A comprehensive review is given on experimental studies of small particles with fivefold symmetry accompanied by an in-depth theoretical description of their characteristics and computer modeling. The cases of uniform and nonuniform deformations (disclination model), stability and relaxation of elastic stresses in pentagonal particles and needle-like crystals, models of their formation are discussed.

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On the basis of continuous elastic models relaxation channels of elastic stresses inside the pentagonal needle-like nanoparticles (PNNPs) are considered. Six models are analyzed: 1. creation of a dislocation inside the PNNP; 2. opening of a gap in the PNNP; 3. creation of a disclination bound with the PNNP surface; 4. splitting of the pentagonal axis; 5. growth of monocrystalline region around the PNNP axis; 6. displacement of the pentagonal axis towards the periphery of the PNNP. An energetic balance and the possibility of realization for each of these channels are discussed.Auf der Grundlage elastischer Kontinuumsmodelle werden Relaxationskanale der elastischen Spannungen ini Inneren von pentagonalen nadelformigen Nanopartikeln (PNNP) untersucht. Sechs Modelle werden analysiert: I. Bildung einer Versetzung im PNNP, 2. Offnung einer Liicke im PNNP, 3. Bildung einer an der PNNP-Oberflache gebundenen Disklination, 4. Aufspaltung der pentagonalen Achse, 5. Wachstum eines einkristallinen Bereiches um die PNNP-Achse, 6. Verschiebung der pentagonalen Achse zur Peripherie der PNNP. Ein Energieausgleich und die Moglichkeit fur die Realisierung jedes dieser Kanale werden diskutiert.') SU-142092 Troitsk, Moscow region, USSR. ' ) SU-194021 Leningrad, USSR.