After J. Roboz, "Introduction to Mass Spectrometry Instrumentation and Techniques", John Wiley and Sons, New York, 1968, p 341. C.A. Andersen and J. R . Hinthorne, Science, 175, 853 (1972). J. M. Morabito and R . K. Lewis, Anal. Chem., 45, 869 (1973). M. Bernheim and G. Slodzian, Surf. Sci., 40, 169 (1973). B. Blanchard, N. Hilleret. and J. Monnier. Mater. Res. Bull.. 6, 1283 (1971). R . J. Blattner, J. E. Baker, and C. A. Evans, Jr.. Anal. Chem., 46, 2171 (1974). R. Bateman and A. E. Banner, private communication, Manchester, England, 1973.
(20)H. W. Werner, H. A. M. deGrefte, and J. Van der Berg, Radiat. E f f . , 18, 269 (1973). (21) V. Leroy J-P. Servais, and L. Habraken, Cent. Rech. Metall, 35, 69 (1973).
RECEIVEDfor review November 15, 1974. Accepted April 21, 1975. This research was supported in part by the National Science Foundation grants GH-33634 and GP-33273.
Spectrum Fitting Technique for Energy Dispersive X-Ray Analysis of Oxides and Silicates with Electron Microbeam Excitation R. J. Gehrke and R. C. Davies Aerojet Nuclear Company, 550 Second Street, ldaho Falls, ldaho 83407
A technique for the rapid, automatic analysis of spectra from electron microanalysis of silicates and oxides with an on-line PDP-11 or a PDP-15 computer is presented. Energy dispersive X-ray spectral data are acquired with a Si(Li) spectrometer mounted on a scanning electron microscope (SEM) or an electron microprobe and are transferred through an interface to the computer for processing. The program locates the X-ray peaks in the spectrum, determines the corresponding elements, and calculates the elemental composition of the sample. The latter computation is accomplished through the use of a linear least-squares fit of the sample (i.e., composite) spectrum with simple oxide (Le., component) spectra. In this technique, the background continuum is not subtracted from the peak but, rather, becomes inherent in the least-squares fit.
The application of energy dispersive Si(Li) X-ray detectors for use on scanning electron microscopes and on electron microprobes to acquire compositional information is extensively discussed in the literature (e.g., Ref. I , 2 ) . Detector resolution has steadily improved over the past few years such. that detectors currently available can completely resolve K a X-ray peaks of adjacent elements. As a result, precise quantitative electron microanalysis should be possible with energy dispersive Si(Li) spectrometry. Further, data accumulation times can be reduced from that of wavelength dispersive spectrometry a t least a factor of ten ( 3 ) . Several techniques have been developed for quantitative reduction of X-ray data from energy-dispersive detectors which claim a quality approaching the accuracy of wavelength dispersive systems (4-6). Although these analysis techniques use different approaches to determine peak areas, each attempts to obtain the net counts in a peak by devising an algorithm to remove the background counts from the gross counts in each peak (4-6). The techniques described in Ref. ( 4 , 5 ) which include innovative peak area determinations, are only described in abstracts. Reed and Ware (6) provide a description of their analysis technique and also have adapted it for routine analysis. Reed and Ware determine the peak areas by summing the contents of groups of channels straddling each peak and by applying corrections for pulse pile-up, dead time, and silicon X-ray escape peaks. Ref. ( 7 ) details the procedure of Ware and
Reed to determine the background under a peak. They describe the background continuum over the whole spectrum by a function which depends on the incident electron energy, the atomic weight and number of the sample, the depth of electron penetration, the various absorption parameters of the sample, and empirically determined instrumental parameters. Peak overlap corrections are also applied. Several commercial suppliers of energy dispersive spectrometers provide minicomputers and the software to reduce and analyze the X-ray data. Often, however, that software is proprietary information and a thorough description of the analysis technique is not available (e.g., Ref. 4 ) . Hence, the user is handicapped in learning how the program operates. Beaman, Solosky, and Settlemeyer ( 8 ) discussed the problems of determining X-ray peak intensities with energy dispersive spectrometers and reviewed the different methods in use in 1973. They concluded that the elimination of peak interferences coupled with an accurate background determination would considerably improve the state-of-the-art of analyzing Si(Li) X-ray fluorescence spectra. In this paper, we describe an analysis technique in which the background continuum becomes inherent in a linear least-squares fit of the sample spectrum by its component spectra. This technique also accounts for Si escape peaks which may underlie the fluorescent X-ray peaks of interest. We have incorporated these techniques into a computer program, X-RAY, which was developed for the Planetary and Earth Sciences Division a t the NASA Lyndon B. Johnson Spacecraft Center, Houston, Texas, to rapidly analyze large numbers of silicate and oxide mineral samples. The program can be used on-line in real time when the computer is directly interfaced to the spectrometer, or it can be used for batch processing of spectra recorded previously on paper tape or magnetic tape. It is written in FORTRAN for a PDP-11 or a PDP-15 computer which has a t least 12K of core in addition to disc and tape storage. The program can automatically locate the X-ray peaks in a spectrum, determine the elements corresponding to the peaks, and calculate the relative elemental intensities. These intensities are determined by performing a linear least-squares f i t to the sample spectrum (Le., composite) with spectra of simple oxide and silicate standards (i.e., components). Ref.