Effects of Specimen Repositioning on Statistics of X-Ray Intensity Measurements from an Electron Microprobe Analyzer James P . Smith and John E. Pedigo Texas Instruments, Inc., P.O. Box 5936, MIS 147, Dallas, Texas 75222
STATISTICS which describe fluctuations in the X-ray photon emission produced in a n electron microprobe analyzer sample are the same as for X-ray fluorescence measurements and nuclear radiation counting (1-5). When electron beam current and energy d o not vary, the X-ray fluctuations are described by the Poisson distribution. The variance of this distribution is equal to the mean and thus defines the ultimate precision available for photon counting. However, the use of this distribution to estimate the precision of electron microprobe analysis has been criticized because it is too optimistic. An experimental evaluation of the actual variance can be used to indicate how close a n analysis can come to the ultimate precision available. The purpose of this investigation is to examine the instrumental parameters which determine the precision of an analysis using measurement procedures identical to those used in actual analysis. The major instrumental factor that limits the precision of the electron microprobe analyzer seems to be the placement of the samples. The precise sample placement is extremely important inasmuch as in a typical analysis, measurements are taken on several points of a specimen as well as on standards, and each point requires a focus adjustment. The X-ray spectrometer is aligned to select a given wavelength of radiation originating at the point that is bombarded by the focused electron beam (see Figure 1). The sample is observed with a microscope through which the spot for analysis is selected by positioning it under a cross-hair. The electron beam, the microscope, and the X-ray spectrometers are all aligned to the point of analysis, thus when new points are selected, the correct position of the sample is chosen simply by focusing the microscope on the sample and positioning the spot under the cross-hair. This is accomplished by x, y , and z movement of the sample. If the depth of focus of the microscope is larger than the effective “depth of focus” of the X-ray spectrometer, then the spectrometer might be slightly out of focus even though the microscope is focused correctly. Therefore, the relative depth of focus of the microscope and spectrometer can be quite critical. The depth of focus of the microscope is the size of the increment in z placement of the sample in which the point of analysis appears to be in focus. The depth of focus of a refractive microscope is approximately inversely proportional to the square of the numerical aperture (N.A.) of the objective and is very small for a high N.A. optical system. The depth
of focus of the X-ray spectrometer might be defined similar to the optical system; that is, it is the size of the increment of z placement of the sample in which no change, other than those due to the Poisson distribution, in mean X-ray intensity can be detected. This value cannot be simply stated because it is dependent on the spectrometer design, the slit sizes, the diffracting crystal, the spectrometer setting, etc. Each commercial electron microprobe analyzer has a different spectrometer design, thus a completely general experimental study is impossible when only one model is available. However, the need for such information is indicated by this evaluation of the precision of the Materials Analysis Company (MAC) Model 400 electron microprobe analyzer and the experimental procedures should be of interest to other analysts who might care to perform a similar evaluation on their instruments.
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(1) K. F. J. Heinrich, in “Advances in X-Ray Analysis,” Vol. 3, W. M. Mueller, Ed., Plenum Press, N. Y.,1960, p 95. (2) H. A. Leibhafsky, H. G . Pfeiffer, and P. D. Zemany, ANAL. CHEM., 27, 1257 (1955). (3) fbid., 31, 1776 (1959). (4) R. C. Stanley, Brit. J. AppL Phy., 12, 503 (1961). (5) T. 0. Ziebold, ANAL.CHEM.,39, 858 (1967).
