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The problem of the decay constant λf of 238U
Nucl. Tracks, Vol. 5, Nos. 1/2, pp. 35-44, 1981. Printed in Great Britain.
0191-278X/81/010035-10502.00/0 © 1981 Pergamon Press Ltd.
THE PROBLEM OF THE DECAY CONSTANT Af OF 238U* G I U L I O BIGAZZI
Laboratorio di Geocronologia e Geochimica Isotopica, CNR, Via Cardinale Mafli 36, 56100-Pisa, Italy (Received 6 November1980; in revised form 20 January 1981) Abstract--More than 40 measurements of the 238Ufission-decay constant ,~! have been performed
since 1940 until now. Sometimes the results disagree with each other; most workers in fission-track dating use one of the two possible values: about 7 x 10-17yr-' and about 8.5 x 10-~7yr-1. Most of the SSTD measurements by solid state, track detector in 2~r geometry agree with the first value, while most of the direct measurements agree with the second one. )tt values obtained by dating samples of well-known ages, or by best-fit between fission-track and other radiometric methods, agree either with the first or with the second value. Measurements by radiochemical or mass-spectrometric analyses give a scatter over a large range. Analysing the measurements obtained by the fission-track method, it is clear that the two focal points are: (I) neutron dosimetry; (2) dating technique and age corrections. The problem of the At value can, thus, be solved only together with other open problems in the fission-track dating, when a standardization of the method is eventually accepted by all fission-track workers. 1. INTRODUCTION
THE 238U fission-decay-constant value is of prime importance for geochronoiogists, as it is one of the components of the formula for the age calculation by the fission-track method. Since the discovery of 23sU spontaneous fission, many measurements have been performed to determine the fissiondecay constant. One of the reasons of the difficulty in measuring At is the fact that the probability of the occurrence of fission is very much lower than of competing radioactive decays: for uranium, for instance the a-decay constant is about 2 x l0 ~ times the fission-decay constant (As (23sU)= 1.551 x 10-'°yr -~, Jaffey et al., 1971; Steiger and Jaeger, 1977). More than 40 values of AI can be listed, which are comprised between 0.7x 10-17yr-' and 28 x l0 -'7 yr-'. When Price and Walker, 1962, proposed that the ages of rocks could be measured by the fission-track method, more than twenty years after the discovery of 23~U fission, there were about twenty Al values; the more acceptable of these ranged between 7 x l0 -~7 yr-' and 12 x 10-27 yr -~. Since that time, the decay-constant value has become of great importance for people working in
geochronology. Some new techniques strongly tied to fission tracks were added to the techniques used until that juncture. In Table I the data from literature that the author is aware of are listed: for each datum, the method by which the value was obtained has been added. Most of them are taken from the list by Thiel and Herr 0976). Methods used to measure AI have been grouped in Table 1 as follows: (1) direct determinations; (2) radiochemical or mass-spectrometry analyses; (3) solid state track detectors (SSTD) and photographic emulsions; (4) fission track, K/Ar and/or Rb/Sr dating comparisons, or dating of samples of well-known ages. In the last fifteen years the range where At could be comprised has been reduced, and two values are commonly accepted by fission-track workers: (1) about 7 x 10-~7yr-I; (2) about 8.5 x 10-17 yr -~. Ages calculated by using these two values differ by about 20%. However, measurements performed on the same samples in different laboratories,
*Introductory lecture for the Pisa FTD Workshop session devoted to the topic of 23sU fission-decay constant. 35
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THE PROBLEM OF THE DECAY CONSTANT Ar OF z3~U using the two At values, do not necessarily differ by 20% from one another, for researchers have not yet found a complete agreement on others parameters which are fundamental to fission-track dating. In each laboratory where fission-track utilization has been developed for dating, a local calibration has been endeavoured, especially during the early 1960s. Different methods have been used for the measurement of the neutron dose, for the counting, and for the age correction of samples which had undergone fossil-track fading. Thus, an evaluation of ages obtained by different laboratories is very difficult, especially if the age determinations date back to the first few years after 1962. It is known for certain that, in each laboratory, age measurements obtained by the fissiontrack method have been compared to those obtained by other radiometric methods (prevalently K/At, Rb/Sr and U/Pb) and/or to the stratigraphic ages. Every calibration has been obviously directed towards the obtaining of data that are most concordant with those obtained in some other way. It thus appears likely that the eventual differences in some aspects or points of dating could have been counterbalanced by differences in other points. For instance, different laboratories where different ,tr values were used may have obtained similar age values on the same sample using different dating methods (for instance, by correcting or not correcting the thermally lowered gas; using different neutron-dose standards; and so on).
The firstiand until now the lastIwide-ranging interlaboratory comparison was performed on a sample distributed by C. W. Naeser of the U.S. Geological Survey (namely, apatite and zircon from the Fish Canyon tuff from San Juan Mountains, Colorado). As a matter of fact, the results obtained using the decay constant 7 × 10 -j7 yr -~ for the age calculation have an average value higher than the results obtained by those laboratories where the constant 8.5 × 10 ~7yr-~ was used; the difference, however, did not reach 20%, though it was not far from it (Naeser and Cebula, 1978). 2. REVIEW OF DATA Excepting the four direct determinations between 1940 and 1946, the distribution of measurements in Table 1 is shown in Fig. 1. We
37
can observe three peaks: the first one is centred around 7 x 10 ~7yr-J, the second peak around 8.5 x 10-~7 yr -' and the third peak falls between 10x and 12x 10 ~7yr-~. The largest part of the measurements connected with the fission tracks comprises the first two peaks. The third peak is predominantly made up of the chemical data. Almost all the measurements performed using detectors in 2~r geometry are in the first peak. In the second peak there are many direct measurements. In both peaks there are radiochemical measurements, just like those obtained by comparing FT, K/Ar and Rb/Sr ages and those obtained by dating samples with a known age. The bad distribution of the At values in Fig. 1 is not due to the reported experimental errors; in fact many standard deviations exist between measurements belonging to different peaks. To show this, Fig. 2 has been drawn by combining the measurements, assuming a normal distribution of the experimental errors; the curve is the addition of standard-area Gaussian curves whose width has been determined by the experimental error relating to the measurements shown in Table I. The four direct determinations between 1940 and 1946, and the At values reported without experimental error, were not taken into account in constructing Fig. 2. The scale of the ordinate is arbitrary. The diagram shows very clearly two different peaks, well distinguished, which can be correlated with two decay-constant values: 7.05 × 10-JTyr ~ and 8.46×10 ~7yr ~. Furthermore the diagram shows another smaller peak, whose maximum corresponds to the 10.65 × 10 ~7yr-, value, The other two peaks, 1.7x 10 ~Tyr-~ and 9.64× 10 z7yr-,, represent single measurements only. In conclusion, such big differences are very probably due to systematic differences which are inherent in the approach. DISCUSSION ON At VALUES OBTAINED BY THE FISSION-TRACK METHOD The analysis of the techniques connected with fission tracks--viz, the SSTD measurements, the measurements by best fit between FT and other ages and the measurements by dating well-known age samples, clearly reveals that the uncertainty in At is strictly tied to the "focal points" of every fissiontrack dating approach: (1) neutron dosimetry; and (2) dating technique and age correction.
