The Berry-Furuta-Rhodes model is used to derive formulae for the characteristic X-ray intensity in specimens of 'non-infinite' thickness, as a function of particle size both for discrete values and for continuous distributions, including the Junge distribution for aerosols. Significant simplifications in otherwise complex formulae are obtained for a number of cases of practical importance, namely, thin specimens, monolayers and low or high packing fractions. The simplified working formulae consist of the equation for a thin, homogeneous specimen, multiplied by a grain size dependent factor. This factor is a function of fluorescent grain size only, so eliminating most inter-element effects. Practical applications of these formulae are discussed, with special reference to energy dispersive X-ray fluorescence analysis of thin briquetted specimens and of aerosols collected on filters.

Standards made up from calibrated solutions deposited on filter paper and dried were measured along with the specimens and blanks. Analytical results were compared with those obtained by atomic absorption spectrophotometry. Air particulate pollution data from a statewide survey in Texas were compared with other available data. The method and equipment has proved itself capable of use for air particulate survey measurements and for pollution source location.

New equations have been derived to describe the dependence of characteristic X-ray intensity on particle size in heterogeneous specimens. The formulae include the effects of continuous size distributions, a problem not covered in earlier theoretical work.

A compact X-ray energy spectrometer has been developed consisting essentially of a radioisotope X-ray source, a lithium-drifted silicon (or germanium) detector and a small computer. Interchangeable sources enable efficient excitation of K X-rays from Na to U and L X-rays from about Ag to U. Energy resolution of K X-rays from adjacent elements down to Na is possible. Depending on the source and the part of the spectrum examined, the characteristic X-rays from up to about 15 elements can be simultaneously excited and measured, for either qualitative or quantitative multi-element analysis. The computer stores detected spectra and performs simple data processing such as peak recognition, background subtraction, peak integration, ratioing and solution of linear equations.The analysis reported in this paper is the determination of V, Cr, Fe, Co, W and Mo in tool steels and is intended to illustrate the capabilities of the radioisotope X-ray fluorescence analysis technique, and the instrument, for multi-element analysis of a system having fairly complex interelement effects.A 100 mCi Pu-238 source was used to excite the K X-rays of V, Cr, Fe, Co and Mb and the L X-rays of W. The count time used was five minutes per sample. Data reduction consisted essentially of peak integration, background subtraction and solution of sixth order linear matrices of a modified Criss-Birks type. The 36 matrix coefficients were determined using six standards, and were then used to analyze seven other analyzed specimens which were treated as unknowns. The measured values of concentration were in very good agreement with the quoted values. An iteration technique was employed to reduce errors in the matrix inversioiis.

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