tion using a mathematical technique based on Simpson's rule for numerical integration. The Simpson's rule technique is described in a number of mathematics and computer science texts (9, IO). Our code was an adaptation for the CDC 7600 of an Algol algorithm given by McKeeman
+
In the modified Simpson's rule used in this evaluation, the interval is integrated by one application of Simpson's rule and then by three applications of Simpson's rule on three equal subintervals. If the sum of the areas of the subintervals do not agree with the area of the interval within a specified limit, then the same procedure is used separately on each of the subintervals. When agreement of the calculated areas is obtained, the program proceeds to the next interval. A maximum of 11 levels of subdivisions is allowed. Thus, the function is evaluated a minimum of 7
or a maximum of 2*311 1 times. The maximum percentage error between the calculated areas allowed in this work was 1 x 10-5. The results of the numerical integration are shown in Figure 3. A detailed tabulation of the results is given in Table I. To demonstrate the error which can result from comparison of solutions with different optical thickness, dilute solutions of quinine sulfate were compared with a quinine standard of relatively large optical density. As shown in Table 11, penetration of the exciting light into the cell volume results in a nonlinear loss of the fluorescent emission out the sides and rear of the cell. Analysis of the experimental data using Equation 10 results in an accurate evaluation of the quantum efficiencies of the dilute solutions.
K. 8. Wiberg, "Computer Programming for Chemists," W. A. Benjamin, New York. N.Y., 1965,p 35. R. H. Pennington, "Introductory Computer Methods and Numerical Analysis," Macmillan, N e w York, N.Y.. 1965,p 193. M . W. McKeeman, Commun. Ass. Computing Machinery, 5, 604 (1962).
Received for review May 29, 1973. Accepted September 4, 1973. Presented in part at the 24th Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Cleveland, Ohio, March 6, 1973. This work was performed under the auspices of the United States Atomic Energy Commission.
(11).
Nondispersive Soft X-Ray Fluorescence Spectrometer for Quantitative Analysis of the Major Elements in Rocks and Minerals A. J. Hebert and Kenneth Street, Jr. Lawrence Berkeley Laboratory, University of California, Berkeley, Calif. 94720
A lithium drifted silicon detector and a multichannel analyzer system have been combined with a multiple anode soft X-ray generator and a high vacuum sample handling system to provide an X-ray fluorescence unit for quantitative analyses of the elements from oxygen to iron. A relatively rapid, accurate, and reproducible sample preparation technique and a method for sample matrix absorption corrections are described.
The use of lithium drifted silicon detectors for the detection of X-rays was reported several years ago (1); however, inadequate resolution for photons of less than 10 keV made even qualitative soft X-ray analysis difficult. The production of better crystals and improvements in electronic detection techniques ( 2 ) have led to the present generator, a simple high vacuum sample transfer and refof detecting and resolving carbon, nitrogen, and oxygen X-rays (3, 4 ) . The spectrometer and techniques described here are the results of efforts to extend the use of these detectors to quantitative analysis of the elements from oxygen to iron (1) H. R. Bowman, E. K. Hyde, S. G . Thompson, and R. C. Jared, Science, 151,562 (1 966) (2) E. Elad. Nucl. Instrum. Methods, 37,327 (1965). (3) D. A. Landis, F. S. Goulding. R. H. Pehl, and J. T. Walton, / € € E Trans. Nucl. Sci.. 18 (l),115,(1971). (4) J . M. Jaklevic and F. S. Goulding, / E € € Trans. Nucl. Sci., 18 (l), 187 (1971).
through the development of a multiple anode soft X-ray generator, a simple high vacuum sample transfer and referencing system, and a relatively rapid, accurate, and reproducible method of sample preparation. In addition, a method of calculating sample matrix absorption effects is described which gives easily applied corrections for compositional differences between a calibration standard and an unknown sample. This, in turn, allows accurate analyses of widely varying types of samples by comparison with a single calibration standard.
