quantitative analysis is, a t present, quite difficult with the technique. Reasons for this difficulty are the existence of several undefined mechanisms in the ion formation process, and the possibility of the superposition of these mechanisms (25). In addition, ion yields vary with parameters such as primary ion energy, residual gas. pressure, nature of the primary ion, temperature, and the chemical nature of the impurity-matrix pair (chemical and matrix effects). Any model of secondary ion emission (7, 32) would have to be modified by the chemical and matrix effects present for the system under analysis. Examples of chemical and matrix effects for the Ta system have been discussed. Experience with the tantalum system suggests, that with the proper use of standards, a quantitative analysis through the use of Equation 14 can be obtained. The most critical parameter in this equation is Krel,the relative ion yield. The estimation of Krel by Equation 13 neglects both chemical and matrix effects. However, with standards of known homogeneous composition and structure (TaZN, Ta205, SiOz, etc.) this number can be measured with sufficient accuracy to perform quantitative analysis provided sputtering rates, primary energy, residual gas pressure, etc. are reproducibly controlled. An example of this approach was discussed for the Ta-02 system, for nitrogen in T a , and for silicon in Ta205. Surface analysis is also possible, but the presence of hydrocarbon compounds and adsorbed gases which cause mass interferences make reliable surface analysis even more difficult than bulk analysis. Despite difficulties due to hydrocarbon interference, we have obtained qualitative agreement between Auger Electron Spectroscopy and the Secondary Ion Emission surface analysis of sputtered tantalum films. The combination of both techniques has given new insight into the surface chemistry of sputtered tantalum and on the lateral and depth distribution of surface impurities on sputtered tantalum thin films. (32) C A Andersen. Proceedings 6th Natlonal Conference on Electron Probe Analysis, July 8.1971
NOMENCLATURE d
a
= diameter of primary ion source = spherical aberration coefficient = semi-angular aperture
i
= current in amps
C
ar
= concentration in ppm at. = absolute ionization yield of isotope i = transmission of instrument = precision = isotopic abundance
P
= density
N
= Avogrado's number =' atomic weight = atom yield/sec. = number of sputtered neutral atoms = time in seconds = number of ionized atoms = ionized atoms/neutral sputtered atoms = sputtering rate (ML/sec.)
cs
Kl
7
P
fR t Il+ fl
i lsec ldef
LP U
= secondary ion current = secondary ion current detected = primary ion current = surface atom density
e
puttered atoms
S ( E ) = sputtering coefficient incident ion Kr,l = relative ionization yield K , = absolute ionization yield of the matrix E = primary ion energy F = correction factor c/s
= counts per second
ACKNOWLEDGMENT It is a pleasure to thank D. Gerstenberg for helpful comments on the manuscript, R. H. Minetti for his help with the Auger measurements, D. Lesher for spark source measurements, and D. Wonsidler for electron probe measurements. Figures 2 and 3, measurements of K , for the respective isotopes of the pure element in Table 11, are courtesy of Cameca, France. Received for review July 31, 1972. Accepted November 30, 1972.
Determination of Lead, Uranium, Thorium, and Thallium in Silicate Glass Standard Materials by Isotope Dilution Mass Spectrometry I. L. Barnes, E. L. Garner, J. W. Gramlich, L. J. Moore, T. J . Murphy, L. A. Machlan, and W. R . Shields Analytical Chemistry Dwision, Institute for Materials Research, National Bureau of Standards, Washington, D C 20234
Mitsunobu Tatsumoto and R. J. Knight U.S. Geological Survey, Denver, Colo. 80225
A set of four standard glasses has been prepared which have been doped with 61 different elements at the 500-, 50-, 1-, and 0.02-ppm level. The concentrations of lead, uranium, thorium, and thallium have been determined by isotope dilution mass spectrometry at a number of points in each of the glasses. The results obtained from independent determinations in two laboratories demonstrate the homogeneity of the samples and that precision of the order of 0.5% (QSYOL.E.) may be obtained by the method even at the 20-ppb level for these elements. The chemical and mass spectrometric procedures necessary are presented. 880
ANALYTICAL CHEMISTRY, VOL. 4 5 , NO. 6, MAY 1973
Approximately six years ago, the staff of the Office of Standard Reference Materials and the Analytical Chemistry Division of the National Bureau of Standards became concerned about the almost complete lack of suitable standard materials for trace element analysis. Efforts involving more than 100 persons within NBS and many others who performed analyses, data comparisons, surveys, etc., have resulted in the availability of about a dozen well characterized standard materials for the areas of ceramics and glasses, clinical, biological, and mineral trace element chemistry. About an equal number are to be released in the near future.
