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Rare-gas dating, III. Evaluation of a double-spiking procedure for potassium-argon dating
Earth and Planetary Science Letters, 34 (1977) 411-418 © Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
411
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RARE-GAS DATING, III. E V A L U A T I O N OF A DOUBLE-SPIKING PROCEDURE FOR POTASSIUM-ARGON DATING C.R. MACEDO, C.V. COSTA, J.T. F E R R E I R A , M.P. F E R R E I R A and J.H. REYNOLDS 1
Laborat6rio de Geocronologia, Departamento de Geologia, Universidade de Coimbra, Coimbra (Portugal)
Revised version received January 1977
A double-spike method for K-Ar dating is described. Use of long-lived 39Ar in addition to the usual 3BAr in the spike permits argon isotopic discrimination occurring after insertion of the spike to be monitored at the same time as ages are determined. A "bootstrap" (self-contained) method of calibrating the spike for isotopic composition is described which, when used appropriately, gives final ages which are independent of the published isotopic composition of the terrestrial atmospheric argon used as a comparison gas. The method calls for a mass spectrometer which resolves adjacent isotopes to a high degree. We have tested the method nevertheless with a mass spectrometer of relatively low resolving power, the AEI MS-10, and found it to be successful in part and without any disadvantages with respect to conventional techniques in those instances where the method fails because of insufficient resolution. That is, we find the discrimination factor inferred in runs on young rocks and blanks to be valid and useful. That factor changes by as much as 1.3% over the life of a filament in the ion source of the MS-10, proving that close control of the discrimination factor is essential for analytical precision with the instrument. These assertions are documented graphically with a compilation of data which represents more than two years experience with the method. We also report measurements of the mass discrimination of the MS-10 and its linearity with mass which indicate that the latter quantity is acceptable when the repeller voltage for the ion source is close to +1 V and is unacceptable otherwise. The spike material is available, upon request, to those laboratories which decide firmly to undertake further testing of the method.
1. Introduction All dating methods have particular problems in precision. In the K - A t method, precise measurements of the ratio 36Ar/4°Ar are required, especially for young rocks, because the percentage error in that ratio is amplified by the factor [atmospheric Ar]/[radiogenic At] to become the percentage error in the amount o f radiogenic argon [1 ]. One o f the essentials in the method is therefore to have good control over the discrimination o f the mass spectrometer. (We leave aside in this paper the question o f natural variations in the ratio 36Ar/4°Ar for the atmospheric or extraneous argon in the samples, which can sometimes lead to even greater errors in determining the radiogenic
1 Permanent address: Department of Physics, University of California, Berkeley, California 94720, U.S.A.
argon content. That is, good control over isotopic discrimination in K - A r dating is a necessary condition for analytical precision in the work but not a sufficient condition for obtaining meaningful age determinations.) The usual method for monitoring the discrimination is to interject runs on argon o f known isotopic composition (atmospheric argon) into the sequence o f runs on argon from rocks. This traditional method is sound, provided the discrimination o f the instrument is relatively stable from day to day, but tedious. Another method to monitor the discrimination, which has been possible since 1959 or before but has not been tried hitherto, is to add long-lived 39Ar to the 38Ar spike. Each measurement made then contains a built-in determination o f mass spectrometer discrimination and of other fractionation processes for the isotopes which took place after the introduction o f the spike. This double-spike technique was first used by Wetherill [2] in a search for
412 molybdenum isotope anomalies in iron meteorites. In establishing a new K - A r laboratory at Coimbra, we instituted some new techniques which we have described in papers I and lI [3,4]. Even though we used a mass spectrometer of limited resolving power, we also included a trial of the double-spike method in the work. This paper reports our findings concerning that method. Failure to test the method under totally favorable conditions is compensated by useful facts we have established about discrimination, its linearity, and its variability in the MS-10, an instrument which is widely used in K - A r dating.
2. The spike gas The spike gas, designated "38Ar", was prepared at some time prior to 1959 by neutron irradiation of a previously outgassed chloride salt. The preparation was "Special Work No. 10591" at the Oak Ridge National Laboratory of what was then the U.S. AEC (now U.S. ERDA). Because of high flux in addition to high fluence for the irradiation, a large amount of long-lived (T1/2 = 265 years) 39Ar was produced by way of the second-order reaction 38Ar + n ~ 39Ar. The content of 36Ar in the sample is low (Table 1). Both these qualities make the spike gas useful for our purpose. The original sample of ~0.4 cm 3 STP 38Ar was split into 12 parts. One of these twelfths was cleaned with a Ti-Zr getter and further split into twelfths, each of which is suitable for filling a pipette which dispenses 10 -4 of the remaining gas per cycle of operation. Several of these 1/144 fractions were consumed in this study. Others remain available (from the Department of Physics, University of California, Berkeley) to other laboratories who firmly decide to institute use of the double-spike technique and who request spike material for that purpose.
3. Determination of the isotopic composition of the spike The double-spike control depends upon knowing accurately the isotopic composition of the spike. Fortunately this composition can be determined, with the same mass spectrometer whose discrimination is to be monitored, by a bootstrap (self-correcting) pro-
cess. First one measures the isotopic composition of the spike gas. With four isotopes present, there are three measured ratios. Next one measures the isotopic composition of a mixture of the spike gas and atmospheric argon. The atmospheric argon is assumed to have the standard isotopic ratios which were determined in 1950 by Nier [5], although this assumption (see below) is not essential. The second measurement provides three more measured ratios. A set of six simultaneous equations can then be written which include six unknowns: the three isotopic ratios for the spike, which we seek; the discrimination factor for the mass spectrometer for the first run (assumed to be linear with mass difference for any pair of isotopes constituting a ratio); the discrimination factor for the second run; and the relative amounts of the two kinds of argon in the mixture. By solving the six equations, one determines the six unknowns. The bootstrap determination was carried out twice In November 1971 large gas samples of spike and spike-air-argon mix were measured in the mass spectrometer. In May 1972 the process was repeated. This time the spike gas was a "large spike" (approximately 16 regular spikes in size) which can be extracted routinely from the pipette on our apparatus. The spike-air mix was contrived by adding a regular spike to the gas released upon melting 2 g of powdered Pyrex glass. The details of these measurements and the results are set out in Table 1 and in the notes for that table. Our final determination of the isotope abundance ratios in the spike is accurate to about 1 part in I000 for 3SAt, 39At,and 4°Ar. The 36AI/38Ar ratio is determined to within 5 parts in 1000 (errors quoted are 0.50 confidence level or 0.67o).
