Determination of the in-plane elastic tensor of crystalline decanol monolayers on water by x-ray diffraction

We show how high-resolution x-ray studies associated with surface tension measurements allow a determination of the elastic constants of crystalline 1-decanol monolayers at the water-air interface. The shape and position of the power-law diffraction peak yield, respectively, the shear and compression elastic constants. At low temperature, rotation scans of the liquid surface around a vertical axis exhibit six sharp peaks, proving the existence of the long-range order of bond orientations, as expected for a hexagonal two-dimensional (2D) crystal. We find a shear elastic constant of (210 +/- 30) mN/m and a compression modulus of (2500 +/- 500) mN/m. These values are compatible with the existence of a 2D solid, according to the Nelson-Halperin melting theory. Between similar to 12 degrees C and melting (T-m = 14.3 degrees C), the drastic broadening of the diffraction line can be interpreted either as the occurrence of a hexatic phase or as a strong decrease of the shear modulus, as expected in the framework of the weak crystallization theory.