One of the first of the materials to be selected for analysis purposes was a silicate matrix containing many elements at a series of graded concentration levels. Since a material such as this did not exist and, in fact, had never before been prepared, the aid of glass chemists at the Central Research Laboratory, Corning Glass Works, Corning, N.Y., was enlisted. This group graciously agreed to make a quantity of material suitable for trace element analyses. Corning materials scientists prepared a large quantity of an extremely pure glass base material. A very high purity silica sand was imported from South Africa, calcium oxide was selected from a lot very low in strontium, and finally a base material, nominally 72% SiOz, 12% CaO, 14% NazO, and 2% A1~03,was prepared and analyzed to ensure that trace elements were a t a very low level. Three 100-kilogram batches of the matrix were prepared and doped with the appropriate amounts of a glass mix containing 61 elements to give nominal concentrations (as the oxide) of 0.02 ppm, 1 ppm, and 50 ppm. A fourth 100-kilogram batch was prepared to contain 500 ppm and does not represent a serial dilution of the original melt as do the other three. Starting with the base glass and progressing to higher concentrations, each batch was remelted in a large platinum crucible and, after stirring for twelve hours, was drawn into approximately 1.2 cm diameter cane using a modified Czochraliski technique. This method was chosen by Corning since it ensured that surface contamination by nozzles, etc., was minimized. Each batch was drawn in an essentially continuous process covering 60 or more hours to give 200 or more meters of cane. During the drawing, the cane was cut into 100 or more two-meter lengths which were carefully numbered serially so that the entire history could be recorded. It is planned that ultimately all of the 61 elements added to these silicate glasses will be determined by two or more analytical methods or, where it is known that a particular method shows no inherent bias, by two separate analysts. The choice of the elements lead, uranium, and thorium for the initial analytical effort was that of the authors who felt that these materials would be suitable as standards for the determination of these elements in rocks and minerals for the Pb-U-Th method of geochronological dating. In this paper, the methods used and the results obtained for the analyses of lead, uranium, thorium, and thallium in these materials are reported.
