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Home All issues Volume 657 (January 2022) A&A, 657 (2022) A127 Full HTML
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Table 1

Polyhedral nano-diamond particle vertex (V), edge (E) and face (F) properties.

Shape V Vertices E Edges F Faces fs{111} reff∕and
T 4 4 isolated CH 6 6 × {111}/{111}, CH2 4 4 × {111} triangular, CH 1 2.013
                 
tT 12 ≡ edge CH2 18 6 × {111}/{111}, CH2 8 4 × {111} hexagonal, CH 1 1.356
12 × {111}/{111}, CH on faces 4 × {111} triangular, CH
                 
O 6 6 isolated CH2 12 12 × {111}/{111}, CH on faces 8 8 × {111} triangular, CH 1 1.465
                 
tO 24 ≡ face CH 36 24 × {111}/{100}, CH2 on faces 14 6 × {100} square, CH2 1.135
12 × {111}/{111}, CH on faces 8 × {111} hexagonal, CH 0.776
                 
cO 12 ≡ face CH2 24 24 × {111}/{100}, CH2 on faces 14 6 × {100} square, CH2 1.211
(all cO edges are equivalent) 8 × {111} triangular, CH 0.366
                 
tC 24 ≡ face CH2 36 24 × {111}/{100}, CH2 on faces 14 6 × {100} octagonal, CH2 1.396
12 × {100}/{100}, CH2 on faces 8 × {111} triangular, CH 0.107
                 
C 8 4 CH2 + 4 CH3 12 12 × {100}/{100}, CH2 on faces 6 6 × {100} square, CH2 0 1.201

Notes. Only {111} and {100} facets are considered in the modelling where fs{111} is the fraction of the particle surface in {111} facets and therefore fs{100} = (1 − fs{111}). The considered regular polyhedral shapes are tetrahedra (T), truncated tetrahedra (tT), octahedra (O), truncated octahedra (tO), cuboctahedra (cO), truncated cubes (tC), and cubes (C). For vertices ‘ ≡ edge(face) CHn ’ indicates that their CHn groups can be considered as forming an integral part of the adjacent edges (faces). The last column gives the ratio of the radius of the circumscribed sphere, reff, with the same volume as a sphere, and (see text fordetails).

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