X-ray spectrometry is an old technique dating back some sixty-odd years and although most of the early interest revolved around the qualitative aspects of the method it wasn't long before attempts were made to obtain quantitative data. One of the first recorded attempts was that by Coster and von Hevesey who in 1923 accurately determined the amount of hafnium in zirconium using tantalum as an internal standard. Glocker and Schreiber were the first to attempt calculation of X-ray characteristic line intensity from first principles although no attempt was made at that time to correct for secondary fluorescence. In von Hevesey's book, “Chemical Analysis by X-Rays,” published in 1932 , a whole chapter is devoted to what is called “Disturbing effects and their avoidance.” Among the effects discussed were primary and secondary absorbtion and third element effects. Matrix correction equations were developed although most of the quantitative work at that time was done using internal standards.

A monochromatic source of X rays for sample excitation permits the use of pure elemental standards and relatively simple calculations to convert the measured fluorescent intensities to an absolute “basis of weight per unit weight of sample. Only the mass absorption coefficients of the sample for the exciting and the fluorescent radiation need be determined. Besides the direct measurement of these absorption coefficients in the sample, other techniques are considered which require fewer sample manipulations and measurements, These fundamental parameters methods permit quantitative analysis without recourse to the time consuming process of preparing nearly identical standards.

The role of statistics in certain areas of X-ray fluorescence analysis is considered. The topics discussed include: calculating the standard deviation associated with the result of an analysis; optimizing experimental parameters for both wavelength and energy dispersive analyses; evaluating limits of detection, limits of decision, and limits of determination; and weighting in the least squares fitting of data in single element polynomial relationships and in multi-element multiple regression analysis.

Empirical algorithms for the treatment of interelement effects in x-ray fluorescence spectrometry are reviewed. It is recommended that the effects of tertiary x-ray emission be treated separately from those of x-ray absorption, and that standard reference materials of composition close to that of the specimen be used.

Performing highly automated, computerized X-ray spectrometric analysis ‘without standards’ calls for accurate matrix correction programs which can be based, essentially, on either the ‘fundamental parameter’ method or improved influence coefficient procedures. The coefficient scheme discussed in this paper was devised to strictly comply with the theoretical relationships for X-ray fluorescence emission, thus connecting, in a way, both approaches. This result is achieved by accurately making allowance for the two complicating factors affecting fluorescent intensities i.e. : (1) the mobility of coefficients, and (2) the occurrence of fluorescence crossed effects. The corresponding algorithm, for practical use, writes

where the (aij + bij ci) terms account for the individual influence coefficients and their variation, and ϵi refers to the overall crossed effect. The essential problem of calibration is then considered, with special emphasis being laid on : (a) experimental coefficient determination, and (b) experimental crossed effect evaluation. Current coefficient methods are briefly surveyed in relation to the present theory.

Finally, the advantages of an experimental, accurate coefficient procedure over the fundamental parameter approach, from a practical standpoint, are emphasized.

Methods for quantitative microprobe analysis of flat samples with energy dispersive spectrometers are reviewed for the case when the electron beam is well contained in the analyzed region. Particular attention is paid to models for background subtraction and peak overlap necessitated by limited energy resolution. Present indications are that careful data collection procedures can often lead to accuracy comparable to crystal diffraction spectrometers.

Energy dispersive X-ray spectrometry has the potential for making very rapid analyses of multi-element samples. In order to fully exploit this capability several studies have been carried out with the goal of improving performance at high input count rates. A refined amplifier permits operation at input count rates up to 80000 per second with minimal peak shift and distortion. Optimum choice of tube parameters and filters permits utilization of a single Mo transmission target tube to analyze a broad range of elements in minimum time. Use of a pulsed tube further reduces the time required for analysis without sacrifice of precision or resolution. Dead time necessarily increases with increasing input count rate. It can be reduced by selecting a short amplifier time constant, but only with a loss of resolution. Digital processing permits recovery of the lost resolution. Some illustrations are given of spectra that have been processed on-line using a computer based multi-channel analyzer.