4. Mass discrimination of the MS-10 mass spectrometer and its linearity One of the essential assumptions in the doublespike method is that the mass discrimination of the mass spectrometer is linear with respect to mass. It was important, therefore, to study that question for the mass spectrometer we used. What was done was to make isotopic measurements of one of our spikeair mixtures under various source conditions. In these measurements we emphasized changing the ion repeller voltage for the source, because the discrimination
413 TABLE 1 Bootstrap determination of isotopic composition of spike. Errors are 0.5 confidence level (0.67cr) Determination
Desig.
2 9 - 3 0 November 1971 3 Spike-air-argon mixed as gases
A
13-17 May 1972 4 Spiked run on powdered Pyrex no overlap 5 corrections with overlap 6 corrections with partial 7 overlap corrections B Combined 8
A +B
(36Ar/38Ar)spike
(39Ar/38Ar)spike
(40Ar/38Ar)spike
FS 1
FM 1
0.0011425 -+0.0000021
0.46484 2 -+0.00020
0.11348 ±0.00013
-0.623% ±0.049
-0.852% ±0.024
0.0011742 -+0.0000016 0.0011796 -+0.0000016 0.0011765 -+0.0000028
0.46453 2 -+0.00025 0.46348 2 -+0.00025 0.46408 2 ~0.00051
0.11759 ±0.00015 0.11706 ±0.00015 0.11737 -+0.00027
-0.411% -+0.062 -0.183% ±0.062 -0.314%
-0.317% -+0.019 -O.311% ±0.019 -0.314~
0.0011660 •+0.0000055
0.46446 2 ±0.00033
0.11737 -+0.00015
t FS = disc. correction calculated for run on spike; F M = disc. correction calculated for run on spike-air mixture. In both cases (MI Ar/M2Ar)true = (MI Ar/M2Ar)apparent [ 1 + F(M2 - MI )]. Ion source settings: 50 ~A, +1 V. 2 Corrected for radioactive decay to November 2 9 - 3 0 , 1971. 3 Large samples. Overlap corrections applied after study of peak shape. Largest correction (to adjacent heavier isotope) was 0.00018 × parent peak. Hydride effect makes small, constant, additive changes in (39Ar/38Ar) and (40Ar/38Ar) in spike gas which we have ignored by treating them as part of the 39Ar and 40Ar in the spike gas. 4 Spike was "large spike" (= ~ 16 regular spikes) from pipette; spike-air mix was evolved by melting 2 g powdered Pyrex glass in presence of regular spike from pipette. 5 For comparison purposes. 6 Affected only ratio (39Ar/38Ar) in run on spike-air mix. 7 Overlap correction in spike-air mix judged excessive, based on discrepancy between F S and F M . Reduced correction by 58% which made calculated F S and F M agree. Difference between corrected and uncorrected spectra compounded as error with other errors. 8 Designate vector composition of A by A, of B by B--',of air argon by "T. Since B sample was from pipette tank, it probably contains a trace of air with respect t o A sample. Revised ~ was vector with terminus on line joining ~ and T which passed closest to B. A + B is average of revised A and B. Oak Ridge analysis of source gas for spike, made in 1959 and corrected for radioactive decay, is 36Ar : 38Ar : 39Ar : 40Ar = 0.0010 : ~ 1 : 0.4650 : 0.1158.
is k n o w n t o c h a n g e s t r o n g l y w i t h t h a t p a r a m e t e r [6]. We also e x p e r i m e n t e d s o m e w h a t w i t h varying t h e e l e c t r o n t r a p c u r r e n t . All d i s c r i m i n a t i o n values inferred are relative t o a s t a n d a r d c o n d i t i o n , i.e. 50 ~tA trap c u r r e n t a n d +1.0 repeller volts. The results are i n t e r p r e t e d as s h o w i n g t h a t t h e l i n e a r i t y in discrimination worsens as o n e m o v e s s u b s t a n t i a l l y a w a y f r o m +1.0 repeller volts. Fig. 1 e x h i b i t s d i s c r i m i n a t i o n ratios (relative t o s t a n d a r d settings) for t h e argon s p e c t r u m as m e a s u r e d w i t h 11 d i f f e r e n t source c o n d i t i o n s . Typical errors are s h o w n . F o r 9 o f t h e s e , t h e t r a p c u r r e n t was 150
/~A a n d t h e repeller voltage varied b e t w e e n e x t r e m e s o f - 1 . 4 V a n d +6 V. F o r the o t h e r t w o s p e c t r a , the trap c u r r e n t was 5 0 / I A . F o r positive values o f the repeller voltage, t h e spectra vary in a regular way, t h e relative d i s c r i m i n a t i o n increasing w i t h repeller voltage. For negative values o f t h e repeller voltage, the disc r i m i n a t i o n o f t h e s y s t e m is m u c h m o r e capricious. At - 1 . 4 repeller volts ( w h i c h m a x i m i z e s t h e sensitivity for a r g o n ) the d i s c r i m i n a t i o n a n d its c u r v a t u r e w h e n p l o t t e d vs. mass b o t h c h a n g e greatly w h e n the trap c u r r e n t is c h a n g e d f r o m 50 t o 150/~A. In o t h e r words, the c o n d i t i o n s for m a x i m u m argon sensitivity
414 1.10]
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--.--o (Discrimination ratio for 36Ar/38ArlMEASURED -- (Discrlminatlon ratio for 36Ar/38Ar)INFERRED
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+2V--J +3V ~ 150 #A unless otherwise indicated
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36
38
39
40
A t o m i c mass, M
Fig. 1. Relative discrimination patterns in the MS-10 mass spectrometer at Coimbra as deduced from runs, under different source conditions, of a spike-air-argon mixture. Electron trap current is 150 ~A unless otherwise stated. Discrimination patterns are relative to the pattern obtained with 50 #A, +1 V repeller. There is evidence from the small discrimination factors found thereby in Table 1 and Fig. 3 that these standard settings do indeed lead to less discrimination than others.
are exceedingly unstable conditions under which to attempt precise argon isotopic measurements. This limitation seems already to be widely appreciated by users of the MS-10 mass spectrometer. At +1.0 V the discrimination changed less between the two trap currents and, more importantly, n o t in its apparent linearity. It is this circumstance that makes us assign zero non-linearity to that value of the repeller voltage. We have no standard gas samples which can be measured with sufficient precision to confirm this supposition otherwise. What would be required would be calibration mixtures, precisely prepared, of separated isotopes such as were employed in Nier's 1950 study [5] in which he established the isotopic composition of argon and other elements using a mass spectrometer calibrated for discrimination by that means. Fig. 2, which was prepared from the data exhibited in Fig. 1, shows the apparent llnearity in discrimina-
L 0
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1 +2 Ion repeller
L
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t +6
voltage
Fig. 2. Linearity of the discrimination patterns for the MS-10 mass spectrometer at Coimbra, based upon data plotted in Fig. 1. "Discrimination ratio" is defined in Fig. 1. Plotted here is the difference between the measured discrimination ratio and that inferred from 39Ar]38Ar measurements, assuming linear discrimination. There is no difference, within experimental error, for +I V and +2 V as choices of repeller voltage. There are significant differences for +6 V, 0 V, -0.7 V and especially - 1.4 V as choices of repeller voltage.
tion for various values of the ion repeller voltage. Error information is included as well. One sees from this figure that there is a range of repeller voltages, extending roughly from +1 to + 2 V where the system is apparently linear within experimental uncertainty. It is in this region that the double-spike method has the best chance of success with an MS-10 mass spectrometer and it is in this region, with a few exceptions, that we made our measurements for this paper.
