The use of cosmic-ray produced ³²Si for dating of ice and water (Reference Lal and SchinkLal and others, 1960; Reference Clausen, Clausen, Buchmann and AmbachClausen and others, 1968; Reference Lal, Venkatavaradan and OlssonLal and others, 1970) has hitherto been complicated by the poor knowledge of the half life. The literature contains several estimates ranging from 60 to 710 years (Reference Turkevich and SamuelsTurkevich and Samuels, 1954; Reference GeithoffGeithof, 1962; Reference Honda and LalHonda and Lal, 1964; Reference JantschJantsch, 1967), all of which are based on assumptions about unknown cross-sections of nuclear processes leading to the formation of ³²Si. Direct measurement of the half life has not been attempted, mainly because of the difficulty in determining the number of ³²Si atoms in the small samples obtainable.

This work presents calibration curves for ³²Si dating of polar ice, independent of the half life and possible temporal changes in the production rate of ³²Si. With reasonable assumptions about the production-rate changes, the calibration curves lead to an estimate of the half life, independent of cross-section considerations.

³²Si is cosmic-ray produced in the atmosphere by argon spallations (Reference Lal and SchinkLal and others, 1960) and is scavenged from the atmosphere by rain and snow. The rate of production has been estimated at 1.7 × 10⁻⁴ atoms cm⁻²s⁻¹ (Reference Lal and SchinkLal and others, 1960) and at 1.2 × 10⁻⁴ atoms cm⁻²s⁻¹ assuming a half life of 300 years (cf. Reference Dansgaard, Dansgaard, Clausen and AarkrogDansgaard and others, 1966 [a], p. 5476). At latitudes higher than 30°, the specific ³²Si activity of precipitation is expected to be approximately 20 dph/ton, essentially independent of latitude (Reference Dansgaard, Dansgaard, Clausen and AarkrogDansgaard and others, 1966[a], p. 5476, [b], fig. 1).

The snow- and ice-pack in the high-altitude regions of the Greenland ice sheet contains many thousands of annual layers of precipitation, accumulated without run-off or mixing. They can be dated by ice-flow considerations (Reference Dansgaard and JohnsenDansgaard and Johnson, 1969) or by counting ¹⁸O/¹⁶O summer maxima downwards from the surface (Reference Johnsen, Johnsen, Dansgaard, Clausen and LangwayJohnsen and others, 1972). A total of 13 firn and ice samples were collected, melted and chemically prepared for extraction of ³²Si. Data obtained on these samples are listed in Table I. Comments on the individual columns are given below.

Table I

1. 1. Sites of collection. Sample Nos. 1–5, 10, 12 and 13 originate from a pit and a bore hole at the Dye 3 station in south Greenland. These bore-hole samples are identical to samples collected for ¹⁴C dating by Hans Oeschger’s group from the University of Bern (¹⁴C data will be reported later). The rest of the samples originate from a 100 m deep trench with slope of 1: 3, at Camp Century, north-west Greenland, but No. 11 is from a bore hole at the same location.

2. 2. The depth is for Camp Century the distance from the 1966 summer layer to the ice sample in situ, for Dye 3 the distance from the 1971 surface to the sample. In order to exclude contamination with bomb-produced ³²Si (Reference Dansgaard, Dansgaard, Clausen and AarkrogDansgaard and others, 1966[a]), the samples were collected from layers below the 1945 horizon, except the surface sample from Dye 3, which represents the accumulation from the summer of 1968 to the summer of 1971. In this period the fall-out of bomb-produced ³²Si has dropped to negligible values (Reference Dansgaard, Dansgaard, Clausen and AarkrogDansgaard and others, 1966[a]).

