Skip to main content
×
Home

Interaction between semicoherent interfaces and Volterra-type dislocations in dissimilar anisotropic materials

  • Aurélien Vattré (a1) and Ernian Pan (a2)
Abstract
Abstract

The interaction between interface dislocation networks and a single lattice Volterra-type dislocation is analyzed by superposition using anisotropic elastic theory in dissimilar materials. The general and nontrivial field solutions for the displacements and stresses are derived by applying the Stroh sextic formalism and Fourier transform in heterogeneous bimaterials. The present approach therefore enables the calculation of the elastic interaction forces for the glide and climb components with different elastic constants and unequal partitioning of elastic fields between adjacent crystals neighboring a semicoherent heterophase interface. Two-dimensional application examples to the pure misfit Au/Cu interface are evaluated, where the infinitely long straight lattice dislocation, parallel to the interface dislocations, is embedded in Au. The repulsive and attractive interaction forces between these two types of (intrinsic and extrinsic) defects are investigated and discussed, for which the results provide a novel basis for examining multiple large-scale dislocation interactions in anisotropic interface-dominated materials with accurate mechanical boundary conditions.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Interaction between semicoherent interfaces and Volterra-type dislocations in dissimilar anisotropic materials
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      Interaction between semicoherent interfaces and Volterra-type dislocations in dissimilar anisotropic materials
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      Interaction between semicoherent interfaces and Volterra-type dislocations in dissimilar anisotropic materials
      Available formats
      ×
Copyright
Corresponding author
a) Address all correspondence to this author. e-mail: aurelien.vattre@cea.fr
Footnotes
Hide All

