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

Russian Federation

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

Russian Federation

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

Russian Federation

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

Russian Federation

References

  1. Genç A., Patarroyo J., Sancho-Parramon J., Bastús N.G., Puntes V., Arbiol, J. Hollow metal nanostructures for enhanced plasmonics: synthesis, local plasmonic properties and applications. Nanophotonics, 2016, vol. 6, no. 1, pp. 193–213. doi: 10.1515/nanoph-2016-0124.
  2. Wang X.Z., Liu F.J., Chen X.Y., Lu G.X., Song X.J., Tian J., Cui H.Z., Zhang G.S., Gao K.D. SnO2 core-shell hollow microspheres co-modification with Au and NiO nanoparticles for acetone gas sensing. Powder Technology, 2020, vol. 364, pp. 159–166. doi: 10.1016/j.powtec.2020.02.006.
  3. Zhu C.Y., Wang H.W., Guan C. Recent progress on hollow array architectures and their applications in electrochemical energy storage. Nanoscale Horizons, 2020, vol. 5, no. 8, pp. 1188–1199. doi: 10.1039/D0NH00332H.
  4. Asset T., Chattot R., Fontana M., Mercier-Guyon B., Job N., Dubau L., Maillard F. A Review on Recent Developments and Prospects for the Oxygen Reduction Reaction on Hollow Pt-alloy Nanoparticles. ChemPhysChem, 2018, vol. 19, no. 13, pp. 1552–1567. doi: 10.1002/cphc.201800153.
  5. Yasun E., Gandhi S., Choudhury S., Mohammadinejad R., Benyettou F., Gozubenli N., Arami H. Hollow Micro and Nanostructures for Therapeutic and Imaging Applications. Journal of Drug Delivery Science and Technology, 2020, vol. 60, article number 102094. doi: 10.1016/j.jddst.2020.102094.
  6. Anderson B.D., Tracy J.B. Nanoparticle conversion chemistry: Kirkendall effect, galvanic exchange, and anion exchange. Nanoscale, 2014, vol. 6, no. 21, pp. 12195–12216 doi: 10.1039/C4NR02025A.
  7. Yu L., Yu X.Y., Lou X.W. The Design and Synthesis of Hollow Micro‐/Nanostructures: Present and Future Trends. Advanced Materials, 2018, vol. 30, no. 38, article number 1800939. doi: 10.1002/adma.201800939.
  8. Zhu M.Y., Tang J.J., Wei W.J., Li S.J. Recent progress in the syntheses and applications of multishelled hollow nanostructures. Materials Chemistry Frontiers, 2020, vol. 4, no. 4, pp. 1105–1149. doi: 10.1039/C9QM00700H.
  9. Belova I.V., Evteev A.V., Levchenko E.V., Murch G.E. The synthesis, stability and shrinkage of hollow nanoparticles: an overview. Journal of Nano Research, 2009, vol. 7, pp. 19–26. doi: 10.4028/ href='www.scientific.net/JNanoR.7.19' target='_blank'>www.scientific.net/JNanoR.7.19.
  10. Yang Z.J., Yang N.L., Pileni M.P. Nano Kirkendall effect related to nanocrystallinity of metal nanocrystals: influence of the outward and inward atomic diffusion on the final nanoparticle structure. Journal of Physical Chemistry C, 2015, vol. 119, no. 39, pp. 22249–22260. doi: 10.1021/acs.jpcc.5b06000.
  11. Glodán G., Cserháti C., Beszeda I., Beke D.L. Production of hollow hemisphere shells by pure Kirkendall porosity formation in Au/Ag system. Applied Physics Letters, 2010, vol. 97, no. 11, article number 113109. doi: 10.1063/1.3490675.
  12. Yu H.C., Yeon D.H., Li X., Thornton K. Continuum simulations of the formation of Kirkendall-effect-induced hollow cylinders in a binary substitutional alloy. Acta materialia, 2009, vol. 57, no. 18, pp. 5348–5360. doi: 10.1016/j.actamat.2009.07.033.
