On the grain size softening in nanocrystalline materials

Materials Science and Engineering Department, North Carolina State University,Raleigh, NC 27695-7907, USA(Received December 17, 1999)(Accepted December 29, 1999)Keywords: Grain boundaries; Thermally activated; Hardness; AtomicIntroductionNanocrystalline materials with grain sizes in the range of 1–100 nm have been found to exhibit noveland often improved physical properties [1–4]. They are thus of considerable interest from bothscientific and technological viewpoints. In the present paper we consider the influence of grain size onthe flow stress (or corresponding hardness) of nanocrystalline materials, with focus on the grain sizesoftening (i.e., the so-called negative or inverse Hall-Petch effect) which has been observed at grainsizes ,;50 nm [5–12].The effect of grain size on the hardness of nanocrystalline materials has been reported to have theform shown schematically in Fig. 1 [5–15]. At the larger grain sizes the hardness increases withdecrease in grain size according to the well-known Hall-Petch relation (with the possibility that theHall-Petch constant k

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