Liquids pair correlation function, observable

Moreover, the sensitivity of pair correlation functions to the potential might not be enough to actually discriminate them. This is apparent in the case of associated liquid, especially water, where rather large differences e.g. of dielectric constant are observed with quite similar pair correlation functions [TIP4P [72] SPC [73], SPC SPC/E [74]. In these cases, the relevant structural information is conveyed by appropriate projections of the distribution function, such as h (r), that monitors the extent of correlation between dipoles as a function of their separation and whose integral is directly related to dielectric permittivity [74],... 

This observation constitutes the basic idea of the local equilibrium model of Prigogine, Nicolis, and Misguich (hereafter referred to as PNM). One considers the case of a spatially nonuniform system and deduces from (3) an integral equation for the pair correlation function that is linear in the gradients. This equation is then approximated in a simple way that enables one to derive explicit expressions for all thermal transport coefficients (viscosities, thermal conductivity), both in simple liquids and in binary mixtures, excluding of course the diffusion coefficient. The latter is a purely kinetic quantity, which cannot be obtained from a local equilibrium hypothesis. 

The strength of the water-metal interaction together with the surface corrugation gives rise to much more drastic changes in water structure than the ones observed in computer simulations of water near smooth nonmetallic surfaces. Structure in the liquid state is usually characterized by pair correlation functions (PCFs). Because of the homogeneity and isotropy of the bulk liquid phase, they become simple radial distribution functions (RDFs), which do only depend on the distance between two atoms. Near an interface, the PCF depends not only on the interatomic distance but also on the position of, say the first, atom relative to the interface and the direction of the interatomic distance vector. Hence, considerable changes in the atom-atom PCFs can be expected close to the surface. 

Fig. 6.8 The Faber-Ziman partial structure factors and partial pair correlation functions for Feg5Ni35. The black lines in the partial structure factors are spline fits to the data. The black lines in the partial pair correlation functions are Lorch modified Fourier transforms of the same data. The poorer conditioning of the FZ matrix results in noisier partial structure factors than for the BT formalism. Despite this there appears to be relatively little difference between the Ni-Ni, Fe-Fe, and Ni-Fe partial structure factors, suggesting that the mixing is close to that of an ideal liquid. The very sharp peak observed in SniNii ) [with corresponding dip in appears to...

The structure factors, S q), and pair correlation functions, g r) of Sb2Tc3 and Sb2Te in the liquid and amorphous phases are shown in Fig. 18.2. If the overall agreement between experiment and simulation is reasonable, it is not as good as in the case of other chalcogenide glasses, such as GeSc2 [22]. It was established [23] that the discrepancy is mostly due to an over coordination of Te atoms in DFT calculations. However, AIMD simulation reproduce all trends observed experimentally. 

Solutions in hand for the reference pairs, it is useful to write out empirical smoothing expressions for the rectilinear densities, reduced density differences, and reduced vapor pressures as functions of Tr and a, following which prediction of reduced liquid densities and vapor pressures is straightforward for systems where Tex and a (equivalently co) are known. If, in addition, the critical property IE s, ln(Tc /Tc), ln(PcVPc), and ln(pcVPc), are available from experiment, theory, or empirical correlation, one can calculate the molar density and vapor pressure IE s for 0.5 < Tr < 1, provided, for VPIE, that Aa/a is known or can be estimated. Thus to calculate liquid density IE s one uses the observed IE on Tc, ln(Tc /Tc), to find (Tr /Tr) at any temperature of interest, and employs the smoothing relations (or numerically solves Equation 13.1) to obtain (pR /pR). Since (MpIE)R = ln(pR /pR) = ln[(p /pc )/(p/pc)] it follows that ln(p7p)(MpIE)R- -ln(pcVpc). For VPIE s one proceeds similarly, substituting reduced temperatures, critical pressures and Aa/a into the smoothing equations to find ln(P /P)RED and thence ln(P /P), since ln(P /P) = I n( Pr /Pr) + In (Pc /Pc)- The approach outlined for molar density IE cannot be used to rationalize the vapor pressure IE without the introduction of isotope dependent system parameters Aa/a. 

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