Dislocation mechanisms of misfit stress relaxation in crystalline nanoheterostructures

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A brief review of theoretical models describing the dislocation mechanisms of misfit stress relaxation in crystalline nanoheterostructures of lower dimension, such as composite nanoparticles, nanowires, and nanolayers is presented. The critical conditions for the appearance of the first misfit dislocations in such nanoheterostructures are determined. The equilibrium distribution density was calculated for the circular prismatic loops of misfit dislocations in core–shell nanowires and proved to be in good agreement with the results of experimental observations. Energy barriers have been found for the nucleation of misfit dislocations in composite nanowires with a core shaped as a rectangular prism and in composite nanolayers with long prismatic inclusions. The lowest barriers are shown to occur upon the emission of partial or perfect dislocation dipoles by the edges of inclusions, depending on the characteristic dimensions of a heterostructure. The directions of further studies in this area were proposed.

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作者简介

M. Gutkin

Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences; ITMO University; Peter the Great St. Petersburg Polytechnic University

编辑信件的主要联系方式.
Email: m.y.gutkin@gmail.com
俄罗斯联邦, Saint Petersburg, 199178; Saint Petersburg, 197101; Saint Petersburg, 195251

A. Kolesnikova

Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences; ITMO University

Email: m.y.gutkin@gmail.com
俄罗斯联邦, Saint Petersburg, 199178; Saint Petersburg, 197101

S. Krasnitckii

ITMO University

Email: m.y.gutkin@gmail.com
俄罗斯联邦, Saint Petersburg, 197101

K. Mikaelyan

Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences

Email: m.y.gutkin@gmail.com
俄罗斯联邦, Saint Petersburg, 199178

D. Mikheev

Peter the Great St. Petersburg Polytechnic University

Email: m.y.gutkin@gmail.com
俄罗斯联邦, Saint Petersburg, 195251

D. Petrov

Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences

Email: m.y.gutkin@gmail.com
俄罗斯联邦, Saint Petersburg, 199178

A. Romanov

ITMO University; Ioffe Institute

Email: m.y.gutkin@gmail.com
俄罗斯联邦, Saint Petersburg, 197101; Saint Petersburg, 194021

A. Smirnov

ITMO University

Email: m.y.gutkin@gmail.com
俄罗斯联邦, Saint Petersburg, 197101

A. Chernakov

Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences; Ioffe Institute

Email: m.y.gutkin@gmail.com
俄罗斯联邦, Saint Petersburg, 199178; Saint Petersburg, 194021

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2. 1. Models of mismatch dislocations in spherical core–shell nanoheterostructures: in solid (a) and hollow (b) monocrystalline nanoparticles, in decahedral nanoparticles (c) and in nanoparticles with hemispherical cores (d, e). Diagrams (a–d) show circular prismatic dislocation loops (PDPs), while diagram (e) shows rectilinear edge dislocation. Here a1 and a2 are the lattice parameters of the core and shell materials; Rp, Rc and R are the radii of the pore, core and shell; b is the Burgers vector of dislocations; ω is the value of the Frank vector of wedge disclosure, which models the stress state in a decahedral particle; (x, y, z) is the Cartesian coordinate system.

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3. Fig. 2. Models of circular prismatic dislocation loops (PDPs) in various cylindrical nanoheterostructures: in a core–shell nanowire (a), around a hollow nanotube embedded in a volumetric matrix (b), and at a flat transverse interface in a segmented nanowire (c). Here a1 and a2 are the parameters lattices of contacting materials; Rp, Rc, Rt, and R are the radii of pores, nuclei, nanotubes, and nanowires; b is the Burgers vector of the dislocation loop.

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4. Fig. 3. Equilibrium distribution of DN loops in a core–shell nanowire. (a) A model of a periodic series of DN loops. (b) The dependence of the energy change of a ΔE nanowire upon the formation of a periodic series of DN loops in it on the reduced distance h/R between the loops for a nanowire consisting of an InAs core and a GaAs shell with a mismatch f = (a1 — a2)/a1 = 0.0717 [58]. The minimum on the curve corresponds to the equilibrium distance between the loops h ≈ 8.35 nm (according to [41]). Here a1 and a2 are the lattice parameters of the core and shell materials, Rc and R are the radii of the core and shell, G and v are the shear modulus and Poisson's ratio, which are the same for core and shell materials, and b is the Burgers vector of the DN loop.

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5. 4. The cross section of the inclusion in the form of a long parallelepiped (nanowires) with dimensions 2l = 2a in a 2d nanolayer. The upper left edge of the nanowire emits a dipole of edge dislocations with Burgers ± b vectors, one of which slides along the inclusion boundary, occupies an equilibrium position x1 on it and becomes a mismatch dislocation, while the second slides to the free surface of the nanolayer and either stops at the equilibrium position x2 or reaches this surface. Here (x, y) is the Cartesian coordinate system in the nanowire cross section.

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6. 5. Energy barriers ΔW for different mechanisms of dislocation nucleation in a model Au–Pd nanowire with a radius of 5, 10, and 50 nm (according to [61]). The diagrams of these mechanisms are shown below the histogram (from left to right): sliding of a partial mismatch dislocation (PD) from the surface of the nanowire along the interface inside the shell, sliding of a complete mismatch dislocation (PD) from the surface of the nanowire along the interface inside the shell, sliding of the PD from the surface of the nanowire along the interface inside the core, sliding of the PD from the surface of the nanowire along the interface inside the core, crawling of the PD from the surface of the nanowire to at the interface, the emission of sliding black holes by the edge of the core of the dipole, the emission of a sliding PDN by the edge of the core of the dipole. Here R is the radius of the nanowire, 2l is the side of the square section of the core.

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