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A D V A N C E D M A T E R I A L S & P R O C E S S E S | J A N U A R Y / F E B R U A R Y 2 0 2 2 2 7 in PbS (with a = 0.594 nm NaCl struc- ture) reports an effective Burgers vector (0.6 ± 0.2 nm), which is also far higher than 0.42 nm for b = a/2<110> [8] . In the case of GeS growth with b = 1.04 nmand b e = 1.75 nm, the fraction of double he- lix is calculated to be 71% and 69% for helix angles of 10 and 5 degrees, re- spectively [7] . Similarly for PbS with b = 0.42 nm and b e = 0.6 nm, the fraction of double helix is calculated to be 45% and 43% for helix angles of 10 and 5 de- grees, respectively [8] . CONCLUSION In summary, the formation of hol- low cores, nanopipes, micropipes, and nanotubes with Eshelby twists with ef- fective Burgers vectors that are much larger than elementary unit Burgers vectors can be explained by the in- troduction of single and double helix screw dislocations. Both dislocation types play an important role in creating novel nanostructured materials with improved properties and in the growth of crystal structures across the scale. A screw dislocation becomes helical by absorption of point defects during crystal growth due to supersaturation during thermal cycling or a supply of va- cancies from the free surfaces in close proximity in nanostructures. Two heli- cal dislocations can lead to the forma- tion of double helix screw dislocations and play a critical role in the growth of one-dimensional nanostructures with Eshelby twists, useful for a variety of applications [20,21] . The discovery of dou- ble helix screw dislocations will impact advanced materials synthesis and pro- cessing from the nanoscale to the me- soscale. ~AM&P For more information: Jagdish Nara- yan, Dept. of Materials Science, North Carolina State University, Raleigh, NC 27695-7907, 919.515.7874, j_narayan@ ncsu.edu. Acknowledgment This work was supported by NSF grant DMR #20162560. References 1. J.P. Hirth and J. Lothe, Theory of Dislocations. New York: McGraw-Hill, 1968. 2. J. Narayan, Discovery of Double Helix of Screw Dislocations: A Per- spective, Mater. Res. Lett., Vol 9(11), p 453-457, 2021. 3. F.C. Frank, The Influence of Dis- locations on Crystal Growth, Discuss. Faraday Soc., Vol 5, p 48-54, 1949. 4. F.C. Frank, Capillary Equilibria of Dislocated Crystals, Acta Crystallogr., Vol 4(6), p 497-501, 1951. 5. J. Narayan, Interface Structures During Solid‐Phase‐Epitaxial Growth in Ion Implanted Semiconductors and a Crystallization Model, J. Appl. Phys., Vol 53, p 8607-8619, 1982. 6. W.W. Webb, Dislocation Mech- anisms in the Growth of Palladium Whisker Crystals, J. Appl. Phys., Vol 36, p 214-221, 1965. 7. Y. Liu, et al., Helical van der Waals Crystals with Discretized Eshelby Twist, Nature, Vol 570, p 358-362, 2019. 8. M.J. Bierman, et al., Dislocation- driven Nanowire Growth and Eshelby Twist, Science, Vol 320, p 1060-1063, 2008. 9. A.S. Nandedkar and J. Narayan, Atomic Structure of Dislocations and Dipoles in Silicon, Philos. Mag., Vol 56, p 625-639, 1987. 10. A.S. Nandedkar and J. Narayan, Atomic Structure of Dislocations in Silicon, Germanium and Diamond, Philos. Mag. A, Vol 61(6), p 873-891, 1990. 11. J. Heindl, et al., Micropipes: Hollow Tubes in Silicon Carbide, Phys. Stat. Sol., Vol 161, p 251-262, 1997. 12. P. Pirouz, On Micropipes and Nanopipes in SiC and GaN, Philos. Mag. A, Vol 78(3), p 727-736, 1998. 13. M. Dudley, et al., Quantitative Analysis of Screw Dislocation in 6H-SiC Single Crystals, Nuovo Cim., Vol 19(D), p 153-164, 1997. 14. J. Giocondi, et al., The Relationship Between Micropipes and Screw Dis- locations in PVT Grown 6H-SiC, MRS Online Proceedings, Vol 423, p 539-544, 1996. 15. S. Morin, et al., Mechanism and Kinetics of Spontaneous Nanotube Growth Driven by Screw Dislocations, Science, Vol 328, p 476-480, 2010. 16. R.W. Balluffi, Mechanisms of Dis- location Climb, Phys. Status Solidi, Vol 31, p 443-463, 1969. 17. J. Narayan and J. Washburn, Self- Climb of Dislocation Loops in Mag- nesium Oxide, Philos. Mag., Vol 26(5), p 1179-1190, 1972. 18. J.D. Eshelby, The Twist in a Crystal Whisker Containing a Dislocation, Philos. Mag., Vol 3(29), p 440-447, 1958. 19. J.D. Eshelby, Screw Dislocations in Thin Rods, J. Appl. Phys., Vol 24, p 176-180, 1953. 20. C.M. Lieber and Z.L. Wang, Func- tional Nanowires, MRS Bulletin, Vol 32, p 99-104, 2007. 21. Y. Xia, et al., One-Dimensional Nanostructures: Synthesis, Characteri- zation, and Applications, Adv. Mater., Vol 15(5), p 353-389, 2003.
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