5. Resolving power of the MS-10 as it affects the double-spike method In order to interpret the results we have obtained in testing the double-spike method, the reader must appreciate the problems arising from the limited resolving power of the small mass spectrometer we used. For the most part our work during the period in question was on young basalts from the Madeira Archipelago. A typical sample might be one gram of basalt, 1.3 m.y. in age, containing 0.7% potassium
415 and enough atmospheric argon (0.15 X 10 - 6 cm 3 STP/g) so that the 4°Ar peak would be 80% air. As we shall see below, the maximum variation, due to discrimination, in the abundance ratio for adjacent masses that one encounters during the life o f a spectrometer filament is about 1.3%. For the example we are considering a 1% error in the abundance ratio for adjacent masses would generate an error in age of 0.3 m.y., which is a considerable error and shows that control o f the spectrometer fractionation is indeed required. We have examined the peak shape in the mass spectrometer very carefully when there were large argon samples being studied for calibration purposes (see above). As in all single-stage mass spectrometers, although to varying degrees depending upon the size of the instrument, there is in ours a broad background extending out from the peak and contributing to adjacent masses both high and low. The slow manner in which this background falls off with mass (only about a factor 3.2 per mass unit) indicates that scattered ions are the source o f the "tail". For argon samples 30 times larger than the argon sample taken above as an example, the tail o f the 40-peak at the mass 39 position is ~ 7 × 10 - s of the parent peak. It seems likely, since gas scattering should in part contribute to the tail, that its fractional size should diminish with sample size. Unfortunately this is a point we have not investigated systematically enough to write about. Thus let us take the 7 × 10 - s tail as an upper limit in our example. The effect o f an extraneous contribution to the 39-peak is to generate a false correction to the discrimination because our knowledge of the discrimination is based upon our measurement o f the 39Ar/38Ar ratio. In the present example (where 40 : 39 : 38 ~ 2 : 0.45 : 1) the error in age so generated is 0.009 m.y., which, one recalls, is an upper limit to the effect. It is clear that the double spike method can be expected to succeed in this instance: it would easily detect a genuinely large change in discrimination and the false correction from the tailing of the 40-peak would constitute at worst a negligible error in comparison with others. But with a sample o f radiogenic argon 30 times larger than the total argon in our example and without correction for the 40-tail at mass 39, the 39Ar/38Ar ratio would be altered very considerably - by 1.6%. In this case a clumsy application o f the double-spike
method can generate errors as large as the errors it is designed to correct.
6. The double-spike method in practice In the mass spectrometer runs made for age deterrninations or blanks, there are three measured isotopic ratios, permitting the determination o f three unknowns: the discrimination factor for the run, the ratio of radiogenic gas to spike gas, and the ratio of atmospheric gas to spike gas. The computer program used to solve this problem at Coimbra prints out all relevant quantities for each run as well as a complete error analysis. From these print-outs we have prepared a plot (Fig. 3) which displays the complete history o f our work with the double-spike method between late 1971 and early 1974. The reader should refer to this figure for the discussion which follows. In Fig. 3 we have plotted the computed value o f 100F (see Table 1 for a precise definition o f F ) vs. the serial number o f the spike used in the run. The meaning of 100F = 1 is that there is a discrimination factor 1.01 for the abundance ratio o f adjacent isotopes; o f 1 0 0 F = 2, a factor 1.02, etc. Every spike used for which there was a value of F obtained has been plotted. The occasional use of large spikes (equivalent to ~ 1 6 regular spikes) leaves a gap of 15 abscissa units in the plot which the reader can, in his mind's eye, close. We chose not to, for simplicity o f plotting. The large spikes occur at a spike nos. 63, 91 (a spike of unorthodox size), 2 9 7 , 3 2 5 , 3 4 1 , 3 5 7 , 3 7 3 , and 390. The gap starting at spike no. 210 occurs because o f unreduced data. The most impressive feature o f Fig. 3 is that for favorable samples - i.e. for young rocks or blanks, in runs where there is good gas cleanup and where no other experimental problems arise - the double-spike technique works, even with a mass spectrometer o f low resolving power. The points in question are plotted as circles, closed for samples and open for blanks. With a few exceptions those circles fit trend lines which drop off towards more negative F values as the filament ages and then rise again discontinuously when a new filament is installed. The mean in the probable error o f 100F in those determinations is very close to 0.1. How the errors are distributed indicate that there may be some residual systematic errors
416 I
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3 Miscellaneous problems I • Large spike, old samples ? Unorthodox settings
• Runs on young rocks o Blanks ' O l d rocks Dirty gas samples
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L- N E W
77 L NEW FILAMENT
-6
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50
100
3
NEW FILAMENT
FILAMENT
J
I
150
200 Spike n u m b e r
I
I
I
250
300
350
400
Fig. 3. A complete plotting of percent discrimination factors for adjacent isotopes, as defined in Table 1, and computed for all runs made at Coimbra between late 1971 and early 1974. Valid trends for the discrimination factor are obtained in runs on young rocks and blanks. The discrimination factor drops with increased filament age.
in the measurement o f F not always under our control. Nevertheless the evidence is strong that the trend lines are valid representations o f F. The excursions in the trend lines are large enough and different enough from one filament to another so that for accurate K - A r dating the mass discrimination must be monitored by some means at frequent intervals. Another striking feature of Fig. 3 is that the old rocks, when run with the regular spike, yield F values which fluctuate widely with respect to the trend lines. These are runs where there is a substantial tail from mass 40 at the 39 position and a corresponding distortion of the 39Ar/38Ar ratio on which the double-spike method depends. We routinely attempt to correct the 39Ar peak for this tail but it is obvious that the correction is insufficiently accurate on the average. Cases o f undercorrection and overcorrection occur with similar frequency. If the quantity o f the spike is increased sixteen-fold as it was for five o f the last six old rocks plotted in Fig. 3, the F values deduced are much closer together and are distributed around a reasonable value as inferred from the runs on young rocks. This
fact indicates that the discrimination o f the mass spectrometer has not been altered by the large gas samples from its usual value, but that our ability to measure it from the 39Ar/38Ar ratio has been impaired The best way to calculate ages for old rocks is by the usual, single-spike method in which the 38At peak is used as an internal standard and the F value is taken from the trend line based on the smaller gas samples. It should be clear from this discussion that, even with the MS-I 0 and under-spiking we have adequate control of the discrimination of the mass spectrometer for old rocks provided we take care to interleave runs on young rocks or blanks into the measuring sequence o f runs on the old rocks. We emphasize that none o f these problems about old rocks arise when using a mass spectrometer of sufficient resolving power for the double-spike method or when dating them by the conventional single-spike method where less resolving power is needed. One notes additional "pathologies" in Fig. 3: gas samples which were not adequately purified give discordant values for F ; samples run with u n o r t h o d o x
417 settings for the ion source gave discordant and fluctuating values of F; samples for which there were abnormal experimental problems (e.g. "much air", "38-peak very unstable", "pump valve open briefly by mistake", "brief ion-gauge pumping of sample by mistake", "vacuum-tube burned out - sample in spectrometer for 8 hours") sometimes gave obviously fallacious values for F.