3. 3. The age T is the time elapsed since the deposition of the samples. As for the Dye 3 samples, the ages are determined by counting summer maxima from the surface in a complete ¹⁸O/¹⁶O record spanning 741 years. The accuracy of these datings is better than ±10 years. The Camp Century samples are dated by using the formula (Reference Dansgaard and JohnsenDansgaard and Johnsen, 1969)

   

   H = 1 367.5 m of ice being the total thickness of the ice sheet, and y m of ice being the present distance of the sample from the bottom, both corrected for the low densities in the upper layers. h = 400 m is the distance from the bottom, above which the horizontal velocity profile is considered uniform (below h = 400 m this profile is assumed to vary proportionally to y, which is not essential for this work). λh/τ = 0.35 m of ice/year is the present annual accumulation rate (Reference Crozaz and LangwayCrozaz and Langway, 1966) which has been shown to be representative for the entire depth interval considered here (Reference Johnsen, Johnsen, Dansgaard, Clausen and LangwayJohnsen and others, 1972, fig. 2). The accuracy of these datings is probably better than ±5%.

4. 4. The time interval ∆ represented in each sample is calculated from the known length of the sample using either the ¹⁸O/¹⁶O record or the formula above. Each sample is collected so as to represent many years of snow accumulation in order to smooth seasonal variations in the ³²Si deposition rate (3.5 times higher in summer than in winter; Reference Dansgaard, Dansgaard, Clausen and AarkrogDansgaard and others, 1966[b]). Furthermore, whenever possible the samples represent two 11 year solar cycles in order to reduce possible influence of short-period variations in the cosmic-ray intensity.

5. 5. Amount of sample. Field preparation. Due to the low specific activity of snow, huge amounts of ice (hundreds of kilograms) are required for dating purposes. In the field, preliminary chemical concentration of ³²Si takes place in drums containing the melt water, acid FeCl₃ solution and inactive silica carrier. Addition of ammonia in excess produces a precipitate of Fe(OH)₃, which scavenges all silica from the water. The field preparation is completed by concentration of the precipitate by filtration.

6. 6. The silicic acid is recovered from the precipitate in the laboratory. After drying, the iron and silicon components are separated in boiling hydrochloric acid. To bring all silica into a soluble state, the remaining precipitate is melted in liquid sodium hydroxide (at c. 320° C) containing a few per cent of sodium nitrate to oxidize possible organic contaminants. After recovering the silicon components as silicic acid by adding hydrochloric acid to the melt dissolved in water, it is heated to 800° C in an electric oven.

7. 7. The net counting rate. The radioactivity measurements are carried out on the daughter ³²P, because it is better suited for detection due to its high β energy 1.7 MeV (compared with 0.1 MeV for ³²Si), and for identification due to the short and well-known half life of 14.3 d. During 2 months of storage, the ignited silicic acid builds up ³²P to more than 95% of the equilibrium value. The chemical extraction of ³²P from the silicic acid has been described in detail by Reference Lal and SchinkLal and others (1960). The β measurement is carried out on approximately 15 mg of Mg₂P₂O₇ in a small counter of the Reference Lal and SchinkLal type (Lal and Schink, 1960) modified by S. J. Johnson. The counter background is ≈1.5 cph for a counting area of 0.5 cm². The counting efficiency is approximately 50% for a 2π geometry with 0.1 mm tungsten backscattering. Figure 1 gives an example of the total counting rate of sample 6 plotted as a function of exp (–λT), λ being the decay constant of ³²P and T the time since separation of ³²P from the silica. The straight line is determined by the method of least squares. The difference between the intersection of this line with ordinates for T = 0 and T = ∞ gives the net counting rate of the sample at the time of isolation. The ordinate for T = ∞ gives the background of the counter plus the contribution of possible long-lived impurities.

   Fig. 1.Total counting rate (cph) of a phosphate sample isolated from the silicates. The net counting rate is due to the ³²Si daughter ³²P that is built up close to equilibrium after 2 months. The ³²Si activity of the ice sample is calculated from the net counting rate for T = 0 after correction for counter efficiency, etc.

   

8. 8. The specific activity is obtained from columns 5 and 7 after correction for counter efficiency and chemical yield. The stated uncertainties include the uncertainties on the latter parameters.

