Thickness a N D Surface Characteristics of Colloidal 2:1 Aluminosilicates Using a N Indirect Fourier T R a N S F O R M of S M a L L - a N G L E X-ray Scattering Data

-An indirect Fourier transformation applied to small-angle X-ray scattering data has been used to determine the thickness and surface properties of two common clay minerals. For an illite system, the particle density distribution function (PDDF) generated by the analysis gave a correct description of particle geometry, and the calculated electron density profile was in accordance with the theoretical electron density distribution for this mineral. This approach provides the opportunity to determine the thickness of fundamental particles of illite while avoiding the difficulties encountered in other methods. Both the PDDF and the electron density profile accurately predict the thickness of Na-montmorillonite layers, and the results suggest that an electron inhomogeneity exists at the interface of this mineral. Key Words--Illite, Indirect Fourier Transform, Montmorillonite, SAXS, Thickness. I N T R O D U C T I O N Small -angle X-ray scattering (SAXS) is a technique widely used to determine the internal and external structure o f colloidal particles over a wide range of length scales (Guinier and Fournet, 1955; Schmidt, 1995). Synthetic and natural clay minerals form colloidal suspensions that are ideal for model testing and studying colloidal behaviors such as swelling, interparticle forces and structural organization (van O1phen, 1963). These studies have both theoretical and industrial significance. The thickness, interparticle spacing in hydrated states, and the influence of interparticle forces fall into the characterization length scale o f S A X S and have been invest igated by this method in the past (Hight et al., 1960, 1962; Taylor and Schmidt, 1969; Morvan et aL, 1994; Pignon et al., 1997; Saunders et al., 1999). In previous studies (e.g. Hight et al., 1960; Saunders et al., 1999), well-character ized smecti tes were used in thickness determinations with the S A X S method based on an assumed particle shape. This approach has l imited application in the determination of thickness of natural clay minerals which often do not have the required regular dimension in at least two coordinates. Hight et al. (1960) also employed the absolute scattering intensity at zero angle to derive the thickness of montmoril lonite , but the method was subject to large experimental errors. Furthermore, the spacing and layer thickness of expandable clays can be measured conveniently by X-ray diffraction (XRD). Illites are a group of non-expandable and micaceous minerals, often present in nature as mixedlayer components with varying proportions of i l l i te-smecti te (I-S) layers. This interstratification makes it difficult to determine the thickness of the fundamental illite particle by convent ional analysis of X-ray data. Various attempts have been made in recent years using TEM, fixed cation content, and X-ray peak broadening (Nadeau et al., 1984; Srodofi et al., 1990, 1992; Drits et al., 1997, 1998). Each of these methods suffers f rom its own uncertainties. As noted by Drits et al. (1997, 1998), the thickness of most illite samples present in nature can be measured by SAXS, and this method offers two advantages over other methods: illite particles in dilute suspensions are independent and free of swell ing problems, and at least one mil l ion particles are scanned and averaged. By comparison, T E M only ' sees ' hundreds of particles. Glatter (1977, 1980) developed a numerical method utilizing an indirect Fourier t ransform (IFT) to calculate the P D D F that describes the averaged geomet ry of all scattering particles. Using this method, it is possible to calculate particle thickness without making any assumptions about particle shape. The IFT minimizes the termination effects encountered when data are conver ted f rom reciprocal space to real space with a direct Fourier t ransformation (Guinier and Fournet, 1955; Hight et al., 1962). Furthermore, deconvolut ion of the P D D F gives the electron density distribution for central symmetr ic scatterers (Glatter, 1982) that reveals their internal structure. Here we report the use of S A X S and the indirect Fourier transform to determine the thickness of the Silver Hill illite and a montmori l loni te (Wyoming bentonite) sample. Use of montmori l loni te serves to verify the numerical method and provides evidence o f surface inhomogenei ty related to surface charge density.