7. Effect on the method of errors in the assumed isotopic composition of terrestrial argon Since we had systematized the computations for this work, it was a simple matter to investigate the effect upon our results of an error in the assumed isotopic composition of terrestrial air argon, which was that published by Nier [5]. We simply had to change the assumed value of (36Ar/4°Ar)terrestrial in two computer programs. We carried out these calculations for two revised values of Nier's atmospheric argon - one in which we increased the 36Ar/4°Ar ratio 2% and one in which we increased it by 4%. The samples we then examined, with these revised data, were (1) a sample of our calibration basalt, BCR-2 [4], (2) a young basalt (sample l-B) [4] from Madeira, and (3) a Precambrian hornblende "HBDE-248" studied both in this laboratory and elsewhere by Berger [7]. Inclusion of the calibration basalt, BCR-2, in this sequence of runs was crucial because it was upon analyses of BCR-2 that our spike pipette calibration depended. It is easy to see that if our calibration of the spike were made in a manner which did not depend upon the discrimination in our mass spectrometer, the error in atmospheric argon would be propagated through the calculations in such a way as to influence our dates. That is, the error in atmospheric argon would cause us to misjudge our spectrometer discrimination, which would cause us tc~ measure falsely the 4°Ar/38Ar ratios in our unknowns, and thereby (since our calibration would be "absolute") measure our ages falsely. Using the mass spectrometer in the calibration process, however, leads to a cancellation of errors. This is illustrated by the ages we obtained, using modified values for the isotopic composition of atmospheric argon, when we carried through the whole process anew, including the calibration o f the spike pipette f r o m the run on BCR-2.
For a +2% change in (36Ar/40Ar)terrestrial the argon content and age of sample Madeira basalt 1-B [4], for which the standard calculations gave an age of 1.2 m.y. and an atmospheric argon content of 80%, changed by only +0.03%. The argon content of HBDE 248, with a standard age of 1364 m.y. and an atmospheric argon content of 1.5% [7], changed by -0.006%. The corresponding changes when the change in the isotopic composition of atmospheric argon was doubled were +0.06% and -0.012%. Since these samples cover an enormous range in age and contamination by atmospheric argon, we can be sure that the method is independent for all practical purposes of any reasonable error in Nier's values for the isotopic composition of air argon, provided the calibration o f the spike constant is based upon measurements made with the same mass spectrometer and not by some absolute means.
8. Summary The double-spike method works. With a mass spectrometer of adequate resolving power there is obtained, along with the dates, a continuous monitoring of mass spectrometer discrimination which is essential for dating, because that discrimination, at least in some mass spectrometers, varies with the age of the filament. With a mass spectrometer of marginal resolving power runs on young rocks and blanks can monitor the discrimination. Provided such runs are interspersed in the measuring sequence, old rocks can be dated with the same amount of spike as used for young rocks. For such determinations on old rocks, the discrimination factor based on runs with young rocks should be used in single-spike calculations. This is because underspiked runs on old rocks give false discrimination factors if there is insufficient resolving power of the mass spectrometer. Unless the laboratory intends to use the 39Ar-4°Ar dating technique [8], there is no disadvantage to employing a double spike of the type used in this work, and there are substantial advantages.
Acknowledgements We thank Dr. G.W. Berger for running the computer programs for section 7. Establishment of the
418 Laborat6rio de Geocronologia in the Departamento de Geologia at Coimbra has been a joint project between the University of Coimbra and the University of California, Berkeley. The work has been supported in part by the Arthur L. Day Fund of the U.S. National Academy of Sciences, by the U.S. National Science Foundation, and by the Instituto de Alta Cultura, Lisbon. One of us (J.H.R.) was a Hays-Fulbright Scholar in Portugal during the early stages of this work and has made subsequent visits supported in part by the Day Fund, by the Instituto de Alta Cultura, and the U.S. Energy Research and Development Administration. With respect to the last, this reports bears Code Number UCB-34P32-103. We express our appreciation to all these institutions for vital support of the project.
References 1 J. Lipson, Potassium-argon dating of sedimentary rocks, Bull. Geol. Soc. Am. 69 (1958) 137-150.
2 G.W. Wetherill, Isotopic composition and concentration of molybdenum in iron meteorites, J. Geophys. Res. 69 (1964) 4403-4408. 3 V. Costa, M.P. Ferreira, R. Macedo and J.H. Reynolds, Rare. gas dating, I. A demountable metal system with low blanks, Earth Planet. Sci. Lett. 25 (1975) 131-141. 4 M.P. Ferreira, R. Macedo, V. Costa, J.H. Reynolds, J.E. Riley, Jr. and M.W. Rowe, Rare-gas dating, II. Attempted uranium-helium dating of young volcanic rocks from the Madeira Archipelago, Earth Planet. Sci. Lett. 25 (1975) 142-150. 5 A.O.C. Nier, A redetermination of the relative abundances of the isotopes of carbon, nitrogen, oxygen, argon, and potassium, Phys. Rev. 77 (1950) 789-793. 6 E. Farrar, R.M. Macintyre, D. York and W.J. Kenyon, A simple mass spectrometer for the analysis of argon at ultra-high vacuum, Nature 204 (1964) 531. 7 G.W. Berger, 40Ar/39Ar step heating of thermally overprinted biotite, hornblende and potassium feldspar from Eldora, Colorado, Earth Planet. Sci. Lett. 26 (1975) 387408. 8 C. Merrihue and G. Turner, Potassium-argon dating by activation with fast neutrons, J. Geophys. Res. 71 (1966) 2852-2857.
