Pair interaction of intersecting dilatation and disclination defects

Keywords: Disclination, Dilatation line, Pair interaction

Abstract

       An elastic interaction of the intersecting dilatation and disclination defects located in an infinite linear isotropic media is investigated. The eigenstrain approach is employed to obtain the analytical expressions describing the pair interaction between intersecting dilatational lines and intersecting wedge disclinations. It is demonstrated that the interaction energy strongly depends on the intersection angle between the defects. The energy reaches the maximum value if the defect lines are coincided while the energy reaches the minimum value if the defect lines are orthogonal. Besides, it is shown that interaction energy of intersecting wedge disclinations strongly depends on the elastic properties of the media: the less the
Poisson ratio, the less the energy. The obtained analytical results seem to be applicable for the theoretical analysis of the residual stress relaxation mechanisms in heterostructures with pentagonal symmetry such as icosahedral particles 

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Author Biographies

Stanislav A. Krasnitckii, ITMO University, 49 Kronverksky pr., bldg. A, St. Petersburg 197101, Russian Federation

Cand. Sci. (Phys.–Math.),
Associate Professor at the Institute of Advanced Data
Transfer Systems, ITMO University (St. Petersburg,
Russian Federation)

Andrei M. Smirnov, ITMO University, 49 Kronverksky pr., bldg. A, St. Petersburg 197101, Russian Federation

Cand. Sci. (Phys.–Math.),
Associate Professor at the Institute of Advanced Data
Transfer Systems, ITMO University (St. Petersburg,
Russian Federation)

References

Martinez A. D., Fioretti A. N., Toberer E. S., Tamboli A. C. Synthesis, structure, and optoelectronic properties of II–IV–V 2 materials. Journal of Materials Chemistry A. 2017;5(23): 11418–11435. https://doi.org/10.1039/C7TA00406K

Zhou H., Xu J., Liu X., … Fan T. Bio-inspired photonic materials: Prototypes and structural effect designs for applications in solar energy manipulation. Advanced Functional Materials. 2018;28(24): 1705309. https://doi.org/10.1002/adfm.201705309

Shao L., Zhuo X., Wang J. Advanced plasmonic materials for dynamic color display. Advanced Materials. 2018;30(16): 1704338. https://doi.org/10.1002/adma.201704338

Matthews J. W., Blakeslee A. E. Defects in epitaxial multilayers: I. Misfit dislocations. Journal of Crystal Growth. 1984;27: 118–125. https://doi.org/10.1016/S0022-0248(74)80055-2

Freund L. B., Suresh S. Thin film materials: stress, defect formation and surface evolution. Cambridge: Cambridge University Press; 2003. 803 p. https://doi.org/10.1017/CBO9780511754715

Gutkin M. Yu., Kolesnikova A. L., Romanov A. E. Nanomechanics of stress relaxation in composite low-imensional structures. Encyclopedia of ContinuumMechanics. 2020: 1778–1799. https://doi.org/10.1007/978-3-662-55771-6_161

Smirnov A. M., Kremleva A. V., Ivanov A. Yu., … Romanov A. E. Stress-strain state and piezoelectric polarization in orthorhombic Ga2O3 thin films depending on growth orientation. Materials and Design. 2023;226: 111616. https://doi.org/10.1016/j.matdes.2023.111616

Kukushkin S. A., Osipov A. V. A new mechanism of elastic energy relaxation in heteroepitaxy of monocrystalline films: Interaction of point defects and dilatation dipoles. Mechanics of Solids. 2013;48: 216–227. https://doi.org/10.3103/S0025654413020143

Ramdani R., Hounkpati V., Chen J., Ruterana P. Stress relaxation in III-V nitrides: investigation of metallic atoms interaction with the N-vacancy. Europhysics Letters. 2022;137(6): 66003. https://doi.org/10.1209/0295-5075/ac6067

Gutkin M. Yu., Kolesnikova A. L., Romanov A. E. Misfit dislocations and other defects in thin films. Materials Science and Engineering: A. 1993;164(1-2): 433–437. https://doi.org/10.1016/0921-5093(93)90707-L

Bobylev S. V., Morozov N. F., Ovid’Ko I. A., Semenov B. N., Sheinerman A. G. Misfit dislocation configurations at interphase boundaries between misoriented crystals in nanoscale film-substrate systems. Reviews on Advanced Materials Science.2012;32(1): 24–33.

