We report a high-resolution synchrotron grazing incidence x-ray diffraction measurement of a surface crystalline monolayer at the liquid-vapor interface of the n-alkane eicosane $\left({\mathrm{C}}_{20}{\mathrm{H}}_{42}\right)$ just above its melting temperature. The peak width of the surface monolayer rotator phase is shown to be resolution limited and implies positional correlations of at least ∼1 μm. The high resolution allowed determination of the temperature dependence of the peak position over the narrow (3 °C) temperature range of the surface crystal phase. The two-dimensional thermal expansion was determined to be $\mathrm{}(dA/dT)/A=1.8(\pm 0.1)\times {10}^{-3}°{\mathrm{C}}^{\mathrm{-}1},$ which is comparable to the expansion in similar chain length bulk n-alkane rotator phases. Our data are consistent with the power-law shaped scattering tails expected from quasi-long-range order in two dimensions.

• Received 10 October 2000

DOI:https://doi.org/10.1103/PhysRevE.63.032602