  13. Puente A.E.P.Y., Erdeniz D., Fife J.L., Dunand D.C. In situ X-ray tomographic microscopy of Kirkendall pore formation and evolution during homogenization of pack-aluminized Ni–Cr wires. Acta Materialia, 2016, vol. 103, pp. 534–546. doi: 10.1016/j.actamat.2015.10.013.
  14. Vara M., Wang X., Howe J., Chi M.F., Xia Y.N. Understanding the Stability of Pt-Based Nanocages under Thermal Stress Using In Situ Electron Microscopy. ChemNanoMat, 2018, vol. 4, no. 1, pp. 112–117 doi: 10.1002/cnma.201700298.
  15. Zhdanov V.P., Kasemo B. On the feasibility of strain-induced formation of hollows during hydriding or oxidation of metal nanoparticles. Nano letters, 2009, vol. 9, no. 5, pp. 2172–2176. doi: 10.1021/nl9008293.
  16. Evteev A.V., Levchenko E.V., Belova I.V., Murch G.E. Formation of a hollow binary alloy nanosphere: a kinetic Monte Carlo study. Journal of Nano Research, 2009, vol. 7, pp. 11–17. doi: 10.4028/ href='www.scientific.net/JNanoR.7.11' target='_blank'>www.scientific.net/JNanoR.7.11.
  17. Svoboda J., Fischer F.D., Vollath D. Modeling of formation of binary-phase hollow nanospheres from metallic solid nanospheres. Acta materialia, 2009, vol. 57, no. 6, pp. 1912–1919. doi: 10.1016/j.actamat.2008.12.038.
  18. Fischer F.D., Svoboda J. Modelling of Reaction of Metallic Nanospheres with Gas. Solid State Phenomen, 2011, vol. 172-174, pp. 1028–1037. doi: 10.4028/ href='www.scientific.net/SSP.172-174.1028' target='_blank'>www.scientific.net/SSP.172-174.1028.
  19. Levitas V.I., Attariani H. Mechanochemical continuum modeling of nanovoid nucleation and growth in reacting nanoparticles. Journal of Physical Chemistry C, 2012, vol. 116, no. 1, pp. 54–62. doi: 10.1021/jp2055365.
  20. Klinger L., Kraft O., Rabkin E. A model of Kirkendall hollowing of core–shell nanowires and nanoparticles controlled by short-circuit diffusion. Acta Materialia, 2015, vol. 83, pp. 180–186. doi: 10.1016/j.actamat.2014.09.050.
  21. Gusak A.M., Zaporozhets T.V., Tu K.N., Gösele U. Kinetic analysis of the instability of hollow nanoparticles. Philosophical Magazine, 2005, vol. 85, no. 36, pp. 4445–4464. doi: 10.1080/14786430500311741.
  22. Fischer F.D., Svoboda J. High temperature instability of hollow nanoparticles. Journal of Nanoparticle Research, 2008, vol. 10, no. 2, pp. 255–261. doi: 10.1007/s11051-007-9242-6.
  23. Evteev A.V., Levchenko E.V., Belova I.V., Murch G.E. Shrinking kinetics by vacancy diffusion of a pure element hollow nanosphere. Philosophical Magazine, 2007, vol. 87, no. 25, pp. 3787–3796. doi: 10.1080/14786430601103005.
  24. Yanovsky V.V., Kopp M.I., Ratner M.A. Evolution of vacancy pores in bounded particles. Functional materials, 2019, vol. 26, no. 1, pp. 131–151. doi: 10.15407/fm26.01.131.
  25. Klinger L., Murch G. E., Belova I.V., Rabkin E. Pores shrinkage and growth in polycrystalline hollow nanoparticles and nanotubes. Scripta Materialia, 2020, vol. 180, pp. 93–96. doi: 10.1016/j.scriptamat.2020.01.029.
  26. Valencia F.J., Ramírez M., Varas A., Rogan J. Understanding the Stability of Hollow Nanoparticles with Polycrystalline Shells. Journal of Physical Chemistry C, 2020, vol. 124, no. 18, pp. 10143–10149. doi: 10.1021/acs.jpcc.0c00258.
  27. Valencia F.J., Ramírez M., Varas A., Rogan J., Kiwi M. Thermal Stability of Hollow Porous Gold Nanoparticles: A Molecular Dynamics Study. Journal of Chemical Information and Modeling, 2020, vol. 60, no. 12, pp. 6204–6210. doi: 10.1021/acs.jcim.0c00785.
  28. Romanov A.E., Polonsky I.A., Gryaznov V.G., Nepijko S.A., Junghanns T., Vitrykhovski N.I. Voids and channels in pentagonal crystals. Journal of crystal growth, 1993, vol. 129, no. 3-4, pp. 691–698. doi: 10.1016/0022-0248(93)90505-Q.
