Reference Intensity Ratio and Mass Absorption Measurements of Eleven Biotites By Randy L. Kath Golder Associates, Inc., 3730 Chamblee-TuckerRoad, Atlanta, Georgia 30341 U.S.A. Michael N. Spilde Institute of Meteoritics, University of New Mexico, Albuquerque, New Mexico 87106 U.S.A. Briant L. Davis Engineering and Mining Experiment Station, South Dakota School of Mines and Technology, Rapid City, South Dakota 57701 U.S.A. Deane K. Smith Department of Geosdences, The Pennsylvania State University, University Park, Pennsylvania 16082 U.S.A. Abstract Pure phase reference intensity ratio determinations were completed on eleven biotites ranging in Fe composition from X Fc = 0.058 to X Fe = 0.695, where X Fc = Fe/ (Fe + Mg). The crys- tal chemistry of biotites requires that the intensity of diffrac- tion for the 00/ reflections, and thus the corresponding ref- erence intensity ratio, correlate with the Fe, Mg and Al in the octahedral sites. As Fe occupancy increases in the octahedral site, the Lkj for the 00/ reflections increases as does the value of IFI 2 computed using the Takeda and Ross (1975) biotite model. The IFI 2 trend closely parallels the experimental re- gression of Lkj = 6.359% Fe + 1.513 (R = 0.91). Observed mass absorption measurements completed by X-ray transmission show a similar trend with /i o = 69.36X Fe + 47.85 (R = 0.97). Cal- culated values of \i from biotite chemical analyses agree well with the measured values. These relationships may be used to predict the appropriate Lkj needed for quantitative analysis of biotite-bearing specimens if the Fe and Mg content of the biotite can be determined. Introduction Quantitative X-ray diffraction is a useful technique for deter- mining modal abundances of minerals in fine grained rocks, construction materials, and atmospheric aerosols (Davis and Walawender, 1982; Shearer et al, 1988; Davis, 1990; Sturges et al., 1989). The single most important parameter in quan- titative X-ray analysis is the reference intensity ratio, I/I c , RIR, or kj. The pure phase reference intensity ratio, de- noted here as Lkj, was determined for eleven biotites, K(Mg,Fe)3(Si s Al)Oio(OH) 2 , in this study, thus avoiding dif- ferential settling of either biotite or corundum standard due to differing aerodynamic sizes. Lkj can vary significantly with elemental composition, particularly when strong scattering elements are involved in solid solution substitution, such as Fe substituting for Mg in octahedral sites in the biotites. Biotites display significant solid solution of Fe and Mg , such that the mole fraction XF C = Fe/ (Fe + Mg) may vary from 0 to 1 for the biotite to an- nite series. Reference Intensity Ratios The fundamental relationship between the weight fraction Wj of any phase j and the diffraction intensity Ij in a multi- phase mixture of n phases was presented by Chung (1974): k i (1) where kj and kj are reference intensity ratios (RIR notation is used in some papers, i.e., Hubbard et al, 1976) for the ith and jth phases, and where all Wj's sum to unity. Intensities must be corrected for transparency and matrix effects as well as for automatic divergence slits, where appropriate. The definition for the ki is the ratio of intensities of ana- lyte and corundum standard reflections for a given hk/when both are present in a 1:1 weight ratio. Davis et al, (1990) have demonstrated the equivalency of the pure phase kj measure- ments with Lkj obtained by measuring intensities of the pure phases and correcting the ratio with calculated or measured mass absorption coefficients. Aerosol suspension was recom- mended to eliminate or reduce preferred orientation; in this case intensities must be corrected for transparency and ma- trix effects resulting from the thin-layer diffraction. Lkj is de- fined for the jth phase, therefore, to be Lkj = (2) where the subscripts c and j refer to corundum standard and pure phase, respectively, and fi is the mass absorption coeffi- cient of each pure phase j and c. Crystal Chemistry The general chemical formula for trioctahedral micas is XY 3 (Z 4 O 10 ) (OH,F,C1,O) 2 The X site is occupied by Ca, Na and K, and is 12-coordi- nated. The octahedrally coordinated Y site is filled by Mg, Fe 2+ , Fe 3+ , Al, Li and minor Ti and Cr. The tetrahedral Z site is occupied by Si and Al. Fluorine, OH, and, to a lesser extent, Cl and O will substitute into specific octahedral anion sites. This study shows the variation of Fe and Mg and their scatter- ing effects within the plane of octahedrally coordinated cations. The dominant feature of the mica structure is comprised of sheets of of pseudohexagonal rings of tetrahedra stacked parallel to the c-axis (Papike, 1988). The tetrahedral sheets are cross-linked by octahedra forming the basic 2:1 layer, and within each 2:1 layer, the tetrahedral sheets have tetrahedra which point in opposite directions. In order to maintain oc- tahedral coordination, the upper tetrahedral sheet is stag- gered by a/3 in either a positive or negative direction along 183 Pomtirr Diffraction, Vol. 6, No. 4, December 1991