The Scherrer equation and the dynamical theory of X-ray diffraction.

The Scherrer equation is a widely used tool to determine the crystallite size of polycrystalline samples. However, it is not clear if one can apply it to large crystallite sizes because its derivation is based on the kinematical theory of X-ray diffraction. For large and perfect crystals, it is more appropriate to use the dynamical theory of X-ray diffraction. Because of the appearance of polycrystalline materials with a high degree of crystalline perfection and large sizes, it is the authors' belief that it is important to establish the crystallite size limit for which the Scherrer equation can be applied. In this work, the diffraction peak profiles are calculated using the dynamical theory of X-ray diffraction for several Bragg reflections and crystallite sizes for Si, LaB6 and CeO2. The full width at half-maximum is then extracted and the crystallite size is computed using the Scherrer equation. It is shown that for crystals with linear absorption coefficients below 2117.3 cm(-1) the Scherrer equation is valid for crystallites with sizes up to 600 nm. It is also shown that as the size increases only the peaks at higher 2θ angles give good results, and if one uses peaks with 2θ > 60° the limit for use of the Scherrer equation would go up to 1 µm.

Problemas de cálcio na água de abastecimento de Nova Olinda - CE / Problems of calcium in the water supply to Nova Olinda - CE

A cidade de Nova Olinda, sul do Estado do Ceará, é abastecida através de quatro poços tubulares profundos que captam num aqüífero confinado, composto, basicamente, por arenito. Na área também afloram calcita e gipsita, que são explotadas por mineradoras instaladas dentro da bacia hidrográfica, onde estão três dos quatro poços. Desde 2006, as tubulações de abastecimento de água estão sendo obstruídas por um precipitado folhear, causando prejuízos. Neste trabalho foi feita uma investigação, usando análises químicas, físico-químicas e de raios X e o índice de saturação de calcita (ISC), para estudar as possíveis causas dos precipitados, identificados, basicamente como calcita. As concentrações de cálcio e os ISCs indicaram que o tratamento da água aplicado na desinfecção aumenta a tendência da precipitação de calcita devido o cálcio contido nos produtos químicos usados.

The township of Nova Olinda, south of Ceará, is supplied with waters from four deep wells exploiting a confined sandstone aquifer. Calcite and gypsum rock outcrop and are being exploited commercially in the watershed where three of the wells are located. Since 2006, public supply pipelines are damaged due to a sheet-like precipitation causing frequent obstruction of the pipes. In this investigation we used chemical analyses, physical chemistry, X-ray analyses and determination of the calcite saturation index - CSI for studying possible causes for the deposits identified, basically, as calcite. Calcium concentrations and CSIs indicate that the water disinfection process adopted increases the tendency of calcite precipitation due to calcium contained in the chemicals used.