38
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THE PROBLEM OF THE DECAY CONSTANT ~,t OF 238U In the SSTD technique, As is normally obtained by using a detector-uranium sandwich and counting the number of tracks produced on the detector, in a known time, by the fissions occurring in the uranium source adjacent to it. The irradiation of the sandwich with thermal neutrons is used, in order to solve two problems: the determination of the efficiency, and the determination of the number of 238U atoms per unit volume in the uranium source. By efficiency one means the ratio between the number of revealable tracks by chemical etching on the detector surface and the number of fissions which occurred in the uranium per unit volume. But the use of the irradiation involves the dose measurement: ai determinations by SSTD were obtained by different laboratories using different dose calibrations. For this reason such measurements, even if they predominantly agree with 7 × 10-b 17yr-', are not easily comparable either with each other or with the data obtained by other techniques. The hypothesis that SSTD values are lower than the real one because of a counting loss due to the low track densities is not well supported; in fact, this would assume the same counting loss for every laboratory. When AI is obtained by the comparison between FT and K/Ar and/or Rb/Sr ages, the neutron-dose calibration and the much-discussed problem of apparent-age correction are focal points. To show this, the curves published by Fleischer and Price (1964)---Fig. 3(a); by Gentner et al. (1972)---Fig. 3(b); and by Naeser et al. (1977)--Fig. 3(c); have been redrawn in Fig. 3. In Fig. 3(a), the best fit between fission track ages and K/Ar-Rb/Sr ages has been obtained by using samples, amongst others, of tektites, obsidians and muscovites. Whoever has analysed such kind of samples knows that thermally-lowered fission-track ages are relatively frequent in them. Owing to the fact that in 1964, age corrections were not yet being used, the value of 6.9 x 10-17 yr-' obtained should be regarded as lower than the real one, as some of the samples examined are likely, to have had a fission-track age lowered by thermal phenomena, i.e. the observed fossil-track density to have been reduced. The above authors observed excessively young ages on some samples, but these were samples with extremely clear fading, which points were significantly distant from the line along which
39
the points relating to the other samples were aligned. In the curve of Fig. 3(b), which has been constructed in the same way as the curve in Fig. 3(a), the ages lowered by some natural thermal phenomena were corrected. It may be noticed that the number of the samples whose age has been corrected is very high (about 70%). Furthermore, the number of cases of thermally-lowered fission-track ages increases with increasing age of the material (glass and minerals) dated. In agreement with the results of Gentner et al. (1972), the fossil-track fading cannot be neglected when comparing FT ages and K/Ar, Rb/Sr or other well-known ages. The above authors used, for the best fit, only the unaffected fission-track ages. The corrected ages of the graph agree perfectly with those obtained by other methods when using the best-fit value: 8.4× 10-~7 yr-% It must be noticed that in both Figs. 3(a) and 3(b), ages of identical materials, namely tektites and obsidians, are shown. Unfortunately, as stated before, the two Aj measurements of Figs. 3(a) and 3(b) are not entirely comparable, owing to the lack of standardization in the neutron dosimetry. Naeser et al. (1977) have built the same kind of curve Fig. 3(c), using samples of zircons. Zircon is very resistant to fading phenomena; the lastnamed authors write: "ages are all from volcanic rocks in which annealing should be absent or minimal". Although Naeser et al. (1977) do not explain in that paper their dating technique, it is very probable that they used the external-detector method, normally applied by Naeser in zircon samples (Naeser, 1969; Naeser and Dodge, 1969). In this method, the fossil tracks are revealed on polished surfaces of the zircons themselves, whereas the induced tracks are observed in an external detector (which could be a muscovite mica or a plastic detector), which is placed in contact with the sample during the irradiation. In this way, the fossil tracks are registered with 4~-geometry, whereas induced tracks are registered with 2~-geometry and in a different material. In addition ages by the external-detector method are not susceptible of being corrected for fossil-track fading. To calculate the age, a factor has to be introduced to correct the induced-track density. This factor should take into account the different
40
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registration geometry as well as the possible differences in etching efficiency and the possible differences in optical counting in the two materials. In the past, ages have been calculated by multiplying by 0.5 the fossil-track density/induced-track density ratio (Naeser and McKee, 1970; Naeser et al., 1971). The FT ages reported in those papers perfectly agree with the K/Ar ages. However, those fission-track-age values are dependent on the
kl value and the neutron dosimeters used by the authors. Reimer et al. (1970) suggested that the "geometry factor" for external detectors had to be higher than 0.5. They based this suggestion on experimental results obtained on the external surfaces of the mineral itself (i.e., apatite, zircon, glass, muscovite and sphene). Gleadow and Lovering (1977) carefully studied the value of the geometry factor for external detectors in fissiontrack dating. They compared the induced-track
THE PROBLEM OF THE DECAY CONSTANT A,, OF 23sU densities on the surface of the external detectors (i.e., muscovite mica) and on the polished surfaces of the crystals themselves. Gleadow and Lovering (1977) conclude "the geometry factor relating track densities on external detectors and internal surfaces is 0.5 for apatite, sphene and zircons, and probably for other minerals as well". They also write "the etching efficiency of zircons, and probably of other minerals, is highly dependent on crystallographic orientation, so that care must be taken when using the external-detector method to choose only the appropriate orientations for counting. For zircon the best orientation is probably parallel to the C-axis. Further work is needed to fully document the variation of etching efficiency with crystallographic orientation in zircon and in other minerals" (p. 105 of the above paper). It means that, when using external-detector method, if for some of the polished surfaces of the zircons an etching efficiency is applicable which is lower than the one corresponding to the probable best orientation, a lower fission-track age could be obtained. Using such lowered ages for the best fit between FT ages and K/Ar ages, a lowered At value could be obtained. However, in their paper Gleadow and Lovering (1977) do not confirm this possibility, as owing to the generally elongated appearance of the zircon crystals, their polished surfaces will mostly be oriented parallel to the C-axis. Even if this statement seems to be reasonable, the problem of the geometry factor for external-detector dating does not seem to be entirely resolved, so that, as stated by the above authors, further work is needed. The external-detector method has been studied by Green and Durrani (1978); they reported experimental data for apatite only, confirming a value of 0.5 for the geometry factor. For the neutron dosimetry, Naeser et al. (1977) used the standard glasses that Carpenter and Reimer (1974) have set up for fission-track dating. In their paper, Naeser et aL (1977) observe that the value found (AI = 6.85 × 10 -17 yr ~) must be referred to such standards. That value must be considered a "conventional" value to be used in connection with NBS standards. This observation is very important and constructive, as it shows a way to solve the problem of the At value to be used for fission-track dating. To summarize: the different best-fit At values
