X-ray diffraction effects by non-ideal crystals of biotite, muscovite, montmorillonite, mixed-layer clays, graphite, and periclase*
Abstract
A Fourier-transform computer program has been developed to calculate the x-ray diffraction effects expected from non-ideal crystals. The program evaluates the function [unk], where G (HKL) is the Fourier transform at a particular H, K, L coordinate in reciprocal space, fn is the atomic scattering factor of the nth atom, and x,y,z its coordinates in direct space. Diffraction profiles were calculated for biotite, muscovite, and montmorillonite crystallites 2, 3, 4, 5, 6, 8, 10, 20 and 30 layers thick, and for various models of graphite and periclase. The apparent basal spacings given by finite muscovite, montmorillonite, graphite, and periclase models deviate from the true values as the platelets become thinner. Diffraction profiles were also calculated for 30-layer packets of random mixed-layer muscovite-montmorillonite clays. The migration curves of the (001), (002), (003), (004) and (005) muscovite maxima and of the (001), (002), (003), (004), (005), (006), (007) and (008) montmorillonite maxima, obtained from those calculations, are in general agreement with the Hendricks-Teller formulation, although certain new details appear giving a more quantitative estimate of the diffraction effects. Diffraction profiles also give a very accurate measure of line broadening. Evaluation of the profiles for graphite gives the following relationship between half-width line broadening and crystal thickness: 2(sin θ′−sin θ″) = 0.90λ/t, where t is the thickness of the crystal and θ′ and θ″ are, respectively, the values of theta at the large- and small- angle sides of the peak.
Articles in the same Issue
- A special case of two-dimensionally disordered crystals
- Die Kristallstruktur des Koenenits, eine Doppelschichtstruktur mit zwei inkommensurablen Teilgittern
- Zur Indizierung von Pulverdiagrammen tetragonaler und hexagonaler Substanzen
- Etch patterns on apophyllite basal cleavages
- Die Kristallstruktur von Li2(Si0,25Ge0,75)2O5
- The crystal structure of LiAlSi2O6-II (“β spodumene”)
- Phase solution of para-chlorophenol
- Crystal structure of an eighteen-layered polytype of cadmium iodide
- X-ray diffraction effects by non-ideal crystals of biotite, muscovite, montmorillonite, mixed-layer clays, graphite, and periclase*
- The crystal structure of alamosite, PbSiO31
- Sauerstoff als Koordinationszentrum in Kristallstrukturen
- Low-iron polymorphs in the pyrrhotite group
- Revised crystal structure of dehydrated Na-Type A zeolite
- Verfeinerung der Tl2O3-Struktur mittels Neutronenbeugung
- The location of hydrogen atoms in crystalline ionic hydrates
- Disorder phenomenon in cadmium iodide crystals
- Crystal structure of single-layer lizardite
- Proof that the pgg packing of ellipses has never the maximum density
- Weighting function in crystal-structure analysis*
- Tetrahedral metal groups in Fe2B and Mn4B structures
- Antisymmetrische OD-Strukturen
- Studies on etching of neutron-irradiated calcium fluoride single crystals
- Matrix methods in Fourier summations
- Electron-optical studies of etch patterns on calcium fluoride
- Structure of etch pattern at helical dislocations in NaCl single crystals
- Crystal structure of l(+)-cysteine hydrochloride monohydrate*
- Eighth International Congress of Crystallography
- Intercongress Meeting, 1968
Articles in the same Issue
- A special case of two-dimensionally disordered crystals
- Die Kristallstruktur des Koenenits, eine Doppelschichtstruktur mit zwei inkommensurablen Teilgittern
- Zur Indizierung von Pulverdiagrammen tetragonaler und hexagonaler Substanzen
- Etch patterns on apophyllite basal cleavages
- Die Kristallstruktur von Li2(Si0,25Ge0,75)2O5
- The crystal structure of LiAlSi2O6-II (“β spodumene”)
- Phase solution of para-chlorophenol
- Crystal structure of an eighteen-layered polytype of cadmium iodide
- X-ray diffraction effects by non-ideal crystals of biotite, muscovite, montmorillonite, mixed-layer clays, graphite, and periclase*
- The crystal structure of alamosite, PbSiO31
- Sauerstoff als Koordinationszentrum in Kristallstrukturen
- Low-iron polymorphs in the pyrrhotite group
- Revised crystal structure of dehydrated Na-Type A zeolite
- Verfeinerung der Tl2O3-Struktur mittels Neutronenbeugung
- The location of hydrogen atoms in crystalline ionic hydrates
- Disorder phenomenon in cadmium iodide crystals
- Crystal structure of single-layer lizardite
- Proof that the pgg packing of ellipses has never the maximum density
- Weighting function in crystal-structure analysis*
- Tetrahedral metal groups in Fe2B and Mn4B structures
- Antisymmetrische OD-Strukturen
- Studies on etching of neutron-irradiated calcium fluoride single crystals
- Matrix methods in Fourier summations
- Electron-optical studies of etch patterns on calcium fluoride
- Structure of etch pattern at helical dislocations in NaCl single crystals
- Crystal structure of l(+)-cysteine hydrochloride monohydrate*
- Eighth International Congress of Crystallography
- Intercongress Meeting, 1968
