The size effect in the mechanical strength of semiconductors and metals: Strain relaxation by dislocation-mediated plast
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The size effect in the mechanical strength of semiconductors and metals: Strain relaxation by dislocation-mediated plastic deformation David J. Dunstana) School of Physics and Astronomy, Queen Mary University of London, London E1 4NS, U.K. (Received 15 April 2017; accepted 7 July 2017)
The Ph.D. work of Jan H. van der Merwe in 1949 established a new paradigm for the understanding of dislocation dynamics in restricted volumes. This led to a comprehensive understanding of plasticity, or strain relaxation, in the context of strained-layer semiconductor structures. However, this understanding was largely overlooked in the context of traditional metallurgy and micromechanics. We identify four reasons for this, the apparent need for an unstrained substrate in van der Merwe’s theory, the supposed inapplicability to strain gradients, the supposed inapplicability to the Hall–Petch effect (dependence of strength on the inverse square root of grain size), and an emphasis on understanding strain hardening rather than the yield point. Addressing these four points in particular, here it is shown how the insights of van der Merwe and of the earlier work by Lawrence Bragg lead to a coherent and unified view of the size-effect phenomena ranging from the Hall–Petch effect to the strain-gradient plasticity theory.
I. INTRODUCTION
While the concept of the dislocation in a continuous elastic media goes back to Volterra in 1907,1 it was in 1934 that the importance of atomic-scale dislocations to crystal plasticity was realised. Taylor,2 Orowan,3 and Polyani4 independently proposed that atomic-scale dislocations provide a mechanism and an explanation for plastic deformation under stresses orders of magnitude below the theoretical strength of solids. Not long after that, it was realised that the dislocation also introduces a length scale, the magnitude b of the Burger’s vector into the plasticity theory, thus enabling size effects. In the continuum plasticity theory, the amount of plastic deformation can be infinitesimal, and the theory predicts behavior independent of the size. By quantising or discretising the amount of plastic slip, the possibility of size effects is opened up. Jan van der Merwe made an early key contribution during his Ph.D. in Bristol in the late 1940s. His work on crystal epitaxy led to the critical thickness theory, which predicts the stability of epitaxial strained layers.5,6 This theory has been fully developed and exploited within the field of semiconductor science and technology. It has been fundamental to underpin the technologies crucial to computers, later the internet, mobile phones, and indeed most of what has been termed as the fourth industrial
Contributing Editor: Artur Braun a) Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2017.300
revolution (after coal and steam, oil and steel, and computing). However, parallel developments in metallurgy and micromechanics, while perhaps less spectacular than the internet, have been just as important in enabling, for examp
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