41
reported in Figs. 3(a), 3(b) and 3(c) are due to systematic differences inherent in the approach, namely: Fig. 3(a)--Neutron dosimetry was by counting the 14°Ba and 99Mo activity in a U foil. Fissiontrack dating was without checking for moderate fossil-track fading. Fig. 3(b)--Neutron dosimetry was by AI-Au and Al-In monitors. Only thermally-unaffected fission-track ages were used for the fit. Fig. 3(c)--Neutron dosimetry was by N.B.S. Standard Reference Material for fission-track dating. Use made of the external-detector method. Zircons, in which annealing should be negligible were used. Hurford and Gleadow (1977) obtained for Af the value (7.00_+0.28)× l0 -17 yr -I by dating standard age-samples and measuring the neutron dose with the NBS glass SRM 962. Many of the laboratories dealing with fission tracks know these samples: they were the apatite and zircon from the alreadymentioned Fish Canyon tuff, and the apatite from the deposit near Cerro de Mercado, Durango, Mexico. Hurford and Gleadow (1977) measured the ages of the zircon samples by the externaldetector method; they selected "only zircons with polished faces approximately parallel to the Caxis", for the reason discussed above. The above authors hypothesize the possibility that apatites from Fish Canyon tuff show a small degree of spontaneous-track fading. However, they did not find any experimentally clear evidence of annealing. Experimental results on the shortening of spontaneous-fission tracks in Durango apatite and Fish Canyon tuff apatite are reported by Green (1980). This author writes that the observed shortening is due to thermal annealing of spontaneous tracks at ambient (room) temperatures. Green (1980) promises to examine the effect of track shortening in fission-track age determination in a further publication. It seems clear that further work is needed on those samples, as conflicting ages were published specially on Durango apatite (M/irk et al., 1971; M/irk et al., 1972; M/irk et al., 1973; Storzer and Poupeau, 1973; Naeser and Fleischer, 1975; Bertel et al., 1976, 1977; Green and Durrani, 1978). In the field of AI determination by the dating of samples of well-known age, Wagner et al. 0975) and Thiel and Herr (1976 have performed two very
42
G. BIGAZZI
important measurements, as they analyzed samples whose age was historically known. The results agree with those obtained by the "rotating bubble chamber" (around 8.5x 10-'Tyr-'). The neutron dose has been measured with great care by Wagner et al. (1975). Nevertheless, the results show that the neutron dosimetry is among the main sources of error. The authors emphasize the possibility of obtaining differences in the decay-constant value which are not easily explainable if different reactors and different irradiations are used. This means that the determination of the neutron dose is one of the main problems in the At measurement by the fission-track method, even if the differences that Wagner et 'al. (1975) observed are far from the percentage (20%) which separates the values clustered around 7 x 10 'Tyr-' from those grouped around 8.5x10--'Tyr -'. Equally important is the partial fading of fossil tracks. As a proof, the higher value of At (about 8.5× 10 ,7 yr ') supported by the fission-track work by Storzer (1970), Gentner et al. (1972), Wagner et al. (1975), M~rk et al. (1975), Thiel and Herr (1976), is used only in laboratories where thermal fading corrections are applied routinely. One could conclude that the use of a lower As value could compensate for the lack of correction of thermally-lowered ages. 4. CONCLUSION As shown in the above discussion it is very difficult to say what the true value of the 238U fission-decay constant is. Many apparently good measurements can be found in the literature, which sometimes agree with one and sometimes with the other of the two values that people working in fission tracks use nowadays. A good calibration, accepted everywhere, is the main aim of geochronologists, so that age measurements performed in different laboratories may be compared with each other and with those obtained by other techniques. The analysis of the At measurements made by the fission-track method has shown that they are not easy to evaluate; this is because of the problems that are still under discussion in connection with this geochronological technique. There are two possibilities in obtaining an interlaboratory calibration: (1) the choice of a standard for the neutron dose measurement which is acceptable to all; or
(2) the choice of one or more standard agesamples. In the first case, the Ar value is needed; the value obtained by the best fit between the fissiontrack ages and ages obtained by other radiometric methods would be recommended. This comparison should be limited to easily controllable samples, for which any fading phenomena of the fossil tracks can, reasonably, be excluded. Not all researchers, in fact, agree with the correction of apparent ages and on which technique to use. It appears reasonable, for instance, to use a value around 7 x 10 ,7 yr-' for At when, for the neutrondose determination the standard glasses SRM 962 and SRM 963 of the National Bureau of Standards, U.S.A., are used. But we must take into account the fact that this At value must be considered a conventional value, referring to the chosen standard. If, on the other hand, an agreement on the choice of one or more age-standards is reached, then problems connected both with the neutron dose measurement and with the At value can be overcome; as the age measured by the fissiontrack method would refer to known ages. The age would be determined by a comparison between the ratios (fossil/induced) track densities of both the sample with a known age and the sample under examination. In any case, the standard-age samples must be chosen with great care as regards the presence of fading phenomena of the fossil tracks. However, there is an arbitrariness in the initial choice, when it is maintained that, in the standard sample, the age measured by the fission-track method is equal to the age measured by other radiometric techniques. A calibration obtained in these two ways does not give an absolute guarantee of the numerical values of the age, but it allows, at least, a comparison to be made amongst the measurements obtained at different laboratories. These points, in relation to the calibration of the fission-track method, are widely discussed in other papers in this special issue. In fact, as we have observed several times in the present paper, the value of the decay constant, the neutron dosimetry and the dating techniques are problems which are strictly tied to each other. Finally, we must not forget the problem of the real value of the 2~8U fission-decay constant--even
THE PROBLEM OF THE DECAY CONSTANT
if an interlaboratory calibration is obtained and convincing age m e a s u r e m e n t s can be performed. In fact, scientists cannot be satisfied with merely accepting a conventional value for a physical quantity, which is capable of being directly measured. Acknowledgements--Figure 3(a) has been reprinted, by permission, from Physical Review, 133, n. IB, B63-B64, Copyright 1964, and by the kind permission of R. L. Fleischer. Figure 3(b) has been reprinted from Trans. Amer. Nucl. Soc., A N S 15, 126--127, Copyright 1972, by the kind permission of D. Storzer. Figure 3(c) has been reprinted by the kind permission, from Nature 267, 649; Copyright 1977, Macmillan Journals Limited.
