Powder x-ray diffraction of turbostratically stacked layer systems
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Powder x-ray diffraction of turbostratically stacked layer systems D. Yang and R. F. Frindt Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6 (Received 3 October 1994; accepted 11 March 1996)
A special form of the Debye formula for calculating the powder x-ray diffraction of a turbostratically stacked layer system is derived, and calculated diffraction patterns for turbostratically stacked graphite and MoS2 layers are presented. Single-molecular-layer MoS2 , prepared by exfoliation of lithium-intercalated MoS2 in water or alcohols, has been deposited on various supports, and x-ray diffraction patterns show that the restacking of the MoS2 layers can be perfectly turbostratic. The restacked MoS2 may or may not have water or organic bilayers between them, depending on the deposition conditions.
I. INTRODUCTION
A turbostratically stacked system is like a pile of randomly stacked cards, where the individual cards are parallel to each other at the same interlayer spacing, but random in translation parallel to the layer and in rotation about the normal to the cards. The powder diffraction patterns for turbostratic stacking consist of two types of peaks: the (00l) peaks and (hk0) peaks. All the mixed (hkl) peaks are suppressed completely by the randomness in translation and rotation. Turbostratic disorder is commonly found in synthetic carbons1,2 and clays.3 Recently, there is interest in synthesizing so-called “nanoscale composites” which can be formed by inclusion of organic or inorganic molecules into the van der Waals gap of MoS2 layers. The methods for synthesizing these intercalated materials include cation exchange,4 direct restacking in the presence of included material,5–7 and a two-phase technique.8 The well-defined c-spacing in x-ray diffraction patterns for these composites implies that the host MoS2 layers are parallel to each other at the same interlayer spacing. The ordering of the composite structure, however, has not been discussed in the literature. From our x-ray studies we believe that in general the stacking of these composites is turbostratic and that the host MoS2 layers in these composites are octahedrally coordinated. To calculate the diffraction pattern for a turbostratically stacked layer system, a common approach is to use numerical integration over reciprocal space or real space.2,9,10 Some time ago Warren and Bodenstein9 calculated the diffraction patterns of fine particle turbostratic carbon black from the general Debye formula. They separated the diffraction into two parts: the twodimensional (hk0) peaks due to the intralayer interference and (001) peaks due to the interlayer interference. They evaluated the (001) peaks for disk-shaped carbon layers using numerical integration in real space. The results were tabulated and diffraction patterns of up to five stacking layers were obtained. J. Mater. Res., Vol. 11, No. 7, Jul 1996
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