Polygonized spiral

On quartz crystals synthesized in a hydrothermal solution of NaOH, KOH series, 1010 faces show polygonal spiral steps, whereas rounded step patterns are observed on 1011 and 0111. ... 

Figure 10.5. (a) Polygonal spiral growth hillocks universally observed on 1010 faces of synthetic quartz. (The arrows indicate the summits of the growth hillocks.) (b) Striation patterns commonly seen on the 1010 faces of natural and synthetic quartz grown in NaCl aqueous solution. 

The anisotropic case of a polygonized spiral has been discussed by many authors [5.15, 5.65-5.67]. The rotation period of a A-cornered polygonized spiral arising from a single screw dislocation is given by... 

The sides of the quadrangular spiral in Fig. 5.30 appear as tangents to the turns of the circular spiral in directions normal to the sides of the nucleus polygon. This result shows that the shape of a polygonized spiral can be approximately estimated by a modified Wulff construction (cf. Section 4.1). 

Figure 6.7. A polygonized spiral on the face of a C36 normal alkane crystal. Courtesy of R. Boistelle)...

The case of polygonized spirals has been discussed by Cabrera, " Kais-chew et and by Chapon and Bonissent. In all these treatments the... 

The assumption i = Uoo for / = Ic and u = 0 for / < /c is an oversimplification. It is obvious that the time lapse Tc and hence the period of rotation should be in reality larger because the step adjacent to the new one propagates with a speed smaller than Doo. The calculation is complicated because the propagation rates of all the adjacent steps are also dependent on / and hence the propagation rate of the spiral is given by a system of differential equations. A numerical calculation on this system of equations was given by Budevski et who found that irrespective of the form of the spiral, the period of rotation of a polygonized spiral is... 

Figure 3.25 Polygonal spiral growth from the giant screw dislocation in Fignre 3.24. Arrows on the side snrface indicate the initial advance directions of the two steps. Each layer of the spiral has a thickness b = 4- Other dimensions are the terrace width y and the size of the smallest surface nucleus...

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