Circular and polygonal spirals

Since the one-dimensional roughness of the steps determines whether a spiral takes circular or polygonal form, these morphologies may be treated similarly to the roughening transition of an interface, as described in Chapter 3. It is possible to predict interface roughness either by Jackson s a factor or by Bennema-Gilmer s generalized factor (see Section 3.8). The coefficients which determine the a 

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.  

The effect of factors which affect the a factor, such as growth temperature or solute-solvent interaction, may be observed by comparing the surface micro- 

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