Comparison of Four Elemental Mass Balance Methods for Clay Mineral Quantification

Abstract

Abstract--The quantification of the relative mineralogical composition of clay mixtures by powder X-ray diffraction or chemical mass balance methods has been severely hampered by a lack of representative standards. The recent development of elemental mass balance models that do not require standards for all minerals in the mixture may help circumvent this problem. These methods, which are based on the numerical optimization of systems of non-linear equations using the Marquardt algorithm, show promise for mineral quantification. The objective of this study is to make a preliminary assessment of the accuracy of these methods and to compare them to linear models that require standards for all mineral phases. Methods 1 and 2 are based on weighted average solutions to simultaneous linear equations solved for single samples with known standards. Solutions were achieved by a matrix decomposition algorithm and the Marquardt algorithm, respectively. Methods 3 and 4 are based on a set of simultaneous non-linear equations with reduced non-linearity solved by least squares optimization based on the Marquardt algorithm for multiple samples. Illite and halloysite compositions were fixed in Method 3, only the halloysite composition was fixed in Method 4. All models yielded relative weight fractions of the three mineral components; additionally, Methods 3 and 4 yielded compositions of smectite, and smectite and illite, respectively. Ten clay mixtures with varying proportions of the <0.2 tzm size fraction of three different reference clays (Wyoming bentonite, Fithian illite, and New Bedford halloysite) were prepared gravimetrically and analyzed by inductively coupled plasma-atomic emission spectroscopy. Accuracy of the four methods was evaluated by comparing the known mineralogical compositions of the mixtures with those predicted by the models. Relative errors of 5 and 10% (randomly +/-) were imposed on the elemental composition of the smectite standard to simulate errors due to lack of good standards. Not surprisingly, the accuracy of Methods 1 and 2 decreased rapidly with increasing error. Because Methods 3 and 4 optimized for the smectite composition and only used it for an initial guess, they were unaffected by the level of introduced error. They accurately quantified the mineralogical compositions of the mixtures and the elemental compositions of smectite, and smectite and illite, respectively.

Effects of grain size distribution on mineralogical and chemical compositions: a case study from size‐fractional sediments of the Huanghe (Yellow River) and Changjiang (Yangtze River)

“…During the early and intermediate weathering stages, K may absorb to clay minerals, partially dissolving into water (Nesbitt et al ., ). Aluminum, Mg, Fe, K, Rb, Cs and Ba are mainly elemental components of, or adsorbed on the clay minerals, whereas Na is primarily removed from weathering sites in solution (Nesbitt et al ., ; Harnois, ; Kolka et al ., ; Mermut and Cano, ; Ohta and Arai, ). Copper and Zn could enhance their concentrations in clay minerals relative to parent rocks (Kogel and Lewis, ).…”

Simultaneous Mineralogical Quantification and Chemical Characterization of Soil Clays

“…Later, Kolka et at (1994) demonstrated that a similar non-linear chemical mass balance model could accurately determine the chemistry of two phases (smectite and illite) and mass proportions for three phases (smectite, illite, and halloysite) in 10 artificial mixtures of reference clays. The model used by Kolka et al (1994) was designed to test the accuracy of the non-linear chemical mass balance approach and was not intended for general use with soil or sediment sampies. In this manuscript, we describe a similar nonlinear chemical mass balance model that is designed for quantification of five clay mineral phases commonly found in temperate region soils.…”