REFERENCES Bertel E., M/irk T. D. and Pahl M. (1976). Spurenl/ingenkorrektur am Durango Apatit. Jahresbericht 1975, Projekt 939 und 1932 des Fonds F6rd. Wiss Forschg. Univ. Innsbruck. Bertel E., M/irk T. D. and Pahl M. (1977) A new method for the measurement of the mean etchable fission track length and of extremely high fission track densities in minerals. Nucl. Track Detection 1, 123126. Carpenter B. S. and Reimer G. M. (1974) Calibrated glass standards for fission track use. N B S Special Publication 260--49. De Carvalho H. G., Martins J. C., De Souza 1. 0. and Tavares O. A. P. (1975) Spontaneous Emission of Heavy Ions from Uranium. Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil, preprint presented to the "Academia Brasileira de Ciencias". Emma V. and Lo Nigro S. (1975) Decay constant for spontaneous fission of 23sU and 232Th. Nucl. Instrum. Methods 128, 355-357. Fleischer R. L. and Price P. B. (1964) Decay constant for spontaneous fission of 23sU. Phys. Rev. 133, IB, B63-B64. Flerov G. N. and Petrzhak (1940) Spontaneous fission of uranium. Z Phys. 3, 275-280. Galliker D., Hugentobler E. and Hahn B. (1970) Spontane Kernspaltung von z3sU and 241Am. Heir. Phys. Acta 43, 593-606. Gentner W., Storzer D., Gijbels R. and Van der Linden R. (1972) Calibration of the decay constant of 23sU spontaneous fission. Trans. Amer. Nucl. Soc. A N S 15, 126--127. Gerling E. K., Shukoljukov A. and Makarotshkin A. (1959) Radiokhimiya 1,223-226. Gleadow A. J. W. and Lovering J. F. (1977) Geometry factor for external detectors in fission track dating. Nuclear Track Detection 1, 99-106. Green P. F. (1980) On the cause of the shortening of spontaneous fission tracks in certain minerals. Nucl. Tracks 4, 91-100.
~,~ O F 23su
43
Green P. F. and Durrani S. A. (1978) A quantitative assessment of geometry factors for use in fission track studies. Nucl. Track Detection 2, 207-213. Von Gunten H. R. (1%9) Distribution of mass in spontaneous and neutron-induced fission. Actinides Rev. 1,275-298. Hoff Lu and Hsuan-Ling Tsao (1952) Spontaneous fission of uranium. Acta Sci. Sinica 1, 77-84. Hurford A. J. and Gleadow A. J. W. (1977) Calibration of Fission Track dating parameters. Nucl. Track Detection 1, 1, 41--48. Ishimori T., Ueno K., Kimura K., Akatsu E., Kobayashi Y., Akatsu J., Ono R. and Hoshi M. (1967) The spontaneous fission of uranium-238. Radiochim. Acta 7, 95-103. Iva~ov K. N. and Petrzhak K. A. (1974) Probability of fission by 1.33MeV-rays and spontaneous fission half-life for 238U. Soy. Atom. Energy 36, 514 (English translation from Atomnaya Energiya 36, 1974, 403). Jaffey A. H., Flynn K. F., Glendenin L. E., Bentley W. C. and Essling A. M. (1971) Precision measurements of half-lives and specific activities of 2~5U and 23sU. Phys. rev. C4, 1889-1906. Khan H. A. and Durrani S. A. (1973) Measurements of spontaneous-fission decay constant of 23sU with a mica solid state track detector. Radiat. Effects 17, 133-135. Kleeman J. D. and Lovering J. F. (1971) A determination of the decay constant for spontaneous fission of natural uranium using fission track accumulation. Geochim. cosmochim. Acta 35, 637--640. Kuroda P. K. and Edwards R. R. (1954) Radiochemical measurements of the natural fission rate of uranium. J. Chem. Phys. 22, 1940. Kuroda P. K. and Edwards R. R. (1957) Radiochemical measurements of the natural fission rate of uranium and the natural occurrence of ~°Ba. J. Inorg. Nucl. Chem. 3, 345-348. Kuroda P. K., Edwards R. R. and Ashizawa F. T. (1956) Radiochemical measurements of the natural fission rate of uranium and the natural occurrence of the short-lived iodine isotopes. J. Chem. Phys. 25, 603. Kuz'minov B. D., Kutsaeva L. S., Nesterov V, G., Prokhorova L. I. and Smirenkin G. P. (1959) Zh. Eksp. Teor. Fiz. (U.S.S.R.) 37,406 (In Russian). Leme M. P. T., Renner C. and Cattani M. (1971) Determination of the decay constant for spontaneous fission of 238U. Nucl. lnstrum. Methods 91,577-579. Maurer W. and Pose H. (1943) Neutronenemission des Urankerns als Folge seiner spontanen Spaltung. Z. Phys. 121,285-292. M/irk E., Pahl M. and M/irk T. D. (1971) Fission Trackalter von Durango Apatit, Mexico. Contr. Miner. and Petrol. 32, 147-148. M/irk E., Pahl M. and M/irk T. D. (1972) Fission Track annealing behaviour of apatite. Trans. Am. Nucl. Soc. 15, 12-127. M~irk E., Pahl M., Purtscheller F. and M/irk T. D. (1973) Annealing behaviour of fission track in apatite corrected fission track ages and contribution to the
44
G. B I G A Z Z I