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RARE-GAS DATING, III. E V A L U A T I O N OF A DOUBLE-SPIKING PROCEDURE FOR POTASSIUM-ARGON DATING C.R. MACEDO, C.V. COSTA, J.T. F E R R E I R A , M.P. F E R R E I R A and J.H. REYNOLDS 1
Laborat6rio de Geocronologia, Departamento de Geologia, Universidade de Coimbra, Coimbra (Portugal)
Revised version received January 1977
A double-spike method for K-Ar dating is described. Use of long-lived 39Ar in addition to the usual 3BAr in the spike permits argon isotopic discrimination occurring after insertion of the spike to be monitored at the same time as ages are determined. A "bootstrap" (self-contained) method of calibrating the spike for isotopic composition is described which, when used appropriately, gives final ages which are independent of the published isotopic composition of the terrestrial atmospheric argon used as a comparison gas. The method calls for a mass spectrometer which resolves adjacent isotopes to a high degree. We have tested the method nevertheless with a mass spectrometer of relatively low resolving power, the AEI MS-10, and found it to be successful in part and without any disadvantages with respect to conventional techniques in those instances where the method fails because of insufficient resolution. That is, we find the discrimination factor inferred in runs on young rocks and blanks to be valid and useful. That factor changes by as much as 1.3% over the life of a filament in the ion source of the MS-10, proving that close control of the discrimination factor is essential for analytical precision with the instrument. These assertions are documented graphically with a compilation of data which represents more than two years experience with the method. We also report measurements of the mass discrimination of the MS-10 and its linearity with mass which indicate that the latter quantity is acceptable when the repeller voltage for the ion source is close to +1 V and is unacceptable otherwise. The spike material is available, upon request, to those laboratories which decide firmly to undertake further testing of the method.
1. Introduction All dating methods have particular problems in precision. In the K - A t method, precise measurements of the ratio 36Ar/4°Ar are required, especially for young rocks, because the percentage error in that ratio is amplified by the factor [atmospheric Ar]/[radiogenic At] to become the percentage error in the amount o f radiogenic argon [1 ]. One o f the essentials in the method is therefore to have good control over the discrimination o f the mass spectrometer. (We leave aside in this paper the question o f natural variations in the ratio 36Ar/4°Ar for the atmospheric or extraneous argon in the samples, which can sometimes lead to even greater errors in determining the radiogenic
1 Permanent address: Department of Physics, University of California, Berkeley, California 94720, U.S.A.
argon content. That is, good control over isotopic discrimination in K - A r dating is a necessary condition for analytical precision in the work but not a sufficient condition for obtaining meaningful age determinations.) The usual method for monitoring the discrimination is to interject runs on argon o f known isotopic composition (atmospheric argon) into the sequence o f runs on argon from rocks. This traditional method is sound, provided the discrimination o f the instrument is relatively stable from day to day, but tedious. Another method to monitor the discrimination, which has been possible since 1959 or before but has not been tried hitherto, is to add long-lived 39Ar to the 38Ar spike. Each measurement made then contains a built-in determination o f mass spectrometer discrimination and of other fractionation processes for the isotopes which took place after the introduction o f the spike. This double-spike technique was first used by Wetherill [2] in a search for
412 molybdenum isotope anomalies in iron meteorites. In establishing a new K - A r laboratory at Coimbra, we instituted some new techniques which we have described in papers I and lI [3,4]. Even though we used a mass spectrometer of limited resolving power, we also included a trial of the double-spike method in the work. This paper reports our findings concerning that method. Failure to test the method under totally favorable conditions is compensated by useful facts we have established about discrimination, its linearity, and its variability in the MS-10, an instrument which is widely used in K - A r dating.
2. The spike gas The spike gas, designated "38Ar", was prepared at some time prior to 1959 by neutron irradiation of a previously outgassed chloride salt. The preparation was "Special Work No. 10591" at the Oak Ridge National Laboratory of what was then the U.S. AEC (now U.S. ERDA). Because of high flux in addition to high fluence for the irradiation, a large amount of long-lived (T1/2 = 265 years) 39Ar was produced by way of the second-order reaction 38Ar + n ~ 39Ar. The content of 36Ar in the sample is low (Table 1). Both these qualities make the spike gas useful for our purpose. The original sample of ~0.4 cm 3 STP 38Ar was split into 12 parts. One of these twelfths was cleaned with a Ti-Zr getter and further split into twelfths, each of which is suitable for filling a pipette which dispenses 10 -4 of the remaining gas per cycle of operation. Several of these 1/144 fractions were consumed in this study. Others remain available (from the Department of Physics, University of California, Berkeley) to other laboratories who firmly decide to institute use of the double-spike technique and who request spike material for that purpose.
3. Determination of the isotopic composition of the spike The double-spike control depends upon knowing accurately the isotopic composition of the spike. Fortunately this composition can be determined, with the same mass spectrometer whose discrimination is to be monitored, by a bootstrap (self-correcting) pro-
cess. First one measures the isotopic composition of the spike gas. With four isotopes present, there are three measured ratios. Next one measures the isotopic composition of a mixture of the spike gas and atmospheric argon. The atmospheric argon is assumed to have the standard isotopic ratios which were determined in 1950 by Nier [5], although this assumption (see below) is not essential. The second measurement provides three more measured ratios. A set of six simultaneous equations can then be written which include six unknowns: the three isotopic ratios for the spike, which we seek; the discrimination factor for the mass spectrometer for the first run (assumed to be linear with mass difference for any pair of isotopes constituting a ratio); the discrimination factor for the second run; and the relative amounts of the two kinds of argon in the mixture. By solving the six equations, one determines the six unknowns. The bootstrap determination was carried out twice In November 1971 large gas samples of spike and spike-air-argon mix were measured in the mass spectrometer. In May 1972 the process was repeated. This time the spike gas was a "large spike" (approximately 16 regular spikes in size) which can be extracted routinely from the pipette on our apparatus. The spike-air mix was contrived by adding a regular spike to the gas released upon melting 2 g of powdered Pyrex glass. The details of these measurements and the results are set out in Table 1 and in the notes for that table. Our final determination of the isotope abundance ratios in the spike is accurate to about 1 part in I000 for 3SAt, 39At,and 4°Ar. The 36AI/38Ar ratio is determined to within 5 parts in 1000 (errors quoted are 0.50 confidence level or 0.67o).
4. Mass discrimination of the MS-10 mass spectrometer and its linearity One of the essential assumptions in the doublespike method is that the mass discrimination of the mass spectrometer is linear with respect to mass. It was important, therefore, to study that question for the mass spectrometer we used. What was done was to make isotopic measurements of one of our spikeair mixtures under various source conditions. In these measurements we emphasized changing the ion repeller voltage for the source, because the discrimination
413 TABLE 1 Bootstrap determination of isotopic composition of spike. Errors are 0.5 confidence level (0.67cr) Determination
Desig.