EXPERIMENTAL Mechanical Preparation. The sections of cane selected for analysis were cut into 10-cm long sections and mounted on glass plates using a pure thermoplastic resin. Using diamond saws and a wafering machine dedicated to this work only, the samples were cut into wafers 1 m m and 3 mm thick. Only particulate-free JP-4 jet engine fuel was used as a coolant. After cutting, the wafers were removed from the plates by refluxing ACS reagent grade acetone over the samples, followed by ultrasonic cleaning in fresh portions of acetone. Particular care was taken to ensure that no cross contamination between the four concentration levels could occur. Chemical Preparation. The chemical preparation and subsequent mass spectrometric analyses were performed independently in two different laboratories. Although many of the steps were similar they were not necessarily identical and where important differences in procedures were used both are given or, where previously published, referenced and identified as steps used at the National Bureau of Standards (NBS) or a t the U.S. Geological Survey (USGS). Each wafer was cleaned by wiping with a lint-free paper towel saturated with ethanol and by immersion in (1 + 9) nitric acid
for five minutes to remove surface contamination. The wafers were then washed with distilled water, air dried, and weighed. The chemical methods used a t USGS for lead, uranium, and thorium have been published by Tatsumoto et al. f l i . Those used at NBS are given below. Each weighed wafer, approximately 1 gram, was transferred t o a 30-ml Teflon (Du Pont) beaker and the appropriate amount of a spike of 206Pb + z03Tl, 235U, or z30Th was added by weight aliquoting from a cleaned plastic syringe (2). Blanks were prepared a t the same time by adding spike solution to beakers without samples. Throughout all of the remaining steps, the blank solutions were treated exactly as the sample solutions. Ten milliliters of (1 + 1) hydrofluoric acid was added to each beaker, the beakers covered with Teflon covers and placed on a hot plate a t low temperature for 16 hours. The solutions then were evaporated to dryness, 5 ml of perchloric acid added, and the solutions slowly evaporated to fumes of perchloric acid to convert insoluble CaFz to soluble C a ( C 1 0 4 ) ~and to remove excess perchloric acid. Following this initial dissolution, the elements were separated for mass spectrometric analysis. Lead and thallium were separated from the sample solutions by electrodeposition with a method modified from t h a t of Muller (3). For this, the sample solutions were evaporated to dryness, taken up in a few milliliters of water, and again evaporated to dryness. The residue was then taken up in 10 ml of water to which was added 1 ml of a 0.5N nitric acid solution containing about l mg of copper. The solution was electrolyzed at 0.02 A (about 2 volts) using 50-mil platinum wires for both anode and cathode. The copper was added during some of the early work to convert the platinum cathode to a copper one which would prevent the formation of nitrous acid; however, it was later determined that this was not necessary and the addition of copper was discontinued. The solution was stirred magnetically during the electrolysis which was continued for 6 to 8 hours. The anode was then washed with water and the PbOz and T1203 were stripped from the electrode with a dilute nitric acid-hydrogen peroxide mixture. After evaporation the residue was taken up with one drop of (2 + 98) nitric acid and reserved for mass spectrometric analysis. This procedure gave recoveries of greater than 90% with samples as small as 1pg. Uranium was separated, after the initial dissolution steps, by dissolving the residue in 1 ml of (1 + 1)nitric acid and adding the solution to a strongly basic anion exchange column (6 mm X 7 cm, AG 1 X 8, 100-200 mesh), previously cleaned with several ml of (1 + 1) nitric acid followed by several milliliters of (1 + 49) nitric acid. The column was washed with a small volume of (1 + l ) nitric acid and then the uranium eluted with (1 + 49) nitric acid. The uranium eluate was evaporated t o dryness, taken up and passed through the column a second time as above. The uranium solution, collected in a Teflon beaker, was evaporated to dryness, dissolved in (1 + 19) nitric acid and reserved for mass spectrometric analysis. Thorium was separated by picking u p the residue from the HF-HC104 sample dissolution in 2 ml of (3 + 1) nitric acid and transferring the solution to an anion exchange column (6 mm X 7 cm, AG 1 X 4, 100-200 mesh), previously cleaned with several milliliters of (3 + 1) and then (1 + 49) nitric acid. Most of the other elements present were removed with 2 ml of (3 + 1) nitric acid and then 4 ml of (1 1) nitric acid. The thorium was then eluted with 7 ml of 0.3N nitric acid. The solution was evaporated to dryness, taken u p in 15 drops of (1 + 1) nitric acid and added to a column as above except the second column was only 2 cm long. Approximately 2.5 ml of (1 + 1) nitric acid was used to re'move remaining traces of most other elements, and then the thorium was eluted with 3 ml of 0.3N nitric acid. After being evaporated to dryness, the residue was redissolved in (1 + 19) nitric acid and reserved for mass spectrometric analysis. Mass Spectrometric Analysis. Each of the elements reported here was analyzed using one or more of a number of 12-inch, 68" radius or 12-inch, 90" radius mass spectrometers available a t NBS or a t USGS. Except for the radius, all instruments are identical being equipped with thermal ionization, thin lens, "z" focus-
+
( 1 ) Mitsunobu Tatsumoto, Roy J. K n i g h t , and Maryse H. Delevaux,
"Uranium, Thorium and Lead Concentrations in Three Silicate Standards and a Method of Lead Isotopic Analysis, Geological Survey Research 1972," U . S . Geol. Surv. Prof. Pap. in press. (2) W . R. Shields, Ed., Nat. Bur. Stand. ( U . S . ) , Tech. Note No. 546 (1970). (3) H . Muller,Z. Anal. Chem., 113, 161 (1938). A N A L Y T I C A L C H E M I S T R Y , VOL. 45, N O . 6, M A Y 1973
881
Table I. The Analytical Results in pprn (micrograms/gram) for Lead, Uranium, Thorium, and Thallium Tabulated YS. the Rod Number Sampled for the 500, 50, 1, and 0.02 ppm Glass Standard Material as Obtained at Two Laboratories 500 ppm Rod No.
