Pentagonal Symmetry in Aperiodic Cyclic Multiply Twinned\nNano- and Mesodiamonds

This\nReview provides the first comprehensive overview of the structure\nand properties of exotic <i>sp</i><sup>3</sup>-crystalline\naperiodic cyclic multiply twinned nano- (10–100 <i>nm</i>) and meso- (up to 1 <i>mm</i>) diamond particles (MTPs)\nexhibiting pentagonal symmetry. It spans their independent experimental\ndiscoveries (1963, 1964, 1972, and 1983) and theoretical structural\ninsights (1993) to recent advancements. The Review focuses on high-symmetry\nMTPs formed by the fusion of multiple cubic diamond fragments through\n[111] facets. The <i>sp</i><sup>3</sup> diamond lattice\nof individual fragments offers a vast range of MTP varieties. These\nparticles are shown to be a special case of aperiodic crystalline\nsolids with limited dimensions and rotational symmetry, leading to\na breakdown of translational invariance. Detailed mathematical analysis\nof the MTPs’ lattices highlights the crucial role of central\ncores in determining the symmetry and effective dimensions of these\nstructures. Both structural and kinetic aspects of the formation mechanisms\nof pentagonal diamond particles are considered, revealing the main\nrole of embryo seeds (low fullerenes, polyhexacyclo[5.5.1.1<sup>2,6</sup>.1<sup>8,12</sup>.0<sup>3,11</sup>.0<sup>5,9</sup>]pentadecane (C<sub>15</sub>), and polyheptacyclo[5.5.1.1<sup>2,7</sup>.1<sup>9,14</sup>.0<sup>3,13</sup>.0<sup>6,11</sup>]octadecane (C<sub>18</sub>)) in\ndetermining the MTPs’ symmetry and structure. The effective\ndimensions of multiply twinned diamonds are shown to be limited by\nstructural stress caused by the mismatch of perfect pentagonal and\ntetrahedral dihedral angles. The extraordinary mechanical and electronic\nproperties of multiply twinned diamonds are discussed, highlighting\nthat hexagonal interfaces between cubic diamond fragments may determine\nexceptional ultrahard and quantum characteristics. The MTP X-ray diffraction\nspectra reveal clear pentagonal patterns with single (diamond decahedrons\nor dodecahedrons) or ten (diamond icosahedra) central 5-fold axes.\nA comparative analysis of experimental structural data and simulations\nat different theoretical levels demonstrates a perfect correspondence\nof theoretical models with crystalline lattices.