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Typical derivations of the Bragg equation in introductory texts do not adequately explain why x-rays are reflected as if by a mirror by crystal planes, and often lead to the mistaken idea that lattice points can be identified with the centres of atoms or ions in the structure. The treatment offered here is a little more demanding, but to compensate for this also has the advantage that it can easily be extended to provide a basic understanding of the use of XRD in structure determination. Comparison of the x-ray powder diffraction patterns obtained from K Cl and K Br is used to illustrate how both the angles and the intensities of diffracted beams are determined by the structure of a solid. A brief discussion of the effects of crystal size on the broadening of diffraction lines is included both for its intrinsic interest, and because it emphasizes that the sharp diffracted beams which are often observed result from the cooperative effect of very large numbers of scattering centers.

The differential molar enthalpy, Gibbs free energy, and entropy of sorption of benzene, toluene, and p-xylene on silicalite were determined at 323.16 K from a set of sorption isochores. The work complements a similar study using H-ZSM-5. The results show that the unusual hysteresis shown in the sorption of p-xylene on low A1 content H-ZSM-5 is a consequence of both the entropy and enthalpy of sorption changing very little over a range of amount sorbed. This arises from the almost constant sorption environment and not from unusual sorbent/sorbate or sorbate/sorbate interactions. In contrast, benzene does display large variations in the enthalpy and entropy of sorption which are associated with dramatic changes in the state of the sorbed material. Paradoxically, this leads to much less noticeable changes in the sorption isotherms. Toluene sorption shows no unexpected features when compared with the behavior of the other systems.Fluorescence parameters of pyrene were employed to investigate the effect of added alkali metal ions, M+, on aqueous solutions of a crown ether surfactant ClOOl8C. It is concluded that M+ ions complex with the nonionic crown ether surfactant to produce an ionic surfactant CloO18CM+ and that the latter forms comicelles with ClOOl8C. The variation of the ratio of the intensity of the first and third vibrational bands (11/13) of pyrene was employed to examine the microscopic polarity of the comicelles (eM), and time-resolved pyrene excimer/monomer fluorescence emission was employed to evaluate the aggregation number, N , of the comicelles. A correlation was found between the binding efficiency of M+ and the fluorescence parameters. The critical micelle concentration, cloud point, micropolarity, and aggregation number were all found to depend in a systematic manner on the fraction of complexed surfactant in the comicelles.

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