Gutkin M. Yu., Kolesnikova A. L., Krasnitckii S. A., Romanov A. E., Shalkovskii A. G. Misfit dislocation loops in hollow core-shell nanoparticles. Scripta Materialia. 2014;83: 1–4. https://doi.org/10.1016/j.scriptamat.2014.03.005

Kukushkin S. A., Osipov A. V., Bessolov V. N., Konenkova E. V., Panteleev V. N. Misfit dislocation locking and rotation during gallium nitride growth on SiC/Si substrates. Physics of the Solid State. 2017;59(4): 674–681. https://doi.org/10.1134/S1063783417040114

Krasnitckii S. A., Smirnov A. M., Gutkin M. Yu. Axial misfit stress relaxation in core-shell nanowires with polyhedral cores through the nucleation of misfit prismatic dislocation loops. Journal of Materials Science. 2020;55: 9198–9210. https://doi.org/10.1007/s10853-020-04401-3

Smirnov A. M., Krasnitckii S. A., Gutkin M. Yu. Generation of misfit dislocations in a core-shell nanowire near the edge of prismatic core. Acta Materialia. 2020;186: 494–510. https://doi.org/10.1016/j.actamat.2020.01.018

Smirnov A. M., Krasnitckii S. A., Rochas S. S., Gutkin M. Yu. Critical Conditions of Dislocation Generation in Core-Shell Nanowires: A Review. Reviews on Advanced Materials and Technologies. 2020;2(3): 19–43. https://doi.org10.17586/2687-0568-2020-2-3-19-4

Smirnov A. M., Young E. C., Bougrov V. E., Speck J. S., Romanov A. E. Stress relaxation in semipolar and nonpolar III-nitride heterostructures by formation of misfit dislocations of various origin. Journal of Applied Physics. 2019;126(24): 245104. https://doi.org/10.1063/1.5126195

Sheinerman A. G., Gutkin M. Yu. Misfit disclinations and dislocation walls in a two-phase cylindrical composite. Physica Status Solidi (a). 2001;184(2): 485–505. https://doi.org/10.1002/1521-396X(200104)184:2<485::AID-PSSA485>3.0.CO;2-4

Kolesnikova A. L., Ovidko I. A., Romanov A. E. Misfit disclination structures in nanocrystalline and polycrystalline films. Solid State Phenomena. 2002;87: 265–276. https://doi.org/10.4028/www.scientific.net/SSP.87.265

Skiba N. V., Ovid’ko I. A., Sheinerman A. G. Misfit disclination dipoles in nanocrystalline films and coatings. Physics of the Solid State. 2009;51(2): 280–285. https://doi.org/10.1134/S1063783409020127

Telyatnik R. S., Osipov A. V., Kukushkin S. A. Pore-and delamination-induced mismatch strain relaxation and conditions for the formation of dislocations, cracks, and buckles in the epitaxial AlN (0001)/SiC/Si (111) heterostructure. Physics of the Solid State. 5015;57(1): 162–172. https://doi.org/10.1134/S106378341501031X

Argunova T. S., Gutkin M. Yu., Mokhov E. N., Kazarova O. P., Lim J. H., Shcheglov M. P. Prevention of AlN crystal from cracking on SiC substrates by evaporation of the substrates. Physics of the Solid State. 2015;57(12): 2473–2478. https://doi.org/10.1134/S1063783415120057

Kukushkin S. A., Osipov A. V., Rozhavskaya M. M., Myasoedov A. V., Troshkov S. I., Lundin V. V., Sorokin L. M., Tsatsul’nikov A. F. Growth and structure of GaN layers on silicon carbide synthesized on a Si substrate by the substitution of atoms: a model of the formation of V-defects during the growth of GaN. Physics of the Solid State. 2015;57(9): 1899–1907. https://doi.org/10.1134/S1063783415090218

Schmidt V., McIntyre P. C., Gцsele U. Morphological instability of misfit-strained core-shell nanowires. Physical Review B. 2008;77(23): 235302. https://doi.org/10.1103/PhysRevB.77.235302

