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 $betaapprox0.1$ 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.
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