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

Valeri S. Harutyunyan; Ashot P. Aivazyan; Andrey N. Avagyan; Valeri S. Harutyunyan; Ashot P. Aivazyan; Andrey N. Avagyan

doi:10.3934/matersci.2017.6.1202

AIMS Materials Science

2017, Volume 4, Issue 6: 1202-1219. doi: 10.3934/matersci.2017.6.1202

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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

Received: 22 September 2017 Accepted: 16 November 2017 Published: 21 November 2017

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.
- 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[J]. AIMS Materials Science, 2017, 4(6): 1202-1219. doi: 10.3934/matersci.2017.6.1202

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Abstract

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.

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