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DOKLADY PHYSICSVol. 46No. 112001ANOMALIES IN MECHANICAL CHARACTERISTICS OF NANOMETER-SIZE OBJECTS827increasing with the reduction in the number of layers.The values of the Poisson’s ratio and Young modulusfor different N are presented in the table. It is worth not-ing that for N = 2 the Poisson’s ratio is smaller than ν∞almost by a factor of 2. As N∞, elastic moduli tendto values corresponding to the infinite crystal, whichare independent of the deformation direction.Based on the studies performed, we can list the basicproperties intrinsic to nanocrystals.1. For the Young modulus of a nanocrystal, only apossible interval of values is determined. This is asso-ciated with the impossibility of unambiguously deter-mining the size of a nanoobject.2. Elastic properties of a nanocrystal substantiallydepend on the number of atomic layers forming it.3. The shape and size of a nanocrystal introduce anadditional anisotropy into its elastic properties.The effects listed are obtained on the basis of arather simplified model. However, as far as they mani-fest themselves for the simplest nanocrystal, they mustall the more play an important role in the case of morecomplicated nanocrystalline objects. The indicatedambiguity in the determination of the Young modulus,evidently, manifests itself for all mechanical character-istics whose definition substantially involves the con-cept of the nanoobject’s size. In particular, the specificdeformation energy per unit volume is determinedambiguously.In the present study, we took into account the inter-action of only neighboring atoms in the crystal lattice.It can be shown that allowance for further neighborsleads to the enhanced effect of the scale factor, espe-cially in the three-dimensional case.Thus, the concepts of classical continuum mechan-ics, including those of the elasticity theory, must beused with great care in the case of their application tonanoobjects. It is necessary to take into account thevariation of mechanical characteristics when scales ofobjects under consideration approach nanometers. Spe-cial attention should be paid to quantities (such as theYoung modulus) that are in principle ambiguous at theNanometer level. Using them, we must clearly definewhat we imply while applying these quantities tonanoobjects.ACKNOWLEDGMENTSThis work was supported by the Russian Foundationfor Basic Research, project nos. 9907-90443 and0001-00489.REFERENCES1. A. L. Volynskiœ, I. V. Chernov, and N. F. Bakeev, Dokl.Akad. Nauk 355, 491 (1997).2. S. L. Bazhenov, A. L. Volynskiœ, E. E. Voronina, andN. F. Bakeev, Dokl. Akad. Nauk 367, 75 (1999).3. Yu. P. Baœdarovtsev, G. N. Savenkov, and V. A. Tara-senko, Vysokomol. Soedin., Ser. A 41, 1302 (1999).4. D. L. Bykov and D. N. Konovalov, in Proceedings of theXXXVI International Workshop “Topical Problems ofStrength,” Vitebsk, 2000, p. 428.5. D. L. Bykov and D. N. Konovalov, Vestn. Tambov. Gos.Univ. 5 (314), 224 (2000).6. A. M. Krivtsov, Tr. S.-Peterb. Gos. Tekh. Univ. 443, 9(1992).7. A. M. Krivtsov, Z. Angew. Math. Mech. 79 (S2), 419(1999).Translated by G. MerzonPoisson’s ratio and Young modulus of a nanocrystal as func-tions of the number of atomic layerNν2ν2/ν∞E2/E∞22.000.180.531.0631.500.230.691.0441.330.260.771.0351.250.270.821.02101.110.300.911.01201.050.320.961.01501.020.330.981.001001.010.330.991.00E1max/E∞