2 9 - 3 0 November 1971 3 Spike-air-argon mixed as gases
A
13-17 May 1972 4 Spiked run on powdered Pyrex no overlap 5 corrections with overlap 6 corrections with partial 7 overlap corrections B Combined 8
A +B
(36Ar/38Ar)spike
(39Ar/38Ar)spike
(40Ar/38Ar)spike
FS 1
FM 1
0.0011425 -+0.0000021
0.46484 2 -+0.00020
0.11348 ±0.00013
-0.623% ±0.049
-0.852% ±0.024
0.0011742 -+0.0000016 0.0011796 -+0.0000016 0.0011765 -+0.0000028
0.46453 2 -+0.00025 0.46348 2 -+0.00025 0.46408 2 ~0.00051
0.11759 ±0.00015 0.11706 ±0.00015 0.11737 -+0.00027
-0.411% -+0.062 -0.183% ±0.062 -0.314%
-0.317% -+0.019 -O.311% ±0.019 -0.314~
0.0011660 •+0.0000055
0.46446 2 ±0.00033
0.11737 -+0.00015
t FS = disc. correction calculated for run on spike; F M = disc. correction calculated for run on spike-air mixture. In both cases (MI Ar/M2Ar)true = (MI Ar/M2Ar)apparent [ 1 + F(M2 - MI )]. Ion source settings: 50 ~A, +1 V. 2 Corrected for radioactive decay to November 2 9 - 3 0 , 1971. 3 Large samples. Overlap corrections applied after study of peak shape. Largest correction (to adjacent heavier isotope) was 0.00018 × parent peak. Hydride effect makes small, constant, additive changes in (39Ar/38Ar) and (40Ar/38Ar) in spike gas which we have ignored by treating them as part of the 39Ar and 40Ar in the spike gas. 4 Spike was "large spike" (= ~ 16 regular spikes) from pipette; spike-air mix was evolved by melting 2 g powdered Pyrex glass in presence of regular spike from pipette. 5 For comparison purposes. 6 Affected only ratio (39Ar/38Ar) in run on spike-air mix. 7 Overlap correction in spike-air mix judged excessive, based on discrepancy between F S and F M . Reduced correction by 58% which made calculated F S and F M agree. Difference between corrected and uncorrected spectra compounded as error with other errors. 8 Designate vector composition of A by A, of B by B--',of air argon by "T. Since B sample was from pipette tank, it probably contains a trace of air with respect t o A sample. Revised ~ was vector with terminus on line joining ~ and T which passed closest to B. A + B is average of revised A and B. Oak Ridge analysis of source gas for spike, made in 1959 and corrected for radioactive decay, is 36Ar : 38Ar : 39Ar : 40Ar = 0.0010 : ~ 1 : 0.4650 : 0.1158.
is k n o w n t o c h a n g e s t r o n g l y w i t h t h a t p a r a m e t e r [6]. We also e x p e r i m e n t e d s o m e w h a t w i t h varying t h e e l e c t r o n t r a p c u r r e n t . All d i s c r i m i n a t i o n values inferred are relative t o a s t a n d a r d c o n d i t i o n , i.e. 50 ~tA trap c u r r e n t a n d +1.0 repeller volts. The results are i n t e r p r e t e d as s h o w i n g t h a t t h e l i n e a r i t y in discrimination worsens as o n e m o v e s s u b s t a n t i a l l y a w a y f r o m +1.0 repeller volts. Fig. 1 e x h i b i t s d i s c r i m i n a t i o n ratios (relative t o s t a n d a r d settings) for t h e argon s p e c t r u m as m e a s u r e d w i t h 11 d i f f e r e n t source c o n d i t i o n s . Typical errors are s h o w n . F o r 9 o f t h e s e , t h e t r a p c u r r e n t was 150
/~A a n d t h e repeller voltage varied b e t w e e n e x t r e m e s o f - 1 . 4 V a n d +6 V. F o r the o t h e r t w o s p e c t r a , the trap c u r r e n t was 5 0 / I A . F o r positive values o f the repeller voltage, t h e spectra vary in a regular way, t h e relative d i s c r i m i n a t i o n increasing w i t h repeller voltage. For negative values o f t h e repeller voltage, the disc r i m i n a t i o n o f t h e s y s t e m is m u c h m o r e capricious. At - 1 . 4 repeller volts ( w h i c h m a x i m i z e s t h e sensitivity for a r g o n ) the d i s c r i m i n a t i o n a n d its c u r v a t u r e w h e n p l o t t e d vs. mass b o t h c h a n g e greatly w h e n the trap c u r r e n t is c h a n g e d f r o m 50 t o 150/~A. In o t h e r words, the c o n d i t i o n s for m a x i m u m argon sensitivity
414 1.10]
I
I
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I\
-
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+0.04
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[
- - +TV
+4V -14V -0.7V
1.05 ~<
+0.02
+5V v 1.00
"~ c
0
-
-0,02 ~.~ 0 . 9 5 --
--.--o (Discrimination ratio for 36Ar/38ArlMEASURED -- (Discrlminatlon ratio for 36Ar/38Ar)INFERRED
OV--0.7V--/ +1V-1
Bars show overage error for plotted ratios o
-0.04
----o (Discrimination ratio for 40Ar/38Ar)MEASURED -- CDiscrimination ratio for 40Ar/38Ar)INFERRED
+2V--J +3V ~ 150 #A unless otherwise indicated
•~ 0 . 9 0 _ (3
.=_
+4V-J +5V ~ +6V --/
-0.06
-1.4V ( 5 O # A ) ~ / -1.4V ~ 0.85
I
I
1
36
38
39
40
A t o m i c mass, M
Fig. 1. Relative discrimination patterns in the MS-10 mass spectrometer at Coimbra as deduced from runs, under different source conditions, of a spike-air-argon mixture. Electron trap current is 150 ~A unless otherwise stated. Discrimination patterns are relative to the pattern obtained with 50 #A, +1 V repeller. There is evidence from the small discrimination factors found thereby in Table 1 and Fig. 3 that these standard settings do indeed lead to less discrimination than others.
are exceedingly unstable conditions under which to attempt precise argon isotopic measurements. This limitation seems already to be widely appreciated by users of the MS-10 mass spectrometer. At +1.0 V the discrimination changed less between the two trap currents and, more importantly, n o t in its apparent linearity. It is this circumstance that makes us assign zero non-linearity to that value of the repeller voltage. We have no standard gas samples which can be measured with sufficient precision to confirm this supposition otherwise. What would be required would be calibration mixtures, precisely prepared, of separated isotopes such as were employed in Nier's 1950 study [5] in which he established the isotopic composition of argon and other elements using a mass spectrometer calibrated for discrimination by that means. Fig. 2, which was prepared from the data exhibited in Fig. 1, shows the apparent llnearity in discrimina-
L 0
i
1 +2 Ion repeller
L
I
I
+4
t +6
voltage
Fig. 2. Linearity of the discrimination patterns for the MS-10 mass spectrometer at Coimbra, based upon data plotted in Fig. 1. "Discrimination ratio" is defined in Fig. 1. Plotted here is the difference between the measured discrimination ratio and that inferred from 39Ar]38Ar measurements, assuming linear discrimination. There is no difference, within experimental error, for +I V and +2 V as choices of repeller voltage. There are significant differences for +6 V, 0 V, -0.7 V and especially - 1.4 V as choices of repeller voltage.
tion for various values of the ion repeller voltage. Error information is included as well. One sees from this figure that there is a range of repeller voltages, extending roughly from +1 to + 2 V where the system is apparently linear within experimental uncertainty. It is in this region that the double-spike method has the best chance of success with an MS-10 mass spectrometer and it is in this region, with a few exceptions, that we made our measurements for this paper.
