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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 5 increasing magnitude, the system can reduce its energy by creating a free sur- face or a hollow core along the disloca- tion. Frank proposed the formation of hollow cores of screw dislocations for crystal structures with large Burgers vectors [3,4] . He derived the size of the hol- low core by equating the incremental change in strain energy density and us- ing linear elasticity theory to determine the change in surface energy of the hol- low core. However, the size of the Burg- ers vectors obtained were too small to account for experimental observations. By empirically accounting for nonlin- ear effects in the elastic region, Frank obtained higher values of the Burgers vectors—yet still not enough to stabilize the formation of hollow cores. However, these estimates do not account for core energy contributions. These can only be handled by atomistic calculations, as shown by Narayan’s group, and not by continuum linear elasticity theory [9,10] . Unfortunately, experimentally ob- served values for the Burgers vectors are considerably higher than these es- timates, as well as elementary Burgers vectors derived from crystal structures. This is particularly relevant to hexag- onal crystal growth along the c-axis having the largest Burgers vector [11,12] . Experimental results show that elemen- tary dislocations in 6H-SiC (c = 1.51 nm) were not hollow, and that the small- est hollow core dislocation had a Burg- ers vector of two unit cells (3.0 nm) [13] . The Burgers vector in the micropipe was found to require a height of at least four to 12 unit cells (18 nm) to stabilize a hollow core dislocation [14] . More recent work on the growth of ZnO nanotubes demonstrates the role of screw disloca- tions, but the effective Burgers vector measured was three to four times high- er than themagnitude of the c-vector [15] . The present work shows that ef- fective super Burgers vectors are pos- sible by the formation of helical screw dislocations, which can pair up to form a double helix and attract additional helical dislocations. A pure screw dis- location can acquire helicity through dislocation self-climb by absorbing point defects during the growth pro- cess or thermal annealing, as shown in Fig. 1a [16,17] . Note that the interaction between hydrostatic stresses of vacan- cies and shear stresses of screw disloca- tions is very weak. However, local jogs and thermal stress fluctuations can in- troduce edge components, which can interact with the hydrostatic stresses of vacancies. With these attractive inter- actions, two helical screw dislocations can pair up to form a double helix of screw dislocations with larger effective Burgers vectors. Figure 1b shows the formation of a double helix, where there is relative shift by λ/4 and for the shift by λ/2, the double helix is shown in Fig. 1c. Two helical dislocations may adjust their relative positions depending on their origin and growth conditions. Addition- al attractive interaction may be derived from vacancy jogs present in the helical dislocations. It is interesting to note the similarity between a single helical screw dislocation and single strand ribonucle- ic acid (RNA), and double helix disloca- tions and deoxyribonucleic acid (DNA) structures with two strands, as shown in Figs. 1a and c, respectively. The two DNA strands are bonded by hydrogen bonds to make a double helix, similar to vacancy jogs in helical dislocations. EXPERIMENTAL RESULTS Formations of single and double helix screw dislocations were studied experimentally in MgO as a function of annealing at high temperatures. Be- fore annealing, these MgO crystals con- tained a high density of screw, mixed, and edge dislocations associated with deformation in MgO. Upon thermal annealing at 1273 K with an ample supply of vacancies from the free sur- face, screw dislocations acquire a heli- cal character by absorbing vacancies. The helical dislocations can pair up and form a double helix, as shown in Fig. 1d. This micrograph was taken with diffraction vector g = [200], with [001] surface normal. The Burgers vec- tor from g.b and g.bxu contrast analy- sis was determined to be a/2[101] with sense vector u = [101]. The higher width of the image is consistent with double helix screw dislocations. With a [200] diffraction vector, dislocation images resulting from strain contrast overlap and produce wider images. The dou- ble helix in Fig. 1d is 780 nm long and contained in the TEM specimen with a thickness of 550 nm. Projected length of the double helix is also 550 nm, as the [101] direction makes an angle of Fig. 1 — (a) Single helical screw dislocation (n=1) at S1 with a constant helix angle ɵ along entire dislocation length; (b) formation of double helix dislocation with another dislocation (S2) shifted by a quarter of a pitch (λ/4) along the axis; (c) shift in Fig. 1c is half (λ/2) of a pitch; and (d) TEMmicrograph of a double helix with two screw dislocations of a/2 [101] Burgers vector. An attractive interaction occurs between the two dislocations through the edge component and vacancy jogs, similar to hydrogen bonding between two DNA strands.