Small-Angle Scattering from Liquid Metals and Alloys and Electronic Correlation Functions

Abstract

The partial structure factors Sii, Sie and See in pure liquid metals are considered at small wave vectorq. Charge neutrality arguments relate the three functions through the valencyZ atq = 0. It is shown that the partial Ornstein-Zernike functions are proportional toq = 0. It is in the long-wavelength limit, and that they are related, not only throughZ, but through a common characteristic energyE. By setting up a model for the dynamic structure factors, and by assuming well-defined plasmon and phonon modes at smallq, the characteristic energy is shown to be dominated by the zero-point energy of the electronic plasma oscillations. In turn, this same energy is shown to dominate the curvature of See atq = 0, the curvature being pronounced and See therefore rising rapidly away fromq = 0. In contrast, because ion masses enter, the coefficients of q2 in Sie and Sii are shown to be orders of magnitude smaller and these structure factors are therefore quite flat nearq = 0. However, the magnitudes of the coefficients of q2 in Sie and Sii are shown to be influenced by the phonon dispersion, though insensitive to phonon damping. For weak electron-ion interaction, Sie(q) and S(q) can be related through an electronic response function, and the resulting expression satisfies the exact limiting relation between Sie andS atq = 0. Finally, the q2-term in See in an alloy is discussed and is shown to be directly related to the average electronic plasma frequency, involving therefore the valencies of the components and the mean atomic volume. The partial structure factors SAe and SBe can also be related to the (measurable) partial ionic structure factors for weak electron-ion interaction.