5. Resolving power of the MS-10 as it affects the double-spike method In order to interpret the results we have obtained in testing the double-spike method, the reader must appreciate the problems arising from the limited resolving power of the small mass spectrometer we used. For the most part our work during the period in question was on young basalts from the Madeira Archipelago. A typical sample might be one gram of basalt, 1.3 m.y. in age, containing 0.7% potassium
415 and enough atmospheric argon (0.15 X 10 - 6 cm 3 STP/g) so that the 4°Ar peak would be 80% air. As we shall see below, the maximum variation, due to discrimination, in the abundance ratio for adjacent masses that one encounters during the life o f a spectrometer filament is about 1.3%. For the example we are considering a 1% error in the abundance ratio for adjacent masses would generate an error in age of 0.3 m.y., which is a considerable error and shows that control o f the spectrometer fractionation is indeed required. We have examined the peak shape in the mass spectrometer very carefully when there were large argon samples being studied for calibration purposes (see above). As in all single-stage mass spectrometers, although to varying degrees depending upon the size of the instrument, there is in ours a broad background extending out from the peak and contributing to adjacent masses both high and low. The slow manner in which this background falls off with mass (only about a factor 3.2 per mass unit) indicates that scattered ions are the source o f the "tail". For argon samples 30 times larger than the argon sample taken above as an example, the tail o f the 40-peak at the mass 39 position is ~ 7 × 10 - s of the parent peak. It seems likely, since gas scattering should in part contribute to the tail, that its fractional size should diminish with sample size. Unfortunately this is a point we have not investigated systematically enough to write about. Thus let us take the 7 × 10 - s tail as an upper limit in our example. The effect o f an extraneous contribution to the 39-peak is to generate a false correction to the discrimination because our knowledge of the discrimination is based upon our measurement o f the 39Ar/38Ar ratio. In the present example (where 40 : 39 : 38 ~ 2 : 0.45 : 1) the error in age so generated is 0.009 m.y., which, one recalls, is an upper limit to the effect. It is clear that the double spike method can be expected to succeed in this instance: it would easily detect a genuinely large change in discrimination and the false correction from the tailing of the 40-peak would constitute at worst a negligible error in comparison with others. But with a sample o f radiogenic argon 30 times larger than the total argon in our example and without correction for the 40-tail at mass 39, the 39Ar/38Ar ratio would be altered very considerably - by 1.6%. In this case a clumsy application o f the double-spike
method can generate errors as large as the errors it is designed to correct.
6. The double-spike method in practice In the mass spectrometer runs made for age deterrninations or blanks, there are three measured isotopic ratios, permitting the determination o f three unknowns: the discrimination factor for the run, the ratio of radiogenic gas to spike gas, and the ratio of atmospheric gas to spike gas. The computer program used to solve this problem at Coimbra prints out all relevant quantities for each run as well as a complete error analysis. From these print-outs we have prepared a plot (Fig. 3) which displays the complete history o f our work with the double-spike method between late 1971 and early 1974. The reader should refer to this figure for the discussion which follows. In Fig. 3 we have plotted the computed value o f 100F (see Table 1 for a precise definition o f F ) vs. the serial number o f the spike used in the run. The meaning of 100F = 1 is that there is a discrimination factor 1.01 for the abundance ratio o f adjacent isotopes; o f 1 0 0 F = 2, a factor 1.02, etc. Every spike used for which there was a value of F obtained has been plotted. The occasional use of large spikes (equivalent to ~ 1 6 regular spikes) leaves a gap of 15 abscissa units in the plot which the reader can, in his mind's eye, close. We chose not to, for simplicity o f plotting. The large spikes occur at a spike nos. 63, 91 (a spike of unorthodox size), 2 9 7 , 3 2 5 , 3 4 1 , 3 5 7 , 3 7 3 , and 390. The gap starting at spike no. 210 occurs because o f unreduced data. The most impressive feature o f Fig. 3 is that for favorable samples - i.e. for young rocks or blanks, in runs where there is good gas cleanup and where no other experimental problems arise - the double-spike technique works, even with a mass spectrometer o f low resolving power. The points in question are plotted as circles, closed for samples and open for blanks. With a few exceptions those circles fit trend lines which drop off towards more negative F values as the filament ages and then rise again discontinuously when a new filament is installed. The mean in the probable error o f 100F in those determinations is very close to 0.1. How the errors are distributed indicate that there may be some residual systematic errors
416 I
I
I
3 Miscellaneous problems I • Large spike, old samples ? Unorthodox settings
• Runs on young rocks o Blanks ' O l d rocks Dirty gas samples
I
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3 1 1 1
222 22 2@
0 L ii
222
o o
n
• e
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4
3
2
-2
o
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?
-4
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I
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L- N E W
77 L NEW FILAMENT
-6
I
I
50
100
3
NEW FILAMENT
FILAMENT
J
I
150
200 Spike n u m b e r
I
I
I
250
300
350
400
Fig. 3. A complete plotting of percent discrimination factors for adjacent isotopes, as defined in Table 1, and computed for all runs made at Coimbra between late 1971 and early 1974. Valid trends for the discrimination factor are obtained in runs on young rocks and blanks. The discrimination factor drops with increased filament age.
