Optimization of Multilayer Soap Crystals for Ultrasoft X-Ray Diffraction

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Abstract
A detailed program for the optimization of the ultrasoft x-ray reflectivity and resolution of multilayer soap crystals is described which is based on classical x-ray diffraction theory and fundamental data concerning monolayer films. New measurements of the conversion factor (fraction of fatty acid converted to soap in a monolayer formed on a liquid substrate containing metal ions) as a function of the metal-ion concentration and liquid substrate pH have been used as the basis of a logical optimization procedure. Full optimization parameters are given for the lead soaps of melissic, lignoceric, stearic, myristic, and lauric acids which have 2d interplanar spacings of 159.6, 131.5, 100.4, 80.5, and 70.0±0.1 Å, respectively. These crystals have a reproducibility of about 10% (mean deviation from mean reflectivity), except in the case of lead stearate where it is 5%. For each soap the optimum lead concentration in the liquid substrate is 3×10−5 M, the pH of this solution is 6.0, and the dipping speed is 0.2 cm sec−1. The resultant crystal is 100% soap and contains no unconverted acid. The necessary surface pressure and temperature are dependent upon the particular soap being produced. The optimum values which give good reproducibility and high reflectivity, for the acids mentioned above, are (1) temperature: 30, 20, 18, 12, and 12°C; (2) pressure: 40, 35, 32, 20, and 15 dyn cm−1, respectively. The relative reflectivity of crystals containing varying amounts of lead are in agreement with diffraction theory. The absolute reflectivities for different thicknesses of all the optimized crystals are presented for various ultrasoft x-ray emission lines and are shown to be in qualitative, but not quantitative, agreement with theory. Crystals of thickness in excess of about 150 monolayers (75 lattice planes) proved impossible to build. The diffraction half-widths of the crystals are found to be in agreement with theory, and the spectral resolution of the crystals has thus been estimated. In general, this is equal to the effective number of diffracting planes and is thus limited by crystal absorption. Resolving powers of 30–60 can be obtained in the 20–120-Å region for the thickest crystals grown. The peak and integrated reflectivities of these crystals were of the order of 1–5% and 1–4×10−4 rad. Detailed measurements are given for all crystals and a variety of emission lines. Reflectivity data is also presented for beryl and potassium acid phthalate (KAP) crystals and a comparison is made between soap crystals and other possible dispersive elements in the ultrasoft x-ray region. Data is presented on peak-to-background ratios, high-order spectra intensity, and the use of mixed fatty acids to achieve intermediate spacing crystals. Because the optimized crystals contain no unconverted acid, they are shown to be particularly stable to a vacuum environment and rises in temperature up to at least 100°C. Spectra are presented to illustrate the use of multilayer soap crystals in ultrasoft x-ray spectrometry.

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