The Influence of Aluminum on Iron Oxides. VIII. Unit-Cell Dimensions of Al-Substituted Goethites and Estimation of Al from them

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Abstract
The unit-cell dimensions of synthetic, Al-substituted goethites showed that the c dimension is a linear function of Al substitution in the range 0–33 mole % Al, but that the a dimension is variable over this same range. The b dimension is also linearly related to Al substitution but is slightly more variable than the c dimension for Al substitutions of 20–33 mole %. The variability of the a dimension is postulated to be the result of structural defects. An improved procedure for estimating Al substitution from x-ray powder diffraction positions requires (1) calculation of the c dimension from the positions of the 110 and 111 diffraction lines using the formula: c = (1/d(111)2 − 1/d(110)2)−1/2, and (2) estimation of Al substitution from the relationship: mole % Al = 1730 − 572.0c. The 95% confidence interval of the estimate is ±2.6 mole % Al when using this procedure, in contrast to ±4.0 mole % Al when the position of the 111 reflection alone is used.