Decay of the pair correlations and small-angle scattering for binary liquids and glasses

The origin of extended-range ordering in binary liquids and glasses is investigated. The starting point is a simple model pair potential which includes both Coulomb and dispersion forces. For this model, the behaviour of the Bhatia–Thornton partial structure factors at small scattering vector values is examined and also the asymptotic behaviour of the associated partial pair correlation functions in real space. The results are compared with the observed real space pair correlation functions for a range of liquid and glassy systems for which accurate partial structure factors have been measured by using neutron diffraction. It is found that the extended range ordering can often be accounted for by using an exponentially damped oscillatory function with a wavelength of oscillation given by ≈2π/kPP, where kPP is the position of the principal peak in the measured partial structure factors. Sometimes this exponentially damped oscillatory function also accounts for the observed behaviour of the real space data at relatively small distances as in the case of the concentration–concentration pair correlation function for molten Ag2Se and for glassy GeSe2, ZnCl2 and GeO2. For these glasses, all of the Bhatia–Thornton pair correlation functions in real space eventually decay with a common wavelength of oscillation and a common decay length. The limitations associated with the use of simple model pair potentials to analyse the experimental data sets are discussed. In addition, the effect on the small-angle scattering and asymptotic decay of the real space pair correlation functions of including a term corresponding to ion-induced dipole interactions in the pair potential is briefly considered. An analytical expression is also given for the real space manifestation of the Lorch modification function.