TABLE OF CONTENTS The transition from bulk crystals or large particles to nanoparticles is accompanied by a change of the interatomic distances and crystal lattice constants [2 5,12]. The main task is to determine whether the lattice constants decrease or increase with a decrease in the particle size, and also to determine that nanoparticle size behind which this change is measurable. The experimental data on the size dependence of the lattice constant reported in the literature are often ambiguous and contradictory.
Analysing the variation of the lattice constant of the nanoparticles, it is important to take into account the possibility of transition from less dense bcc and hexagonal structures to more dense fcc structures accompanying by a decrease in the particle size, mentioned in Section 5.1. According to electron diffraction data [55], the hexagonal close-packed structure and the lattice constants, which are characteristic of bulk metals, remains unchanged with a decrease of diameter D of the particles Gd, Tb, Dy, Er, Eu and Yb from 8 to 5 nm. With a further decrease of the particle size, the lattice constants decrease rapidly. However, these changes are accompanied by a change of electron diffraction patterns, indicating a structural transformation, i.e. transition from the hcp to fcc structure, and not a decrease of the interplanar distances of the hcp lattice. In fact, investigation of nanoparticles of rare-earth metals by the X-ray diffraction technique showed a structural transition from the hcp to fcc lattice [15,16]. Thus, to ensure reliable detection of...
