Basic Aspects of X-Ray Absorption in Quantitative Diffraction Analysis of Powder Mixtures

Alexander, Leroy E.; Klug, Harold P.

doi:10.1021/ac60022a002

Cited by 302 publications

(118 citation statements)

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“…Although a standard calibration approach (see, for example, Alexander & Klug, 1948) is clearly preferable for quantitative analysis purposes since it is independent of absorption in the sample, it does require a time-consuming and often tedious precalibration. We see that such a precalibration is not essential using the present method.…”

Section: Resultsmentioning

confidence: 99%

Quantitative analysis of multicomponent powders by full-profile refinement of Guinier–Hägg X-ray film data

Werner¹,

Salomé²,

Malmros³

1979

J Appl Cryst

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Full-profile analysis of microdensitometer-measured Guinier-H~igg X-ray powder film data (strictly monochromatized Cu K~I radiation) [see Malmros & Thomas (1977). J. Appl. Cryst. 10,[7][8][9][10][11] is here extended to treat a multicomponent system where two of the components are refinable. The method is demonstrated for the case of: (a) ~-Bi203/KC1 (standard), and (b) CaF2/SiO2 (s-quartz) together with a Mg(OH)2 matrix. In (a), a weight ratio BizO3/KCI of 1:1 gave an experimental result of 0-96(9):1. In (b), a number of admixtures have been studied in the range 1-60 wt% SiO2 all with 10 wt % CaF2. The agreement between weight ratios and profile refinement results suggests that the formal temperature factors function as effective absorption correction parameters. It is thus shown that approximate quantitative analysis is feasible from Guinier-H~igg diffraction data without any previously determined calibration curve. Moreover, the method permits the use of all available overlapping data in the refinement of a structure without needing to exclude data from known impurities [see Waltersson, Werner & Wilhelmi (1977). Cryst. Struct. Commun. 6,[231][232][233][234][235].This feature is likely to prove the most common application of the method.

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Section: Resultsmentioning

confidence: 99%

Quantitative analysis of multicomponent powders by full-profile refinement of Guinier–Hägg X-ray film data

Werner¹,

Salomé²,

Malmros³

1979

J Appl Cryst

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“…It can be noticed immediately that in the limit 12D ~ 0 and v0 = 0 then Fo = 1 and (15) remains in the form derived by Alexander & Klug (1948) for the homogeneous case, apart from the correction ~-, which also approaches unity when/z~Ol vanishes.…”

Section: Kok )mentioning

confidence: 76%

“…According to the experimental results for graphite, the model is qualitatively and also quantitatively consistent within certain limits. Also, as was demonstrated in the derivation of the theoretical formulae, this model has as limiting cases the ideal case of Alexander & Klug (1948) and the empirical expressions of Cooper (1965) and Weiss (1966).…”

Section: Resultsmentioning

confidence: 99%

“…An expression for the intensity from ideally homogeneous crystalline powders was derived by Alexander & Klug (1948). However, in actual powders the following heterogeneities exist and must be taken into account: (a) heterogeneity of the diffracting phase (distribution of crystals); (b) heterogeneity of the crystalline material (presence of cavities or holes); (c) heterogeneity of composition (presence of several phases in unequal concentrations); (d) heterogeneity of the shape and size of particles; and (e) heterogeneity of the distribution of holes.…”

Section: Introductionmentioning

confidence: 99%

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General theory of the effect of granularity in powder X-ray diffraction

González¹

1987

Acta Cryst Sect A

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The effect of granularity in powder X-ray diffraction is reviewed, and the shortcomings of previously developed models in explaining this effect are described. A new physical model encompassing all aspects of this phenomenon is proposed. Mathematical formulae based on the model are derived, and their limit cases are discussed. Values of the theoretical intensities from the model are compared with results from a specially designed experiment.

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“…Without going into the mathematics, a detailed discussion of which can be found in ref. 7, the following equations are obtained:…”

Section: Internal Standard Methodsmentioning

confidence: 99%

X-ray methods for quantitative determination of inorganic fillers in paper

Bluhm¹,

Jones²,

Deslandes³

1985

Can. J. Chem.

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. 63, 243 (1985). X-ray diffraction methods have been investigated as means of quantifying filler contents of paper. Both an "internal standard method" and an "absorption-diffraction method" were applied. Because of preferential orientation of the filler particles in commercial paper samples, the "internal standard method" was modificd to include an empirical evaluation of the proportionality constant, K . Values of K specific for each filler material investigated (clay, calcite. talc, and titanium dioxide) were obtained by X-ray diffraction intensity measurements on standard papers containing different amounts of each filler. These values of K were then used to calculate the filler content of various commercial papers. The filler contents of these same commercial papers were also determined using the X-ray "absorption-diffraction method" and ash determination. Comparisons made among results from all these methods indicated that both X-ray methods give acceptable agreement with ash determination, but that the "absorption-diffraction method" is preferred due to its ease of application. In addition, the X-ray methods are more rapid and versatile than ash determination. 243 (1985). Deux mCthodes de diffraction des rayons-X, "mCthodc du standard interne" et "absorption-diffraction," ont C t t utilistes pour la quantification des pigments inorganiques dans le papier. A causc dc la presence d'une orientation prtftrentielle des particules de pigments dans des feuilles de papier commerciaux, la "mCthode du standard interne" a CtC modifiCe en utilisant une tvaluation empirique de la constante dc proportionalitt K . Pour chaquc pigment ttudit (argile, calcite, talc et dioxide de titane) une valeur de K a C t t obtenue par la mesure des intensitts rayons-X obtcnus dc papicrs exptrimentaux qui contenaient difftrentes quantitts dc pigments. Ces valcurs dc K ont ensuite tt6 utilisees pour Cvaluer la quantitt en pigments dans des papiers commcrciaux. Les contenus en pigments de ces dernicrs ont Cgalement tte dttcrmints par la mtthode "absorptiondiffraction" et par dttermination des cendres. Aprks comparaison des rtsultats obtenus par ces trois mtthodes, il apparait que la mtthode "absorption-diffraction" soit prtftrte h cause de sa facilitt d'application. De plus, les mirthodes utilisant la diffraction des rayons->( sont plus rapides et plus versatiles quc la mtthode classique de determination des cendres.

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Basic Aspects of X-Ray Absorption in Quantitative Diffraction Analysis of Powder Mixtures

Cited by 302 publications

References 9 publications

Quantitative analysis of multicomponent powders by full-profile refinement of Guinier–Hägg X-ray film data

Quantitative analysis of multicomponent powders by full-profile refinement of Guinier–Hägg X-ray film data

General theory of the effect of granularity in powder X-ray diffraction

X-ray methods for quantitative determination of inorganic fillers in paper

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