geothermochronology of minerals. Tschermaks Mineral Petrog. Mitt. 20, 131-154. M~irk T. D., Mark E., Bertel E. and Pahl M. (1977) Fission Track measurement of the decay constant for spontaneous fission of 238U. Ber. nat.-med. Ver. lnnsbruck 64, 7-11. Naeser C. W. (1969) Etching fission tracks in zircon. Nature 165, 388. Naeser C. W. and Cebula G. T. (1978) Fission Track dating of apatite and zircon: an interlaboratory comparison. United States Geolocical Survey-Report 78, 107. Naeser C. W. and Dodge F. C. W. (1969) Fission Track ages of accessory minerals from granitic rocks of central Sierra Nevada batholith, California. Bull. Geol. Soc. Amer. 80, 2201-2212. Naeser C. W. and Fleischer R. L. (1975) Age of the apatite at Cerro de Mercado, Mexico: a problem for fission-track annealing corrections. Geophys. Res. Lett. 2, 67-70. Naeser C. W., Kistler R. W. and Dodge F. C. W. (1971) Ages of coexisting minerals from heat flow borehole sites, Central Sierra Nevada Batholit. J. Geophys. Res. 76, 6462-6463. Naeser C. W., Hurford A. J. and Gleadow A. J. W. (1977) Fission-Track dating of pumice from the KBS Tuff, East Rudolf, Kenya. Nature 267, 649. Naeser C. W. and McKee E. H. (1970). Fission Track and K-Ar ages of Tertiary ash-flow tufts, NorthCentral Nevada.. Bull. Geol. Soc. Am. 81, 33753384. Nishimura S. (1972) On the value of the decay constant for spontaneous fission of 238U. Ganseki Kobutsu Kosho Gakkai-Shi 67, 139-142 (In Japanese). Nishimura S. (1978) On the value of the decay constant for spontaneous fission of Uranium-238. Short Papers of the Fourth International Conference, Geochronology, Cosmochronology, Isotope Geology 1978. Geological Survey Open-File Report 78-701,306-307. Parker P. L. and Kuroda P. K. (1956) Molybdenum-99 in uranium salts and the spontaneous fission half-life of uranium-238. J. Chem. Phys. 25, 1084--1085. Parker P. L. and Kuroda P. K. (1958) The occurrence of molybdenum-99 in natural and in depleted uranium salts and the spontaneous fission half-life of uranium-238..L Inorg. Nucl. Chem. 5, 153-158. Perfilov N. A. (1947) Zh. Eksp. Teor. Fiz. (U.S.S.R.) 17, 476-484 (In Russian). Podgurskaia A. V., Kalashnikova V. I., Stoliarov G. A., Vorob'ev E. D. and Flerov G. N. (1955) Zh. Eksp. Teor. Fiz. (U.S.S.R.) 23, 503 (In Russian).
Pose H. (1943) Spontane Neutronemission von Uran und Thorium. Z. Phys. 121,293-297. Price P. B. and Walker R. M. (1962) Observation of fossil particle tracks in natural micas. Nature 196. 732-734. Rao M. N. and Kuroda P. K. (1966) Decay constant and mass-yield curve for the spontaneous fission of 238U. Phys. Rev. 147,884-886. Reimer G. M., Storzer D. and Wagner G. A. (1970) Geometry factor in fission track counting. Earth Planet. Sci. Letters 9, 401--404. Roberts J. H., Gold R. and Armani R. J. (1968) Spontaneous-fission decay constant of 238U. Phys. Rev. 174, 1482-1484. Segr6 E. (1952) Spontaneous fission. Phys. Rev. 86, 2128. Scharft-Goldhaber G. and Klaiber G. S. (1946) Spontaneous emission of neutrons from uranium. Phys. Rev. 70, 229. Shukoljukov Yu. A., Ashkinadze G. S., Levchenkov O A. and Ovchinnikova G. V. (1968) Geokhimiya 3, 265-274 (In Russian), Spadavecchia A. and Hahn B. (1967) Die Rotationskammer und einige Anwendungen. Heir. Phys. Acta 40, 1063-1079. Steiger R. H. and Jaeger E. (1977) Subcommission on Geochronology: Convention on the use of Decay Constants in Geo- and Cosmochronology. Earth Planet. Sci. Lett. 36,359-362. Storzer D. (1970) Spaltspuren des 238-Urans und ihre Bedeutung fiJr die geologische Geschichte natiirlicher Gl~iser. Thesis, Universit~it Heidelberg. Storzer D. and Poupeau G. (1973) Plateau ages of minerals and glasses by the fission track method. C. R. Acad. Sci. (Paris) 276, 137-139, Suzuki M. (1973) Chronology of Prehistoric Human Activity in Kanto, Japan. Part 1. Framework Reconstructing Prehistoric Human Activity in Obsidian. J. Faculty of Science, The University of Tokyo, Sec. V, IV, Part 3, 241-318, pls. I-XII. Thiel K. and Herr W. (1976) The 238U spontaneous fission decay constant redetermined by fission track. Earth Planet. Sci. Lett. 30, 50-56. Wagner G. A., Reimer G. B., Carpenter B. S., Faul H., Van der Linden R. and Gijbels R. (1975) The spontaneous fission rate of U-238 and fission track dating. Geochim. cosmochim. Acta 39, 1279-1286. Whitehouse W. J. and Galbraith W. (1950) Energy spectrum of fragments from the spontaneous fission of natural uranium. Phil. Mag. 41. 429-443.
0191-278X/81/010035-10502.00/0 © 1981 Pergamon Press Ltd.
