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The Physical Nature of Changes of Lattice Parameters in Small Particles
Author(s) -
Ya Gamarnik M.
Publication year - 1993
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221780105
Subject(s) - perpendicular , condensed matter physics , lattice (music) , lattice constant , lattice energy , crystal structure , crystal (programming language) , monolayer , sign (mathematics) , bond length , ionic bonding , materials science , chemistry , crystallography , molecular physics , ion , diffraction , physics , geometry , nanotechnology , mathematics , optics , quantum mechanics , programming language , computer science , mathematical analysis , acoustics
The nature of size‐related changes of lattice parameters is determined by the difference in bond energies of surface and inner unit cells of a particle, which (the difference) leads to an excess or a deficit of the intracrystalline pressure in a small particle, stipulating a compession or tension of its lattice. It is shown that the size‐related change of the length of each lattice edge is determined by crystal sizes in perpendicular direction and practically does not depend on the crystal size along this edge. This property, called transversality, is explained by an energetic non‐equivalence of different unit cells, which is realized within cell monolayers or columns perpendicular to the edge. It is shown that the sign of the size effect – decrease or increase of the lattice parameter – is determined by the sign of the interaction energy v c ′of a unit cell with crystal unit cells excepting the nearest ones. To the positive sign of this energy there corresponds compression, to the negative sign tension of a small particle. The structural features are analysed for substances with ionic, covalent, and metallic bond types, determining the sign of v c ′and therefore the sign of the size effect.