Lead NBS
USGS
---__
2 13 18 48 56 66 78 106
426.5 426.2 425.6 426.1 426.9 426.0 462.2 425.7
425.9 426.0 425.0 425.4 425.6
Average
426.15 t0.41 10.98
0
95% L.E.
NBS
Uranium USGS
_---_-__-
461.5 461.8 461.3 461.2 462.2 461.1
461.1 462.0 460.3 462.7
--_-_
461.6
425.58 t o . 40
461.5 t0.4 t1.0
-_-__
t1.11
Thorium USGS
-----
Thallium NBS
__--_
456.70 457.67 457.72 457.88 456.64 457.27 456.63 457.34
457.1 453.5 456.2 453.8 456.5
-_-_-
63.6 60.2 61.5 61.2 62.3 61.4 62.3 62.0
461.3 11.0 t3.1
457.23 to. 52 21.2
455.4 t1.6 24.6
61.8 11.0 t2.4
-----
-----
NBS
-----
50 P P Rod No.
Lead
Uranium USGS
NBS
USGS
NBS
2 37 44 68 75 114
38.57 38.68 38.64 38-51 38.41 38.62
38.62 38.58 38.64 38.50 38.48
_-_--
37.35 37.37 37.36 37.36 37.39 (37.63)a
37.36 37.35 37.33 37.54 37.48
Average
38.57 to.09 t o . 25
38.56 t0.07 10.19
37.37 to. 015 10.042
0
95% L.E. Special Cuts: 90 99
NBS
Thorium USGS 37.36 37.52 37.60 37.53
-----
37 .79 37 -78 37 .80 37.82 37.80 37.78
37.41 to.09 20.26
37.79 20. 017 20.045
37.55 t0.04 10.12
---_-----
Thallium NBS 15.66 15.81 15.75 15.59 15.54
15.73 15.68 t0.10
20.26
a Excluded from average. 37.41 37.42 1 PPm
NB S
USGS
Uranium NBS USGS
2 36 40 69 76 114
2.32
2.30 2.33 2.31 2.32 2.29
0.824 0.823 0.822 0.823
2.33
Aver age
2.33 t0.006
Rod No.
U
95% L.E.
Lead
---_
-_-2.33
-___
-____
NBS
Thorium USGS
----
__--_
0.828 0.831 0.828 0.824 0.827
0.823
----_
0.751 0.750 0.749 0.750 0.748 0.745
2.32 10.016 t0.044
0.823 +0.0007 tO.0020
0.827 t0.0025 r0.0070
0 .*749 co.002 k0.006
0.746 0.745 0.749 0.742 0.748.
_____
0.746 r0.003 10.008
Thallium NBS
_____ 0.270
-----
0.269 0.268 0.269 001
to.
0.02 ppm Lead
Rod No. NBS
USGS
2 33 43 51 61 76 130
1.87 1.89 1.90 1.86 1.87 1.88 1.98
1.87 1.86 1.83 1.83 1.84
Average
1.88 k0.014 t0.035
1.85 tO.018 10.050
0
95% L.E.