EXPERIMENTAL Apparatus. Multiple A n o d e Soft X - R a y Generator. A schematic sketch of the spectrometer is shown in Figure 1. The rotating anode mount accepts six hollow cylindrical anodes which are held in place by copper screws passing through the center of each anode. Each anode has two nickel plated copper partitions between it and its neighbors to eliminate cross contamination from line of sight sputtering. A summary of the anodes, filters, electron energies, and observed X-rays is given in Table I. A cross sectional schematic diagram of the electron gun is shown in Figure 2 . The interior of the nickel plated soft iron case is lined with tantalum foil. The back of the gun has a large opening which allows the outer tantalum surface, with its higher emissivity, to radiate to the chamber interior. Thorium oxide coated iridium filaments readily provide adequate electron currents a t a power input of roughly 4 watts and a n estimated filament temperature of 1400 "C. The stable nature of the filament input power level indicates little, if any, appreciable filament deterioration during several months of operation. For most analyses, 150 pA of current to the anode is sufficient
ANALYTICAL CHEMISTRY, VOL. 46, NO. 2, FEBRUARY 1974
203
+-2.54cm---i
water
ROlatinQ anode and falter assembly
-_
eclron gun mounting sulalors and rods
Electron g u n mountlnp l"SYlot0lS
c
mple transfer and g shaft
/-
icoI filter position
/
Sample c e l l ond holding
spring
wive
To VAC-ion pump
Figure 3. Cross sectional sketch of the spectrometer vacuum chamber Figure 1. Schematic sketch of the spectrometer
Table I. Anode and Filter Data
Kovar i n s u l a t e d f e e d throughs
Cross
section
back
view
Anode
Filter element
Mg
M g ( K edge)
0.015
AI
Al(K edgej S i ( K edge) A g ( L edge) T i ( K edge) N i ( K edge)
0.013 7 1 . 4 9 0,015 7 1 . 7 4 7 2.98 0.001 0.025 7 4.51 0 . 0 2 5 10 7 . 4 8
--1
k-22.54cm --4i
T a n t a l u m foil
Electron flux Electron - d i f f u s e r ~
-
Water coaled mount Cross section tap view
Figure 2. Cross sectional sketch of the electron gun and rotating anode mount to generate several thousand detected events per second. Higher data acquisition rates are possible, but the present level of amplifier and analyzer dead time corrections make such rates undesirable when comparing quite different samples, such a s a granite and a peridotite, where the counting rates may differ appreciably. Pulsed operation of the electron gun in a synchronous mode with the detector amplifiers may alleviate this restriction. Experiments on X-ray flux reproducibility indicate variations on the order of 0.5% or less for each anode when rerun in place over a period of 1 hour. The reproducibility from day to day with anode rotation and sample changes is on t h e order of 1to 2%. Vacuum S y s t e m . A cross sectional sketch of the spectrometer vacuum chamber is shown in Figure 3. T h e chamber walls are made of soft iron plate. The plate acts as a n effective magnetic shield so t h a t the electron gun and X-ray source geometry are constant even though conditions in the laboratory may vary. The chamber volume of roughly 2 liters is pumped with a 50-liter-persecond ion p u m p and a liquid nitrogen cold finger. The chamber interior is nickel plated to preserve a relatively noise-free background spectrum. The low fluorescent yield for nickel L X-rays (-0.005) is especially helpful in this respect. Under normal operating conditions, no noticeable Ni L X-rays or other unexpected background signals are observed. All moving parts are provided with double or multiple O-ring seals which provide continuous differential pumping. T h e areas 204
7
Elements determined
1 . 2 5 0, F, Na, and L X - r a y s of s o m e heavier elements
Si Ag Ti Ni
