Frontier Materials & Technologies. 2021; : 27-38
Релаксация остаточных напряжений в декаэдрических частицах путем образования центральной сферической поры
https://doi.org/10.18323/2782-4039-2021-4-27-38Аннотация
Малые металлические частицы с объемно-центрированной кристаллической решеткой (ОЦК) часто принимают форму многогранников с осями симметрии пятого порядка, таких как икосаэдр, декаэдр и пятиугольная призма. Оси симметрии пятого порядка, запрещенные законами классической кристаллографии, вызывают в таких частицах неоднородные упругие напряжения и деформации. При некоторых условиях эти напряжения и деформации могут релаксировать за счет изменения структуры частицы, а именно образования частичных и полных дислокаций, слоев несоответствия, зарождения трещин и пор. В рамках квазиравновесного энергетического подхода предложена теоретическая модель, описывающая релаксацию неоднородных упругих напряжений и деформаций в декаэдрических частицах за счет формирования центральной сферической полости. Найдены явные аналитические выражения для энергий сплошных и полых декаэдрических частиц. Упругая энергия полой декаэдрической частицы определена как работа, затраченная на зарождение в упругой сферической оболочке положительной клиновой дисклинации мощностью ω≈0,0163 рад (≈7°20') в поле ее собственных напряжений. Изменение поверхностной энергии за счет формирования поры определено с учетом влияния эффекта релаксации первой координационный сферы, окружающей вакансию, на изменение объема частицы. Определено изменение энергии декаэдрических частиц при образовании сферической поры, установлены оптимальные и критические параметры этого процесса. Показано, что существует некоторый критический радиус частицы, при достижении которого формирование центральной сферической поры становится энергетически выгодным. Кроме того, показано, что зародыш поры будет расти, пока не достигнет некоторого оптимального размера, соответствующего наибольшему изменению энергии системы. Численные расчеты согласуются с экспериментальными наблюдениями нестабильных пор в относительно малых серебряных и золотых декаэдрических частицах диаметром 30–40 нм и стабильных пор в относительно больших медных декаэдрических частицах диаметром ~1 мкм.
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Frontier Materials & Technologies. 2021; : 27-38
Resiadual stress relaxation in decahedral particles through the formation of a central spherical void
https://doi.org/10.18323/2782-4039-2021-4-27-38Abstract
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.
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