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DETECTOR
Figure 1. Illustration of MAC Model 400 electron microprobe showing the light, electron, and X-ray optical systems properly focused to point of analysis
Table I. Electron Microprobe Analyzer Experimental Conditions for Precision Determination Runs Spectrometer No. 2 Spectrometer No. 3 Spectrometer No. 1 Crystal Line Mean" Crystal Line Meana Meana Crystal Line Run No. Sample ADP Kai(1) 6.4 ADP Kai(1) 6.5 1 AI KAP Kai(2) 4.2 Kai(2) 5.9 KAP ADP Kai(1) 6.2 Kai(2) 7.8 2 AI KAP Kai(1) 14.2 KAP Kai(1) 6.4 Kai(1) 17.0 ADP 3 A1 KAP Kai(1) 6.6 KAP Kai(1) 15.2 Kai(1) 6.8 ADP 4 A1 ADP Kai(2) 3.0 ADP LiF Kai(1) 12.9 Kai(2) 2.6 5 Ti ADP Kai(1) 13.3 LiF ADP Kai(2) 2.1 Kai(1) 13.1 6 Ti Li F Kai(2) 3.6 Kai(1) 26.3 ADP LiF Kai(2) 3.3 7 Fe ADP Kai(1) 28.6 LiF Kai(2) 3.2 Kai(1) 27.9 ADP 8 Fe Li F LCudl) 12.9 ADP Lad 1) 11.2 KAP Lad21 5.1 9 SI1 ADP L42) 6.0 LQl(2) 4.8 ADP LUl(1) 8.3 LiF 10 Sn ADP Lffl(2) 5.6 KAP Lffl(1) 10.8 La1(2) 6.5 ADP 11 Sn KAP Ladl) 9.6 L42) 5.7 Lffl(1) 8.6 LiF ADP 12 Sn LiF Mai(1) 2.6 M~i(1) 2.8 ADP LiF LCul(1) 17.3 13 Au ADP LCYl(1) 17.8 LiF Mffdl) 2.4 LCul(1) 17.5 ADP 14 Au LiF Counts/sec X lo-" ti
EXPERIRIENTAL The electron microprobe analyzer was equipped with three X-ray spectrometers, thus allowing three simultaneous measurements. Several sets of measurements were made, each consisting of a series of detepinations simultaneously recorded from each of the three X-ray spectrometers. In this way, over 10,000 individual measurements were obtained. The measurements were recorded o n paper tape and processed by an IBM 7044 computer. An initial set of determinations, consisting of 280 measurement^ of 0.66-meV gamma radiation from standard sources placed near each of the three detectors exhibited Poisson distributions. Thus the three detectors and their associated electronics were assumed to be functioning properly. Other sets of measurements were made employing various instrumental parameters chosen to evaluate the effects o n precision of the following: the 20 settings of the spectrometer, the diffracting crystal, and the microscope objective N.A. The microscope on the M A C model 400 instrument was equipped with a three-lens objective turret allowing a choice of magnification and N.A. The three N.A. values available on the microscope were 0.13, 0.28, and 0.33. Three different diffracting crystals were also available; these were the LiF, ADP, and K A P crystals. The experimental conditions chosen for the precision determination runs are outlined in Table I. At least four sets of measurements were made for each condition. The first set consisted of 240 determinations (80 measurements made simultaneously by three spectrometers), taken while analyzing the same spot with no instrumental adjustments made between the counts. The other sets were made by moving the sample out of focus and then back into focus between each measurement. This procedure was followed using each of the three microscope objectives. In this way, the loss of precision caused by the uncertainty in reproducing the focus could be evaluated for each diffracting crystal and various 28 setting. Thus, for each run outlined in Table I, an initial set of three simultaneous series of 80 determinations (one series from each spectrometer) was obtained with no instrument adjustments made between the measurements. Next, while observing the sample through the 0.33 N . A . objective, three series of 80 measurements were obtained with optical refocusing the sample between each measurement. Then three series of 80 measurements were made using the 0.28 N.A. objective and refocusing the sample between each measurement. Finally, three series of 80 measurements were made while refocusing through the 0.13 N.A. objective. Pure element standards were used for the measurements; they were high purity semiconductor grade metals. The
metals chosen were gold, tin, iron, titanium, and aluminum. These were mounted in Bakelite molds and polished, the final polish being made with 0.3-micron polishing alumina immediately before the measurements were made. The X-ray emission was excited by a slightly defocused electron beam at 5-micron diameter spots near the center of the polished metal surfaces. The beam was defocused to reduce any possible specimen surface contamination during the measurement. An absorbed beam current of not more than 50 n A and an accelerating potential of 25 kV were used throughout the study. The counts were all accumulated during 1-second intervals. Therefore, a complete set of 80 measurements did not require more than 5 minutes. During this short period of time, the formation of a contamination at the point of the analysis was not detected either visually or by a general decrease in X-ray intensity as time progressed. The absorbed beam current did not vary more than 1% during the run. RESULTS AND DISCUSSION The computer program used to evaluate the count distributions calculated the basic statistical quantities: mean count, standard deviation, variance, and chi-square for each set of counts. If the counts followed the Poisson distribution characteristic of radiation emission, then the variance should approximate the mean count. Therefore, the data have been organized on the basis of the ratio of the variance to the mean ( K ) . The total variance ( V T )of a series of X-ray intensity measurements can be expressed as the sum of a variance due to the Poisson distribution of photon emission ( V p )and the variance produced by the random instrumental settings (V,). The variance of a Poisson distribution is equal to the mean (&TI.
