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

Abstract

The origin of extended-range ordering in binary liquids and glasses is investigated. Thestarting point is a simple model pair potential which includes both Coulomb and dispersionforces. For this model, the behaviour of the Bhatia–Thornton partial structure factors at smallscattering vector values is examined and also the asymptotic behaviour of the associatedpartial pair correlation functions in real space. The results are compared with the observedreal space pair correlation functions for a range of liquid and glassy systems for whichaccurate partial structure factors have been measured by using neutron diffraction. It isfound that the extended range ordering can often be accounted for by using anexponentially 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 theobserved behaviour of the real space data at relatively small distances as in thecase of the concentration–concentration pair correlation function for moltenAg2Se and forglassy GeSe2, ZnCl2 and GeO2. For these glasses, all of the Bhatia–Thornton pair correlation functions in real spaceeventually decay with a common wavelength of oscillation and a common decay length. Thelimitations associated with the use of simple model pair potentials to analyse theexperimental data sets are discussed. In addition, the effect on the small-angle scatteringand asymptotic decay of the real space pair correlation functions of including a termcorresponding 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 Lorchmodification function.