882
-.---__
Uranium NBS USGS
NBS
0.0715 0.0708 0.0716 0.0722 0.0721 0.0716 0.0721
0.0724 0.0722
0.0250 0,0249 0.0251 0.0256 0.0256 0.0254 0.0250
0.0278 0.0237 0.0251 0.0256 0,0254
0.0717 rO.0005 10.0012
0.0726 tO.0004 t0.0013
0.0252 10,0003 tO.0007
0.0255 10.0015 t0.0041
ANALYTICAL CHEMISTRY, VOL. 45, NO. 6, MAY 1973
--_-_-
0.0730 0.0730
-________--
Thorium USGS
------
Thallium NBS
___.__
ing ion sources, multielement, deep cage Faraday collectors, and a measuring circuit consisting of a calibrated vibrating reed electrometer, a constant zero expanded scale circuit, and a specially modified recorder. A detailed description of the instruments and the various components has been published (4-61. The mass spectrometric method used for lead was the so-called "silica gel" procedure used for small samples (Le.. up to 20 fig) of lead. This procedure suggested by Akishin et al. (7) and by Cameron et al. 181 has been modified [Shields (21, Tatsumoto ( I ) ] and while there are slight differences in the modifications the results of each are nearly identical with the lead 204/206, 207/206 and 208/206 ratios determined with an accuracy of &0.1%, 0.0770, and 0.1% respectively (95% L.E.). Thallium is determined mass spectrometrically on the same filament loading as the lead but a t a much lower temperature. This combined procedure has been previously published (2). The mass spectrometric procedure for lead, uranium, and thorium (USGS) has been described by Doe et al. (91. The uranium (NBS) procedure has been extensively studied and has recently been reported in detail by Garner et al. (10). Thorium (NBS) is determined by a procedure which is similar to the uranium procedure in all respects except for the final filament currents used. The final setting of filament current was made at 25 minutes and a current of 2.5-2.7 amperes was used.
RESULTS AND DISCUSSION The analytical results for the determination of lead, uranium, and thorium as obtained a t the two laboratories and for thallium as obtained at NBS are shown in Table I. Also shown on the table are the average, the standard deviation, and, where meaningful, the 95% limit of error for each of the groups of analyses. Since materials such as those used in this study had not been made previously, one of the major objectives was to examine the homogeneity of the glass rods. Within the experimental limits shown in Table I, the results indicate that this material, on the basis of 1-gram samples, is remarkably homogeneous for the four elements analyzed over a length of 400 or more feet. A small exception to this is shown in the uranium analyses for the 50-ppm glass where there appears to be a slight trend toward increasing uranium concentration with increasing rod number, and a t rod number 114 the value obtained is considerably outside the limits of experimental error. Many subsequent analyses have confirmed this high value while analyses of rods Number 90 and 99 which were made as special cuts gave values well within the range expected. No reasonable explanation can be offered for the apparent increase, especially when the amount present is well within the solubility limits for uranium in silicate glass and when such an effect was not noted either in the 500 ppm glass or in the 1- and 0.02-ppm material. We had deliberately chosen samples from the start and finish of the entire lot of this material for this set of analyses so that the maximum effects of any variation in concentration of an element would appear; however, it is intended that the first and last 10 meters of each material will be discarded and will never be used except in such studies. W . R. Shields, E d . , Nat. Bur. Stand. (U.S.), Tech. Note No. 277
(1966). Shields, Ed., Nat. Bur. Stand. (U.S.), Tech. Note No. 426 (1967). W. R. Shields, Ed., Nat. Bur. Stand. (U.S.), Tech. Note No. 456
W . R.
