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Nanomechanics of defects in solids: applications to nanolayers, nanoparticles, nanocrystals and biomaterials

Final Report Summary - MATERIALS NANOMECH (Nanomechanics of defects in solids: applications to nanolayers, nanoparticles, nanocrystals and biomaterials)

Project context and objectives

The main objectives of the project, were as follows:
-(1) Theory of crystal lattice defects in nanoscale metal particles and nanorods and the defect influence on the catalytic activity of metal clusters and nanorods;
-(2) Mechanics of crystal lattice defects in core/shell nanostructures and nanoscale thin film electronic materials with special emphasis to the defect stability in such objects;
-(3) Theory of structural defects (in particular disclinations) in ultrafine grained bulk nanostructures for the clarification of the mechanisms of plastic deformation and fracture of such bulk nanostructured materials prepared by severe plastic deformation (SPD);
-(4) Theory of structure defects in crystalline nanotubes and their influence on mechanical properties of both carbon nanotubes and protein membrane nanotubes

The scientific results on the above topics are included in nine published articles in scientific journals, and one more article and the planned monograph are under preparation. The highlights of the project are listed below.

Physical and mechanical properties of spherical and equiaxial pentagonal nanoparticles (PNPs) and elongated pentagonal nanorods (PNRs) have been theoretically investigated. It was demonstrated that the properties of such objects strongly depend on the elastic distortions of their crystal lattice caused by the disclination defects. Therefore new exact solutions for the elastic field of defects in elastic spheroids were delivered [2][3] and stability of pentagonal nano- and nanoparticles were addressed [5].

The fundamental mechanisms of dislocation nucleation and evolution in nanoscale films and core/shell nanostructures were also investigated. Particular issues involved the development of original physical models of mechanical stress calculation and dislocation formation in growing island films and core/shell nanostructures. The obtained results could be separated into two groups: (i) thin island-like lattice mismatched films [4], [7] and (ii) core-shell PNPs and PNRs [5]. In analysing (i) we performed theoretical analysis of transmission electron microscopy (TEM) images of surface InSb quantum dots (QDs) coherently grown on InAs substrate. A finite element method (FEM) was used to calculate elastic fields and total displacements in a QD and an adjusted region of the substrate. The effects of QD form factor and QD aspect ratio on displacements and TEM images were analysed. A quasilinear dependence of radial displacements on radial coordinate for spherical, elliptical, and truncated spherical QDs was demonstrated. The total displacements were used for computation of TEM diffraction contrast associated with QDs. Calculated TEM images of heavily strained QDs demonstrate the picture of pseudo-moire with a strong dependence of moire-like fringe distance D on aspect ratio d. This dependence gives the possibility to determine the aspect ratio and height of QDs from the results of TEM experiments.

Pentagonal nanorods (PNRs) and nanoparticles (PNPs) covered by mismatched shell layers were theoretically investigated [5]. Mechanical stresses and elastic energies of such objects were calculated analytically and analysed in the framework of linear isotropic elasticity. Difference between elastic modules of core and shell was taken into account. The threshold radii, as the minimal radii of PNR and PNP for which the formation of the shell layer is energetically favourable, were found. The threshold radius was approximately 10 nm for PNPs and 100 nm for PNRs of typical face-centred cubic (FCC) metals. The optimal magnitudes of mismatch parameter giving the maximal energy release for shelled PNRs and PNPs were determined. In the recent publication [9] various relaxation mechanisms in pentagonal nano-objects were examined.

Theory of structural defects (in particular disclinations) was used for the clarification of the mechanisms of plastic deformation and fracture bulk nanostructured materials prepared by severe plastic deformation (SPD) [1], [6]. The concept of disclinations (rotational linear defects) was proven to be useful in the description of grain subdivision and the related work hardening, as well as to the prediction of fracture of metals [8]. The goal of the third case-problem was for the further development of the fundamental concept of disclinations for such SPD materials, and its application to the description of the grain structure, mechanical and diffusion properties of heavily deformed nanostructured metals and alloys. The role of disclinations in deformation behaviour and structure formation of nanocrystalline materials (NCMs) was discussed [1]. A number of disclination-based models were advanced for the explanation of NCM mechanical properties. The relay dislocation-disclination model of plastic shear propagation in NCM is developed in detail. This model was based on the switching between translation and rotation deformation modes of plastic deformation. It was argued that the translation mode in NCM is due to the grain boundary dislocation sliding and the rotation mode is due to the formation of wedge junction disclinations which emerge by co-operation processes of intergrain dislocation motion or co-operative grain boundary diffusion. The dependence of deforming stress on the grain size for various grain aspect ratios was demonstrated in the case of relay dislocation-disclination mechanism operation. It was shown that the transition from one mode to another may contribute to the inverse Hall-Petch relationship observed in NCM below a critical grain size.

