Modes of Appearance

The mode of appearance of fivefold twinned particles depends on both their orientation with respect to a planar substrate (or a matrix) and the evolution of their surface morphology as influenced by the growth conditions. With respect to a planar substrate, there are four possible high symmetry orientations for both types of MTPs. Decahedra may be situated (i) with their fivefold axis perpendicular to the substrate plane, as in "fivefold" orientation or (011); (ii) with the fivefold axis parallel to the substrate plane, as in "parallel" or (001); (iii) with one tetrahedral bounding face resting on the substrate, as in "face" orientation or (111); and (iv) with the common edge of two tetrahedra resting on the substrate, as in "edge" orientation or (112). As can be seen from Figure 3, this gives as projection on the substrate (or imaging) plane a regular pentagon, a rhombic, a shortened pentagon, or a slightly less shortened pentagon, respectively. Icosahedra may be situated (i) with the common edge of two tetrahedra resting on the substrate and two fivefold axes parallel to it, as in "edge" orientation or (112); (ii) with one corner resting on the substrate and one fivefold axis parallel to it, as in "parallel" orientation or (001); (iii) with one fivefold axis perpendicular to the substrate, as in "fivefold" orientation, or (011); and (iv) with one tetrahedral bounding face resting on the substrate, as in "face" orientation or (111). Figure 4 shows the corresponding projections on the imaging plane giving a hexagon shortened along a diagonal, a hexagon elongated along a diagonal, a regular decagon, or a regular hexagon, respectively. The assignment of orientations in terms of crystal axes indices (in braces)

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