Use of the Nye tensor in analyzing HREM images of bcc screw dislocations

Abstract

The Nye tensor characterizes the strength of infinitesimal dislocations at each point in a continuously dislocated crystal, and provides a measure of the Burgers vector and the extent of dislocation dissociation. The present work employs this description to analyze ½ screw dislocations in bcc Mo obtained by Finnis–Sinclair, Bond Order Potential and first-principles simulations in an attempt to detect misfit in the core region. The spatial distribution and strength of the fractional dislocations are calculated and compared between the different simulated core structures. The Nye tensor technique is also applied to HREM images of end-on screw dislocations in Mo to detect the edge fractional dislocations predicted by simulation. The advantage of the Nye tensor for this purpose arises from its insensitivity to the Eshelby twist due to surface relaxation in a thin TEM foil (this is not the case for the more conventional methods of depicting misfit, such as direct and differential displacement maps). Although the Eshelby twist was removed from the experimental HREM images, some residual, mottled contrast structure was observed in the Nye tensor plots. This contrast was found to be due to the experimental noise, which masks the true structure of the dislocation core and precludes experimental characterization of screw dislocations in Mo by HREM.

Acknowledgements

The research has been funded by an AFOSR grant (Grant No. F49620-02-1-0105). The authors are grateful to V. Vitek for providing atomic coordinates for the FS and BOP dislocation cores, to C. Woodward for the first-principles core and to D. H. Lassila for supplying the deformed Mo single crystals. B.G.M would also like to thank D. C. Elbert for helpful discussions on multislice image simulations. The focus determination for figure 7 was carried out using the NCEM public domain software developed by R. Kilaas.

Notes

† By convention the vector originates from the perfect lattice position of the atom of interest.

† Summation from 1 to 3 over repeated Latin suffixes is implied.

† Repeated Latin indices indicate summation from 1 to 3 in the dislocated lattice, while repeated Greek indices imply summation from 1 to 3 in the perfect reference lattice.

† The shear modulus is μ.

† The metastability arises because there is a zero restoring force, hence an energy barrier must be overcome to remove the higher energy fault.

† The mean of the Gaussian distribution is 16 pm; the standard deviation is approximately 7.5 pm.