Grid mount
Rotating anodes
Electron X-Ray enenergy, ergy, keV keV
Filter thicknew, mm
0, Na, Mg 0, Na, Mg, A1 Al, Si, P, S, C1 Si, CI, K, Ca, Sc C1, K, Ca, Sc, T i , V, C r , Mn, F e
between the atmosphere and the spectrometer chamber are pumped with a cryo pump (5) that maintains a vacuum of l o - * Torr or better. Movements of the rotating anode, the sample transfer shaft, or the detector window gate valve cause only minor fluctuations in the analysis chamber pressure. which usually and 1 X 10 - 6 Torr. holds a t between 5 X When it is necessary to bring the spectrometer chamber u p to air, a 0.13-mm thick beryllium window is moved in place of the 56 pg/cm2 aluminum window in order to maintain the detector a t a high vacuum. The aluminum window between the detector and sample must be pinhole free to white light in order to provide a n optical barrier to visible photons which generate interfering signals in the detector. T h e window also serves as a barrier to condensable molecules in the spectrometer chamber. The sample transfer shaft has a series of seven O-rings surrounding two sets of six sample referencing cells. This allows insertion of a new set of six samples with maintenance of differential pumping while the set previously analyzed is being removed. Sample transfer is accomplished with the turn of a single crank, and roughing of the sample cells to 10 * Torr or better occurs automatically as the transfer shaft moves the cells over roughing ports. In cases of rock, mineral, alloy, or other low vapor pressure material analyses, the total time necessary to place six samples in their cells and transfer them to the analysis chamber, including a 4-minute stay in the roughing position, is 5 minutes. Analyses are Torr or less. usually performed a t 8 x Detector. T h e lithium drifted silicon detector was built a t Lawrence Berkeley Laboratory and is similar to those described previously (3, 4 ) , with the exception that it uses a side mount detector arrangement with crystal cooling occurring cia copper battery cable. The detector is of standard "top-hat'' design with pulsed opto feedback circuitry. It has a resolution of 190 eV FWHM for iron K a X-rays, a Fano factor of 0.12, and electronic resolution of 108 eV. The observed FWHM for sodium X-rays a t 1.04 keV is approximately 140 eV. ( 5 ) R. Hintz and R Parsons, UCRL-17299 (March 1 9 6 7 ) . distributed by National Technical Information Service, U.S. Department of Commerce, 5285 Port Royal Road, Springfield, Va. 22151
ANALYTICAL CHEMISTRY, VOL. 46, NO. 2, FEBRUARY 1974
Table 11. Comparison of Present XRF Results and Preferred Values for Major Elements i n USGS Standard Rocks as Per Cent Oxidea Sample
G-2
XRF Preferred values Difference
GSP-1
XRF Preferred values Difference
AGV-1
XRF Preferred values Difference
PCC-1
Na2O
Source
XRF Preferred
DTS-1 X R F Preferred values Difference
BCR-1 X R F Preferred values Difference
AliOa
4 . 1 7 (5) 4.15
0 . 7 7 (2) 0.77
15 .26 (9) 15.31
+0.5% 2.84(5) 2.86
0 0.99(2) 0.95
-0.7% 4.36(5) 4.32
+o
Si02
CaO
Ti02
FeO
1.98(2) 2 .oo
0.51(1) 0.48
-0.3% 15.02(9) 14.92
-0.1% -0.2% 67.1(2) 5.54(2) 67.32 5.52
-1.0% 2.08(2) 2.06
+6% 0.67(1) 0.66
+0.8%
+3.9% 1 .51(2) 1.53
+O . 6 %
-0.4% +0.3% 59.6(2) 2.93(2) 59.10 2.92
+1.1% 4.97(2) 4.98
+2% 1.03(1) 1.05
-0.1% 6.03(1) 6.04
.9% 0.02(5) 0 ,0077
-1.5% 43 .42 (8) 43.26
-0.1% 0.67(9) 0.72
-0.3% +0.8% +0.3% 41.2(2) 0.007(17) 0.54(2) 41.84 0.0031 0.54
-2% O.Ol(1) 0.01
-0.2% 7.42(1) 7.34
... 0.007(5) 0 .0084
+o
.4% 49 .68 ( 8 ) 49.83
-6.7% 0.41(9) 0.30
-1.5% 40.2(2) 40.48
0.009(17) 0.0015
-0.3% 3.52(2) 3.46
+37% 13.42(9) 13.44
-0.5% 55.0(2) 54.22
1.68(2) 1.70
.
.
I
3 .30(5) 3.32 -0.7%
+1.9%
16.90 (9) 16.92
-0.2%
69.2(2) 69.29
KzO
4.50(2) 4.51
values Difference
Mu0
+1.5%
...
...
