Grain size dependence of mechanical properties in nanocrystalline selenium
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Grain size dependence of mechanical properties in nanocrystalline selenium K. Lu and H. Y. Zhang State Key Laboratory for RSA, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110015, People’s Republic of China
Y. Zhong and H. J. Fecht Technical University of Berlin, Institute for Metals Research, Hardenbergstr. 36, D-10623 Berlin, Germany (Received 26 January 1996; accepted 8 November 1996)
Porosity-free nanocrystalline element selenium (nc-Se) samples with the mean grain sizes ranging from 8 to 70 nm were synthesized by complete crystallization of the melt-quenched amorphous Se solid. Mechanical properties including microhardness sHn d and elastic modulus (E) of the nc-Se samples were measured by means of nanoindentation tests and microhardness tests, respectively. With a reduction of grain size, the nc-Se samples were found to be substantially hardened. But the grain size dependence of Hn does not follow a simple Hall–Petch relation over the whole grain size range, exhibiting three distinct stages corresponding to three different Hall–Petch slopes. The maximum Hall–Petch slope was found to be in the grain size range of 15–20 nm, corresponding to large values of the elastic modulus. This behavior can be explained in terms of the lattice distortion in the nc-Se samples that was experimentally determined by using quantitative x-ray diffraction measurements. A conclusion is drawn that the lattice structure of the nm-sized crystallites may play an important role in mechanical properties of nanocrystalline materials.
I. INTRODUCTION
Nanocrystalline materials, or polycrystalline materials with grain sizes in the nanometer regime, provide new opportunities to extend our understanding of the structure-property relationship in solid materials. As the nanocrystalline material is structurally characterized by ultrafine grains and a large volume fraction of associated interfaces, many properties of nanocrystalline materials are significantly different from, and frequently superior to, those of their coarse-grained counterparts, and therefore have drawn much attention in recent years.1,2 It is known that grain size has a profound effect on the mechanical properties of materials. The grain size dependence of strength or hardness of conventional polycrystalline materials is usually described by the wellknown Hall–Petch (H-P) relation3 : Hn Hn0 1 kd 21/2 ,
(1)
where Hn0 and k are constants. Normally the value of k is positive, so that the polycrystal will be hardened with a refinement of its grains. This relationship has been well studied and confirmed in both theory and practice in many systems of metals and ceramics with grains coarser than micrometers. For nanocrystalline materials, however, the H-P relation is not found to be always valid.4–6 Experimental obJ. Mater. Res., Vol. 12, No. 4, Apr 1997
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servations indicated that both the normal (with positive k values) and the abnormal (with negative k va
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