Gradient nanomechanics was discussed in [6] by developing appropriate differential equations for the plastic strain and/or the structural defects that bring this about. The effectiveness of the approach was illustrated by considering size-dependent stress-strain curves for nanopolycrystals with varying grain size.

The solutions attained for structural defects (in particular disclinations) in ultrafine grained bulk nanostructures were based on continuum elasticity theory, diffusion-reaction defect kinetics were performed in conjunction with TEM images [7]. Further systematic theoretical studies of disclinations were reported in [8].

More recently a complete analytical solution of the plane elasticity problem for the concentrated force acting at the half-space weakened by a circular hole [10]. It proposed to use the results of this theoretical work for the interpretation of nanoindentation experiments conducted at AUT.

Preliminary results have also been obtained for gradient elasticity considerations of the above problems. These were extensions of previous results obtained by the SI dealing with the elimination of singularities from dislocation and disclination lines [12 and references therein]. These extensions and implications of gradient elasticity in nano-objects will be included in the planned monograph by Romanov and Aifantis [11].

[1] A.E. Romanov, A.L. Kolesnikova, I.A. Ovid'ko, and E.C. Aifantis, Disclinations in nanocrystalline materials: Manifestation of the relay mechanism of plastic deformation", Materials Science and Engineering A 503, 62-67, 2009.

[2] A.L. Kolesnikova and A.E. Romanov, Twist disclination loop in an elastic spheroid, Technacal Physics Letters 35, 985-989, 2009.

[3] A.L. Kolesnikova and A.E. Romanov, Representations of elastic fields of circular dislocation and disclination loops in terms of spherical harmonics and their application to various problems of the theory of defects, International Journal of Solids and Structures 47, 58-70, 2010.

[4] N.A. Bert, A.B. Freidin, A.L. Kolesnikova, I.K. Korolev, and A.E. Romanov, On strain state and pseudo-moiré TEV contrast of InSb quantum dots coherently grown on InAs surface, Physica Status Solidi (a) 207 2323-2326, 2010.

[5] L.M. Dorogin, S. Vlassov, A.L. Kolesnikova, I. Kink, R. Lohmus, and A.E.Romanov Crystal mismatched layers in pentagonal nanorods and nanoparticles, Physica Status Solidi (b) 247, 288-298, 2010.

[6] X. Zhang, A.E. Romanov, and E.C. Aifantis, On gradient nanomechanics: plastic flow in nanopolycrystals, Materials Science Forum 667-669, 991-996, 2011.

[7] N.A. Bert, A.L. Kolesnikova, I.K. Korolev, A.E. Romanov, A.B. Freidin, V.V. Chaldyshev, and E.C. Aifantis, Elastic fields and physical properties of surface quantum dots, Physics of the Solid State 53, 2091–2102, 2011.

[8] A.E. Romanov, A.L. Kolesnikova, and E.C. Aifantis, "Disclinations and materials Structure", in Advanced Materials, Tutorial vol.4 D.L. Merson Ed., Togliatti, TSU, 2011, pp. 251-316 /in Russian/.

[9] A.E. Romanov, A.A. Vikarchuk, A.L. Kolesnikova, L.M. Dorogin, I. Kink, and E.C. Aifantis, Structural transformations in nano- and microobjects triggered by disclinations, Journal of Materials Research 27, 545-551, 2012.

[10] A.V.Proskura A.B. Freidin, A.L. Kolesnikova, N.F. Morozov, and A.E. Romanov, Plane elasticity problem for the concentrated force acting on the half-space weakened by a circular hole, Journal of Applied Mechanics, to be submitted 2012.

[11] A.E. Romanov and E.C. Aifantis, "Defects at the Nanoscale", in preparation.

[12] E.C. Aifantis, Non-singular dislocation fields, in: Proc. Dislocations 2008, Ed. A.H.W. Ngan, IOP Conf. Series: Mater. Sci. Engng. 3, 012026/1-10 (2009).