Quantitative Clay Mineral Analysis Using Simultaneous Linear Equations

Abstract

Abstraet--A program of simultaneous linear equations has been developed to calculate component proportions and/or component property values for mineral mixtures in soil clays and sediments. The analysis is based on quantitatively measured chemical and physical properties of samples and involves (1) qualitative idemification of the mineral components in the mixture by any appropriate means; (2) quantitative measure of the sample property values selected for use in the program; (3) estimation of the proportion of each component in the mixture by a technique such as X-ray powder diffraction; (4) assignment of limits to component property ranges; (5) selection of one of four available calculation options and application of the simultaneous linear-equations program; (6) examination of the residuals of the analysis and, if appropriate, adjustment of the initial estimates for component proportions or property ranges and then repeating step 5; and (7) verification of the final component proportions by comparison with information from step 1. Completeness and/or accuracy of the final results for component proportions may be checked by the closeness of approach to 1.0 for the sum of the component proportions. The method requires that, at minimum, the number of properties measured must equal the number of components in the samples being analyzed and that the minimum number of samples must equal the number of properties measured.Using the clay fractions of 15 Pennsylvania soils containing kaolinite, illite, smectite, vermiculite, chlorite, interstratified vermiculite/chlorite, quartz, and noncrystalline material, and measuring methylene blue cation-exchange capacity, the amount of Ca displaced by Mg from a Ca-saturated clay, the amount of K displaced by NH4 from a K-saturated clay heated to 110~ % I(20, % SiO2, % MgO, and weight loss at 1100--300~ and 300"-950~ the adjustment of property va!ues was found to have the lowest residual value and the most consistent results. The source of analytical errors was also located by examination of residual tables. Samples that were similar in composition gave more reliable component proportions.

Data report: clay mineral assemblages from the Nankai Trough accretionary prism and the Kumano Basin, IODP Expeditions 315 and 316, NanTroSEIZE Stage 1

“…The presence of a specific detrital and/or authigenic mineral can be detected easily through visual recognition of characteristic peak positions. It is more problematic, however, to estimate the relative abundance of a mineral in bulk sediment or the claysize fraction with meaningful accuracy (e.g., Moore, 1968;Heath and Pisias, 1979;Johnson et al, 1985). The most common semiquantitative approach for analyzing marine clays has been to apply the Biscaye (1965) weighting factors to the peak areas of basal reflections (McManus, 1991).…”

Calibration of an X-Ray Diffraction Method to Determine Relative Mineral Abundances in Bulk Powders Using Matrix Singular Value Decomposition: A Test from the Barbados Accretionary Complex

“…Like Johnson et al (1985), we used linear algebra to determine factors for converting XRD data to relative mineral abundances. Absolute abundances are virtually impossible to quantify without identifying every mineral phase in the specimen, along with the weight percentages of each amorphous constituent; this is an unrealistic goal for ODP shipboard investigations.…”

“…Many of the software packages that support modern digital XRD systems also can be calibrated using results from known mixtures of standard minerals (e.g., Mascle et al, 1988); unfortunately, the inner workings of these programs are generally protected by proprietary status, so they are impossible to evaluate. A final method involves the use of simultaneous linear equations, and the input parameters can include both XRD and chemical data (Johnson et al, 1985). With this approach, the minimum number of properties measured must equal the number of components in the samples being analyzed, and the minimum number of samples analyzed must equal the number of properties measured (e.g., peak intensity for three minerals in three standards).…”

Comparison of Four Elemental Mass Balance Methods for Clay Mineral Quantification

“…Chemical methods have been used alone or in conjunction with powder XRD data for clay mineral quantification (McNeal and Sansoterra, 1964;Hussey, 1972;Johnson et al, 1985;Calvert et al, 1989;Slaughter, 1989;Hodgson and Dudeney, 1984;Braun, 1986). The majority of these methods have used simultaneous linear equations (SLEs) to solve for the quantities of each phase in a mixture.…”