Atomic environments solid-like

Fig. 1.7 A schematic representation of the free-energy function/(v), which is dependent primarily on the atomic volume at an atom site (a) the binding-energy plot showing equilibrium volume Vq and inflexion point vi (b) division of/(v) into two parts, consisting of a central, strongly bonded harmonic part with v < Vc and a linear part with v > Vc used to define solid-like, SL, and liquid-like, LL, atomic environments (from Cohen and Grest (1979) courtesy of the APS).

Fig. 1.21 Radial distribution functions and bond-angle distribution functions of the solid-like atom environments (a) and (b) and of the liquid-like environments (c) and (d)...

Two partly complementary, partly overlapping concepts, namely free volume and liquid-like (LL) atomic environments, have been used over the years to explain the increased fluidity or ease of local plastic accommodations of imposed shape changes in glassy solids. They were first discussed in Sections 1.5 and 1.14. The concept of free volume, which was introduced by Fox and Flory (1950) and has been further elaborated by many others since, is based on a local excess of... 

Since the LL atomic environments and the complementary solid-like (SL) types bifurcate, cp always represents the LL-environment fraction as a well-defined parameter characterizing the disorder of the amorphous state in simple glasses. 

A suitable order parameter r) should distinguish locally between the ordered (solid-like) and disordered (liquid-like) environment of an atom. Usually it is taken to be a function adapted to the symmetry of the solid phase, so that it takes nonzero values in the crystal-like configurations and zero in the liquid-like ones (ideal liquids are isotropic). One possible choice is a linear combination of spherical harmonics in a similar fashion as the popular Steinhardt order parameter Qi [26] defined in the Sect. 3.2.1 Angioletti-Uberti et al. instead chose polynomials adapted to the face-centered cubic (fee) symmetry of Ar, since they are cheaper to compute than spherical harmonics. Their polynomials have the form (using the same notation as in [27]) ... 

For interfacial systems, potential functions should ideally be transferrable from the gas-phase to the condensed phase. Aqueous-mineral interfaces are not in the gas phase (although they may be close, see (7)), but both the water molecules and the atoms/ions in the substrate are in contact with an environment that is very different from their bulk environment. The easiest different environment to test, especially when comparing with electronic structure calculations, is a vacuum, so there is likely to be a great deal of information available on either the surface of the solid or the gas-phase polynuclear ion or the gas-phase aquo complex (i.e., Fe(H20)63+, C03(H20)62-). The gas-phase transfer-ability requirements on potential functions are challenging, but it is difficult to imagine constructing effective potential functions for such systems without using gas-phase systems in the construction process. This means that any water molecules used on these complexes must also transfer from the gas phase to the condensed phase. A fundamental aspect of this transferability is polarization. 

The formation of alkaline earth metal bis[bis(tiialkylsilyl)amides] has been discussed in detail elsewhere." Like all heavier group 2 metal bis[bis(tiisalkylsilyl)amides], the complex [(Ca N(SiMe3)2 2)2] has a dimeric structure both in solution and the solid state (Figure 3.8), in which the calcium atoms are in a distorted trigonal planar environment. 

The first explanation and use of such a pseudopotential is due to Heilman5 (1935) who used it in atomic calculations. More recently the pseudopotential concept was reformulated by Phillips and Kleinman7 who were interested in its application to the solid state.8-10 Research in both solid- and liquid-state physics with pseudopotentials was reviewed by Ziman,11 and work in the fields of atomic spectroscopy and scattering has been discussed by Bardsley.12 For an earlier review on applications to the molecular environment the reader is referred to Weeks et a/.13 In this article we shall concentrate on molecular calculations, specifically those of an ab initio nature. Our objective in Section 2 has been to outline the theoretical origins of the pseudopotential approximation, and in Section 3 we have described some of the techniques which have been used in actual calculations. Section 4 attempts to present results from a representative sample of pseudopotential calculations, and our emphasis has been to concentrate on particular molecules which have been the subjects of investigation by the various approaches, rather than to catalogue every available calculation. Finally, in Section 5, we have drawn some conclusions on the relative merits of the different methods and implementations of pseudopotentials. Some of the possible future developments are outlined in the context of the likely progress in quantum chemistry. 

Adducts ofB(C6F5)3 that have been studied in detail either in solution or the solid state are collected in Table I along with selected solution NMR spectroscopic data and metrical parameters. In particular, both the nB NMR chemical shift35 and the separation between the resonances for the meta and para fluorine atoms in the 19F NMR spectrum109 are quite sensitive to the environment about the boron center and the strength of the LB-B(C6F5)3 interaction. Indeed, as shown in Fig. 1, a rough empirical correlation between these two NMR parameters is observed. Anomalies arise for two classes of LB more linear bases like nitriles or isonitriles that do not pyramidalize the boron center as severely and the RM1 adducts (M = Al, Ga). 

Like Mossbauer spectroscopy, positron spectroscopy is a nuclear process for probing the chemical and physical environments of solid materials. It is a more versatile technique than Mossbauer spectroscopy, but it does not provide as much information on the structure surrounding the nucleus or the immediate environment of the atom. 

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