Resiadual stress relaxation in decahedral particles through the formation of a central spherical void

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Abstract

Small metal particles with a body-centered crystal lattice (BCC) often take the form of polyhedrons with fifth-order symmetry axes such as the icosahedron, decahedron, and pentagonal prism. The quintic symmetry axes, forbidden by the traditional crystallography laws, cause inhomogeneous elastic stress and strain in these particles. Under certain conditions, these stress and strain could relax through the change in the particle structure: the formation of partial and perfect dislocations, misfit layers, and the nucleation of cracks and voids. Within the quasi-equilibrium energy approach, the authors proposed a theoretical model of residual stress relaxation in decahedral particles due to the formation of a central spherical void. The explicit analytical expressions for energies of solid and hollow decahedral particles are found. The elastic energy of a hollow decahedral particle is defined as the work spent on the nucleation of a positive wedge disclination with the power ω≈0.0163 rad (≈7°20') in the elastic spherical shell under its own stress field. The authors determined the change in the surface energy due to the formation of a void considering the influence of the relaxation effect of the first coordination sphere surrounding the vacancy on the particle volume change. The energy change of decahedral particles during the formation of a spherical void is calculated and the optimal and critical parameters of this process are determined. The study shows that there some critical radius of a particle, if reached the formation of the central spherical void becomes energetically favorable. Moreover, the study shows that a pore germ will grow until it reaches a certain optimal size corresponding to the greatest change in the system energy. The numerical calculations correspond with experimental observations of unstable voids in the rather small silver and gold decahedral particles with the diameter of 30–40 nm and stable voids in relatively large copper decahedral particles with the diameter of ~1 μm.

About the authors

Stanislav A. Krasnitsky

Peter the Great St. Petersburg Polytechnic University, St. Petersburg (Russia)

Author for correspondence.
Email: krasnitsky@inbox.ru
ORCID iD: 0000-0003-4363-8242

PhD (Physics and Mathematics), senior researcher

Россия

Anna L. Kolesnikova

Institute of Problems of Mechanical Engineering of the Russian Academy of Sciences, St. Petersburg (Russia)

Email: fake@neicon.ru
ORCID iD: 0000-0003-4116-4821

Doctor of Sciences (Physics and Mathematics), leading researcher

Россия

Mikhail Yu. Gutkin

Institute of Problems of Mechanical Engineering of the Russian Academy of Sciences, St. Petersburg (Russia)

Email: fake@neicon.ru
ORCID iD: 0000-0003-0727-6352

Doctor of Sciences (Physics and Mathematics), chief researcher

Россия

Aleksey E. Romanov

ITMO University, St. Petersburg (Russia)

Email: fake@neicon.ru
ORCID iD: 0000-0003-3738-408X

Doctor of Sciences (Physics and Mathematics), Professor

Россия

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