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An X-ray analysis of stacking disorder in kaolinite by fourth moment

  • A. K. De (a1) and S. Bhattacherjee (a1)

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Mathematically, it is well established that besides the Fourier coefficients, the natural characteristics of any distribution are its moments. The use of the second moment, called variance, as a measure of line broadening has already gained wide popularity because of its several merits relative to other empirically devised parameters. In recent decades, the fourth moment has been recognized as an important parameter; its theoretical significance has been discussed by Mitra (1964), who developed the moment range function for the estimation of crystallite size and distortion in cold-worked metal. However, owing to the requirements of high degree of accuracy of intensity measurement coupled with cumbersome calculations, this parameter did not find much general application. Modern diffractometers and sophisticated computers have helped ease the problem and in recent years several workers (Kagan & Snovidov, 1965; Kulshreshtha et al., 1971; Mukherjee, 1981) have successfully used this parameter for defect analysis in various non-ideal forms of materials.

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Brindley, G.W. (1961) X-ray diffraction by layer lattices with random layer displacements. Pp. 446466 in: X-ray Identification and Crystal Structures of Clay Minerals (G. Brown, editor). Mineralogical Society, London.
De, A.K., Bhattacherjee, S. & Mitra, G.B. (1983) Structure defects in layer silicate clay minerals. Clays Clay Miner. 3l, 315316.
Ghosh, T.B. (1981) X-ray diffraction studies of lattice defects in metals and alloys including those rapidly quenched from metal. PhD thesis, Indian Institute of Technology, Kharagpur, India.
Kagan, A.S. & Snovidov, V.M. (1965) Analysis of the shape of the diffraction lines of low-temperature tempered martensite. Fiz. Metal. Metalalloved 19, 191198.
Kulshreshtha, A.K., Kothari, N.R. & Dweltz, N.E. (1971) Analysis of polymeric X-ray diffraction profiles II. The significance of the Fourth Moment Range Function of the diffraction profile in the analysis of first order reflexions. J. Appl. Cryst. 4, 125130.
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Mitra, G.B. (1964) Determination of particle size and strain in a distorted polycrystalline aggregate by the method of variance. Acta Cryst. 17, 764771.
Mitra, G.B. & Bhattacherjee, S. (1969) X-ray diffraction studies on the transformation of kaolinite into metakaolin. I. Variability of interlayer spacing. Am. Miner. 54, 14031418.
Mitra, G.B. & Bhattacherjee, S. (1970) X-ray diffraction studies on the transformation of kaolinite into metakaolin. Acta Cryst. B26, 21242128.
Mukherjee, P.S. (1981) Studies on fibrous polymers by X-ray diffraction techniques. PhD thesis, Indian Institute of Technology, Kharagpur, India.
Plançon, A. & Tchoubar, C. (1977) Determination of structural defects in phyllosilicates by X-ray powder diffraction II. Nature and proportion of defects in natural kaolinites. Clays Clay Miner. 25, 436450.

An X-ray analysis of stacking disorder in kaolinite by fourth moment

  • A. K. De (a1) and S. Bhattacherjee (a1)

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