BOLS Notation

The bond nature index m correlates the bond energy to the bond length. For Au, Ag, Ni, and Cu metals, m = 1 for alloys and compounds, m is around four for C and Si, the optimal m value is 2.56 [10] and 4.88 [11], respectively. The m value may change with the coordination environment of group 111 and group IV elements [12]. The C z) is anisotropic and varies with the effective CN rather than the apparent CN value. The Zi labels the atomic CN of atoms in the rth layer of a substance. The curvature dependent zt takes the following form [11]  

The curvature takes all possible values from infinity to negative infinity. The BOLS correlation illustrated in Fig. 11.2 is independent of the particular form of the pairing potential as the approach involves only atomic distance and bond energy at equilibrium u(4-, E.  

---

BOLS notation holds for defects, skins of solids and liquids, as well as molecules... 

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] ... 

The BOLS notation considers variation of atomic coh from atoms in the skin only. Using the same spherical dot containing N atoms with N, atoms in the fth surface shell, the average ( coh( )) ( b(N)) is. 

Interspin interaction and the spin momentum dictate the magnetism of nanoferromagnetic system, following the BOLS notation, Ising premise, and Brillouin functions. 

A broken bond shortens and strengthens its neighbors globally and spontaneously, which follows the BOLS notation, irrespective of structural phase of a... 

From the analytical expression of binding energy per unit area, EyT, and the current T-BOLS notation, the shortened and strengthened bonds of the undercoordinated surface atoms dictate the smface tension, surface stress, and surface energy. Correspondingly, one may also clarily the difference between surface stress and surface tension as the energy gradient in the surface normal and in the surface plane directions, respectively, as summarized in Table 24.2. The d,surface tension is a vector with x and y components because dFx/dy = dFy/dx = 0 instead of a second-rank tensor. 

Fig. 28.4 The V-P profile for nanostructured Ti02 shows the IHPR transition at 15 nm size, as the slope is inversely ptoportional to the bonding energy density of yield stress, according to the present T-BOLS notation. (Reprinted with permission from [89])...

The currently defined T ni(x)/7)n(0)-BOLS curve overlaps the curve derived from Born s criterion, T ni(x)/ri (0)-Bom, which indicates the consistency in the respective physical mechanisms of melting. BOLS notation suggests that the melting is governed by the skin-resolved depression of the atomic cohesive energy (I m oe zE but the Born s criterion Eq. (28.5) requires that the shear modulus or mechanical strength disappears at T [90]. The trend of the 7 m(x)/rm(0) curves also agree with the models derived from Lindermann s criterion of atomic vibration [91-93], surface lattice/phonon instability [94, 95], liquid drop [96], and surface area difference [97]. Therefore, all the models are correct despite different perspectives. 

The encapsuled and the free-standing (H20)n molecular clusters, surface skins, or ultrathin films of water should share the same entity of bond order deficiency to follow the BOLS premise without exception. However, the involvement of the weak lone pair interaction and the interelectron-pair repulsion prevents the two segments of the H-bond from following the BOLS mechanism simultaneously. The binding energy difference between the 0 H and H-O and the presence of the interelectron-pair repulsion define the H-O covalent bond to be the master that contracts by a smaller degree than which the BOLS notation predicts. The contraction of the H-O bond lengthens and softens the slave 0 H bond by repulsion. 

The currently described knowledge about localized charge entrapment and polarization associated with the skin of both the liquid and the solid specimen provides an electronic mechanism for the 4S. According to the BOLS-NEP notation, the small fluidic drop can be viewed as a liquid core covered with a solid-like, densely charged, and elastic sheet with pinned dipoles. The energy density, charge density, polarizability, and the trap depth are bond order dependence. 

As demonstrated, the impact of the often overlooked event of atomic CN imperfection and the associated local quantum entrapment and polarization is indeed profoundly tremendous. The BOLS and NEP notations enable one to view the performance of a defect, surface, a nanosolid, and a solid in amorphous state consistently in a way from the perspective of bond and non-bond formation, dissociation, relaxation, and vibration and the energetic and dynamic process of electron densification, localization, polarization, and redistribution. The following features the progress made in this part ... 

Consistency between the BOLS prediction and the measurements evidences not only the essentiality and validity of the BOLS-NEP notation but also the significance of atomic CN imperfection to the low-dimensional and disordered systems that are dominated by atomic CN deficiencies. Understanding gained insofar should be able to help us in predicting nanosolid performance and hence provide guideline in designing process and fabricating materials with desired functions. 

---