Hofmeister H. Shape variations and anisotropic growth of multiply twinned nanoparticles. Zeitschrift fer Kristallographie. 2009;224(11): 528–538. https://doi.org/10.1524/zkri.2009.1034

Ruditskiy A., Peng H. C., Xia Y. Shape-controlled metal nanocrystals for heterogeneous catalysis. Annual Rview of Chemical and Biomolecular Engineering. 2016;7: 327–348. https://doi.org/10.1146/annurev-chembioeng-080615-034503

Romanov A. E., Kolesnikova A. L. Application of disclination concept to solid structures. Progress in Materials Science. 2009;54(6): 740–769. https://doi.org/10.1016/j.pmatsci.2009.03.002

Romanov A. E., Kolesnikova A. L. Elasticity boundary-value problems for straight wedge disclinations. A review on methods and results. Reviews on Advanced Materials and Technologies. 2021;3(1): 55–95. https://doi.org/10.17586/2687-0568-2021-3-1-55-95

Yasnikov I. S., Vikarchuk A. A. Voids in icosahedral small particles of an electrolytic metal. JETP Letters. 2006;83(1): 42–45. https://doi.org/10.1134/S0021364006010103

Huang J., Yan Y., Li X., Qiao X., Wu X., Li J., Shen R., Yang D., Zhang H. Unexpected Kirkendall effect in twinned icosahedral nanocrystals driven by strain gradient. Nano Research. 2020;13: 2641–2649. https://doi.org/10.1007/s12274-020-2903-9

Romanov A. E., Polonsky I. A., Gryaznov V. G., Nepijko S. A., Junghanns T., Vitrykhovski N. J. Voids and channels in pentagonal crystals. Journal of Crystal Growth. 1993;129(3-4): 691–698. https://doi.org/10.1016/0022-0248(93)90505-Q

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. 2013;52(12): 1756–1769. https://doi.org/10.1080/00222348.2013.808929

Krasnitckii S. A., Gutkin M. Yu., Kolesnikova A. L., Romanov A. E. Formation of a pore as stress relaxation mechanism in decahedral small particles. Letters on Materials. 2022;12(2): 137–141. https://doi.org/10.22226/2410-3535-2022-2-137-141

Khramov A. S., Krasnitckii S. A., Smirnov A. M., Gutkin M. Yu. The void evolution kinetics driven by residual stress in icosahedral particles. Materials Physics and Mechanics. 2022;50(3): 401–409. https://doi.org/10.18149/MPM.5032022_4

Mura T. Micromechanics of defects in solids. Boston: Martinus Nijhoff Publishers; 1987. 587 p.

Kolesnikova A. L., Soroka R. M., Romanov A. E. Defects in the elastic continuum: classification, fields and physical analogies. Materials Physics and Mechanics. 2013;17(1): 71–91.

De Wit R. Partial disclinations. Journal of Physics C: Solid State Physics. 1972;5(5): 529–534. https://doi.org/10.1088/0022-3719/5/5/004

Vladimirov V. I., Romanov A. E. Disclinations in Crystals. Leningrad: Izdatel’stvo Nauka; 1986. 224p.

Kolesnikova A. L., Gutkin M. Yi., 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;99: 82–96. https://doi.org/10.1016/j.ijsolstr.2016.06.029

Prudnikov A. P., Brychkov I. A., Marichev O. I. Integrals and series: special functions (Vol. 2). Amsterdam: Gordon and Breach Science Publishers; 1998. 740p.

Polonsky I. A., Romanov A. E., Gryaznov V. G., Kaprelov A. M. Disclination in an elastic sphere. Philosophical Magazine A. 1991;64(2): 281–287. https://doi.org/10.1080/01418619108221185

Mayoral A., Barron H., Estrada-Salas R., Vazquez-Duran A., Josй-Yacamбn M. Nanoparticle stability from the nano to the meso interval. Nanoscale. 2010;2(3): 335–342. https://doi.org/10.1039/B9NR00287A

Published
2023-10-12
How to Cite
Krasnitckii, S. A., & Smirnov, A. M. (2023). Pair interaction of intersecting dilatation and disclination defects. Condensed Matter and Interphases, 25(4), 505-513. https://doi.org/10.17308/kcmf.2023.25/11473
Section
Original articles