Pair Distribution Function as a Probe for Zeolite Structures
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Pair Distribution Function as a Probe for Zeolite Structures María M. Martínez-Iñesta and Raúl F. Lobo Center for Catalytic Science and Technology, Department of Chemical Engineering University of Delaware Newark, DE 19716 USA ABSTRACT In this article we describe how we have used the pair distribution function of zeolites to solve complex structural problems. A first study was dedicated to refining the structure of disordered zeolite beta, a zeolite that is used in the alkylation of benzene. A second study is a work in progress geared toward the determination of the mechanism of negative thermal expansion of zeolite chabazite, which has been found to be one of the most contracting materials known. Preliminary results suggest that the individual Si-Ox distances and Ox-Si-Ox angles in the tetrahedral are deformed with temperature while the average tetrahedra dimensions stay constant. INTRODUCTION A zeolite is a crystalline aluminosilicate with a three-dimensional framework structure of linked tetrahedra that forms uniformly sized pores of molecular dimensions. Zeolites are often cited as examples of perfect crystals with ideal periodic long-range order. In practice, however, disorder is introduced in many forms. The way this is usually dealt with, using standard crystallographic methods, is by the development of models that describe the distortions caused by disorder in an average way. At the atomic level methods such as solid state NMR and optical spectroscopies are used to gain knowledge about the local chemical environments and geometry surrounding selected atoms in a sample. However, these approaches still do not help solve many problems associated with understanding diffusion and the catalytic and adsorptive properties of zeolites, mainly because the need of precise atomic models to understand these problems. The objective of my research is to adapt the a technique called Pair-Distribution Function (PDF) to the study of local structure in zeolites in order to fill the information gap that currently exists for the understanding of zeolite physical and chemical processes. The Pair Distribution Function (PDF) is a scattering technique in which all the information from a powder diffraction pattern, Bragg and diffuse scattering, is Fourier transformed into real space by ∞ 2 (1) G (r ) = 4πr ( ρ (r ) − ρ o ) = ∫ Q[S (Q) − 1]sin(Qr )dQ
π
0
where S(Q) is the corrected and reduced intensity data, r is the interatomic distance, ρ(r) is the microscopic pair density and ρo is the average atomic density of the material. This used to be a technique used to study only liquids and amorphous materials mainly due to the technical limitations to get to high enough Q to get useful information for crystalline materials. Recently, however, with the advent of second, and soon third generation, synchrotron facilities, there are sources available that can reach higher maximum Q’s with high enough flux to be able to get information not available before for crystalline materials. A pair distribution function describes the distri
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