X-ray scattering from a two-dimensional liquid modulated by its periodic host

We present a treatment of the x-ray scattering from a two-dimensional (2D) liquid modulated by its periodic host. While this is general for all fluids within (or upon) periodic lattices, we concentrate on alkali metals intercalated in graphite to reveal the origin of the following: (a) the alkali-metal contribution to the graphite Bragg peaks, (b) the replication of the alkali-metal liquid scattering about the graphite reciprocal-lattice points, and (c) the anisotropic sixfold angular modulation of the normally isotropic 2D liquid scattering. While the first is linear in the relevant Fourier coefficients of the modulation potential, the latter two appear to second order. Finally we indicate a method for accurately evaluating the above Fourier coefficients from graphite Bragg peak intensities in the disordered (liquid) state of the intercalated alkali-metal species, which includes corrections for correlations in the liquid.