Terraces, spiral

Fig. 4. AFM deflection image of the Cu(lll) surface during deposition of copper. The steps are one atom in height. In the upper left are two nested spiral terraces. 

From this expression we observe that R > / hc- The terrace connecting two spirals, one left-handed and the other right-handed, will grow indefinitely if the diameter of the critical 2D nucleus, 2Rc, is less than the distance between the emerging points of the two spirals (Frank, 1949). The minimum measured separation between coupled spirals is about 50 nm, so that R < 25 nm (see Section 5.1). Asymmetric hollow cores can be clearly seen in Fig. 5.13 and are in fact composed of two single hollow cores of the same sign separated by about 2/ hc, as can be inferred from the figure. 

Fig. 24 Transmission electron micrograph of linear polyethylene crystallised at 127 °C for 2.5 min showing spiral terraces in the 110 sectors. Scale bar represents 1 pm. From Toda and Keller [37] with permission from Springer, Berlin Heidelberg New York...

Fig. 6.9. Image of a 2 j-m X 2 j-m area of a 450 nm thick, sputter-deposited YBCO film grown on MgO. Note the growth spirals including doubles with opposite spin directions (arrows), the one-unit-cell-high terraces, and other defect structures.

The form of this growth law, quadratic tending to linear, is shown by curve (b) in fig. 5.1. The same law applies to surfaces from which emerge a whole distribution of screw dislocations, though the geometry is naturally more complex. The existence of these spiral growth terraces has, of course, been amply verified by observation. 

The nature of the surface was observed as liquid was circulated continuously through the cell. The flow velocity had no effect on crystal growth, confirming that the growth was not diffusion limited at the 10 jrl s flow rate employed. The crystal plane observed was the (1014) face which does not cross any of the strong covalent bonds, i.e. the C-O bonds, in the material. The images revealed the flat terraces of the crystal with spiral step patterns standing out from the surface, as shown below in Fig. 6.18. 

Banded spherulites, eg in PE (179,180), poly(vinylidene fluoride) (PVDF) (181), or polyhydroxyalkanoates (182), have also been studied in detail. The periodic bands detected in optical microscopy correspond typically to periodic corrugations along the radial direction of the spherulite. Particularly interesting is the case of PVDF (181). On the basis of a careful analysis it was found that the slopes of the observed multilayer terraces of lamellar crystals are retained in each half of a banded spherulite. This evidence confirmed the macroscopic selection of one-handedness in the formation of spiral terraces in each growth direction of the sheaf at the center of banded spherulites of PVDF (181). 

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