Measurement of Smectic-A-Phase Order-Parameter Fluctuations near a Second-Order Smectic-A—Nematic-Phase Transition

The anisotropic liquid-structure factor of $p$ -cyanobenzylidene-amino-$p$-$n$-octyloxybenzene has been measured in the nematic phase using $\mathrm{Cu} K\alpha$ x rays. This material exhibits a second-order phase transition to the smectic $A$ phase at $T_c=82.8\mathrm{}$ °C. The liquid-structure factor shows a non-Lorentzian peak at a wave number of $q_0=0.179\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$ (equivalent $d$ spacing 35.0 Å) of the following form: $S_q=1+{\{3.5\mathrm{}{\epsilon }^{\gamma }+10\mathrm{}{\left[\frac{(q_{\parallel }-q_0)}{q_0}\right]}^2+0.6\mathrm{}{\left(\frac{q_{\perp }}{q_0}\right)}^{\eta }\}}^{-1\mathrm{}}$, where $\epsilon =\frac{(T-T_c)}{T_c}$, $\gamma =1.49\mathrm{}\pm 0.1$, $\eta =2.5\mathrm{}\pm 0.2$, and $\hslash q_{\parallel }\left(\hslash q_{\perp }\right)$ are the momentum transfers parallel (perpendicular) to the orienting field.