Diffraction by a one-dimensionally disordered crystal. I. The intensity equation

Kakinoki, Jiro; Komura, Y.

doi:10.1107/s0365110x65002888

Cited by 130 publications

(90 citation statements)

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“…The theory of X-ray diffraction by close-packed crystals with stacking faults was developed, among others, by Wilson (1942), Hendricks & Teller (1942), Jagodzinski (1949a, b), Paterson (1952), Gevers (1954), Johnson (1963), Allegra (1961Allegra ( , 1964, Kakinoki & Komura (1965), Kakinoki (1967), Howard (1977) and Frey & Boysen (1981). A satisfactory solution has been obtained for simple cases of X-ray diffraction by 3 C and 2H crystals with stacking faults.…”

Section: Introductionmentioning

confidence: 99%

“…Gevers (1954) developed the theory only for 4H and 6H(33) crystals containing deformation faults. More general methods formulated by Hendricks & Teller (1942) and developed by Kakinoki & Komura (1965), Kakinoki (1967), Takaki & Sakurai (1976) and Takaki (1977) are quite complicated and they have not been widely used for polytypic structures. Minagawa (1977Minagawa ( , 1978 used these methods to study the structural changes from 2H to 4H in CdI2 crystals and the stacking faults in CdI2-4H crystals.…”

Section: Introductionmentioning

confidence: 99%

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The diffraction of X-rays by close-packed polytypic crystals containing single stacking faults. I. General theory

Michalski¹

1988

Acta Cryst Sect A

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A general theory of X-ray diffraction by onedimensionally disordered close-packed polytypic crystals has been developed. A random distribution of all possible single stacking faults for arbitrary n-periodical structure is taken into consideration. Exact expressions for measurable parameters of changes in the intensity distribution caused by faults are given. Initial equations of the theory have been formulated by applying Holloway's [J. Appl. Phys. For the mathematical description of disorder, successive layers of the perfect structure have been denoted by an additional subscript j. The probability of occurrence of the faulted layer with subscript k after the layer with subscript j has been denoted by ajk. A set of recurrence relations is developed for average phase factors of layers with subscript j on m positions. An arbitrary sequence of layers is written in these relations by using the so-called phase-change factors (after layer with subscript j), determined by H~igg's structure symbols. Terms of the coefficients of the characteristic equation and boundary conditions which are necessary to describe the change in the intensity distribution are given for small values of ark. Finally, the shifts and broadenings of the reciprocal-lattice points and the changes in the intensity of peak maxima are derived in terms of ark.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The diffraction of X-rays by close-packed polytypic crystals containing single stacking faults. I. General theory

Michalski¹

1988

Acta Cryst Sect A

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“…In an alternative and also widely used mathematical approach to mixed-layering (Kakinoki and Komura, 1965), the above-listed types ofinterstratification are also recognized and called Reichweite 0, 1, and 3, respectively.…”

Section: Introductionmentioning

confidence: 99%

X-Ray Powder Diffraction Identification of Illitic Materials

Środoń

1984

Clays and clay miner.

258

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Abstract--The 10-/~ clay components of sedimentary rocks ("iUites") are commonly mixtures of 100% nonexpandable illite and an ordered illite/smectite mixed-layer mineral. If the proportion of the illite/ smectite in a mixture is sufficient to produce a measurable reflection between 33-35*20 (CuKa radiation) that is noncoincident with an illite reflection, the ratio of component layers and type of interstratification for the mixed-layer mineral can be determined. The identification technique developed in this study rests upon the following experimental findings for ordered illite/smectites of diagenetic origin: (1) the thickness of the illite layer in illite/smectites is 9.97/~; (2) the thickness of smectite-ethylene glycol complex ranges from 16.7 to 16.9/~; (3) illite/smectites form a continuous sequence ofinterstratification types--random, random/IS, IS, IS/ISII, ISII--and each type is related to a specific range of expandability.The new technique broadens the computer simulation method developed by R. C. Reynolds and J. Hower to include those sedimentary materials which are dominated by the presence of discrete illite, are low in illite/smectite, and, as such, have been described previously only by an "illite crystallinity index."

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“…Obviously this is never possible and intensity calculations should be carried out for models characterized by average structural parameters. As in previous works (Kakinoki and Komura, 1965;Drits and Sakharov, 1976;Plançon and Tchoubar, 1976;Plançon, 1981;Sakharov et al, 1982a, b) it is assumed in the present study that the layer type distributions in powdered mixed-layer samples obey Markovian statistics. ) s Int( r An important parameter in this model is the short-range order factor R defined as the number of preceding layers that influence the occurrence probability for a final layer of a given type.…”

Section: Amplitude and Intensity Diffracted By A Crystal Consisting Omentioning

confidence: 53%

Influence of the Outer Surface Layers of Crystals on the X-Ray Diffraction Intensity of Basal Reflections

Sakharov

Plançon

Lanson

et al. 2004

Clays and clay miner.

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This study presents a mathematical formalism describing diffraction effects from periodic and mixed-layer minerals in which the outer surface layers of crystals differ from layers forming the core of the crystals. XRD patterns calculated for structure models of chlorite and irregular chlorite-smectites terminated on both sides of the crystals by either brucite-like or 2:1 layers show the strong influence that different outer surface layers make on the distribution of basal reflection intensities. Simulation of the experimental XRD patterns from two chlorite samples having different Fe-content shows that in these two samples the chlorite crystals were terminated by brucite-like layers on both sides. In contrast, crystals in a corrensite sample were terminated by water molecules and exchangeable cations. The nature of diffraction effects due to outer surface layers is discussed.

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Diffraction by a one-dimensionally disordered crystal. I. The intensity equation

Cited by 130 publications

References 1 publication

The diffraction of X-rays by close-packed polytypic crystals containing single stacking faults. I. General theory

The diffraction of X-rays by close-packed polytypic crystals containing single stacking faults. I. General theory

X-Ray Powder Diffraction Identification of Illitic Materials

Influence of the Outer Surface Layers of Crystals on the X-Ray Diffraction Intensity of Basal Reflections

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