Size Effect in the Dielectric Permittivity of Crystals

2 Changes of the Atomic Structure on Transition from Bulk Solids to Nanophases 

This topic will be discussed in two steps, firstly the crystals with 3-dimensional structures (metal nanoparticles and 4-coordinate semiconductors) and then those with a layered stmcture (Bi, Se, Te, etc). A decrease in the crystal sizes can result in a change of the stmcture type if the surface energy gain exceeds the enthalpy of the corresponding phase transition. Thus, Co has the structure of the hep type in the bulk, the/cc type in 10-20 nm particles and the bcc type in 2-5 nm particles [33], Particles of In with the diameter of 5 nm have the/cc structure, and those from 5 nm upward to the bulk have the fecf-lattice [34]. Agl adopts the cubic stmcture in the particles larger than 50 nm and the hexagonal one in smaller crystals [35]. In As has the wurtzite (w) stmcture up to 40 nm and the sphalerite (zb) structure in grains of 80 nm [36]. Nano-CdS has the the zb stmcture for D = 4 nm, while the w-phase is stable for the bulk material [37, 38]. On the contrary, MnSe was obtained in the w-form in nanoparticles, whereas the zb phase is stable for bulk crystals [37, 39]. 

The study of stmctural parameters of the Ge nanophase [49] shows that 9 nm nanoparticles have = 4, similar to that of the bulk, but this parameter decreases (down to 3.3) as grains become smaller. At the same time, the interatomic distance increases and approaches that for bulk amorphous Ge. This contradicts the observations for metallic nanophases where a decrease in the size is accompanied by a contraction of the mean interatomic distance due to capillary pressure. For the present case, the increase in interatomic distance apparent in semiconductor samples results from the increase in amorphous fraction with decreasing grain sizes. At the same time, crushing of Te crystals reduces both the and bond lengths, and increases the force constants (A b) [50], Fig. 8.1. These results indicate that nanosamples of Te are close to the covalent state. 

The dielectric permittivity (e) of solids often changes with the particle size. The dependence is a result of a complicated interplay of several factors, it can vary widely in magnitude and even have different sense. Let us consider the influence of different factors on e under transition from bulk solids to nanophases. 

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