Static Structure Factor for a Finite Incommensurate Monolayer

Abstract

The static structure factor for a finite two-dimensional classical harmonic lattice is evaluated, including finite-size effects from both lattice sums and the lower $k$ cutoff on the phonon spectrum. The numerical results show that the power-law behavior of $S\left(\overrightarrow{\mathrm{q}}\right)$ expected in an infinite two-dimensional crystal should be already quite apparent in crystallites of size $L\sim 1000-5000$ Å.