THE PROBLEM OF THE DECAY CONSTANT Af OF 238U* G I U L I O BIGAZZI
Laboratorio di Geocronologia e Geochimica Isotopica, CNR, Via Cardinale Mafli 36, 56100-Pisa, Italy (Received 6 November1980; in revised form 20 January 1981) Abstract--More than 40 measurements of the 238Ufission-decay constant ,~! have been performed
since 1940 until now. Sometimes the results disagree with each other; most workers in fission-track dating use one of the two possible values: about 7 x 10-17yr-' and about 8.5 x 10-~7yr-1. Most of the SSTD measurements by solid state, track detector in 2~r geometry agree with the first value, while most of the direct measurements agree with the second one. )tt values obtained by dating samples of well-known ages, or by best-fit between fission-track and other radiometric methods, agree either with the first or with the second value. Measurements by radiochemical or mass-spectrometric analyses give a scatter over a large range. Analysing the measurements obtained by the fission-track method, it is clear that the two focal points are: (I) neutron dosimetry; (2) dating technique and age corrections. The problem of the At value can, thus, be solved only together with other open problems in the fission-track dating, when a standardization of the method is eventually accepted by all fission-track workers. 1. INTRODUCTION
THE 238U fission-decay-constant value is of prime importance for geochronoiogists, as it is one of the components of the formula for the age calculation by the fission-track method. Since the discovery of 23sU spontaneous fission, many measurements have been performed to determine the fissiondecay constant. One of the reasons of the difficulty in measuring At is the fact that the probability of the occurrence of fission is very much lower than of competing radioactive decays: for uranium, for instance the a-decay constant is about 2 x l0 ~ times the fission-decay constant (As (23sU)= 1.551 x 10-'°yr -~, Jaffey et al., 1971; Steiger and Jaeger, 1977). More than 40 values of AI can be listed, which are comprised between 0.7x 10-17yr-' and 28 x l0 -'7 yr-'. When Price and Walker, 1962, proposed that the ages of rocks could be measured by the fission-track method, more than twenty years after the discovery of 23~U fission, there were about twenty Al values; the more acceptable of these ranged between 7 x l0 -~7 yr-' and 12 x 10-27 yr -~. Since that time, the decay-constant value has become of great importance for people working in
geochronology. Some new techniques strongly tied to fission tracks were added to the techniques used until that juncture. In Table I the data from literature that the author is aware of are listed: for each datum, the method by which the value was obtained has been added. Most of them are taken from the list by Thiel and Herr 0976). Methods used to measure AI have been grouped in Table 1 as follows: (1) direct determinations; (2) radiochemical or mass-spectrometry analyses; (3) solid state track detectors (SSTD) and photographic emulsions; (4) fission track, K/Ar and/or Rb/Sr dating comparisons, or dating of samples of well-known ages. In the last fifteen years the range where At could be comprised has been reduced, and two values are commonly accepted by fission-track workers: (1) about 7 x 10-~7yr-I; (2) about 8.5 x 10-17 yr -~. Ages calculated by using these two values differ by about 20%. However, measurements performed on the same samples in different laboratories,
*Introductory lecture for the Pisa FTD Workshop session devoted to the topic of 23sU fission-decay constant. 35
36
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THE PROBLEM OF THE DECAY CONSTANT Ar OF z3~U using the two At values, do not necessarily differ by 20% from one another, for researchers have not yet found a complete agreement on others parameters which are fundamental to fission-track dating. In each laboratory where fission-track utilization has been developed for dating, a local calibration has been endeavoured, especially during the early 1960s. Different methods have been used for the measurement of the neutron dose, for the counting, and for the age correction of samples which had undergone fossil-track fading. Thus, an evaluation of ages obtained by different laboratories is very difficult, especially if the age determinations date back to the first few years after 1962. It is known for certain that, in each laboratory, age measurements obtained by the fissiontrack method have been compared to those obtained by other radiometric methods (prevalently K/At, Rb/Sr and U/Pb) and/or to the stratigraphic ages. Every calibration has been obviously directed towards the obtaining of data that are most concordant with those obtained in some other way. It thus appears likely that the eventual differences in some aspects or points of dating could have been counterbalanced by differences in other points. For instance, different laboratories where different ,tr values were used may have obtained similar age values on the same sample using different dating methods (for instance, by correcting or not correcting the thermally lowered gas; using different neutron-dose standards; and so on).
The firstiand until now the lastIwide-ranging interlaboratory comparison was performed on a sample distributed by C. W. Naeser of the U.S. Geological Survey (namely, apatite and zircon from the Fish Canyon tuff from San Juan Mountains, Colorado). As a matter of fact, the results obtained using the decay constant 7 × 10 -j7 yr -~ for the age calculation have an average value higher than the results obtained by those laboratories where the constant 8.5 × 10 ~7yr-~ was used; the difference, however, did not reach 20%, though it was not far from it (Naeser and Cebula, 1978). 2. REVIEW OF DATA Excepting the four direct determinations between 1940 and 1946, the distribution of measurements in Table 1 is shown in Fig. 1. We
37
can observe three peaks: the first one is centred around 7 x 10 ~7yr-J, the second peak around 8.5 x 10-~7 yr -' and the third peak falls between 10x and 12x 10 ~7yr-~. The largest part of the measurements connected with the fission tracks comprises the first two peaks. The third peak is predominantly made up of the chemical data. Almost all the measurements performed using detectors in 2~r geometry are in the first peak. In the second peak there are many direct measurements. In both peaks there are radiochemical measurements, just like those obtained by comparing FT, K/Ar and Rb/Sr ages and those obtained by dating samples with a known age. The bad distribution of the At values in Fig. 1 is not due to the reported experimental errors; in fact many standard deviations exist between measurements belonging to different peaks. To show this, Fig. 2 has been drawn by combining the measurements, assuming a normal distribution of the experimental errors; the curve is the addition of standard-area Gaussian curves whose width has been determined by the experimental error relating to the measurements shown in Table I. The four direct determinations between 1940 and 1946, and the At values reported without experimental error, were not taken into account in constructing Fig. 2. The scale of the ordinate is arbitrary. The diagram shows very clearly two different peaks, well distinguished, which can be correlated with two decay-constant values: 7.05 × 10-JTyr ~ and 8.46×10 ~7yr ~. Furthermore the diagram shows another smaller peak, whose maximum corresponds to the 10.65 × 10 ~7yr-, value, The other two peaks, 1.7x 10 ~Tyr-~ and 9.64× 10 z7yr-,, represent single measurements only. In conclusion, such big differences are very probably due to systematic differences which are inherent in the approach. DISCUSSION ON At VALUES OBTAINED BY THE FISSION-TRACK METHOD The analysis of the techniques connected with fission tracks--viz, the SSTD measurements, the measurements by best fit between FT and other ages and the measurements by dating well-known age samples, clearly reveals that the uncertainty in At is strictly tied to the "focal points" of every fissiontrack dating approach: (1) neutron dosimetry; and (2) dating technique and age correction.