( 1968). P. A. Akishin, 0. T. Mikitin, and 8. M . Panchenkov, Geokhimiya, 5, 425-9 (1957). A. E. Cameron, D. H. Smith, and R. L. Walker, Anal. Chem., 41, 525-6 (1969). 6.R . Doe, Mitsunobu Tatsumoto. M . H. Deievaux, and 2. E. Peterman, "Isotope-dilution Determination of Five Elements in G.-2 (Granite), with a discussion of the Analysis of Lead, Geological Survey Research," U.S. Geol. Surv., Prof. Pap., 575-6, 61 70-81 77 (1967). E. L. Garner, L. A. Machlan, and W. R . Shields, Naf. Bur. Stand. (U.S.), Spec. Pub/., 260-27 (1971).
470
I-
URANIUM A
*Av "Av
= 461.5
"Av
= 455 4
= 461.3
460
a
THORIUM
450
0
420
410
400
1
LEAD
t 0
20
40
60
80
100
ROD NUMBER
Figure 1.
Analytical results for lead, uranium, and thorium in the
500 ppm glass plotted as concentration ( p g / g ) vs. increasing rod number obtained at two different laboratories *NBS, Section 310.06, all sample points. **USGS,Denver, M . Tatsumoto, five sample points
The error limits increase from about 0.2% for the 500ppm material to about 2% for the 0.02-ppm glass as would be expected but even in the case of the uranium and thorium where the actual concentration is about 70 and 25 ppb, respectively, the error has not increased significantly. Even for the vast majority of individual sample points (rods), the agreement between laboratories is quite good. The largest disagreement between laboratories both for the average and for sample points occurs in the case of the analyses for thorium in the 50-ppm glass. Such a systematic error is probably the result of a small error in the calibration of the isotopic spike used. The homogeneity of the glass materials as well as the level of interlaboratory agreement may be further demonstrated by plotting these data in graphical form. Such a plot for lead, uranium, and thorium for the 500-ppm glasses is shown in Figure 1 where the concentration in micrograms/gram us. rod numbers (each rod number represents about one meter of glass with rod Xumber one the start of the production process and the higher numbers, the finish of the pulling or cane making procedure). The same plot of concentration us. rod number is shown for lead, uranium, and thorium for the material with nominal concentration of 50 ppm in Figure 2. Note that the trend for increasing concentration of uranium for rods above Number 100 is shown in this plot. In Figure 3 the data for lead, uranium, and thorium in the 1-ppm glass are shown as a plot of concentration us. length of material and included in this figure are the data for uranium obtained by track counting. The wide spread in these data is undoubtedly the result of some radial inhomogeneity across the face of a single wafer (see below). The result of performing analyses at the ppm level or lower with even a moderately uncontrolled overall laboratory blank is demonstrated in Figure 3 and also in Figure 4 where the equivalent plot for the data obtained in the analyses of the 0.02-ppm glass is shown. During the early part of this work, the laboratory blank for a lead analyses was 4-20 nanograms (with approximately a 1ANALYTICAL C H E M I S T R Y , VOL. 45, NO. 6, M A Y 1973
883
=‘O
t
NBS High Blank
“Av
185
1.80
4
f ‘Av
a
*‘A”
= 37 79 = 37.55
THORIUM
= 185
L
,
NlUM
074
NBS Nuclear Track Counting
‘A“ =Oo717
E 072 *’A“
0
5
0 0729
u 070
I
URANIUM
% .
’
l3 ,‘ ’Av ~37.38
“Av
= 37 41
@ Spacial Cuts-aII rods numbered abova 1 0 0 discarded I
37.0 20
40
80
60
100
0
120
20
40
60
80
io0
120
R O D NUMBER ROD NUMBER
Figure 2. Analytical results for lead, uranium, and thorium in the 50 ppm glass plotted as concentration (pglg) vs. increasing rod number obtained at two different laboratories *NBS, Section 310.06, all sample points. **USGS, Denver, M. Tatsumoto. five sample points
2.4
2.3
2.2
.
URANLUM
0.84
cn
5
0 0.82 0
.
