January_February_2022_AMP_Digital

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 6 45° with the surface normal [001]. The helical angle for the double helix from Fig. 1d is estimated to be 35°, which is close to the point where single helix dis- locations break into a stack of vacancy loops, as discussed below. The vacancy dislocation interac- tion increases with vacancy absorption, consequently increasing the edge com- ponent [16,17] . With continued vacancy absorption, helical dislocations trans- form into a stack of vacancy loops with separation equal to the pitch and loop radius, which is equal to the radius of the helix (Fig. 2). From the contrast analysis, it was determined that the stacks of prismatic loops on (101) planes at S3, Fig. 2a, re- sult from a single helix along the [101] direction and (101) plane, which lies at 45° from the surface normal [001]. The stacks at S4, Figs. 2a and b, are from the a/2[110] screw dislocation along the [110] direction, whereas the stacks at S5 are from the a/2[1-10] screw dislo- cation along the [1-10] direction. These a/2[110] and a/2[1-10] loops lie edge- on in the [001] sample orientation. It is interesting to note that the length of stacks at S4 and S5 is larger as these dis- locations lie nearly parallel to the (001) specimen. The pitch of the helix is esti- mated to be 50 nm and r h = 5 nm (Fig. 2, S4 and S5). This gives a helix angle of 30-35°, and vacancy supersaturation of c/c 0 2.5 during annealing at 1273 K, as- suming Ω ~ b 3 and τ = 20 eV/nm [9,10] . The smaller λ at S5 compared to S4 is con- sistent with the presence of a double helix and a single helix, respectively. NANOTUBE FORMATION Formation of nanopipes and mi- cropipes requires formation of dislo- cations with large Burgers vectors. The author proposes that this can occur by formation of single helix and double he- lix screw dislocations, which can start the nucleation process, with other heli- cal dislocations joining in through sur- face interaction with the hollow core, as suggested in reference 12. In view of the previous discussion on the forma- tion mechanism, what are the strate- gies to reduce the number density of nanopipes and micropipes? To reduce formation of these undesirable struc- tures, formation of helical dislocations should be reduced. This can be accom- plished by controlling the supply of va- cancies via reducing the temperature during the initial stages of growth. In ZnO, nanotube growth is found to be driven by axial screw dislocations, where self-perpetuating growth spi- rals enable formation of hollow tubes. However, the magnitude of the Burgers vector estimated from surface height measurements was found to be three to four times higher than the magni- tude of the elementary Burgers vector (0.520 nm in ZnO) [15] . These results can be rationalized by a combination of the single and double helix screw disloca- tions involved in nanotube growth. ESHELBY TWISTS Another interesting aspect regard- ing the role of screw dislocations during crystal growth is worth noting. In the course of crystal growth, a coaxial screw dislocation in a finite cylinder with end surfaces produces counteractive shear stresses, which produce a torque and a twist, known as an Eshelby twist [18,19] . Because the Eshelby twist is inversely proportional to the square of the cyl- inder radius, it does not play a signif- icant role in large crystals. However, with screw-dislocation-aided growth of nanostructures such as nanowires, the Eshelby twist can lead to some interest- ing, helically twisted nanostructures [7,8] . Again, the same difficulty arises regard- ing interpretation of the Eshelby twist. The magnitudes of Burgers vectors de- rived from experimentally measured Eshelby twists are considerably higher than the Burgers vectors of elementary screw dislocations. ResultsbyLiuet al. on thegrowthof GeS nanowires (c = 1.04 nm with ortho- rhombic crystal structure) show that ax- ial screw dislocations produce a discret- ized crystallographic twist along the c-axis [7] . These results in helically twist- ed nanowire structures were interpret- ed using the Eshelby twist model [18,19] . However, the effective Burgers vector (b e = 1.75 nm) was found to be far higher than b = 1.04 nm for the [0001] disloca- tion expected from the Eshelby model. Similarly, earlier work by Bierman et al. on screw dislocation nanowire growth Fig. 2 — Formation of helical screw dislocations as a result of vacancy diffusion and punching into a stack of vacancy loops in (001) MgO during high-temperature annealing: (a) TEM micrograph taken with diffraction vector [200], showing a/2[101] loops at S3 and a/2[110] loops at S4; (b) TEMmicrograph taken with diffraction vector [200], showing a/2[110] loops at S4 and a/2[1-10] loops at S5.