Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials
Founded at 2009

Contribution of grain boundaries with matching planes to internal friction

V.G. Kul’kov

University «Moscow Power Engineering Institute» in Volzhsky

DOI: 10.26456/pcascnn/2023.15.264

Original article

Abstract: In nanocrystalline metals, there are grain boundaries that, under the influence of shear stresses applied along them, move along the normal. Such boundaries combine two types of the grain boundary deformation – mutual grain slippage along the boundary and its migration. This relationship is easily explained in the model of intercrystalline boundaries with mating crystallographic planes. By solving the differential equation under the action of alternating voltage, the functional dependence of the boundary displacement on the coordinate and time is found. Based on this, the value of the energy dissipated during the oscillation period and the expression for the internal friction caused by the contribution of such boundaries are found. It has the character of a Debye peak. The activation energy of the process is equal to the activation energy of the grain boundary self-diffusion. An atomic mechanism of the boundary motion is proposed, which is based on diffusion processes between extended steps of atomic scale in the boundary.

Keywords: grain boundaries, crystallites, matching planes, boundary migration, diffusion, vacancies, relaxation time

  • Viktor G. Kul’kov – Dr.Sc., Professor, Branch of the National Research, University «Moscow Power Engineering Institute» in Volzhsky


Kul’kov, V.G. Contribution of grain boundaries with matching planes to internal friction / V.G. Kul’kov // Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials. — 2023. — I. 15. — P. 264-273. DOI: 10.26456/pcascnn/2023.15.264. (In Russian).

