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The interplay between grain boundaries and disclinations in condensed matter physics

  • Maurice Kleman

Abstract

The concept of grain boundary, much studied for its relationship with dislocation motion in plastic deformation, is here developed and associated with that of disclination. After defining a disclination in terms of a Volterra process, we investigate the nature of the interplay between both, with application to two cases: i) in polycrystals the triple junctions result from the stress free merging of disclinations bordering the incident grain boundaries; the plastic properties of nanocrystals, which cannot be attributed directly to dislocations, are related to these disclinations; ii) in lamellar liquid crystalline phases grain boundaries are often the place not only of dislocations, but also of focal conic domains, a stunning disclination system described by G. Friedel one hundred years ago.


* Correspondence address, Dr. Maurice Kleman Institut de Physique du Globe de Paris. 4, place Jussieu - 75252 Paris cédex 05 Tel.: 33(0)1 4427 2188 Fax: 33(0)1 4427 2830 E-mail:

Dedicated to the late Prof. Charles Crussard (1916–2008)


References

[1] C.Crussard: Rev. Met.41 (1944) 118, 139.10.1051/metal/194441040111Search in Google Scholar

[2] F.C.Frank: Discuss. Faraday Soc.25 (1958) 19.10.1039/df9582500019Search in Google Scholar

[3] G.Friedel: Ann. Phys. (Paris)18 (1922) 273.10.1051/anphys/192209180273Search in Google Scholar

[4] F.C.Frank, in: Pittsburgh Conference, Office of Naval Research, 2 (1949) 542.Search in Google Scholar

[5] M.Kleman, J.Friedel: Rev. Mod. Phys.80 (2008) 61.10.1103/RevModPhys.80.61Search in Google Scholar

[6] J.Friedel, M.Kleman: J. de Physique30 (1969) C4:43.10.1051/jphyscol:1969412Search in Google Scholar

[7] F.C.Frank, in: Report on the Symposium on the Plastic Deformation of Crystalline Solids, Carnegie Institute of Technology, Pittsburgh, (1950) 150.Search in Google Scholar

[8] X.Huang, N.Hansen, N.Tsuji: Science312 (2006) 249.10.1126/science.1124268Search in Google Scholar PubMed

[9] K.S.Kumar, H.Van Swygenhoven, S.Suresh: Acta Mater.51 (2003) 5743.10.1016/j.actamat.2003.08.032Search in Google Scholar

[10] H.Van Swygenhoven, P.M.Derlet, A.G.Froseth: Acta Mater.54 (2006) 1975.10.1016/j.actamat.2005.12.026Search in Google Scholar

[11] I.A.Ovid'ko: Rev. Adv. Mater. Sci.10 (2005) 89.Search in Google Scholar

[12] S.Van Petegem, S.Brandstetter, H.Van Swygenhoven, J.-L.Martin: Appl. Phys. Lett.89 (2006) 073102.10.1063/1.2336726Search in Google Scholar

[13] P.G.de Gennes, J.Prost: The Physics of Liquid Crystals, 2nd edn, Clarendon Press, Oxford (1993).Search in Google Scholar

[14] C.Blanc, N.Zuodar, I.Lelidis, M.Kleman, J.-L.Martin: Phys. Rev. E69 (2004) 011705.10.1103/PhysRevE.69.011705Search in Google Scholar PubMed

[15] C.Meyer, S.Asnacios, M.Kleman: Eur. Phys. J. E6 (2001) 245.10.1007/s101890170007Search in Google Scholar

[16] G.Friedel, F.Grandjean: Bull. Soc. Fr. Mineral.33 (1910) 409.Search in Google Scholar

[17] M.Kleman, O.D.Lavrentovich, Yu.A.Nastishin, in: F.R.N.Nabarro, J.P.Hirth (Eds.), Dislocations in Solids, Vol. 12, Elsevier, Amsterdam (2004) 147.10.1016/S1572-4859(05)80005-1Search in Google Scholar

[18] D.Hilbert, S.Cohn-Vossen: Geometry and the Imagination, Chelsea Pub. Cy, New York (1964).Search in Google Scholar

[19] R.Bidaux, N.Boccara, G.Sarma, L.de Sèze, P.G.de Gennes, O.Parodi: J. Physique34 (1973) 661.Search in Google Scholar

[20] C.Blanc, M.Kleman: Phys. Rev. E62 (2000) 6739.10.1103/PhysRevE.62.6739Search in Google Scholar PubMed

[21] M.Kleman, O.D.Lavrentovich: Eur. Phys. J. E2 (2000) 47.10.1007/s101890050039Search in Google Scholar

[22] M.Kleman, O.D.Lavrentovich: Phys. Rev. E61 (2000) 1574.10.1103/PhysRevE.61.1574Search in Google Scholar

[23] N.Clark, private communication (2005).Search in Google Scholar

[24] C.Blanc, M.Kleman: Eur. Phys. J. B10 (1999) 53.10.1007/s100510050829Search in Google Scholar

[25] J.Friedel, private communication (2008).Search in Google Scholar

[26] S.R.Renn, T.C.Lubensky: Phys. Rev. A38 (1988) 2132.10.1103/PhysRevA.38.2132Search in Google Scholar PubMed

[27] M.Schlenker, M.Kleman: J. Appl. Phys.43 (1972) 3184.10.1063/1.1661683Search in Google Scholar

Received: 2008-9-16
Accepted: 2009-7-25
Published Online: 2013-06-11
Published in Print: 2009-10-01

© 2009, Carl Hanser Verlag, München

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