38
G. BIGAZZI [~
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THE PROBLEM OF THE DECAY CONSTANT ~,t OF 238U In the SSTD technique, As is normally obtained by using a detector-uranium sandwich and counting the number of tracks produced on the detector, in a known time, by the fissions occurring in the uranium source adjacent to it. The irradiation of the sandwich with thermal neutrons is used, in order to solve two problems: the determination of the efficiency, and the determination of the number of 238U atoms per unit volume in the uranium source. By efficiency one means the ratio between the number of revealable tracks by chemical etching on the detector surface and the number of fissions which occurred in the uranium per unit volume. But the use of the irradiation involves the dose measurement: ai determinations by SSTD were obtained by different laboratories using different dose calibrations. For this reason such measurements, even if they predominantly agree with 7 × 10-b 17yr-', are not easily comparable either with each other or with the data obtained by other techniques. The hypothesis that SSTD values are lower than the real one because of a counting loss due to the low track densities is not well supported; in fact, this would assume the same counting loss for every laboratory. When AI is obtained by the comparison between FT and K/Ar and/or Rb/Sr ages, the neutron-dose calibration and the much-discussed problem of apparent-age correction are focal points. To show this, the curves published by Fleischer and Price (1964)---Fig. 3(a); by Gentner et al. (1972)---Fig. 3(b); and by Naeser et al. (1977)--Fig. 3(c); have been redrawn in Fig. 3. In Fig. 3(a), the best fit between fission track ages and K/Ar-Rb/Sr ages has been obtained by using samples, amongst others, of tektites, obsidians and muscovites. Whoever has analysed such kind of samples knows that thermally-lowered fission-track ages are relatively frequent in them. Owing to the fact that in 1964, age corrections were not yet being used, the value of 6.9 x 10-17 yr-' obtained should be regarded as lower than the real one, as some of the samples examined are likely, to have had a fission-track age lowered by thermal phenomena, i.e. the observed fossil-track density to have been reduced. The above authors observed excessively young ages on some samples, but these were samples with extremely clear fading, which points were significantly distant from the line along which
39
the points relating to the other samples were aligned. In the curve of Fig. 3(b), which has been constructed in the same way as the curve in Fig. 3(a), the ages lowered by some natural thermal phenomena were corrected. It may be noticed that the number of the samples whose age has been corrected is very high (about 70%). Furthermore, the number of cases of thermally-lowered fission-track ages increases with increasing age of the material (glass and minerals) dated. In agreement with the results of Gentner et al. (1972), the fossil-track fading cannot be neglected when comparing FT ages and K/Ar, Rb/Sr or other well-known ages. The above authors used, for the best fit, only the unaffected fission-track ages. The corrected ages of the graph agree perfectly with those obtained by other methods when using the best-fit value: 8.4× 10-~7 yr-% It must be noticed that in both Figs. 3(a) and 3(b), ages of identical materials, namely tektites and obsidians, are shown. Unfortunately, as stated before, the two Aj measurements of Figs. 3(a) and 3(b) are not entirely comparable, owing to the lack of standardization in the neutron dosimetry. Naeser et al. (1977) have built the same kind of curve Fig. 3(c), using samples of zircons. Zircon is very resistant to fading phenomena; the lastnamed authors write: "ages are all from volcanic rocks in which annealing should be absent or minimal". Although Naeser et al. (1977) do not explain in that paper their dating technique, it is very probable that they used the external-detector method, normally applied by Naeser in zircon samples (Naeser, 1969; Naeser and Dodge, 1969). In this method, the fossil tracks are revealed on polished surfaces of the zircons themselves, whereas the induced tracks are observed in an external detector (which could be a muscovite mica or a plastic detector), which is placed in contact with the sample during the irradiation. In this way, the fossil tracks are registered with 4~-geometry, whereas induced tracks are registered with 2~-geometry and in a different material. In addition ages by the external-detector method are not susceptible of being corrected for fossil-track fading. To calculate the age, a factor has to be introduced to correct the induced-track density. This factor should take into account the different
40
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registration geometry as well as the possible differences in etching efficiency and the possible differences in optical counting in the two materials. In the past, ages have been calculated by multiplying by 0.5 the fossil-track density/induced-track density ratio (Naeser and McKee, 1970; Naeser et al., 1971). The FT ages reported in those papers perfectly agree with the K/Ar ages. However, those fission-track-age values are dependent on the
kl value and the neutron dosimeters used by the authors. Reimer et al. (1970) suggested that the "geometry factor" for external detectors had to be higher than 0.5. They based this suggestion on experimental results obtained on the external surfaces of the mineral itself (i.e., apatite, zircon, glass, muscovite and sphene). Gleadow and Lovering (1977) carefully studied the value of the geometry factor for external detectors in fissiontrack dating. They compared the induced-track
THE PROBLEM OF THE DECAY CONSTANT A,, OF 23sU densities on the surface of the external detectors (i.e., muscovite mica) and on the polished surfaces of the crystals themselves. Gleadow and Lovering (1977) conclude "the geometry factor relating track densities on external detectors and internal surfaces is 0.5 for apatite, sphene and zircons, and probably for other minerals as well". They also write "the etching efficiency of zircons, and probably of other minerals, is highly dependent on crystallographic orientation, so that care must be taken when using the external-detector method to choose only the appropriate orientations for counting. For zircon the best orientation is probably parallel to the C-axis. Further work is needed to fully document the variation of etching efficiency with crystallographic orientation in zircon and in other minerals" (p. 105 of the above paper). It means that, when using external-detector method, if for some of the polished surfaces of the zircons an etching efficiency is applicable which is lower than the one corresponding to the probable best orientation, a lower fission-track age could be obtained. Using such lowered ages for the best fit between FT ages and K/Ar ages, a lowered At value could be obtained. However, in their paper Gleadow and Lovering (1977) do not confirm this possibility, as owing to the generally elongated appearance of the zircon crystals, their polished surfaces will mostly be oriented parallel to the C-axis. Even if this statement seems to be reasonable, the problem of the geometry factor for external-detector dating does not seem to be entirely resolved, so that, as stated by the above authors, further work is needed. The external-detector method has been studied by Green and Durrani (1978); they reported experimental data for apatite only, confirming a value of 0.5 for the geometry factor. For the neutron dosimetry, Naeser et al. (1977) used the standard glasses that Carpenter and Reimer (1974) have set up for fission-track dating. In their paper, Naeser et aL (1977) observe that the value found (AI = 6.85 × 10 -17 yr ~) must be referred to such standards. That value must be considered a "conventional" value to be used in connection with NBS standards. This observation is very important and constructive, as it shows a way to solve the problem of the At value to be used for fission-track dating. To summarize: the different best-fit At values
