  We report on X-ray studies of freely suspended hexatic films of three
different liquid crystal compounds. By applying angular X-ray cross-correlation
analysis (XCCA) to the measured diffraction patterns the parameters of the
bond-orientational (BO) order in the hexatic phase were directly determined.
The temperature evolution of the BO order parameters was analyzed on the basis
of the multicritical scaling theory (MCST). Our results confirmed the validity
of the MCST in the whole temperature range of existence of the hexatic phase
for all three compounds. The temperature dependence of the BO order parameters
in the vicinity of the hexatic-smectic transition was fitted by a conventional
power law with a critical exponent $\beta\approx0.1$ of extremely small value.
We found that the temperature dependence of higher order harmonics of the BO
order scales as the powers of the first harmonic, with exponent equal to
harmonic number. This indicates a nonlinear coupling of the BO order parameters
of different order. It is shown that compounds of various composition,
possessing different phase sequences, display the same thermodynamic behavior
in the hexatic phase and in the vicinity of the smectic-hexatic phase
transition.
