BOLS Formulation

The BOLS notation indicates that the contraction of the mean lattice constant of the entire solid originates from the CN imperfection-induced bond contraction of surface atoms and the fraction of the surface atoms of the entire solid. The following expressions formulate the surface strain and nanosolid densihcation [82, 83]  

Among several methods, XRD is the most efficient method to determine the crystal size D and the lattice constant d for a bulk and nanostructured materials, as illustrated in Fig. 12.3, based on Bragg diffraction and Scherrer s equation, 

Given the shape and size of a solid and the known atomic diameters of the constituent atoms, one can easily predict the lattice contraction of the nanosolid using Eq. (12.2). For the ZnMnTe spherical nanosolid instance [70], the diameters of the constituent atoms are 0.1306(Zn), 0.1379(Mn), and 0.1350(Te) nm, and the effective CN of the outermost three atomic layers are taken as 4, 6, and 8, respectively. The resultant bond length is d = xd with x being the fraction of the component element. Calculation results agree fairly well with the observation ( 8 % contraction for 12.5 nm-sized ZnMnTe solid) and show that the lattice constant reaches its bulk value only when the solid dimension is sufficiently large. At the lower end of the size limit, the mean lattice contraction of the solid approaches the value for a dimer of the same atomic constituents. Furthermore, predictions based on the BOLS premise also agree with the observed trends of lattice contraction for ZnS Mn films [85] and Sn and Bi nanoparticles [69]. 

Measurements [11] show that for the 2.0, 2.5, and 3.5 nm-sized Ag crystals, the Ag-Ag atomic distance is shorter than the bulk value. For the 5.0 nm crystal, 60 % of the atoms have the bulk value but 40 % have shorter atomic distances. 

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Figure 19.7 compares BOLS predictions with measured size dependence of Ms at low T. As the measured data are much scattered, it is hard to reach a conclusion though the trends generally match however, the close match of Tc(K) suppression and lattice contraction, as shown earlier in this report evidences sufficiently the validity of the BOLS formulation as the origin of the unusual magnetic behavior of the ferromagnetic nanosolids at different temperatures. 

The BOLS formulation enables reproduction of the measured P y-Kc- Figure 28.9a shows the typical V-P profiles [89] measured at the ambient temperature for Sn02 bulk and powders of 14, 8, and 3 nm across, which demonstrates clearly the size... 

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