-1%
0 0.12(2) 0.03
... 7 .02 (2) 7 .OO
+o . 2 %
2.40(1) 2.38 3.81(1) 3.82
0 O.Ol(1) 0.01
+1.1% 7 . 7 3 (t ) 7.79
0 2.20(1) 2.22
-0.8%
-1%
12.06(1) 12.08 -0.2%
Numbers in parentheses represent one standard deviation at the last digit for the observed counting statistics.
Procedure. Sample Preparation. Rocks and Materials Suitable for LiBOz Fusion: Sample powder with a particle size of the order of 0.1 mm or less is mixed with spectroscopic grade lithium metaborate (Southwestern Analytical Chemicals, Austin, Texas), LiB02, in a 10:1 ratio of LiBOz to sample. At present 200 mg of powdered sample is fused with 1.80 grams of LiB02. Each bottle of LiBOz is checked for weight loss on fusion and the correction, which is usually less than 270, is applied to the ratio. The fusion is performed over a Fisher burner with air and natural gas inlets, The weighed powders are carefully mixed in a gold plated platinum crucible. The mixture is then slowly brought to approximately 900 "C for 4 minutes. During this time, the crucible is swirled with tongs over the burner with a gloved hand. The liquid mass is also stirred with a 3-mm diameter vitreous carbon rod (Beckwith Carbon Corp., 16140 Raymer St., Van Nuys, Calif. 91406) which is rotated in a small battery powered stirrer. Following a final 5- or 10-second stir, the glass is poured into a nickel plated copper ring resting on a polished vitreous carbon disk (Beckwith Carbon Corp.) which is at 250 "C. A thick flat gold foil that is silver soldered to a copper block is then brought down on the molten glass to press it into the ring and against the carbon. T h e gold foil press is removed after 2 seconds and the glass pill is allowed to anneal a t 250 "C for several minutes. The nickel plated copper rings which retain the glass preserve an analyzable surface in the event of cracking during the annealing process, The polished vitreous carbon surface appears to be free of detectable major element contaminants, as judged from analysis in the spectrometer of pure LiB02 samples. The polished vitreous carbon surface is easily cleaned with distilled water and alcohol. The time necessary to weigh and prepare a glass fusion sample is usually less than 10 minutes with a failure rate of less than 10%. Most failures in preparing a usable pill result from an incomplete transfer of molten glass from the gold plated platinum crucible. An improved crucible surface, which the molten glass does not adhere to, can usually be obtained by dipping the crucible for 2 seconds in a solution containing 3 parts of concentrated and 4 parts of H20, and then HCI, 1 part of concentrated "03, quickly rinsing with distilled H20. Fusions are carried out a t temperatures less than 950 "C. At higher temperatures, both the sample and the vitreous carbon disk may be damaged by sticking and thermal shock chipping of the carbon. Vitreous carbon has a hardness close to that of silicon carbide, and damaged carbon disks may be reground and polished in the same manner as glass. In addition to sticking and thermal shock, we have observed significant losses of sodium and potassium from standard rock samples in cases where the fusion temperature has exceeded 1000 "C.
The glass sample pills are stored in a vacuum desiccator to minimize the effects of long term exposure to the laboratory atmosphere. Moisture pickup by the glass is less than 1 part in lo4 per day; however, surface changes have been observed for some samples after several months of laboratory exposure. If less than 200 mg of sample is available, a ring or cup which requires less volume of glass may be used to scale down requirements, or the pill and standard may be made a t a higher LiBOz to sample ratio. Other Samples: Biological samples may be prepared by drying and powdering t h e solid or by freeze drying t h e liquid. The resultant powder is pressed into a 25-mm diameter by 0.75-mm thick pill. The pills are then held between thin aluminum washers for analysis. For oxygen analyses on rocks or other minerals, powder is dusted onto a Scotch brand (3M) tape surface with a sample ringacting as a frame. Filter paper disks from air monitors or other filtration procedures may be analyzed by simply placing the disks between aluminum washers. The filter papers may be backed up with additional thicknesses of paper or with a pure nickel foil if the sample does not constitute a n infinite thickness for some of the higher energy X-rays. In cases where the samples have high moisture content or other volatiles present, they are stored in a vacuum desiccator prior to being placed in the spectrometer.
