Absolute X-Ray Reflectivity Studies of Finite and Imperfect Systems: Thin Liquid Crystal Films and Imperfect Graphite
Abstract
X-ray reflectivity has been used to obtain bulk defect information for natural single crystal graphite and pyrolytic graphite, and to study the critical behavior of the correlation length for smectic-A freely suspended liquid crystal films of butoxybenxylidene octylaniline (40.8). Detailed information about the stacking faults in natural graphite and the twist defects in pyrolytic graphite can be obtained from the enhancement of the reflectivity. X -ray reflectivity formulas are derived which include the effects of bulk defects, and the sensitivity of x-ray reflectivity to the bulk defects is established for the first time. For natural graphite, the probability of growth-twin fault occurrence at any given layer is (4.5 +/- 0.4) times 10^{ -4} while the probability of deformation fault occurrence is close to 0 (<10^ {-5}). For pyrolytic graphite, the variation in the lattice constant due to twist defects is (5 +/- 1) times 10^ {-3} A. Due to the finite x-ray absorption, the number of defect planes detected by the x-rays increases as the incidence angle increases and the reflectivity shows an extra incidence angle dependence. In the liquid crystal film studies, measurements of 11, two 46, 60 and 81 layer films were performed at more than ten different temperatures each in the smectic -A phase. Detailed analysis of the reflectivity showed that the film density developed pronounced profiles due to the two free surfaces. However, the profiles could not be explained by the order parameter phase fluctuations, which is the origin of the lower marginal dimensionality for bulk smectic-A phase. The phase fluctuations are quenched by the two free surfaces and are negligibly small in thin films. Instead, the order parameter amplitude develops a static spatial profile in thin films. A mean field theory is developed to explain the order parameter amplitude profiles. Excellent agreement between the results from the mean field theory and the density profiles was found and the correlation lengths of the profiles were derived. The critical behavior of the correlation length near the nematic-to-smectic-A phase transition is studied in the smectic-A phase. The correlation length and order parameter exponents, nu and beta are in excellent agreement with the simple mean field predictions.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- 1994
- Bibcode:
- 1994PhDT........57Z
- Keywords:
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- THIN FILMS;
- Physics: Condensed Matter; Engineering: Materials Science