Full article (in Russian): download PDF file


1. Orlov A.N., Perevezentsev V.N., Rybin V.V. Granitsy zeren v metallakh [Grain boundaries in metals], Moscow, Metallurgiya Publ., 1980, 154 p. (In Russian).
2. Gleiter H., Chalmers B. High-angle grain boundaries, New York, Pergamon Press, 1972, 274 p.
3. Molodov D.A., Gorkaya T., Günster C., Gottstein G. Migration of specific planar grain boundaries in bicrystals: application of magnetic fields and mechanical stresses, Frontiers of Materials Science in China, 2010, vol. 4, issue 3, pp. 291-305. DOI: 10.1007/s11706-010-0080-6.
4. Sheikh-Ali A.D., Szpunar J.A. Sliding behaviour of symmetric tilt near ∑=25 {1 2 16} boundary in zinc bicrystals, Materials Science and Engineering: A, 1998, vol. 245, issue 1, pp. 49-54. DOI: 10.1016/s0921-5093(97)00697-7.
5. Sheikh-Ali A. D., Lavrentyev F. F., Kazarov Y. G. Sliding behaviour of ∑= 9 {1 2 12} symmetric tilt boundary in zinc bicrystals, Acta Materialia, 1997, vol. 45, issue 11, pp. 4505-4512. DOI: 10.1016/S1359-6454(97)00119-5
6. Sheikh-Ali A.D. Coupling of grain boundary sliding and migration within the range of boundary specialness, Acta Materialia, 2010, vol. 58, issue 19, pp. 6249-6255. DOI: 10.1016/j.actamat.2010.07.043.
7. Gorkaya T., Molodov K.D., Molodov D.A., Gottstein G. Concurrent grain boundary motion and grain rotation under an applied stress, Acta Materialia, 2011, vol. 59, issue 14, pp. 5674-5680. DOI: 10.1016/j.actamat.2011.05.042.
8. Molodov D.A, Gorkaya T, Gottstein G. Mechanically driven migration of 〈100〉 tilt grain boundaries in Albicrystals, Materials Science Forum, 2007, vol. 558-559, pp. 927-932. DOI: 10.4028/
9. Suzuki A., Mishin Y. Atomic mechanism of grain boundary migration, Materials Science Forum, 2005, vol. 502, pp. 157-162. DOI: 10.4028/
10. Kar'kina L.E., Kar'kin I.N., Kuznetsov A.R., Gornostyrev Y.N. Grain-boundary shear-migration coupling in al bicrystals. Atomistic modeling, Physics of the Solid State, 2018, vol. 60, issue 10, pp. 1916-1923. DOI: 10.1134/S1063783418100104.
11. Rahman M.J., Zurob H.S., Hoyt J.J. A comprehensive molecular dynamics study of low angle grain boundary mobility in a pure aluminum system, Acta Materialia, 2014, vol. 74, pp. 39-48. DOI: 10.1016/j.actamat.2014.03.063.
12. Cahn J.W., Mishin Y., Suzuki A. Coupling grain boundary motion to shear deformation, Acta Materialia, 2006, vol. 54, issue 19, pp. 4953-4975. DOI: 10.1016/j.actamat.2006.08.004.
13. Maier A.-K., Mari D., Tkalcec I., Schaller R. Theoretical modelling of grain boundary anelastic relaxations, Acta Materialia, 2014, vol. 74, pp. 132-140. DOI: 10.1016/j.actamat.2014.04.016.
14. Ovid'ko I.A., Sheinerman A.G. Free surface effects on stress-driven grain boundary sliding and migration processes in nanocrystalline materials, Acta Materialia, 2016, vol. 121, pp. 117-125. DOI: 10.1016/j.actamat.2016.08.082.
15. Berbenni S., Paliwal B., Cherkaoui M. A micromechanics-based model for shear-coupled grain boundary migration in bicrystals, International Journal of Plasticity, 2013, vol. 44, pp. 68-94. DOI: 10.1016/j.ijplas.2012.11.011.
16. Hadian R., Grabowski B., Race C.P., Neugebauer J. Atomistic migration mechanisms of atomically flat, stepped, and kinked grain boundaries, Physical Review B, 2016, vol. 94, issue 16, pp. 165413-1-165413-10. DOI:10.1103/PhysRevB.94.165413.
17. Gorelik S.S., Dobatkin S.V., Kaputkina L.M. Rekristallizatsiya metallov i splavov [Recrystallization of metals and alloys], Moscow, MISIS Publ., 2005, 432 p. (In Russian).
18. Caillard D., Mompiou F., Legros M., Grain-boundary shear-migration coupling. II. Geometrical model for general boundaries, Acta Materialia, 2009, vol. 57, issue 8, pp. 2390-2402. DOI: 10.1016/j.actamat.2009.01.023.
19. Ralphp B., Howell P.R. Page T.F. The structure of grain boundaries. A model based on planar watching, Physica Status Solidi b, 1973, vol. 55, issue 2, pp. 641-652. DOI: 10.1002/pssb.2220550220.
20. Gronsky R., Thomas G. Direct observations of plane matching by lattice imaging electron microscopy, Scripta Metallurgica, 1977, vol. 11, issue 9, pp. 791-794. DOI: 10.1016/0036-9748(77)90077-1.
21. Pumphrey P.H. A plane matching theory of high angle grain boundary structure, Scripta Metallurgica, 1972, vol. 6, issue 2, pp. 107-114. DOI: 10.1016/0036-9748(72)90260-8.
22. Schindler R., Clemans J.E., Balluffi R.W. On grain boundary dislocations in plane matching grain boundaries, Physica Status Solidi a, 1979, vol. 56, issue 2, pp. 749-761. DOI: 10.1002/pssa.2210560243.
23. Randle V., Ralph B. The coincident axial direction (CAD) approach to grain boundary structure, Journal of Materials Science, 1988, vol. 23, issue 3, pp. 934-940. DOI: 10.1007/BF01153992.
24. Fedorov Y.A. Mezhkristallitnoe proskal'zyvanie po granitse s sopryagayushchimisya ploskostyami [Intercrystallite gliding on boundary with conjugate planes], Fizika metallov i metallovedenie [The Physics of Metals and Metallography], 1991, no. 7, pp. 67-72. (In Russian).
25. Darinskii B.M., Kul'kov V.G. Dvizhenie mezhkristallitnoi granitsy sopryagayushchikhsya ploskostei [Movement of the intercrystalline boundary of the matching planes], Sbornik nauchnykh trudov «Fizika i tekhnologiya materialov elektronnoi tekhniki» [Collection of scientific papers «Physics and technology of electronic equipment materials»], Voronezh, VPI Publ., 1992, pp. 114-117. (In Russian).
26. Hirth J., Lothe J. Theory of Dislocations, New York, John Wiley & Sons Publ., 1982, 857 p.
27. Kul'kov V.G. Migratsiya nesorazmernoi mezhkristallitnoi granitsy i granichnaya samodiffuziya, [Migration of a disproportionate intercrystalline boundary and boundary self-diffusion], Kondensirovannye sredy i mezhfaznye granitsy [Condensed Matter and Interphases], 2022, vol. 24, no. 4, pp. 475-482. DOI: 10.17308/kcmf.2022.24/10552. (In Russian).
28. Nowick A.S., Berry В.S. Anelastic Relaxation in Crystalline Solids, New York, London, Academic Press Publ., 1972, 677 p. DOI: 10.1016/B978-0-12-522650-9.X5001-0.
29. Blunter M.S., Piguzov Yu.V., Ashmarin G.M. et al. Metod vnutrennego treniya v metallovedcheskikh iscledovaniyakh [The method of internal friction in metal studies], Moscow, Metallurgiya Publ., 1991, 248 p. (In Russian).
30. Chuvil'deev V.N. Neravnovesnye granitsy zeren v metallakh. Teoriya i prilozheniya [Nonequilibrium grain boundaries in metals. Theory and Applications], Moscow, Fizmatlit Publ., 2004, 304 p. (In Russian).

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