Atomic environments liquid-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)...

Fig. 1.22 Dependence of the liquid-like (LL) atom environment fraction cp on the normalized density, pjpQ, of amorphous silicon (from Demkowicz and Argon (2005a) courtesy of the APS).

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... 

Demkowicz, M. J. and Argon, A. S. (2005a) Liquid-like atomic environments act as plasticity carriers in amorphous silicon, Phys. Rev. B, 72, 245205 (1-16). 

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]) ... 

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. 

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