Contributing Editor: Johan Brand Malherbe

Footnotes
References
Hide All
1. Frank F.C. and van der Merwe J.H.: One-dimensional dislocations. I. Static theory. Proc. R. Soc. A 198(1053), 205 (1949).
2. van der Merwe J.H.: On the stresses and energies associated with inter-crystalline boundaries. Proc. Phys. Soc., London, Sect. A 63(6), 616 (1950).
3. van der Merwe J.H.: Crystal interfaces. Part I. Semi-infinite crystals. J. Appl. Phys. 34(1), 117 (1963).
4. van der Merwe J.H.: Crystal interfaces. Part II. Finite overgrowths. J. Appl. Phys. 34(1), 123 (1963).
5. Peierls R.: The size of a dislocation. Proc. Phys. Soc. 52(1), 34 (1940).
6. Nabarro F.R.N.: Dislocations in a simple cubic lattice. Proc. Phys. Soc. 59(2), 256 (1947).
7. Sutton A.P. and Balluffi R.W.: Interfaces in Crystalline Materials (Oxford University Press, Oxford, 1995).
8. van der Merwe J.H.: Equilibrium structure of a thin epitaxial film. J. Appl. Phys. 41(11), 4725 (1970).
9. People R. and Bean J.C.: Calculation of critical layer thickness versus lattice mismatch for Ge x Si1−x /Si strained-layer heterostructures. Appl. Phys. Lett. 47(3), 322 (1985).
10. van der Merwe J.H. and Jesser W.A.: An exactly solvable model for calculating critical misfit and thickness in epitaxial superlattices: Layers of equal elastic constants and thicknesses. J. Appl. Phys. 63(5), 1509 (1988).
11. Jesser W.A. and van der Merwe J.H.: An exactly solvable model for calculating critical misfit and thickness in epitaxial superlattices. II. Layers of unequal elastic constants and thicknesses. J. Appl. Phys. 63(6), 1928 (1988).
12. Chou Y.T. and Pande C.S.: Interfacial screw dislocations in anisotropic two-phase media. J. Appl. Phys. 44(7), 3355 (1973).
13. Chou Y.T. and Pande C.S.: Erratum: Interfacial screw dislocations in anisotropic two-phase media. J. Appl. Phys. 44(12), 5647 (1973).
14. Barnett D.M. and Lothe J.: An image force theorem for dislocations in anisotropic bicrystals. J. Phys. F: Met. Phys. 4(10), 1618 (1974).
15. Chou Y.T., Pande C.S., and Yang H.C.: Interfacial edge dislocations and dislocation walls in anisotropic two-phase media. J. Appl. Phys. 46(1), 5 (1975).
16. Hirth J.P., Barnett D.M., and Lothe J.: Stress fields of dislocation arrays at interfaces in bicrystals. Philos. Mag. A 40(1), 39 (1979).
17. Dupeux M. and Bonnet R.: Stresses, displacements and energy calculations for interfacial dislocations in anisotropic two-phase media. Acta Metall. 28(6), 721 (1980).
18. Bonnet R.: Periodic elastic fields in anisotropic two-phase media. Application to interfacial dislocations. Acta Metall. 29(2), 437 (1981).
19. Willis J.R., Jain S.C., and Bullough R.: The energy of an array of dislocations: Implications for strain relaxation in semiconductor heterostructures. Philos. Mag. A 62(1), 115 (1990).
20. Bonnet R.: Evaluation of surface strain due to the reconstruction of atomically close-packed crystalline surfaces. Phys. Rev. B 61, 14059 (2000).
21. Stroh A.N.: Dislocations and cracks in anisotropic elasticity. Philos. Mag. 3(30), 625 (1958).
22. Ting T.C.T.: Anisotropic Elasticity: Theory and Applications (Oxford University Press, New York, Oxford, 1996).
23. Frank F.C.: Martensite. Acta Metall. 1(1), 15 (1953).
24. Bilby B.A., Bullough R., and Smith E.: Continuous distributions of dislocations: A new application of the methods of non-riemannian geometry. Proc. R. Soc. A 231(1185), 263 (1955).
25. Bilby B.A.: Types of dislocation sources. In Report of the Conference on Defects in Crystalline Solids (Physical Society, London, 1955); p. 124.
26. Vattré A.J. and Demkowicz M.J.: Determining the Burgers vectors and elastic strain energies of interface dislocation arrays using anisotropic elasticity theory. Acta Mater. 61(14), 5172 (2013).
27. Vattré A.J., Abdolrahim N., Kolluri K., and Demkowicz M.J.: Computational design of patterned interfaces using reduced order models. Sci. Rep. 4, 6231 (2014).
28. Vattré A.J. and Demkowicz M.J.: Partitioning of elastic distortions at a semicoherent heterophase interface between anisotropic crystals. Acta Mater. 82, 234 (2015).
29. Vattré A.: Mechanical interactions between semicoherent heterophase interfaces and free surfaces in crystalline bilayers. Acta Mater. 93, 46 (2015).
30. Vattré A.: Elastic interactions between interface dislocations and internal stresses in finite-thickness nanolayered materials. Acta Mater. 114, 184 (2016).
31. Vattré A.: Elastic strain relaxation in interfacial dislocation patterns: I. A parametric energy-based framework. J. Mech. Phys. Solids 105, 254 (2017).
32. Vattré A.: Elastic strain relaxation in interfacial dislocation patterns: II. From long- and short-range interactions to local reactions. J. Mech. Phys. Solids 105, 283 (2017).
33. Beyerlein I.J., Demkowicz M.J., Misra A., and Uberuaga B.P.: Defect-interface interactions. Prog. Mater. Sci. 74, 125 (2015).
34. Chu H. and Pan E.: Elastic fields due to dislocation arrays in anisotropic bimaterials. Int. J. Solids Struct. 51(10), 1954 (2014).
35. Pan E.: Three-dimensional Green’s functions in an anisotropic half-space with general boundary conditions. J. Appl. Mech. 70(1), 101 (2003).
36. Pan E.: Some new three dimensional Green’s functions in anisotropic piezoelectric bimaterials. Electron. J. Boundary Elem. 1(2), 236 (2003).
37. Gray D.E.: American Institute of Physics Handbook (McGraw-Hill, New-York, 1957).
38. Hirth J.P. and Lothe J.: Theory of Dislocations, 2nd ed. (Kriger, Melbourne, 1992).
39. Eshelby J.D., Read W.T., and Shockley W.: Anisotropic elasticity with applications to dislocation theory. Acta Metall. 1(3), 251 (1953).
40. Ting T.C.T. and Minzhong W.: Generalized Stroh formalism for anisotropic elasticity for general boundary conditions. Acta Mech. Sin. 8(3), 193 (1992).
41. Pan E. and Chen W.Q.: Static Green’s Functions in Anisotropic Media (Cambridge University Press, Cambridge, 2015).
42. Balluffi R.W.: Elasticity Theory for Crystal Defects (Cambridge University Press, Cambridge, 2012).
43. Peach M. and Koehler J.C.: The forces exerted on dislocations and the stress fields produced by them. Phys. Rev. Lett. 80(3), 436 (1950).
44. Freund L.B. and Suresh S.: Thin Film Materials: Stress, Defect Formation and Surface Evolution (Cambridge University Press, Cambridge, 2004).
45. Chen Z., Jen Z., and Gao H.: Repulsive force between screw dislocation and coherent twin boundary in aluminum and copper. Phys. Rev. B 75, 212104 (2007).
46. Wang J. and Misra A.: An overview of interface-dominated deformation mechanisms in metallic multilayers. Curr. Opin. Solid State Mater. Sci. 15(1), 20 (2011).
47. Wang J., Hoagland R.G., and Misra A.: Room-temperature dislocation climb in metallic interfaces. Appl. Phys. Lett. 94(13), 131910 (2009).
48. Han X., Pan E., and Sangghaleh A.: Fields induced by three-dimensional dislocation loops in anisotropic magneto-electro-elastic bimaterials. Philos. Mag. 93(24), 3291 (1979).
49. Gao Y. and Larson B.C.: Displacement fields and self-energies of circular and polygonal dislocation loops in homogeneous and layered anisotropic solids. J. Mech. Phys. Solids 83, 104 (2015).
50. Vattré A., Jourdan T., Ding H., Marinica M-C., and Demkowicz M.J.: Non-random walk diffusion enhances the sink strength of semicoherent interfaces. Nat. Commun. 7, 10424 (2016).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Materials Research
  • ISSN: 0884-2914
  • EISSN: 2044-5326
  • URL: /core/journals/journal-of-materials-research
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 3
Total number of PDF views: 47 *
Loading metrics...

Abstract views

Total abstract views: 158 *
Loading metrics...

* Views captured on Cambridge Core between 7th August 2017 - 23rd November 2017. This data will be updated every 24 hours.