9. 9. The weighted mean specific activities are plotted versus age T in Figure 2. The (extrapolated) surface value is 23±2 dph/ton at Camp Century and 16.5±1.5 dph/ton at Dye 3. The former value may be representative for north and north-west Greenland, because another sample from mid north Greenland (Inge Lehmann) indicates 27±3 dph/ton. Similarly, the Dye 3 value may be representative for East and south Greenland, because a sample from mid East Greenland (Jarl Joset) indicates 19±3 dph/ton.

   Fig. 2.The specific ³²Si activity (disintegrations per hour per ton) of firn and ice samples plotted as a function of the time since deposition. Dating of old ice should be based on the apparent half life of 295 years and on the specific activity of a sample of recent deposits.

   

The two lines are calculated by the method of least squares. The slopes of the two lines correspond to apparent half lives of 260±40 and 330±35 years for ³²Si. The difference is not significant and 295±25 years is adopted as the best estimate of the apparent half life of ³²Si for dating of ice in Greenland. As to west Antarctic ice, the same apparent half life can probably be used along with a specific ³²Si activity of recent precipitation of 25±2 dph/ton, as indicated by a preliminary measurement on pre-bomb firn from “Byrd” station.

When used on up to 1 000 year old ice samples of the order of 1 ton, the technique described above gives datings with an estimated uncertainty of ±60 years. Ice older than 1 000 years may be dated by using correspondingly higher amounts (a factor of 2 higher for each 300 years beyond 1 000 years).

Measurements on recent material from temperate glaciers in Norway (Reference Dansgaard, Dansgaard, Clausen and AarkrogDansgaard and others, 1966[b]) and Austria (Reference Clausen, Clausen, Buchmann and AmbachClausen and others, 1968) gave somewhat higher values (28 and 50 dph/ton). These samples were collected in 1962 and 1966 respectively and were probably contaminated with bomb-produced ³²Si. Therefore, if the technique is applied outside Greenland and west Antarctica, a recent reference sample should be collected so as to represent net accumulated material from prior to 1952, or, if impossible, after 1970, assuming negligible fall-out of bomb-produced ³²Si in the present decade. If only a short time interval of deposition can be represented, it must be a whole number of years. In all cases, any kind of solid matter present in the samples should be included in the chemical preparation to account for possible adhesion of ³²Si to solid particles.

The apparent half life of 295 ± 25 years, suggested by the data in Figure 2, should be applied for dating of cold as well as temperate glaciers.

The true half life of ³²Si is probably a little higher due to secular changes of the cosmic-ray flux and, therefore, of the natural ³²Si production in the atmosphere. Unfortunately, the temporal change in the cosmic-ray flux is still an unsolved problem. However, short time variations (i.e. up to several hundred years) would show up in Figure 2, if essential. For example, one may expect that the 400 year oscillation observed in the ¹⁴C/¹²C ratio in tree rings (Reference Suess and OlssonSuess, 1970) would appear in Figure 2, if due to cosmic-ray flux variations, the more so as the ³²Si fall-out is not subject to attenuation, as is the ¹⁴C/¹²C ratio in the atmosphere (due to CO₂ exchange with the oceans). The reason why the data do not oscillate with a period of 400 years may be either that the corresponding variation in the ¹⁴C/¹²C ratio is not caused by varying cosmic-ray flux or that the cosmic-ray component producing ³²Si varies much less than that producing ¹⁴C.

On the other hand, the slope of the line in Figure 2 may be influenced by the long-term variation (8 900 year period) in the cosmic-ray flux caused by oscillating geomagnetic moment (Reference Bucha and NeustupnyBucha and Neustrupny, 1967). During the last 700 years the geomagnetic moment seems to have decreased by 25% (Reference Bucha and OlssonBucha, 1970), which corresponds to a 10% increase of the ¹⁴C production, according to Reference Lal, Venkatavaradan and OlssonLal and Venkatavarandan’s (1970, fig. 4) calculations.

Let us assume that the production and fall-out of ³²Si has also increased by 10%. This means that the half life of 295±25 years from Figure 2 is a little lower than in the case of the unchanged ³²Si production rate. The corrected half life therefore appears to be 330±40 years, the higher uncertainty being used to account for the difficulty in estimating the correction term.