Vicinal faces

On a so-called vicinal face there are many steps running in parallel with almost the same separation or terrace width in between. At a finite temperature, these steps also fluctuate. But due to the high energy cost for the formation of overhangs on the crystal surface, steps cannot cross each other. This non-crossing condition suppresses the step fluctuation. 

S. R. Coriell, B. T. Murray, A. A. Chernov, G. B. McFadden. Step bunching on a vicinal face of a crystal growing in a flowing solution. J Cryst Growth 169 773, 1996. 

Weidler, P.G. Hug, S.J. Wetche,T.P. Hiem-stra, T. (1998 a) Determination of growth rates of (100) and (110) faces of synthetic goefhite by scanning force microscopy. Geochrm. Cos-mochim. Acta 62 21-22 Weidler, P.G. Schwinn, T. Gaub, H.E. (1996) Vicinal faces on synthetic goefhite observed by atomic force microscopy. Clays Clay Min. 44 437-442... 

Weidler, P. G., Schwinn, T., and Gaub, H. E. (1996) Vicinal faces on synthetic goethite observed by atomic force microscopy. Clays Clay Min. 44 437-443. 

A high-indexed surface zone with a high density of steps or growth sites (kink positions) would follow the same growth law as liquid metals, i.e., the Butler-Volmer relation. Vicinal faces, characterized by low-index surface zones separated by uniformly distributed monatomic steps show an intermediate behavior. 

Figure 8. Top right Definition of vicinal faces. Top left examples of vicinal faces on GaAs. Bottom right Development of vicinal faces due to nutrient flow. Bottom left Wulff construction showing possible metastable low angle faces near principle directions, Ai and A2. From www.fhi-berlin.mpg.de/th/member/kratzer p.html.

For the fee system for each of the three families of planes 111, 100, and 110 there is only one type of site where an atom could be added in the nearest-neighbor position they are called singular faces (Fig. 9). Atomically flat surfaces nearly parallel to a singular face are called vicinal faces. The vicinal faces can be described by the composition of terraces of singular faces and by monoatomic steps (Fig. 11). The monoatomic steps are either densely packed in atoms or kinked. This model is called the TLK model (terrace, ledge, kink) and it can be easily extended to all faces on the three main zones of the unit triangle. 

A more obvious but perhaps underappreciated problem with surface roughness is the existence of defect sites on a surface, i.e., sites that would not be exposed on a perfectly smooth surface. This type of defect is separate from classical defects like stacking faults, subgrain boundaries and dislocations, and is due just to non-uniform expression of the substrate structure in an uneven surface (Fig. 9) such as could occur with the local development of vicinal faces. As surface characterization methods are generally poor except in the case of a small suite of oxides and silicates, this effect has probably not been fully considered to date. For example, it is possible to imagine a low roughness (hkl) surface that is entirely terminated by small faces with other (hkl) orientations, so that the exposed surface functional groups differ both in density and orientation from what is expected. 

Figure 9. Development of vicinal faces on surfaces as a pathway to a more stable surface. Top thermodynamic description. Middle (A1-A3) examples of GaAs vicinal surfaces. Bottom left Wulff construction showing positions of vicinal faces. Adapted from Waychunas (2001).

Figure 6 (left), (a) Differential interference contrast (DIC) photomicrograph of a trigonal growth hillock on a 100 face of apatite from the Golconda Mine, Minas Gerais Brazil. The three vicinal faces of the hillock exhibit macrosteps. The horizontal steps run in the [001] direction. The three step orientations are parallel to the three dominant step orientations of the spiral in Figure 5. Image is approximately 666 pm across, (b) Schematic of the face symmetry with respect to the hillock in a. Steps on the basal vicinal face parallel [001]. Lines within each vicinal face represent the orientations of growth steps. Arrows indicate the directions of advancement of steps during growth. [Modified after Rakov an and Reeder (1994)].

The dotted lines indicate the sector associated with the prism face and the subsector of the basal vicinal face of the hillock is shaded, (b) A DIG photomicrograph of an actual hillock on the (100) face of a fluorapatite from the Golconda Mine, Minas Gerais, Brazil. Image is -666 pm vertical. [Modified after Rakovan and Reeder (1996).]... 

Figure 22. Plots of the concentration of selected REEs between symmetrically noneqnivalent vicinal faces, and their associated snbsectors, along the line a-b shown in Fignre 21a. [Used by permission of Elsevier Science Ltd., from Rakovan and Reeder (1996) Geochimica et Cosmochimica Acta, Vol. 60, Fig. 3, p. 4439.]...

Occasionally, after careful goniometric measurement, crystals may be found to exhibit plane surfaces which appear to be crystallographic planes, being symmetrical in accordance with the symmetry of the crystal, but which cannot be described by simple indices. These are called vicinal faces. A simple method for determining the existence of these faces is to observe the reflection of a spot of light on the face four spot reflections, for example, would indicate four vicinal faces. 

The number of vicinal faces corresponds to the symmetry of the face, and this property may often be used as an aid to the classification of the crystal. For example, a cube face (fourfold axis of symmetry) may appear to be made up of an extremely flat four-sided pyramid with its base being the true (100) plane but its apex need not necessarily be at the centre of the face. An octahedral face (threefold symmetry) may show a three-sided pyramid. These vicinal faces most probably arise from the mode of layer growth on the individual faces commencing at point sources (see section 6.1). 

Hamelin A, Katayama A (1981) Lead imderpotential deposition on gold single-crystal surfaces the (100) face and its vicinal faces. J Electroanal Chem 117(2) 221-232... 

---