A method of quantitative phase analysis without standards

Zevin, L.

doi:10.1107/s0021889877013144

Cited by 52 publications

(22 citation statements)

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“…Subsequently, Alexander developed practical XRD methods and derived the related theoretical basis [2]. With the improvements of XRD analysis, different quantitative methods have been presented in succession, such as reference intensity ratio (RIR) method [3], external standard method [4], matrix-flushing method [5], non-standard method [6], doping method [7], and Rietveld method [8]. The Rietveld method, as proposed by Hugo M. Rietveld, is widely accepted due to its whole-pattern fitting approach instead of single-peak analysis.…”

Section: Introductionmentioning

confidence: 99%

Error Analysis and Correction for Quantitative Phase Analysis Based on Rietveld-Internal Standard Method: Whether the Minor Phases Can Be Ignored?

Zhao

Liu

et al. 2018

Crystals

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The Rietveld-internal standard method for Bragg-Brentano reflection geometry (θ/2θ) X-ray diffraction (XRD) patterns is implemented to determine the amorphous phase content. The effect of some minor phases on quantitative accuracy is assessed. The numerical simulation analysis of errors and the related corrections are discussed. The results reveal that high purity of crystalline phases in the standard must be strictly ensured. The minor amorphous or non-quantified crystalline phases exert significant effect on the quantitative accuracy, even with less than 2 wt% if ignored. The error levels are evaluated by numerical simulation analysis and the corresponding error-accepted zone is suggested. To eliminate such error, a corrected equation is proposed. When the adding standard happens to be present in sample, it should be also carefully dealt with even in low amounts. Based on that ignorance, the absolute and relative error equations (∆ AE , ∆ RE) are derived, as proposed. The conditions for high quantitative accuracy of original equation is strictly satisfied with a lower amount of standard phase present in sample, less than 2 wt%, and a higher dosage of internal standard, larger than 20 wt%. The corrected equation to eliminate such quantitative error is suggested.

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Section: Introductionmentioning

confidence: 99%

Error Analysis and Correction for Quantitative Phase Analysis Based on Rietveld-Internal Standard Method: Whether the Minor Phases Can Be Ignored?

Zhao

Liu

et al. 2018

Crystals

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“…(a) Standardless analysis methods based on X-ray data only (MOORE, 1965;SALYN & DRITS, 1972;ZEVIN, 1977;FIALA, 1980;STARKS et al, 1984;FANG and ZEVIN, 1985;RIUS et al 1987;BISH and POST, 1993;ESTEVE et al, 1997b;ZANGALIS, 1998). Below are presented two different cases of these methods, described for quantitative X-ray analysis.…”

Section: Introductionmentioning

confidence: 99%

Quantitative Phase Analysis of Mixtures of Three Components using Rietveld and Rius Standardless Methods. Comparative Results

Esteve

Ochando

Reventós

et al. 2000

Cryst. Res. Technol.

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“…This method has been shown to be reasonably accurate, as two-phase mixtures agree within + 2% and three-phase mixtures within about + 5-10%. The generalized version of this method (Zevin, 1977) requires n 2 intensities for n phases as well as mass attenuation coefficients of each phase, a significant drawback for clay mixtures with more than two phases. Additionally, minor and amorphous components cannot be quantified by standardless methods based on powder XRD.…”

confidence: 99%

“…A standardless XRD method of quantification was developed by Salyn and Drits (1972) and refined by Zevin (1977). This method requires partial separation of phases in two or more fractions, usually accomplished by centrifugation.…”

confidence: 99%

Comparison of Four Elemental Mass Balance Methods for Clay Mineral Quantification

Kolka

Laird²,

Nater

1994

Clays and clay miner.

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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.

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A method of quantitative phase analysis without standards

Abstract: It is shown that to determine the quantitative phase composition of n samples each of which contains n phases it is sufficient to obtain a set of n 2 intensities values of analytical lines, I~j, where 1 < i < n is the phase number in a sample of number 1 Show more

Cited by 52 publications

References 1 publication

Error Analysis and Correction for Quantitative Phase Analysis Based on Rietveld-Internal Standard Method: Whether the Minor Phases Can Be Ignored?

Error Analysis and Correction for Quantitative Phase Analysis Based on Rietveld-Internal Standard Method: Whether the Minor Phases Can Be Ignored?

Quantitative Phase Analysis of Mixtures of Three Components using Rietveld and Rius Standardless Methods. Comparative Results

Comparison of Four Elemental Mass Balance Methods for Clay Mineral Quantification

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