in the measurement o f F not always under our control. Nevertheless the evidence is strong that the trend lines are valid representations o f F. The excursions in the trend lines are large enough and different enough from one filament to another so that for accurate K - A r dating the mass discrimination must be monitored by some means at frequent intervals. Another striking feature of Fig. 3 is that the old rocks, when run with the regular spike, yield F values which fluctuate widely with respect to the trend lines. These are runs where there is a substantial tail from mass 40 at the 39 position and a corresponding distortion of the 39Ar/38Ar ratio on which the double-spike method depends. We routinely attempt to correct the 39Ar peak for this tail but it is obvious that the correction is insufficiently accurate on the average. Cases o f undercorrection and overcorrection occur with similar frequency. If the quantity o f the spike is increased sixteen-fold as it was for five o f the last six old rocks plotted in Fig. 3, the F values deduced are much closer together and are distributed around a reasonable value as inferred from the runs on young rocks. This
fact indicates that the discrimination o f the mass spectrometer has not been altered by the large gas samples from its usual value, but that our ability to measure it from the 39Ar/38Ar ratio has been impaired The best way to calculate ages for old rocks is by the usual, single-spike method in which the 38At peak is used as an internal standard and the F value is taken from the trend line based on the smaller gas samples. It should be clear from this discussion that, even with the MS-I 0 and under-spiking we have adequate control of the discrimination of the mass spectrometer for old rocks provided we take care to interleave runs on young rocks or blanks into the measuring sequence o f runs on the old rocks. We emphasize that none o f these problems about old rocks arise when using a mass spectrometer of sufficient resolving power for the double-spike method or when dating them by the conventional single-spike method where less resolving power is needed. One notes additional "pathologies" in Fig. 3: gas samples which were not adequately purified give discordant values for F ; samples run with u n o r t h o d o x
417 settings for the ion source gave discordant and fluctuating values of F; samples for which there were abnormal experimental problems (e.g. "much air", "38-peak very unstable", "pump valve open briefly by mistake", "brief ion-gauge pumping of sample by mistake", "vacuum-tube burned out - sample in spectrometer for 8 hours") sometimes gave obviously fallacious values for F.
7. Effect on the method of errors in the assumed isotopic composition of terrestrial argon Since we had systematized the computations for this work, it was a simple matter to investigate the effect upon our results of an error in the assumed isotopic composition of terrestrial air argon, which was that published by Nier [5]. We simply had to change the assumed value of (36Ar/4°Ar)terrestrial in two computer programs. We carried out these calculations for two revised values of Nier's atmospheric argon - one in which we increased the 36Ar/4°Ar ratio 2% and one in which we increased it by 4%. The samples we then examined, with these revised data, were (1) a sample of our calibration basalt, BCR-2 [4], (2) a young basalt (sample l-B) [4] from Madeira, and (3) a Precambrian hornblende "HBDE-248" studied both in this laboratory and elsewhere by Berger [7]. Inclusion of the calibration basalt, BCR-2, in this sequence of runs was crucial because it was upon analyses of BCR-2 that our spike pipette calibration depended. It is easy to see that if our calibration of the spike were made in a manner which did not depend upon the discrimination in our mass spectrometer, the error in atmospheric argon would be propagated through the calculations in such a way as to influence our dates. That is, the error in atmospheric argon would cause us to misjudge our spectrometer discrimination, which would cause us tc~ measure falsely the 4°Ar/38Ar ratios in our unknowns, and thereby (since our calibration would be "absolute") measure our ages falsely. Using the mass spectrometer in the calibration process, however, leads to a cancellation of errors. This is illustrated by the ages we obtained, using modified values for the isotopic composition of atmospheric argon, when we carried through the whole process anew, including the calibration o f the spike pipette f r o m the run on BCR-2.
For a +2% change in (36Ar/40Ar)terrestrial the argon content and age of sample Madeira basalt 1-B [4], for which the standard calculations gave an age of 1.2 m.y. and an atmospheric argon content of 80%, changed by only +0.03%. The argon content of HBDE 248, with a standard age of 1364 m.y. and an atmospheric argon content of 1.5% [7], changed by -0.006%. The corresponding changes when the change in the isotopic composition of atmospheric argon was doubled were +0.06% and -0.012%. Since these samples cover an enormous range in age and contamination by atmospheric argon, we can be sure that the method is independent for all practical purposes of any reasonable error in Nier's values for the isotopic composition of air argon, provided the calibration o f the spike constant is based upon measurements made with the same mass spectrometer and not by some absolute means.
8. Summary The double-spike method works. With a mass spectrometer of adequate resolving power there is obtained, along with the dates, a continuous monitoring of mass spectrometer discrimination which is essential for dating, because that discrimination, at least in some mass spectrometers, varies with the age of the filament. With a mass spectrometer of marginal resolving power runs on young rocks and blanks can monitor the discrimination. Provided such runs are interspersed in the measuring sequence, old rocks can be dated with the same amount of spike as used for young rocks. For such determinations on old rocks, the discrimination factor based on runs with young rocks should be used in single-spike calculations. This is because underspiked runs on old rocks give false discrimination factors if there is insufficient resolving power of the mass spectrometer. Unless the laboratory intends to use the 39Ar-4°Ar dating technique [8], there is no disadvantage to employing a double spike of the type used in this work, and there are substantial advantages.
Acknowledgements We thank Dr. G.W. Berger for running the computer programs for section 7. Establishment of the
418 Laborat6rio de Geocronologia in the Departamento de Geologia at Coimbra has been a joint project between the University of Coimbra and the University of California, Berkeley. The work has been supported in part by the Arthur L. Day Fund of the U.S. National Academy of Sciences, by the U.S. National Science Foundation, and by the Instituto de Alta Cultura, Lisbon. One of us (J.H.R.) was a Hays-Fulbright Scholar in Portugal during the early stages of this work and has made subsequent visits supported in part by the Day Fund, by the Instituto de Alta Cultura, and the U.S. Energy Research and Development Administration. With respect to the last, this reports bears Code Number UCB-34P32-103. We express our appreciation to all these institutions for vital support of the project.
References 1 J. Lipson, Potassium-argon dating of sedimentary rocks, Bull. Geol. Soc. Am. 69 (1958) 137-150.
2 G.W. Wetherill, Isotopic composition and concentration of molybdenum in iron meteorites, J. Geophys. Res. 69 (1964) 4403-4408. 3 V. Costa, M.P. Ferreira, R. Macedo and J.H. Reynolds, Rare. gas dating, I. A demountable metal system with low blanks, Earth Planet. Sci. Lett. 25 (1975) 131-141. 4 M.P. Ferreira, R. Macedo, V. Costa, J.H. Reynolds, J.E. Riley, Jr. and M.W. Rowe, Rare-gas dating, II. Attempted uranium-helium dating of young volcanic rocks from the Madeira Archipelago, Earth Planet. Sci. Lett. 25 (1975) 142-150. 5 A.O.C. Nier, A redetermination of the relative abundances of the isotopes of carbon, nitrogen, oxygen, argon, and potassium, Phys. Rev. 77 (1950) 789-793. 6 E. Farrar, R.M. Macintyre, D. York and W.J. Kenyon, A simple mass spectrometer for the analysis of argon at ultra-high vacuum, Nature 204 (1964) 531. 7 G.W. Berger, 40Ar/39Ar step heating of thermally overprinted biotite, hornblende and potassium feldspar from Eldora, Colorado, Earth Planet. Sci. Lett. 26 (1975) 387408. 8 C. Merrihue and G. Turner, Potassium-argon dating by activation with fast neutrons, J. Geophys. Res. 71 (1966) 2852-2857.