The unit cell structures of two ferrielectric liquid-crystal phases are determined from ellipsometric studies of freestanding films in a nondistorting rotatable electric field. A highly biaxial mode with out-of-plane distortions describes all of the data from two different compounds. Qualitative and quantitative features of the data rule out alternate models. We also present a detailed explanation for apparent inconsistencies between previous resonant x-ray and optical experiments.

We describe a model for the layer-thinning transition in free-standing liquid-crystal films based on the successive, spontaneous formation of dislocation loops. As the film temperature increases and the smectic order and layer compressional modulus decrease, the condition for creating a dislocation loop of critical radius is met and a thinning is nucleated. The resulting equation for N, the number of smectic layers, as a function of temperature yields good fitting results to the thinning transitions obtained from several fluorinated compounds.

The kinetic behavior of dislocation loops in overheated free-standing smectic-A films is reported. The loops open at velocities that are much faster than those seen in nonoverheated films. The velocities increase dramatically as a function of temperature and vary slightly as a function of film thickness. The behavior of dislocation loops induced with a pulsed resistive wire heater is identical to that of the loops giving rise to the layer-thinning transition. In addition, the interaction between two simultaneously nucleated dislocation loops is analyzed. The observed interactions give evidence that thinning occurs in the interior of the film. The results support a model for the layer-by-layer thinning transition based on the nucleation of dislocation loops.

Both optical reflectivity and ellipsometry data obtained from freestanding films in the Sm-C ‫ء‬ a phase of one liquid-crystal compound display characteristic oscillations as a function of temperature. A model for the film consisting of surface anticlinic layers and an interior short-pitched azimuthal helix provides an excellent description of our data. Our results show a linear evolution with temperature of the relative interlayer azimuthal angle. The data enable us to place an upper bound on the degree of distortion in the short-pitched helix. PACS numbers: 61.30.Eb, 77.84.Nh, 83.70.Jr The surprising discoveries of ferroelectric and antiferroelectric behavior in liquid crystal Sm-C ‫ء‬ [1] and Sm-C ‫ء‬ A[2] phases without long range positional order are fundamental to condensed matter physics. Three phases showing more complicated electric field responses (Sm-C ‫ء‬ FI1 , Sm-C ‫ء‬ FI2 , and Sm-C ‫ء‬ a ) have also been identified [3]. While the structure of the Sm-C ‫ء‬ and Sm-C ‫ء‬ A phases are now well understood, the underlying structures of these intermediate phases is still the subject of debate. Recent resonant x-ray experiments [4] have for the first time resolved the structural periodicity of these phases. Furthermore, the polarization analysis [5] gives direct evidence for the clock model [6] unit cell in the Sm-C ‫ء‬ FI1 and Sm-C ‫ء‬ FI2phases. In this paper we study the detailed structure of the Sm-C ‫ء‬ a phase found in the 10OTBBB1M7 compound [7] (Fig. 1) using optical reflectivity and ellipsometry. The clock model with a continuously evolving helix is the only model that is consistent with our data. Our results also confirm the periodicity measured by x rays for this phase [4]. Alternative models, in particular, the proposed Ising model devil's staircase [3,8], conflict with even the gross features of our data. We also propose that surface anticlinic layers [9] coexist with the helical Sm-C ‫ء‬ a phase in our freestanding films. Our results also allow us to place an upper bound on the degree of distortion in the shortpitched helix should such a distortion exist.The Sm-C ‫ء‬ a phase, like all of the Sm-C ‫ء‬ variant phases, is known to possess a tilted smectic structure. The average orientation of the long axis of the molecules (the director) within the ith layer may be described by the tilt angle ͑u i ͒ with respect to the layer normal and the azimuthal angle ͑f i ͒. Each layer possesses a net dipole, oriented perpendicular to the layer normal and the director. Our results allow us to model ͓u i ͔ and ͓f i ͔ as continuous functions of temperature in the Sm-C ‫ء‬ a phase in freestanding films.The liquid-crystal freestanding film is prepared in a double stage temperature controlled oven with a temperature resolution of 0.01 K. The film is drawn across a 7 3 5 mm rectangular hole in a horizontal glass coverslip [10]. Two gold electrodes produce an aligning electric field in the plane of the film The 10OTBBB1M7 compound studied is isolated in a 5 6 atm argon environment. The ellipsometry optical comp...

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