41
reported in Figs. 3(a), 3(b) and 3(c) are due to systematic differences inherent in the approach, namely: Fig. 3(a)--Neutron dosimetry was by counting the 14°Ba and 99Mo activity in a U foil. Fissiontrack dating was without checking for moderate fossil-track fading. Fig. 3(b)--Neutron dosimetry was by AI-Au and Al-In monitors. Only thermally-unaffected fission-track ages were used for the fit. Fig. 3(c)--Neutron dosimetry was by N.B.S. Standard Reference Material for fission-track dating. Use made of the external-detector method. Zircons, in which annealing should be negligible were used. Hurford and Gleadow (1977) obtained for Af the value (7.00_+0.28)× l0 -17 yr -I by dating standard age-samples and measuring the neutron dose with the NBS glass SRM 962. Many of the laboratories dealing with fission tracks know these samples: they were the apatite and zircon from the alreadymentioned Fish Canyon tuff, and the apatite from the deposit near Cerro de Mercado, Durango, Mexico. Hurford and Gleadow (1977) measured the ages of the zircon samples by the externaldetector method; they selected "only zircons with polished faces approximately parallel to the Caxis", for the reason discussed above. The above authors hypothesize the possibility that apatites from Fish Canyon tuff show a small degree of spontaneous-track fading. However, they did not find any experimentally clear evidence of annealing. Experimental results on the shortening of spontaneous-fission tracks in Durango apatite and Fish Canyon tuff apatite are reported by Green (1980). This author writes that the observed shortening is due to thermal annealing of spontaneous tracks at ambient (room) temperatures. Green (1980) promises to examine the effect of track shortening in fission-track age determination in a further publication. It seems clear that further work is needed on those samples, as conflicting ages were published specially on Durango apatite (M/irk et al., 1971; M/irk et al., 1972; M/irk et al., 1973; Storzer and Poupeau, 1973; Naeser and Fleischer, 1975; Bertel et al., 1976, 1977; Green and Durrani, 1978). In the field of AI determination by the dating of samples of well-known age, Wagner et al. 0975) and Thiel and Herr (1976 have performed two very
42
G. BIGAZZI
important measurements, as they analyzed samples whose age was historically known. The results agree with those obtained by the "rotating bubble chamber" (around 8.5x 10-'Tyr-'). The neutron dose has been measured with great care by Wagner et al. (1975). Nevertheless, the results show that the neutron dosimetry is among the main sources of error. The authors emphasize the possibility of obtaining differences in the decay-constant value which are not easily explainable if different reactors and different irradiations are used. This means that the determination of the neutron dose is one of the main problems in the At measurement by the fission-track method, even if the differences that Wagner et 'al. (1975) observed are far from the percentage (20%) which separates the values clustered around 7 x 10 'Tyr-' from those grouped around 8.5x10--'Tyr -'. Equally important is the partial fading of fossil tracks. As a proof, the higher value of At (about 8.5× 10 ,7 yr ') supported by the fission-track work by Storzer (1970), Gentner et al. (1972), Wagner et al. (1975), M~rk et al. (1975), Thiel and Herr (1976), is used only in laboratories where thermal fading corrections are applied routinely. One could conclude that the use of a lower As value could compensate for the lack of correction of thermally-lowered ages. 4. CONCLUSION As shown in the above discussion it is very difficult to say what the true value of the 238U fission-decay constant is. Many apparently good measurements can be found in the literature, which sometimes agree with one and sometimes with the other of the two values that people working in fission tracks use nowadays. A good calibration, accepted everywhere, is the main aim of geochronologists, so that age measurements performed in different laboratories may be compared with each other and with those obtained by other techniques. The analysis of the At measurements made by the fission-track method has shown that they are not easy to evaluate; this is because of the problems that are still under discussion in connection with this geochronological technique. There are two possibilities in obtaining an interlaboratory calibration: (1) the choice of a standard for the neutron dose measurement which is acceptable to all; or
(2) the choice of one or more standard agesamples. In the first case, the Ar value is needed; the value obtained by the best fit between the fissiontrack ages and ages obtained by other radiometric methods would be recommended. This comparison should be limited to easily controllable samples, for which any fading phenomena of the fossil tracks can, reasonably, be excluded. Not all researchers, in fact, agree with the correction of apparent ages and on which technique to use. It appears reasonable, for instance, to use a value around 7 x 10 ,7 yr-' for At when, for the neutrondose determination the standard glasses SRM 962 and SRM 963 of the National Bureau of Standards, U.S.A., are used. But we must take into account the fact that this At value must be considered a conventional value, referring to the chosen standard. If, on the other hand, an agreement on the choice of one or more age-standards is reached, then problems connected both with the neutron dose measurement and with the At value can be overcome; as the age measured by the fissiontrack method would refer to known ages. The age would be determined by a comparison between the ratios (fossil/induced) track densities of both the sample with a known age and the sample under examination. In any case, the standard-age samples must be chosen with great care as regards the presence of fading phenomena of the fossil tracks. However, there is an arbitrariness in the initial choice, when it is maintained that, in the standard sample, the age measured by the fission-track method is equal to the age measured by other radiometric techniques. A calibration obtained in these two ways does not give an absolute guarantee of the numerical values of the age, but it allows, at least, a comparison to be made amongst the measurements obtained at different laboratories. These points, in relation to the calibration of the fission-track method, are widely discussed in other papers in this special issue. In fact, as we have observed several times in the present paper, the value of the decay constant, the neutron dosimetry and the dating techniques are problems which are strictly tied to each other. Finally, we must not forget the problem of the real value of the 2~8U fission-decay constant--even
THE PROBLEM OF THE DECAY CONSTANT
if an interlaboratory calibration is obtained and convincing age m e a s u r e m e n t s can be performed. In fact, scientists cannot be satisfied with merely accepting a conventional value for a physical quantity, which is capable of being directly measured. Acknowledgements--Figure 3(a) has been reprinted, by permission, from Physical Review, 133, n. IB, B63-B64, Copyright 1964, and by the kind permission of R. L. Fleischer. Figure 3(b) has been reprinted from Trans. Amer. Nucl. Soc., A N S 15, 126--127, Copyright 1972, by the kind permission of D. Storzer. Figure 3(c) has been reprinted by the kind permission, from Nature 267, 649; Copyright 1977, Macmillan Journals Limited.
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