  29. Yasnikov I.S., Vikarchuk A.A. Evolution of the formation and growth of a cavity in pentagonal crystals of electrolytic origin. Physics of the Solid State, 2006, vol. 48, no. 8, pp. 1433–1438.
  30. Vlasov N.M., Dragunov Y.G. Phase transformations in pentagonal nanocrystals. Technical Physics, 2013, vol. 58, no. 2, pp. 218–222.
  31. Vlasov N.M., Zaznoba V.A. Kinetics of migration (deposition) of fission products and interstitial impurities to sinks with different singularities. Physics of the Solid State, 2014, vol. 56, no. 3, pp. 518–521.
  32. Yasnikov I.S. Mechanism of the formation of cavities in icosahedral metallic small particles of electrolytic origin. Physics of the Solid State, 2007, vol. 49, no. 7, pp. 1224–1228.
  33. Yasnikov I.S., Vikarchuk A.A. The formation of cavities in icosahedral small particles formed in the process of metal electrocrystallization. Pisma v Zhurnal tekhnicheskoy fiziki, 2007, vol. 33, no. 19, pp. 24–31.
  34. Tsagrakis I., Yasnikov I.S., Aifantis E.C. Gradient elasticity for disclinated micro crystals. Mechanics Research Communications, 2018, vol. 93, pp. 159–162. doi: 10.1016/j.mechrescom.2017.11.007.
  35. Yasnikov I.S., Vikarchuk A.A. Concerning the existence of cavities in icosahedral small metal particles of electrolytic nature. Pisma v Zhurnal eksperimentalnoy i teoreticheskoy fiziki, 2006, vol. 83, no. 1-2, pp. 46–49.
  36. Wang X., Figueroa-Cosme L., Yang X., Luo M., Liu J., Xie Z.X., Xia Y.N. Pt-based icosahedral nanocages: using a combination of {111} facets, twin defects, and ultrathin walls to greatly enhance their activity toward oxygen reduction. Nano letters, 2016, vol. 16, no. 2, pp. 1467–1471. doi: 10.1021/acs.nanolett.5b05140.
  37. Han L., Long P., Bai J.F., Che S.N. Spontaneous formation and characterization of silica mesoporous crystal spheres with reverse multiply twinned polyhedral hollows. Journal of the American Chemical Society, 2011, vol. 133, no. 16, pp. 6106–6109. doi: 10.1021/ja110443a.
  38. Hou P.F., Cui P.L., Liu H., Li J.L., Yang J. Nanoscale noble metals with a hollow interior formed through inside-out diffusion of silver in solid-state core-shell nanoparticles. Nano Research, 2015, vol. 8, no. 2, pp. 512–522. doi: 10.1007/s12274-014-0663-0.
  39. Huang H.W., Zhang L., Lv T., Ruditskiy A., Liu J.Y., Ye Z.Z., Xia Y.N. Five-Fold Twinned Pd Nanorods and Their Use as Templates for the Synthesis of Bimetallic or Hollow Nanostructures. ChemNanoMat, 2015, vol. 1, no. 4, pp. 246–252. doi: 10.1002/cnma.201500042.
  40. Tehuacanero-Cuapa S., Palomino-Merino R., Reyes-Gasga J. CBED electron beam drilling and closing of holes in decahedral silver nanoparticles. Radiation Physics and Chemistry, 2013, vol. 87, pp. 59–63. doi: 10.1016/j.radphyschem.2013.02.023.
  41. Tehuacanero-Cuapa S., Reyes-Gasga J., Brès E.F., Palomino-Merino R., García-García R. Holes drilling in gold and silver decahedral nanoparticles by the convergent beam electron diffraction electron beam. Radiation Effects and Defects in Solids, 2014, vol. 169, no. 10, pp. 838–844. doi: 10.1080/10420150.2014.958747.
  42. Tehuacanero-Cuapa S., Reyes-Gasga J., Rodríguez-Gómez A., Bahena D., Hernández-Calderón I., García-García R. The low-loss EELS spectra from radiation damaged gold nanoparticles. Journal of Applied Physics, 2016, vol. 120, no. 16, article number 164302. doi: 10.1063/1.4965862.
