Quantification Curves for Mica/smectite Interstratifications by X-ray Powder Diffraction

-X-ray powder diffraction (XRD) patterns for many interstratified mica/glycolated smectites were calculated by changing combinations of probabilities and transition probabilities of two-component layers. Three basal XRD reflections, 5.1L7.6~ (P l), 8.9 ~ 0.2~ (P2), and 16.1~176 (P3) were selected for the quantification curves. A distinct relationship exists between a20~ (p2 Pl) and A202 (P3 -P2) which shows systematic changes with expandability at constant Reichweite values. The calculated values were plotted with A20~ and A20: as the axes of coordinates, and quantification curves were calculated. The components and stacking parameters of mica/smectites were estimated easily using this diagram. Probabilities of existence of component layers and their transition probabilities for Reichweite (R=0) and (R= 1) structures, and special cases of R=2 and R=3 structures were obtained. Key Words--Ethylene glycol, Interstratification, Mica/smectite, Reichweite structures, X-ray powder diffraction. /'e. o ~ I_/ ~ C , 5 . 1 7 . 6 ~ ( p l ) , 8 . 9 10.2~ ( P 2 ) ~: 1 6 . 1 ~" o A 201 (P2 P l ) ~ A 202 (P3 P2 ) ~D~"~I~-~ 1 "909~t)]]~2"3~,~. R e i c h w e i t e ( R = 0 ) ~ ( R = 1 ) 0 3 ~ : ' E ( D ~ , 1R = 2 ~ R = 3 I N T R O D U C T I O N Many papers have been published on the calculation of X-ray powder diffraction (XRD) patterns of interstratified laminar systems. Mrring (1949) presented simplified methods for the analysis of interstratified structures; MacEwan (1958) and Reynolds (1967) were able to correct the frequency terms, g, into easily computed groups for different types of random interstratification; and Reynolds and Hower (1970) calculated pattems for ordered structures. Kakinoki and Komura (1952, 1954a, 1954b, 1965) showed how matrix methods can be used to obtain XRD profiles of interstratified structures that contain any number of compoCopyright 9 1988, The Clay Minerals Society nents. Allegra (1964) showed that the order of the matrices of the intensity equation can be reduced by introducing displacement vectors. Allegra's equation is similar to that of Kakinoki and Komura (1965). A comprehensive summary of the theoretical treatment of XRD for interstratified structures was given by Reynolds (1980). Sato (1969, 1973), Sato et al. (1965), Cradwick (1975), Drits and Sakharov (1976), and Watanabe (1981) applied the equation of Kakinoki and Komura (1954a, 1954b, 1965) for interstratified minerals and tried to quantify their interstratifications. Tomita and Takahashi (1985) derived XRD quantification curves for mica/smectite and ch lor i t e / smec t i t e