Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Stress field of a near-surface basal screw dislocation in elastically anisotropic hexagonal crystals

1 Department of Solid State Physics, Yerevan State University, 0025 Yerevan, Armenia
2 Almaz Synthesis LTD, 0069 Yerevan, Armenia

Topical Section: Crystalline Materials

In this study, we derive and analyze the analytical expressions for stress components of the dislocation elastic field induced by a near-surface basal screw dislocation in a semi-infinite elastically anisotropic material with hexagonal crystal lattice. The variation of above stress components depending on “free surface–dislocation” distance (i.e., free surface effect) is studied by means of plotting the stress distribution maps for elastically anisotropic crystals of GaN and TiB2 that exhibit different degrees of elastic anisotropy. The dependence both of the image force on a screw dislocation and the force of interaction between two neighboring basal screw dislocations on the “free surface–dislocation” distance is analyzed as well. The influence of elastic anisotropy on the latter force is numerically analyzed for GaN and TiB2 and also for crystals of such highly elastically-anisotropic materials as Ti, Zn, Cd, and graphite.
The comparatively stronger effect of the elastic anisotropy on dislocation-induced stress distribution quantified for TiB2 is attributed to the higher degree of elastic anisotropy of this compound in comparison to that of the GaN. For GaN and TiB2, the dislocation stress distribution maps are highly influenced by the free surface effect at “free surface–dislocation” distances roughly smaller than ≈15 and ≈50 nm, respectively. It is found that, for above indicated materials, the relative decrease of the force of interaction between near-surface screw dislocations due to free surface effect is in the order Ti > GaN > TiB2 > Zn > Cd > Graphite that results from increase of the specific shear anisotropy parameter in the reverse order Ti < GaN < TiB2 < Zn < Cd < Graphite. The results obtained in this study are also applicable to the case when a screw dislocation is situated in the “thin film–substrate” system at a (0001) basal interface between the film and substrate provided that the elastic constants of the film and substrate are the same or sufficiently close to each other.
  Figure/Table
  Supplementary
  Article Metrics

Keywords elastic anisotropy; screw dislocation; stress field; stress distribution map; free surface effect; gallium nitride; titanium diboride; graphite

Citation: Valeri S. Harutyunyan, Ashot P. Aivazyan, Andrey N. Avagyan. Stress field of a near-surface basal screw dislocation in elastically anisotropic hexagonal crystals. AIMS Materials Science, 2017, 4(6): 1202-1219. doi: 10.3934/matersci.2017.6.1202