  43. Kolesnikova A.L., Romanov A.E. Stress relaxation in pentagonal whiskers. Pisma v Zhurnal tekhnicheskoy fiziki, 2007, vol. 33, no. 20, pp. 73–79.
  44. Gutkin M.Y., Kolesnikova A.L., Krasnitckii S.A., Dorogin L.M., Serebryakova V.S., Vikarchuk A.A., Romanov A.E. Stress relaxation in icosahedral small particles via generation of circular prismatic dislocation loops. Scripta Materialia, 2015, vol. 105, pp. 10–13. doi: 10.1016/j.scriptamat.2015.04.015.
  45. Gutkin M.Y., Kolesnikova A.L., Krasnitckii S.A., Romanov A.E., Shalkovskii A.G. Misfit dislocation loops in hollow core–shell nanoparticles. Scripta Materialia, 2014, vol. 83, no. 1-4, pp. 1–4. doi: 10.1016/j.scriptamat.2014.03.005.
  46. Krauchanka M.Y., Krasnitckii S.A., Gutkin M.Y., Kolesnikova A.L., Romanov A.E. Circular loops of misfit dislocations in decahedral core-shell nanoparticles. Scripta Materialia, 2019, vol. 167, pp. 81–85. doi: 10.1016/j.scriptamat.2019.03.031.
  47. Gutkin M.Y., Kolesnikova A.L., Yasnikov I.S., Vikarchuk A.A., Aifantis E.C., Romanov A.E. Fracture of hollow multiply-twinned particles under chemical etching. European Journal of Mechanics A-Solids, 2018, vol. 68, pp. 133–139. doi: 10.1016/j.euromechsol.2017.11.004.
  48. Dorogin L.M., Vlassov S., Kolesnikova A.L., Kink I., Lõhmus R., Romanov A.E. Crystal mismatched layers in pentagonal nanorods and nanoparticles. Physica status solidi B-basic solid state physics, 2010, vol. 247, no. 2, pp. 288–298. doi: 10.1002/pssb.200945385.
  49. Gutkin M.Yu., Panpurin S.N. Spontaneous formation and equilibrium distribution of cylindrical quantum dots in atomically inhomogeneous pentagonal nanowires. Journal of macromolecular science part B-physics, 2013, vol. 52, no. 12, pp. 1756–1769. doi: 10.1080/00222348.2013.808929.
  50. Ding Y., Sun X.L., Wang Z.L., Sun S.H. Misfit dislocations in multimetallic core-shelled nanoparticles. Applied Physics Letters, 2012, vol. 100, no. 11, article number 111603. doi: 10.1063/1.3695332.
  51. Bhattarai N., Casillas G., Ponce A., Jose-Yacaman M. Strain-release mechanisms in bimetallic core–shell nanoparticles as revealed by Cs-corrected STEM. Surface science, 2013, vol. 609, pp. 161–166. doi: 10.1016/j.susc.2012.12.001.
  52. Khanal S., Casillas G., Bhattarai N., Velázquez-Salazar J.J., Santiago U., Ponce A., Mejia-Rosales S., José-Yacamán M. CuS2-Passivated Au-Core, Au3Cu-shell nanoparticles analyzed by atomistic-resolution Cs-corrected STEM. Langmuir, 2013, vol. 29, no. 29, pp. 9231–9239. doi: 10.1021/la401598e.
  53. De Wit R. Partial disclinations. Journal of Physics C: Solid State Physics, 1972, vol. 5, pp. 529–534. doi: 10.1088/0022-3719/5/5/004.
  54. Romanov A.E., Kolesnikova A.L. Application of disclination concept to solid structures. Progress in Materials Science, 2009, vol. 54, no. 6, pp. 740–769. doi: 10.1016/j.pmatsci.2009.03.002.
  55. Polonsky I.A., Romanov A.E., Gryaznov V.G., Kaprelov A.M. Disclination in an elastic sphere. Philosophical magazine A-physics of condensed matter structure defects and mechanical properties, 1991, vol. 64, no. 2, pp. 281–287. doi: 10.1080/01418619108221185.
  56. Kolesnikova A.L., Gutkin M.Yu., Proskura A.V., Morozov N.F., Romanov A.E. Elastic fields of straight wedge disclinations axially piercing bodies with spherical free surfaces. International Journal of Solids and Structures, 2016, vol. 99, pp. 82–96. doi: 10.1016/j.ijsolstr.2016.06.029.
  57. Khirt Dzh., Lote I. Teoriya dislokatsiy [Dislocation theory]. Moscow, Atomizdat Publ., 1972. 599 p.

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