X-Ray Study of the Nematic Phase and $\mathrm{Smectic}-A_1-\mathrm{to}-\mathrm{Smectic}-\tilde{A}$ Phase Transition in Heptylphenyl Nitrobenzoloxybenzoate (DB7N${\mathrm{O}}_2$)

We report a high-resolution x-ray study of the fluctuations in the nematic and smectic-$A_1$ phases in heptylphenyl nitrobenzoloxybenzoate. As a function of decreasing temperature, the fluctuations evolve from an incommensurate region, through an intermediate region of coexisting (competing) incommensurate and smectic-$\tilde{C}$ fluctuations, to a region dominated by pretransitional smectic-$\tilde{A}$ fluctuations which exhibit a phase-lockin $\mathrm{smectic}-A_1-\mathrm{smectic}-\tilde{A}$ transition. This behavior directly confirms the current theoretical description of the smectic-$\tilde{A}$ and smectic-$\tilde{C}$ phases as alternatives to the incommensurate phase.