( 9- 11 ) report the earlier application of this linear least-squares ANALYTICAL CHEMISTRY, VOL. 47, NO. 9, AUGUST 1975
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method to the analysis of y-ray pulse-height spectra. The present program, X-RAY, was developed from SISYP H U S ( 1 1 ) , the fitting program used a t INEL for the analysis of NaI(T1) y-ray spectra. Not only can X-RAY perform the above functions automatically, it has the advantage of not requiring a number of empirical instrumental factors t o be supplied by the user (6). The elemental concentrations are determined by correcting the least-squares fit results for the matrix effects within the sample by the method of Bence and Albee (12). Analyses have been carried out for the oxides of elements from sodium (2 = 11) to zinc (2 = 30) with this program. The accuracy achievable by this technique has not yet been established. An extensive evaluation of the data accumulation techniques, the stability of the electron beam current and system electronics, and the matrix correction procedure would be necessary in order to define their contributions to the total uncertainty in the calculated concentrations. This is beyond the scope of this paper. The entire analysis of a spectrum takes about 60 seconds with the PDP-11. In the “automatic” mode, the program sequences through all the steps in the analysis, prints the results, and continues to the analysis of the next spectrum. In the “stepping” mode, the program stops after executing a command and waits for the next command to be given. A description of the techniques incorporated in the program follows. A more detailed description of the program together with a user handbook is presented in Ref. (13).
COMPUTATIONAL METHODS Peak Identification. The peak identification routine determines which elements are present within a sample. This is done by automatically locating the X-ray peaks present, determining the channel positions of these peaks, converting the channel positions to energies and comparing these energies to a table of energies of K X-rays. This information then is used to select the appropriate component spectra (element oxide standards) for the least-squares fit of the composite spectrum. A cross-correlation of a Gaussian function with the data is used to locate the peaks within a spectrum ( 1 4 ) . The effect of the cross-correlation is to enhance the portions of the data where the search Gaussian correlates best with the data. The cross-correlation function C, is given by: m-1
C, =
I Y ~[exp(-(t C
- t o ) 2 / b 2 ) ] [ ~-t +(,B , + iZ)]
t=O
(1) where exp - ( t - t ~ ) ~ / / is b ’the Gaussian function, m = the number of channels over which the correlation function is computed, No = the height of the Gaussian, t o = m/2, b = FWHM/2(ln2)1/2, FWHM = full-width-at-half-maximum of Gaussian function, T = channel number of the correla~ the tion spectrum, Yt+T= the counts in channel t + of data spectrum, and B , = the background associated with channel 7.The background B , is determined by
The cross-correlation given by Equation 1 causes the correlation spectrum to be positive in the vicinity of peaks and negative or zero elsewhere. A peak in the correlated spectrum is defined by the presence of one, or more, positive points. A peak located in channel i of the data spectrum is computed by Equation 1 to be approximately in channel i - m/2 of the correlation spectrum. Once a peak is found, its position is calculated from the original data as the first moment or centroid. The energy of the peak is calculated 1538
ANALYTICAL CHEMISTRY, VOL. 47, NO. 9, AUGUST 1975
OLIVINE 174-1
3
t
0
100
200
300
4 00
CHANQEEL NUMBER
Figure 1. Results of least-squares fit of Mg, Si, Fe, and bremsstrahlung spectra (Le., lined spectra) to composite spectrum of olivine 174-1. These X-ray fluorescence spectra are produced by electron microbeam excitation
from this centroid and the gain and zero (from a prior calibration) of the spectrometer system. Once the energy has been found for a particular peak, a binary search is performed on a table of K a and K/3 X-ray energies and element names (for 11 5 2 I30). All elements with energies within 0.08 keV of the calculated energy are selected. For elements from calcium through iron, two possible identifications will often be made because the KP X-ray energy of one element differs by
