Synthesis of vaterite CaCO3 as submicron and nanosized particles using inorganic precursors and sucrose in aqueous medium

It is reported the synthesis of CaCO₃ vaterite as stable nanoparticles and submicron-sized by a simple and relatively rapid procedure. XRD, SEM and FTIR techniques have been used to characterize the precipitated products. The synthesis is based on chemical precipitation of inorganic salt precursors, calcium nitrate tetrahydrate and sodium bicarbonate, and using the disaccharide sucrose as an additive in aqueous medium. The role of the disaccharide sucrose is to control the vaterite precipitation after nucleation and growth. It has been found that an increase in sugar concentration promotes the crystal precipitation of vaterite with spherulitic morphology, as revealed by SEM, and changed the surface of the precipitated particles. There is a significant difference between CaCO₃ precipitation in the absence and presence of sucrose. Addition of 0% of sucrose leads to 83% of calcite as identified by XRD methods. In contrast, addition of 67% of sucrose in aqueous medium produces 100% vaterite. The present results may be useful to provide a quick, simple, inexpensive and novel method for the controlled synthesis of new advanced biomaterials based on vaterite particles without hazardous chemicals and inert atmosphere, with great possibilities for industrial scale production.     

Effects of Dry Grinding on the Structural Changes of Kaolinite Powders

The present study examined the effects of dry grinding, using ball-milling, on the structure of reference well-crystallized (KGa-1) and poorly crystallized (KGa-2) kaolinite powders from Georgia. Grinding produced a strong structural alteration, mainly along the c axis, resulting in disorder and total degradation of the crystal structure of the kaolinite and the formation of an amorphous product. The surface area increased with grinding time, mainly in KGa-2 (maximum value 50.27 m²/g), a result associated with particle-size reduction. These particles became more agglomerated with grinding, and the surface area decreased after 30 min, as confirmed by scanning electron microscopy and particle-size-distribution analysis. There was a limit to particle-size reduction with grinding time. When grinding time was increased, the original endothermic differential thermal analysis (DTA) effects of dehydroxylation in both samples shifted to lower temperatures, decreased in intensity, then disappeared completely after 120 min of grinding. The temperature of the characteristic first exothermic effect shifted slightly to lower temperatures with grinding, although the DTA effects did not increase with grinding time in either kaolinite sample, at least up to 325 min. The amorphous, mechanically activated kaolinite converted into low-crystalline mullite nuclei at a lower temperature than did the unground samples, as deduced by thermal and X-ray observations. This effect was especially important for the KGa-2 sample. Grinding did not seem to influence the formation of silicon-aluminum spinel from kaolinite. The present results may explain why ground kaolinite samples prepared via different routes—e.g., with differences in grinding—behave differently during high-temperature transformations, as reported in the related literature.     

Absorbing beam splitter in a Michelson interferometer

The equality of the reflected and the transmitted irradiances by a beam splitter that consists of a thin absorbing coating (typically a metallic film) on a transparent plate is considered. The absorption and the phase difference between the reflected and transmitted fields are also studied. The lack of reversibility of this beam splitter introduces an asymmetry that is discussed for a Michelson interferometer.     

Characterizing the reflectance near the Brewster angle: a Padé-approximant approach

We characterize the reflectance peak near the Brewster angle for both an interface between two dielectric media and a single slab. To approach this problem analytically, we approximate the reflectance by a first-order diagonal Padé. In this way, we calculate the width and the skewness of the peak, and we show that although they present a well-resolved maximum they are otherwise not so markedly dependent on the refractive index. As an application of interest, we derive simple expressions for the precision of the Abelès Brewster-angle method.     

Understanding multilayers from a geometrical viewpoint

We reelaborate on the basic properties of lossless multilayers. We show that the transfer matrices for these multilayers have essentially the same algebraic properties as the Lorentz group SO(2, 1) in a (2 + 1)-dimensional space-time as well as the group SL(2, R) underlying the structure of the ABCD law in geometrical optics. By resorting to the Iwasawa decomposition, we represent the action of any multilayer as the product of three matrices of simple interpretation. This group-theoretical structure allows us to introduce bilinear transformations in the complex plane. The concept of multilayer transfer function naturally emerges, and its corresponding properties in the unit disk are studied. We show that the Iwasawa decomposition is reflected at this geometrical level in three simple actions that can be considered the basic pieces for a deeper understanding of the multilayer behavior. We use the method to analyze in detail a simple practical example.     

Hyperbolic reflections as fundamental building blocks for multilayer optics

We re-elaborate on the basic properties of lossless multilayers by using bilinear transformations. We study some interesting properties of the multilayer transfer function in the unit disk, showing that hyperbolic geometry turns out to be an essential tool for understanding multilayer action. We use a simple trace criterion to separate multilayers into three classes that represent rotations, translations, or parallel displacements. Moreover, we show that these three actions can be decomposed as a product of two reflections in hyperbolic lines. Therefore, we conclude that hyperbolic reflections can be considered as the basic pieces for a deeper understanding of multilayer optics.