The necessary first step in using an x-ray fluorescence spectrometer for quantitative analysis is to obtain the intensities for the various elements. With a wavelength dispersive system this usually requires simply setting the crystal to the proper angle (and possibly adjusting the pulse height selector) and making a dead-time correction. With the energy dispersive x-ray fluorescence analyzer it is necessary to take into account the presence of erroneous peaks in the spectrum, to obtain true intensity values.

False peaks due to diffraction of white tube radiation from the sample can usually be shifted to portions of the energy spectrum where they do not interfere with emission lines of interest by selection of the proper tube-sample-detector geometry. Modern amplifier design provides a built – in dead time correction and greatly reduces the effects of pulse-pile-up, although the latter phenomenon will still produce small peaks at exact multiples of major peaks.

Simplified models are “being used, at the College Park Metallurgy Research Center for six popular methods for matrix correction in X-ray analysis, including Lachance-Traill, Lucas-Tooth and Pyne, and Rasberry-Heinrich procedures. A choice of models provides the broader data-handling capability required for processing information obtained by both energy-dispersive and wavelength-dispersive X-ray systems. The selection of model for each problem depends on the system and the availability of standard reference materials. Programming developed at College Park using the simplified models has been formulated for use by analytical chemists with minimal computer training. Some of the considerations involved in developing a versatile computer program for matrix correction will be presented, as well as applications of the procedures to iron-nickel-chromium alloys, aluminum alloys, and low-alloy steels.

A quantitative X-ray fluorescence method for single or multielement analysis is reported. It requires no calibration curve and covers a wide concentration range. The sample is dispersed into a film-forming polymer solution from which a thin specimen is made. A simple intensity-concentration equation free from matrix factors is derived. The simplicity and versatility of this method are demonstrated with eighteen examples. The precision of this method is statistically estimated to be 5% relative.

A procedure and program are described for rapid, economical and simple production of fully quantitative, multi-element analyses from energy dispersive microprobe data. Methods are outlined for background shaping and scaling, comprehensive overlap correction, and adjustment for instrumental drift. Program facilities include the output of all coefficients required, built-in standard data, the option to use default standards when no working standards have been measured, and the ability to respecify standards during data processing.

The U. S. Steel Research x-ray spectrometric laboratory performs between 7,000 and 10,000 analytical determinations each month for alloying elements in all types of steels and raw -materials. The spectrometer is automatically controlled by a DEC PDP 8/1 minicomputer utilizing vari ations of software packages provided by Siemens Corporation. As many as 256 individual analytical measurements can be sequentially performed. The minimal interelemental effects encountered in low-alloy steel analyses are corrected in a separate program written in FOCAL language. Correction coefficients for the program were established by multiple linear regression analyses.

Stainless and multialloy steels are analyzed with a two-part control and correction program. The control program controls all functions of the spectrometer automatically and stores parabolic calibration coefficients. Following a sequential determination of the alloying elements control is switched to a correction program written in FOCAL. The correction program prints a tabular listing of the elements determined, followed by a listing of the corrected concentrations of elements adjusted for interelemental effects. Orthogonal polynomial analyses were performed to determine σ values for all constituents determined.

For analysis of raw materials, the samples are fused prior to analysis by use of a flux and heavy absorber technique that essentially eliminates interelement effects and permits linear calibrations up to 100 percent. Samples are ground and pelletized after fusion for better reproducibility. Single sets of calibration standards are used regardless of raw materials mineralogical history. Synthetic standards can be produced for ranges where no calibration standards exist.

A rapid multielement analysis procedure for cement and ceramic type materials has been developed which uses pelletized powders and an exponential correction to the observed x-ray intensities. Only the more significant interactions are considered in an iterative process requiring a minimum of standards. The interaction coefficients are determined by a nonlinear multiple least squares fit of the standards. Average deviations obtained for the analysis of light elements in cement ranged from a low of 0.006% for K2O to a high of 0.13% absolute for SiO2.