0
z
THORIUM
075
t+y>,
‘Av “Av
= 0.749
= 0.746
0 74
0
20
40
60
80
1W
120
Figure 4. Analytical results for lead, uranium, and thorium in the 0.02 ppm glass plotted as concentration (pg/g) vs. increasing
rod number obtained at two different laboratories *NBS, Section 310.06, all sample points. **USGS, Denver, M . Tatsumoto, five sample points
small inhomogeneities will be demonstrated if the overall laboratory errors were to be reduced by about an order of magnitude. In contrast, although a formal program of analyses has not been established, some evidence of radial inhomo‘geneity has been obtained. At USGS a quarter of a wafer of the 500-ppm material was used for analysis and the results indicate that the concentrations do vary across a single wafer. Carpenter (11) has also shown this same effect for uranium and boron using a nuclear track counting technique. For this reason, a single whole wafer is always used as a sample and no sub-sampling of a wafer is permitted. This rule includes grinding, crushing, etc., for subsequent sampling errors would invalidate the entire sample. Also demonstrated during the above analyses was the importance of a knowledge of the isotopic composition of the element. It was at first assumed that the isotopic composition of the uranium present was that of “natural” uranium or that:
234U= 0.0054 atom per cent 235U= 0.7200 atom per cent 238U= 99.2746 atom per cent
ROD NUMBER
Figure 3. Analytical results for lead, uranium, and thorium in t h e 1 ppm glass potted as concentration ( p g l g ) v s . increasing rod
An actual composition analysis indicated that the uranium in the 500-ppm glass was:
number obtained at two different laboratories
234U= 0.0010 atom per cent
*NBS, Section 310.06, all sample points. **USGS, Denver, M. Tatsumoto, five sample points
235U=
gram sample) at NBS but 3-4 nanograms a t USGS. With constant effort, this has been reduced to 2-3 nanograms at NBS and 1-2 nanograms or lower at USGS. This continuous effort is always necessary for analytical work at the trace levels. It may be seen in Figures 1-4 that while the material is homogeneous and the results of the two laboratories agree to within the error limits stated, there are definitely regions where the results fall on trends and both values tend to be high or low for certain rod groups. It is felt that 884
ANALYTICAL C H E M I S T R Y , VOL. 45, NO. 6, MAY 1973
0.2376 atom per cent
0.0043 atom per cent 238U= 99.7571 atom per cent 236U=
The uranium composition in the 50-, 1-, and 0.08-ppm glasses was intermediate between these limiting values. This change, of course, has a marked effect on an isotope dilution analysis where the 2351238 ratio is used and subsequent investigation showed that nearly all uranium now supplied as reagent chemicals is uranium depleted in 235U and the atomic weight of each batch cannot be assumed if an accurate value is needed. (11) 8.S. Carpenter, Anal. Chem., 44, 600-602 (1972)
The agreement between laboratories for these analyses was particularly gratifying and we feel demonstrates both that isotope dilution mass spectrometry can be a very precise and accurate technique and, more importantly, that though techniques or methods may vary, if these are carefully evaluated, reproducible results may be obtained a t different laboratories. We are now confident that even the small differences that are shown here are due almost entirely to differences
in laboratory blank values and that because of substantial improvements made in this area since this work was done, even better agreement would be obtained were the work to be repeated. Received for review, October 26, 1972. Accepted December 15, 1972. Publication authorized by the Director, U S . Geological Survey.
Multicategory Prediction Using Arrays of Binary Pattern Classifiers Wayne L. Felty’ and Peter C. Jurs
Department of Chemistry, The Pennsylvania State University, University Park, Pa. 76802
Arrays of binary pattern classifiers have been used previously in a branching tree and parallel manner for predictive purposes, and recently the use of Hamming-type binary codes has been suggested. In the present work, prediction of carbon number for a set of C3-C10 organic compounds and a subset of c4-c10 hydrocarbons, using mass spectrometric data, has been shown to be feasible by means of three types of binary codes, two with errorcorrection capability. Carbon number prediction was also carried out by the parallel and branching tree methods and the predictive abilities and ease of implementation for the various classification schemes compared. The highest prediction, 95.4%, was obtained for the hydrocarbon data set using both the branching tree and Hamming (7,4) binary code.
