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. Author manuscript; available in PMC: 2013 Sep 10.
Published in final edited form as: J Biomed Nanotechnol. 2013 Sep;9(9):1441–1470. doi: 10.1166/jbn.2013.1642

Figure 2.

Figure 2

(a) A hypothetic curve illustrating deviation (—) from a theoretically predicted dependence of a physical quantity on the particle size of a material (- - -) once the latter enters the domain of nanosizes (< 100 nm); (b) hardness or strength of a material as a function of normalized grain size, demonstrating the deviations of experimentally obtained values from those predicted by the Hall-Petch law at sufficiently low, sub-100-nm grain sizes. Reprinted with permission from [5], C. S. Pande and K. P. Cooper, Nanomechanics of hall-petch relationship in nanocrystalline materials. Progress Mat. Sci. 54, 689 (2009). © 2009, Elsevier.