A procedure is presented for the chemical analysis of rocks by x-ray fluorescence. Rocks are grouped within a set of twelve empirical standard compositions, prepared by sintering to 1200°C appropriate mixes of minerals and chemicals. For the major rock components silica, alumina, calcia, magnesia, potash, and ferric oxide, and the trace elements silver, copper, lead, zinc, molybdenum, manganese, tin, and antimony, quadratic equations are derived correlating concentration and intensity ratios corrected for dead time, background, and equipment drift. Interelemental effects are computed as a series of correcting factors modifying the basic analytical equations.

The X-ray fluorescent analyzer for identification of every piece of steel product in the production line has. been developed and its accuracy and utility has teen ascertained from practical applications.

It has also been applied to thickness measurement of zinc coating and color coating on steel sheets in the coating lines. In the severe environment of steel works for four years, there has been no instrumental trouble, and the reliability of the analyzer has been confirmed.

An energy dispersive X-ray fluorescence spectrometer using pulsed X-ray excitation has been developed for use in large-scale environmental analysis programs. A grid controlled X-ray tube is coupled with variable secondary fluorescence targets to analyze for a wide variety of elements with almost optimum sensitivity. The operation of the pulsed tube in a feedback loop with the semiconductor detector spectrometer results in a substantial increase in output counting rates without pile-up. The loop functions by turning off the excitation immediately upon detection of an event by the spectrometer. Pileup events are virtually eliminated and the X-ray tube's available anode power is better utilized.

The electronic control of this feedback mode results in some unique features in the response of the system to varying sample mass. These features are discussed in detail. Experimental results for sensitivity and accuracy over the range of elements measured are presented. Early operating experience with the unit indicates increases of counting rates of a factor of five compared with similar conventional systems.

X-ray fluorescence spectroscopy is new becoming a tool in research and. industry. Semiconductor detectors are proving valuable in measuring fluorescent X rays, and so are providing a versatile tool for rapid multielement analysis of many types of samples. This paper will mainly be concerned with, different types of copper ore. An experimental setup has been designed to determine Cu, Fe and Pb of concentration ranging from 0.1 to 20, to 5, and to 4 percent, respectively, with analytical precision of 20% relative at 0.1% Cu, and 3% relative at 20% Cu. For excitation a 100 mCi Pu-238 source and/or a low power air-cooled X-ray tube were used. Data acquisition and “on-line” evaluation for each sample takes about 100 seconds. Electronics blocks and sub-systems used In the set-up are available commercially. The most important benefit to be obtained from the setup is the ability to provide precise, reproducible determinations of large numbers of samples day after day.

Upgrading a manual X-ray spectrograph, interfacing with an 8K computer, and employment of interelement correction programs have resulted in a several-fold increase in productivity for routine quantitative analysis and an accompanying decrease in operator bias both in measurement procedures and in calculations. Factors such as dead time and self-absorption also are now computer corrected, resulting in improved accuracy. All conditions of analysis except for the X-ray tube voltage are controlled by the computer, which enhances precision of analysis. Elemental intensities are corrected for matrix effects, and from these the percent concentrations are calculated and printed via teletype.

Interelement correction programs utilizing multiple linear regression are employed for the determination of the following minor and trace elements; K, S, Rb, Sr, Y, and Zr in silicate rocks, and Ba, As, Sb, and Zn in both silicate and carbonate rock samples. The last named elements use the same regression curves for both rock types. All these elements are determined in concentrations generally ranging from 0.0025% to 4.00%, The sensitivities obtainable range from 0.0001% for barium to 0.001% for antimony. The accuracy, as measured by the percent relative error for a variety of silicate and carbonate rocks, is on the order of 1-7%. The exception is yttrium (13.8%).