Pentagonal Symmetry in Aperiodic Cyclic Multiply Twinned Nano- and Mesodiamonds

This
Review provides the first comprehensive overview of the structure
and properties of exotic sp3-crystalline
aperiodic cyclic multiply twinned nano- (10–100 nm) and meso- (up to 1 mm) diamond particles (MTPs)
exhibiting pentagonal symmetry. It spans their independent experimental
discoveries (1963, 1964, 1972, and 1983) and theoretical structural
insights (1993) to recent advancements. The Review focuses on high-symmetry
MTPs formed by the fusion of multiple cubic diamond fragments through
[111] facets. The sp3 diamond lattice
of individual fragments offers a vast range of MTP varieties. These
particles are shown to be a special case of aperiodic crystalline
solids with limited dimensions and rotational symmetry, leading to
a breakdown of translational invariance. Detailed mathematical analysis
of the MTPs’ lattices highlights the crucial role of central
cores in determining the symmetry and effective dimensions of these
structures. Both structural and kinetic aspects of the formation mechanisms
of pentagonal diamond particles are considered, revealing the main
role of embryo seeds (low fullerenes, polyhexacyclo[5.5.1.12,6.18,12.03,11.05,9]pentadecane (C15), and polyheptacyclo[5.5.1.12,7.19,14.03,13.06,11]octadecane (C18)) in
determining the MTPs’ symmetry and structure. The effective
dimensions of multiply twinned diamonds are shown to be limited by
structural stress caused by the mismatch of perfect pentagonal and
tetrahedral dihedral angles. The extraordinary mechanical and electronic
properties of multiply twinned diamonds are discussed, highlighting
that hexagonal interfaces between cubic diamond fragments may determine
exceptional ultrahard and quantum characteristics. The MTP X-ray diffraction
spectra reveal clear pentagonal patterns with single (diamond decahedrons
or dodecahedrons) or ten (diamond icosahedra) central 5-fold axes.
A comparative analysis of experimental structural data and simulations
at different theoretical levels demonstrates a perfect correspondence
of theoretical models with crystalline lattices.