RESULTS AND DISCUSSION Analyses of three s e p a r a t e l y pr-epared sets of six USGS s t a n d a r d rock p o w d e r s i n d i c a t e r e p r o d u c i b i l i t y and a c c u r a c y on the o r d e r of 1 t o 2% for e i g h t m a j o r e l e m e n t s w h e n c a l i b r a t e d a g a i n s t published w e t c h e m i c a l r e s u l t s (6). A c o m p a r i s o n of v a l u e s is given in T a b l e 11. These results are not d e r i v e d from o u r o w n c a l i b r a t i o n s , but were obt a i n e d for a n y one USGS standard s a m p l e b y a s s u m i n g that the listed p r e f e r r e d v a l u e s are correct for the s i x standards and c o m p a r i n g t h e a b s o r p t i o n c o r r e c t e d i n t e n sities. The r e p o r t e d v a l u e s were o b t a i n e d w i t h a 5 - m i n u t e a v e r a g e a n a l y s i s t i m e p e r e l e m e n t , o r 40 m i n u t e s per sample. The d e v i a t i o n s i n the t h r e e sets are i n a g r e e m e n t w i t h t h e expected statistical uncertainties. (6) I . S. E. Carmichael, J. Hampel. and R. N. Jack, Chem. Geol.. 3, 59 (1968).
ANALYTICAL CHEMISTRY, VOL. 46, N O . 2, FEBRUARY 1974
205
,*{l
f
1O:l LiB02
+ f(MgYTiKMp+
+
AIYT~,~' "'
-L)}IK (1)
where f = weight fraction of sample in LiBOz matrix (7) K. Norrish and B. W . Chappell, "Physical Method9 in Determinative Mineralogy." J. Zussman, Ea., Academic Press New York. N.Y., p 196.
206
+
+
ATiK = 1 /(MgYTiKMp A I Y T ~ K +... ~' -L) (2) where Mg = weight fraction of MgO in the original sample. Al = weight fraction of A1203 in the original sample, etc. L = loss, i e . , weight fraction of volatiles lost in the fusion. The Ys are given by expressions like
where YTi KMg corrects for the absorption due to MgO in the sample when the incoming X-rays are Ti X-rays and the outgoing X-rays are those of potassium. GTiMg = mass absorption coefficient for Ti X-rays in MgO. P T ~ L B = mass absorption coefficient for Ti X-rays in LiBOz. G K M g = mass absorption coefficient for potassium X-rays in MgO. = mass absorption coefficient for potassium X-rays in LiB02. 4 = Sec cr/Sec p where a is the angle of the incoming X-rays to the sample normal and (3 is the outgoing angle. In the present apparatus 4 = 1.233. The mass absorption coefficients tabulated by McMaster et ai. (8)were used in the work reported here. (8)
w.
ANALYTICAL CHEMISTRY, VOL. 46, NO. 2. FEBRUARY 1974
H. McMaSter et al.. UCRL-50174 (May 1969). distributed by National Technical Information Service. U.S. Department of Commerce, 5285 Port Royal Road. Springfield, Va. 22151.