Previous studies have demonstrated the usefulness of learning machines utilizing binary pattern classifiers for the interpretation of complex chemical data, particularly low-resolution mass spectra ( I ) . In the present work, several methods of combining binary decision makers to yield quantitative prediction are investigated. Binary pattern classifiers, or threshold logic units, have been described in detail by Nilsson ( Z ) , and some chemical applications have been discussed by Isenhour and Jurs ( I ) . A multidimensional piece of data, e.g., a mass spectrum, is represented by a pattern vector, X = ( x l , x z , . . . , x d ) , where the xi's are, for example, the intensities of selected m l e positions. The decision surface is given by the weight vector, W E (wl,wZ,. . .,wd+l).The classification process involves taking the dot (inner) product of these two vectors to give a scalar, X.W = s. The algebraic sign of the scalar indicates into which of two categories the pattern vector is classified. The weight vector for a particular decision is obtained by means of a training algorithm employing error-correction feedback, iteratively modifying some initial weight vector so as to correctly classify the members of a known set of pattern vectors. Present address, Department of Chemistry, Mansfield State College, Mansfield, Pa. 16933. (1) T. L. Isenhour and P. C. Jurs, Anal. Chem., 43(9). 20A (1971) and references cited therein. ( 2 ) N. J. Nilsson, “Learning Machines,” McGraw-Hill, New York, N.Y., 1965.
While a number of chemically significant questions can be answered by a binary decision, such as the presence or absence of a certain functional group or element, multicategory decisions, such as the number of certain groups or atoms per molecule, must also be made. One means of achieving multicategory classification is through the use of an array of binary classifiers. Perhaps the most obvious manner of combining binary classifiers is the branching tree method, which has been applied to the determination of empirical formulas ( 3 ) . More often, a parallel arrangement of classifiers, each with a different cutoff, has been used ( 4 ) . A third method, utilizing Hamming-type binary codes and offering the interesting possibility of self-detection and -correction of errors, has been recently suggested by Lytle ( 5 )but was not implemented. While the use of binary codes has several inherent advantages, the feasibility of the method depends upon whether the weight vectors for the pertinent binary pattern classifiers can be successfully trained. The present investigation answers this crucial question, using the test problem of carbon number prediction. The three methods of pattern classification, branching tree, parallel, and. binary code, are then compared with respect to carbon number prediction as well as general features.
DATA AND COMPUTATIONS Data Set. Low resolution mass spectra were obtained from a collection purchased on magnetic tape from the Mass Spectrometry Data Centre, Atomic Weapons Research Establishment, United Kingdom Atomic Energy Commission. Six hundred spectra, pertaining to compounds of molecular formula C3-10H2-zz00-4N0-2, were taken from that portion of the tape comprised of American Petroleum Institute Research Project 44 spectra. The spectra were randomly divided into a training set of 200 and a prediction set of 400. A second data set, consisting of the hydrocarbon subset of the 600 spectra, was also used. Five C3 hydrocarbons were deleted because of the low population of this category. The remaining 372 C4-ClO hydrocarbons were randomly divided into a training set of 200 and a prediction set of 172. The same training and (3) P. C. Jurs, E. R. Kowalski, and T. L. Isenhour, Anal. Chem., 41, 21 (1969). (4)
P. C. J u r s , B. R . Kowalski, T . L. Isenhour. and C. N. Reilley, ibid.,
42, 1387 (1970). (5) F. E. Lytle. ibid., 44, 1867 (1972).
ANALYTICAL CHEMISTRY, VOL. 45, NO. 6, M A Y 1973
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