Superspherical-shape approximation to describe the morphology of small crystalline particles having near-polyhedral shapes with round edges

Superspheres: Intermediate Shapes between Spheres and Polyhedra

“…The shapes of small metal particles observed in previous studies have been discussed previously using the superspherical approximation [8]. Menon and Martin reported the production of ultrafine Ni particles by vapor condensation in an inert gas plasma reactor [11].…”

“…Although the original superspheres discussed in [2][3][4] are intermediate shapes between a sphere and a cube, now the superspheres can refer to shapes intermediate between various convex polyhedra and a sphere [8].…”

“…Superspheres have been used to discuss the shapes of small crystalline particles and precipitates [2,3,5,8,9]. The planes of crystal facets are indicated by their Miller indices.…”

“…The boundary between Regions 1 and 2, expressed by the line from P to R, is written as: Figure 6 is essentially the same as Figure 3 in [7,8] where the parameters α = 1/a and β = 1/b are used instead of a and b. In the appendix, the volume and surface area of the polyhedra shown in Figure 6 are written as a function of a and b.…”

“…As shown in Figure 7, the change in N with increasing p becomes smaller as the number of faces of polyhedra increases from the {100} cube with 6 to the {100}-{111}-{110} polyhedron with 26. Among the various polyhedra shown in Figure 3 ≈ 5.05 has the minimum total surface area S for the same V [8,10]. The a and b dependence of N can be calculated easily using the results shown in the appendix.…”