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The accuracy of the Scherrer crystallite size equation is limited in part by the uncertainty in p, the experimentally deduced pure diffraction broadening. Currently used procedures for estimating {3 from the observed breadth of a Debye-Scherrer line are not, in general, applicable to the x-ray spectrometer.By making use of a scheme of convolution analysis for analyzing the effect of geometrical factors in broadening the pure diffraction contour, a correction curve is developed for determining p from the experimentally measured line breadths band B (Jones' notation). The degree of reliability of this correction procedure is ascertained by applying Stokes' direct Fourier transform procedure for determining the form of the pure diffraction contour free of instrumental effects. Suggestive procedures are given for crystallite size determination with the x-ray spectrometer in different size ranges, and several examples are described.

1 he mathetiidtical relatioriships are deteloped which are pertinent to the quantitative analysis of powder mixtures for the case of diffraction from the surface of a flat powder specimen. These formulas relate the diffracted intensity to the absorptive properties of the sample.(1) -Mixture of n components; absorbing power of the unknown equal to that of the matrix; concentration proportional to intensity. Direct analysis is permitted.(2) Binary mixture; absorbing power of the unknown not equal to that of the diluent; concentration not proportional to intensity. Direct analysis is possible by means of calibration curves prepared from synthetic mixtures. (3) Mixture of n components; absorbing power of the unknown not equal to that of the matrix; general case. Analysis is accomplished by the addition of an internal standard. Concentration is proportional to the ratio of the intensitj of a selected reflection from the unknown to tbe intensity of a reflection from the Three important cases are treated: internal Standard.URING recent years x-lag diffraction methods have been D extensively applied to problems of quantitative analysis Diffraction methods possess the unique advantage of detecting not only the presence of chemical elements but also their state 'If chemical combination. Quantitative measurements of greatly improved quality can now be made with the aid of Geigercounter tubes for receiving the diffracted energy. Finally, particular impetus has been given to the use of quantitative diffraction techniques by the development and widespread commercial distribution of the Norelco Geiger-counter x-ray spectrometer.In spite of this extensive activity in the field of diffraction analysis, no investigator to date has published a detailed statement of the simple but important mathematical relationships Ehich relate the diffracted intensity to the absorptive properties of the sample and thereby determine the particular procedure that is suitable for the analysis of any given sample. This communication presents these mathematical considerations for the case of liffraction from the surface of a flat powder specimen, the arrangement employed in the Norelco x-ray spectrometer.The measurement of the absolute intensities of x-rays diffracted by the components of a binary powder mixture has been discussed theoretically by Brentano (4, 6), and he has applied the results io the measurement of atomic scattering factors. Glocker (8) and Schafer (IO) have shown in a similar manner that the fundamental intensity formulas of Laue can be used as a basis for the quantitative d8raction analysis of binary powder mixture5 and alloys. However, they did not extend their mathematical treatment to the point of evolving a systematic practical wheme if analysis. INTENSITY DIFFRACTED BY ONE COMPONENT OF A POWDER MIXTUREI t will be initially assumed that the sample is a uniform mixture of 1c components, that the particle size is very small so that extinction and so-called microabsorption effects (6) are negligible, and that the thickness of the ...

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