when the value of K is near unity, the variance V iis insignificant. The value of chi-square gives a n objective estimate as to the extent the distribution of counts corresponds to a Poisson distribution. Each set of measurements taken for this study consisted of three series of 80 determinations; therefore, chisquare values between 60 and 100 for a series would indicate that a Poisson count distribution was predominate. Values VOL. 40, NO. 13, NOVEMBER 1968
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OBJECTIVE NUMERICAL A P E R T U R E
Figure 2. Variance to mean ratio observed while using various light optical objectives and ADP and LiF diffracting crystals 0.1
much greater than 100 would indicate that the distribution of counts was determined also by factors other than random photon emission. Chi-square for the 80 member series is the product of the ratio of variance to mean times 80; thus the value of K should vary between 0.75 and 1.25 if the fluctuations follow a Poisson distribution. The values of K larger than 1.25 indicate that the precision of the measurements is not as good as one would expect if the Poisson distribution of the photon emission were the only cause of intensity fluctuations. These larger values of Kshould indicate a loss in precision that arises from the random settings of the instrument. The statistical distribution which gives rise to Vt has not been characterized by this study, since V iis not important when the measurements exhibit the Poisson distribution (ultimate precision available). There are no significant differences between the results obtained with the A D P and the LiF diffracting crystals. The ratio of the variance to the mean obtained for all of the runs (regardless of the 26' settings) listed in Table I are diagramed in Figures 2 and 3 as a function of the objective numerical aperture. The ratios obtained with no refocusing adjustments are arbitrarily shown to have a large N.A. value indicating no error in reproducing the sample position. These data clustered about a value of one. This means that the ultimate precision was achieved when no change in sample position was made between the measurements. If instrumental variations such as drifting beam current or erratic detector sensitivity were significant, then these data would be significantly greater than unity. The majority of the sets of refocusing measurements taken with the 0.33 N.A. objective and either the A D P or LiF crystal resulted in precision very close to the ulitmate available. All but one of these series produced a variance to mean ratio less than two. The results obtained using the K A P diffracting crystal were quite pronounced (Figure 3). Any quantitative analysis made using the KAP crystal would be very questionable when the 0.13 N.A. objective is used and even the use of the 0.33 N.A. objective would produce a precision much poorer than that obtained using the A D P or LiF crystals. NO significant differences were obtained by exchanging the crystals between the spectrometers. I n Figure 4 the ratio of the variance t o the mean count is plotted as a function of the spectrometer 26' setting for the LiF and A D P crystals. If the 0.33 N.A. objective is used and the 2030
ANALYTICAL CHEMISTRY
'
0.2 0.3 0.4 OBJECTIVE NUMERICAL A P E R T U R E
Figure 3. Variance to mean ratio observed while using various light optical objectives and KAP diffracting crystal
28 setting remains above 50°, then the ultimate precision is obtained by the instrument. At lower 26' settings, the precision becomes poorer. If the M series is used for the heavy elements, most elements can be analyzed by the MAC instrument by using a n A D P or LiF crystal and a 28 setting above 50". Therefore, for these elements the ultimate precision should be obtainable if the 0.33 N.A. objective is used. Those elements which cannot be analyzed within these specifications are: Zn, Ga, Ge, As, Pd, Ag, Cd, and all those below atomic number 13.