In the analysis of the USGS standard rocks, the largest absorption corrections occur in the determination of iron using nickel X-rays. The extreme values are AN,Fe(PCC-l) = 1.381 and AN,Fe(BCR-l) = 1.592. For the lighter elements, the absorption corrections are typically much smaller. For example, in analysis for magnesium using aluminum X-rays, the lowest and highest corrections are A41Mg(G-2) = 1.010 andAAIMg(DTS-1) = 1.042. The consistency obtained in the analysis of the six USGS standards, which vary widely in composition, indicates that the calculated absorption corrections are adequate. The sodium and magnesium analyses required 10 minutes each per sample. Under the same conditions, if 2 to 4% standard deviations are adequate for Na, Mg, and Ti at these levels, then 1% standard deviations can be obtained for the remaining elements that are present at or above the 1% level in a total analysis time of 10 minutes per sample. Results obtained for manganese and chromium during these analyses have not been included in Table I1 because of uncertainties in absolute calibration. Once an accurate calibration is obtained, the spectrometer should yield 1% standard deviations for Mn or Cr analyses at the 1000ppm level in less than 5 minutes, and at the same time provide analyses for the rest of the elements from potassium to iron. The sensitivity corresponding to three standard deviations of the observed counting statistics for a 5-minute analysis at 1 O : l dilution of rock in LiB02 varies from 0.09% for Na to 0.01% for Fe. The variation is due to differences in cross sections, absorption effects, and fluorescent yields. The present sensitivity for biological samples such as pressed protein powder or freeze dried blood varies from
0.8% for oxygen to 0.001% for iron in a 5-minute analysis. Preliminary experiments indicate that 1 to 2% standard deviations for oxyggn analyses may be obtained for rock or mineral powders in 10 minutes with the sample on tape procedure described above. Examples of observed spectra are shown in Figure 5 . In obtaining these results, we purposely operated the spectrometer below its design capabilities in order to guard against any changes in spectrometer efficiency or other uncertainties which arise from higher counting rates while analyzing the three standard rock sets. This also allowed an accurate check on our sample preparation technique. The spectrometer is now being tested under more efficient operating conditions. The preliminary experiments indicate that it will perform reliably and provide analyses comparable to or better than those reported here in 15 minutes per unknown fused rock or mineral sample. The present results are comparable to those obtained with conventional dispersive systems. One advantage that similar nondispersive systems may provide over dispersive ones is a significantly lower cost for the equipment. The present spectrometer was produced for a fraction of the cost of a conventional dispersive system.
ACKNOWLEDGMENT We wish to thank Robert D. Giauque, H. R. Bowman, Frank Asaro, Joseph M. Jaklevic, and William L. Searles for many informative and useful discussions. We also thank Gardener G. Young for his expert advice and help in fabricating the spectrometer. Received for review May 23, 1973. Accepted August 30, 1973. This work was performed under the auspices of the U.S. Atomic Energy Commission.
Automatic Correction System for Light Scatter in Atomic Fluorescence Spectrometry T. C. Rains, M. S. Epstein, and Oscar Menis Analytical Chemistry Division, National Bureau of Standards, Washington, D. C. 20234
Light scattering of incident radiation by solvent droplets and unvaporized solute particles in the flame is a major interference in atomic fluorescence spectrometry (AFS). A technique for the automatic correction of light scatter is described which increases the speed and accuracy of analysis. The light from an electrodeless discharge lamp and a 150-W xenon lamp is alternately passed through the flame. The resulting signal from the multiplier phototube is fed to a lock-in amplifier which corrects for the contribution of the light scattering to the fluorescence signal. The principles of the technique and apparatus for making the automatic correction are described. To accomplish this correctiop, scatter of the incident radiation from the electrodeless discharge and xenon lamps is balanced initially while aspirating a 1% lanthanum solution. The method has been applied to the determination of 0.11 and 0.26 p g Cd/ gram in SRM's Orchard Leaves and Liver, respectively, without any prior separation or preconcentration.
Atomic fluorescence spectrometry (AFS) has been shown to be a very sensitive analytical technique for the determination of many elements ( 2 - 5 ) . However, the number of published applications of AFS for the determination of trace elements is limited (6). This can be attributed, in part, to a number of factors such as the unavailability of commercial instrumentation, the need for a highintensity radiation source. and the effect of chemical and physical interferences. While commercial instruments for AFS are not available, flame photometers and atomic ab11) A. Syty. chapter in "Flame Emission and Atomic Absorption Spectrometry," Voi. 2, J. A. Dean and T. C. Rains, Ed., Marcel Dekker, New York, N.Y., 1971. (2) J. B. Willis, Spectrosc. Lett.. 2, 191 ( 1 9 6 9 ) . (3) R . L. Miller. L. M . Fraser, and J. D. Winefordner, Appi. Spectrosc., 25, 477 (1971). (4) J. D. Winefordner, V. Svoboda, and L. J , Cline, CRC Crit Rev Ana/ Chem , p 233 (August 1 9 7 0 ) . ( 5 ) G. F. Kirkbright, Anaiyst. ( L o n d o n ) ,96, 609 (1971). (6) J. D. Winefordner and T. J. Vickers, Anal. Chem , 44, 150R ( 1 9 7 2 ) .
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