POWDER X-RAY-DIFFRACTION OF 2-DIMENSIONAL MATERIALS

An analytic solution for the normalized intensity for powder x-ray dif fraction has been obtained for a simple two-dimensional lattice using a linear approximation for the interference function. The analytic sol ution, where the Bragg peaks are strongly asymmetric, is compared to c omputer simulations using the Debye formula, and is shown to be in clo ser agreement than earlier numerical solutions by Warren and others. F or a two-dimensional structure consisting of more than one monolayer o f atoms, the shape of the Bragg peaks is modulated by the structure fa ctor. This structure factor modulation provides a continuous plot of t he structure factor over the range of the diffraction tail and thus pr ovides valuable information about the structure of the layer. It is de monstrated that because of structure factor modulation the Warren expr ession which relates the width of Bragg peaks to layer size cannot be used for a two-dimensional sheet with more than one layer of atoms, an d it is proposed in such cases that measuring the low-angle side width of half-maximum intensity can be used for determination of the layer size. Single molecular layer MoS2 and WS2 suspensions, prepared by exf oliation, provide excellent randomly oriented two-dimensional systems for demonstrating the unique features of powder x-ray diffraction patt erns of two-dimensional materials and for structure identification usi ng Bragg peak profiles. (C) 1996 American Institute of Physics.