netherlands Organization for Scientific Research (NWO). I.C. and N.Y.C.L. were supported by NSF DMR-CMP Award No. 1507607.
Author information
Authors and Affiliations
Contributions
N.Y.C.L., M.B., J.P.S. and I.C. conceived and designed the research, with later contributions from P.S.; N.Y.C.L. conducted the vacancy and polycrystal experiments, and P.S. conducted the dislocation experiment. M.B. conducted the simulations and developed the underlying theory. N.Y.C.L. and M.B. analysed the data. All authors discussed the results and wrote the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Supplementary Information
Supplementary Information (PDF 6556 kb)
Supplementary Information
Supplementary Movie 1 (MP4 10484 kb)
Rights and permissions
About this article
Cite this article
Lin, N., Bierbaum, M., Schall, P. et al. Measuring nonlinear stresses generated by defects in 3D colloidal crystals. Nature Mater 15, 1172–1176 (2016). https://doi.org/10.1038/nmat4715
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/nmat4715
This article is cited by
-
Dislocation interactions during plastic relaxation of epitaxial colloidal crystals
Nature Communications (2023)
-
Emergent solidity of amorphous materials as a consequence of mechanical self-organisation
Nature Communications (2020)
-
Doping colloidal bcc crystals — interstitial solids and meta-stable clusters
Scientific Reports (2017)
-
Stresses come to light
Nature Materials (2016)