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Figure 4. Variance to mean ratio observed while using various objectives and wavelength settings for ADP and LiF crystals The open figures identify measurements made using the 0.33 N.A. objective, the solid figures show that the 0.28 N.A. objective was used and the partially solid figures identify the measurement made using the 0.13 N.A. objective
A qualitative explanation of these data is possible. The spectrometers o n the M A C electron microprobe analyzer are fully focusing as shown in Figure 1. The source, the diffracting crystal, and the detector all lie in a Rowland circle. As lower 20 settings are selected, the crystal moves toward the sample along a straight line and rotates about its center. Thus, at the lower 28 settings, where precision is relatively poor, the crystal is very close to the source. Therefore, a n incremental change in the z sample placement results in a larger 20 error as compared to the error if the spectrometer were set at a much higher 20 value. F o r the M A C instrument, a change in the sample placement, AZ, along the optical axis produces a change of approximately
in the measured wavelength (d is the crystal spacing in angstroms, 0 is the correct reflected angle, and Z is expressed in microns). This simplified equation explains the qualitative characteristics of Figure 4 which shows that the precision is poor at the lower 20 settings. Furthermore, if the d spacing is relatively large as is the case for the K A P crystal, a given AZ increment results in a relatively large increment in diffracted wavelength. Diffracting crystals with the largest d spacings
should therefore produce the poorest precision, this effect is illustrated by the data plotted in Figures 2 and 3. More experimental and theoretical work is required in order t o fully characterize the precision of electron microprobe analysis. Yet this study has definitely demonstrated that there are major sources of scatter in electron microprobe data other than X-ray intensity fluctuations but that a careful evaluation of these sources of scatter can show how to avoid a loss in precision. It has been shown that the ulitmate precision available (that determined by the photon emission statistics) can be obtained in the M A C electron microprobe analyzer for many analyses of homogeneous metals. This can be accomplished by positioning the specimen through the 0.33 N.A. microscope objective and by chosing X-ray lines for monitoring which allow optimum 20 spectrometer settings. Of course, many sources of scatter which have not been considered here are inherent in routine analytical work. The sample preparation, surface contamination, inhomogeneities in the sample, shifting position of the point of electron impact, and sample charging can all cause poor precision. Since the samples used in this study were pure elemental metals, these other causes were isolated from the effect of specimen repositioning. RECEIVED for review May 1,1968. Accepted August 20, 1968
Determination of Trace Elements in Organic Material by the Oxygen Bomb Method Shizuo Fujiwara Department of Chemistry, Faculty of Science, The Uniaersity of Tokyo, Hongo, Tokyo
Hisatake Narasaki Department of Chemistry, Faculty of Science and Engineering, Saitama University, Shimoskubo, Urawa SEVERAL METHODS have been developed for determining trace elements in organic substances. Dry or wet ashing procedures are the most simple, and have been most widely used. However, they include serious sources of error; for example, with the dry method one cannot prevent the loss of some elements by volatilization, and with the wet method, contamination often results from concentration of impurities in the digesting reagents employed. The present paper describes a method of ashing in which a n oxygen bomb is used. The advantages of this method are: the sample is decomposed in a closed system, the procedure of decomposition is simple and rapid, and contamination originating in the digesting reagents is eliminated.
in the bomb was brought up to 25 kg/cm2, and the samples were ignited by passing a small ac current through the platinum wire coil under a potential difference of 10 volts. The combustion products from 1 gram of polyethylene were examined in a preliminary study. Analysis of both the liquid and vapor phases in the bomb was made before and after combustion. Determination of the components in the gas phase was made by mass spectrometry. Nitric and nitrous acids in aqueous solutions produced after combustion (as a result of using liquid-air oxygen) were determined by ultraviolet spectrometery ( I ) . (1) H. Hamaguchi, R. Kuroda, and S. Endo, Bunseki Kagaku, 7, 409 (1958).
EXPERIMENTAL
The construction of the bomb, which is made of 18-8 Cr-Ni stainless steel, is shown in Figure 1. The capacity is 300 ml. [The values have been chosen for the convenience of the bomb used in this experiment. They are intermediate of the values of bombs in the literature (Appendix).] The electrodes and the combustion cup are of platinum. Use of fused silica is an alternative. As will be explained later, it is recommended that the interior of the bomb be platinumplated. Analytical samples were tied u p in a sheet of rice paper by means of cotton thread and put in the cup. Then the remaining parts of the thread were passed through a coil of platinum wire between the electrodes. Oxygen pressure
Table I. Analyses of Combustion Gas of Polyethylene in an Oxygen Bomb by Mass Spectrometry( % v/v) Mean value of two determinations Oxygen Gases in the bomb supplied Before ignition After ignition 0 2 99.02 95,84 68.76 N2 0.77 3.77 1.99 0.15 0.29 Ar 0.21 coz 0.02 28.95 co 0.15
VOL. 40, NO. 13, NOVEMBER 1968
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