References

  • 1. Hirth JP, Lothe J (1982) Theory of Dislocations, New York: John Wiley & Sons.
  • 2. Morkoc H (2008) Handbook of Nitride Semiconductors and Devices, Berlin: Wiley-VCH.
  • 3. Telling RH, Heggie MI (2003) Stacking fault and dislocation glide on basal plane of graphite. Phil Mag Lett 83: 411–421.
  • 4. Jagannadham K, Marcinkowski MJ (1978) Comparison of the image and surface dislocation models. Phys Status Solidi A 50: 293–302.    
  • 5. Cheng X, Shen Y, Zhang L, et al. (2012) Surface effect on the screw dislocation mobility over the Peierls barrier. Phil Mag Lett 92: 270–277.    
  • 6. Gars B, Markenscoff X (2012) The Peierls stress for coupled dislocation partials near a free surface. Philos Mag 92: 1390–1421.    
  • 7. Lee CL, Li S (2007) A half-space Peierls–Nabarro model and the mobility of screw dislocations in a thin film. Acta Mater 55: 2149–2157.    
  • 8. Liu L, Meng Z, Xu G, et al. (2017) Surface effects on the properties of screw dislocation in nanofilms. Adv Mater Sci Eng 2017.
  • 9. Eshelby JD, Read WT, Shockley W (1953) Anisotropic elasticity with applications to dislocations theory. Acta Metall 1: 251–259.    
  • 10. Spence GB (1962) Theory of extended dislocations in symmetry directions in anisotropic infinite crystals and thin plates. J Appl Phys 33: 729–733.    
  • 11. Chou YT (1962) Interaction of parallel dislocations in a hexagonal crystal. J Appl Phys 33: 2747–2751.    
  • 12. Chou YT (1963) Characteristics of dislocation stress fields due to elastic anisotropy. J Appl Phys 34: 429–433.    
  • 13. Holec D (2008) Multi-Scale Modeling of III-Nitrides: from Dislocations to the Electronic Structure [PhD thesis]. University of Cambridge.
  • 14. Chu HJ, Pan E, Wang J, et al. (2011) Three-dimensional elastic displacements induced by a dislocation of polygonal shape in anisotropic elastic crystals. Int J Solids Struct 48: 1164–1170.    
  • 15. Chu HJ, Wang J, Beyerlein IJ, et al. (2013) Dislocation models of interfacial shearing induced by an approaching glide dislocation. Int J Plasticity 41: 1–13.    
  • 16. Barnett DM, Lothe J (1974) An image force theorem for dislocations in anisotropic bicrystals. J Phys F Metal Phys 4: 1618–1635.    
  • 17. Wang J, Hoagland RG, Hirth JP, et al. (2008) Atomistic modeling of the interaction of glide dislocations with "weak" interfaces. Acta Mater 56: 5685–5693.    
  • 18. Wang L, Liu Z, Zhuang Z (2016) Developing micro-scale crystal plasticity model based on phase field theory for modeling dislocations in heteroepitaxial structures. Int J Plasticity 81: 267–283.
  • 19. Chou YT (1966) On dislocation–boundary interaction in an anisotropic aggregate. Phys Status Solidi B 15: 123–127.    
  • 20. Chu H, Pan E (2014) Elastic fields due to dislocation arrays in anisotropic biomaterials. Int J Solids Struct 51: 1954–1961.    
  • 21. Shahsavari R, Chen L (2015) Screw dislocations in complex, low symmetry oxides: Core structures, energetics, and impact on crystal growth. ACS Appl Mater Interfaces 7: 2223–2234.    
  • 22. Ruterana P, Albrecht M, Neugebauer J (2003) Nitride Semiconductors: Handbook on Materials and Devices, Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA.
  • 23. Munro RG (2000) Material properties of titanium diboride. J Res Natl Inst Stan 105: 709–720.
  • 24. Cheng TS, Davies A, Summerfield A, et al. (2016) High temperature MBE of graphene on sapphire and hexagonal boron nitride flakes on sapphire. J Vac Sci Technol B 34: 02L101.
  • 25. Chung DH, Buessem WR (1968) The Elastic Anisotropy of Crystals, In: Vahldiek FW, Mersol SA, Anisotropy in Single-Crystal Refractory Compounds, New York: Plenum, 217–245.
  • 26. Lethbridge ZAD, Walton RI, Marmier ASH, et al. (2010) Elastic anisotropy and extreme Poisson's ratios in single crystals. Acta Mater 58: 6444–6451.
  • 27. Kube CM (2016) Elastic anisotropy of crystals. AIP Adv 6: 095209.    
  • 28. Specht P, Harutyunyan VS, Ho J, et al. (2004) Anisotropy of the elastic properties of wurtzite InN epitaxial films. Defect Diff Forum 226–228: 79–90.
  • 29. Vurgaftman I, Meyer JR (2003) Band parameters for nitrogen-containing semiconductors. J Appl Phys 94: 3675–3696.    
  • 30. Wang HY, Xue FY, Zhao NH, et al. (2011) First-principles calculation of elastic properties of TiB2 and ZrB2. Adv Mater Res 150–151: 40–43.
  • 31. Polian A, Grimsditch M, Grzegory I (1996) Elastic constants of gallium nitride. J Appl Phys 79: 3343–3344.    
  • 32. Spoor PS, Maynard JD, Pan MJ, et al. (1997) Elastic constants and crystal anisotropy of titanium diboride. Appl Phys Lett 70: 1959–1961.    
  • 33. Peselnick L, Meister R (1965) Variational method of determining effective moduli of polycrystals: (A) hexagonal symmetry, (B) trigonal symmetry. J Appl Phys 36: 2879–2884.    
  • 34. Watt JP, Peselnick L (1980) Clarification of the Hashin-Shtrikman bounds on the effective elastic moduli of polycrystals with hexagonal, trigonal, and tetragonal symmetries. J Appl Phys 51: 1525–1531.    
  • 35. Simmons G, Wang H (1971) Single crystal elastic constants and calculated aggregate properties: a Handbook, Cambridge, Massachusetts: The MIT Press.
  • 36. Cousins CSG, Heggie MI (2003) Elasticity of carbon allotropes. III. Hexagonal graphite: Review of data, previous calculations, and a fit to a modified anharmonic Keating model. Phys Rev B 67: 024109.

 

Reader Comments

your name: *   your email: *  

Copyright Info: 2017, Valeri S. Harutyunyan, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved