10  K)Ar and Ar)Ar dating

 

Potassium is one of the eight most abundant chemical elements in the Earth’s crust and a major constituent of many rock-forming minerals. However, the radioactive isotope, 40K, makes up only 0.012% of total potassium, so it effectively falls in the low ppm concentration range. 40K exhibits a branched decay scheme to 40Ca and 40Ar. The major branch leads to 40Ca, but in most rocks the daughter product is swamped by common (non-radiogenic) 40Ca, which makes up 97% of total calcium. Because variations in the abundance of radiogenic 40Ca are very limited in most rock systems, this method has a restricted application as a dating tool (section 9.5). Only 11% of 40K decays lead to 40Ar, but since this is a rare gas, the radiogenic component is dominant. It makes up 99.6% of atmospheric argon, equal to 0.93% of dry air by volume.

 

            Decay to 40Ar is by three different routes (section 1.3.1), two of which involve capture of an orbital electron by the nucleus. The third route (positron emission) makes up only 0.01% of decays to 40Ar. Therefore, the electron capture (EC) decay constant can be taken to represent all of the routes from 40K to 40Ar. This decay constant has a recommended value of 0.581 H 10!10 yr!1, equivalent to a half-life of 11.93 Byr (Steiger and Jager, 1977), based on a weighted mean of the six best counting determinations evaluated by Beckinsale and Gale (1969).

 

            Decay to 40Ca is by emission of a $ particle, and the $ decay constant has a recommended value of 4.962 H 10!10 yr!1, equivalent to a half-life of 1.397 Byr. The sum of the decay constants for the two branches yields the total 40K decay constant of 5.543 H 10!10 yr!1, equivalent to a half-life of 1.25 Byr. The possible need for revision to this value is discussed in section 10.4.3.

 

 

10.1     The K)Ar dating method

 

            The fraction of 40K atoms that decay into 40Ar is given by the expression 8EC /(8EC + 8$). Hence, substituting into the general decay equation [1.10], the growth of 40Ar in a K-bearing rock or mineral can be written as:

 

                                    8EC

 40Artotal  =  40ArI   +     )))  @  40K (e8total t ! 1)                                   [10.1]

                                    8total

 

However, if the system was completely outgassed of Ar at the time of formation, the initial Ar term disappears, and the equation is simplified to:

 

    40Ar* = (8EC / 8total) @ 40K (e8 total t ! 1)                                              [10.2]

 

where 40Ar* signifies radiogenic argon only. As will be seen below, this is the situation which is normally assumed in K)Ar dating.

 

 

10.1.1  Analytical techniques

 

The isotopic composition of naturally occurring potassium has been found to be effectively constant in all types of rock throughout the Earth, with a few minor exceptions (e.g. Garner et al., 1976). Therefore the 40K content of a mineral or rock is usually found by straightforward chemical analysis for total potassium, followed by multiplication by 1.2 H 10!4 to derive the concentration of the radioactive isotope. Various methods can be used to determine potassium, including ICP-OES (inductively coupled plasma – optical emission spectrometry), X-ray fluorescence, and isotope dilution. In the past, a commonly used method was flame photometry (Vincent, 1960), a form of optical emission spectrometry especially suitable for the alkali metals. This technique was less accurate than isotope dilution but could achieve precisions of ca. 1% and was quick and inexpensive.

 

            Argon trapped in a geological sample is released and purified in an argon extraction line, ‘spiked’ with an enriched isotope, and then fed into a mass spectrometer for isotopic analysis (Fig. 10.1). Samples must have the minimum possible surface area for absorption of atmospheric argon; therefore mineral separates or whole-rock chips are not powdered. After loading the sample(s) in the extraction line, the whole line, and especially the sample itself, must be baked under vacuum to extract all possible atmospheric argon from the system. Next, after isolating the pump, the sample is manoeuvred into a disposable molybdenum crucible, which is positioned in a radio frequency induction furnace. The crucible is heated to ca. 1400 oC, whereupon the sample melts and releases all of the trapped gases. These consist mostly of H2O and CO2, with a very small amount of argon and other rare gases. All gases except the rare gases can be removed by reaction with titanium vapour in a Ti sublimation pump or by using a zeolite ‘getter’. Activated charcoal fingers may be used for temporary absorption of gases during their manipulation.

Fig. 10.1. Schematic diagram of an argon extraction line coupled to a static gas mass spectrometer. After Dalrymple and Lanphere (1969).

 

            Highly enriched 38Ar spike is usually stored in a large glass reservoir bulb. This is connected to a length of capillary tube of fixed volume, between two valves with low dead-space (Fig. 10.1). The capillary is opened to the reservoir while valve 1 is closed. Valve 2 is then closed, and the known volume of spike between the two valves is added to the sample by opening valve 1. Because the reservoir pressure falls with each gas withdrawal, successive spike aliquots contain smaller and smaller fractions of 38Ar. However, aliquots are periodically calibrated by mixing with a known volume of atmospheric argon and performing an isotope dilution analysis. The amount of 38Ar spike added to each sample is determined by noting its order in the sequence and interpolating between the calibration runs (Lanphere and Dalrymple, 1966). The amount of argon released from a typical sample of a few hundred milligrams is very small, generally less than 10!6 cc (cm3) at STP (standard temperature and pressure = 25 oC at 1 atm). For this reason the isotopic analysis is performed statically; in other words, the entire sample is fed into the mass spectrometer at once, after isolation from the pumps. The 40Ar/36Ar ratio in the air may be measured between unknown samples as a check on the calibration of the machine, and normally has a value of 295.5 " 0.5.

 

            Two different types of mass spectrometer are in common use. Modern rare gas machines tend to be very similar to solid source TIMS machines, with a high accelerating potential of several kilovolts, and peak-switching by changing the magnetic field. The problem with this type of machine is that the high velocities of the ions makes them implant into metal components in the vacuum system whenever these are struck by the ion beam. Such ions diffuse back out of the metal surfaces during analysis of the next sample, and this memory effect must be carefully corrected. The effect may be reduced by polishing metal components which the beam is likely to strike. Many older instruments used a low accelerating potential of a few hundred volts and a small permanent-field magnet. The accelerating potential was then switched to focus different nuclides into the collector. This type of machine suffered from very little memory effect but was capable of much poorer precision in the measurement of isotope ratios. Since the source is gaseous, there is no problem of mass-dependent fractionation in either type of machine.

 

            A typical argon isotope mass spectrum is shown in Fig. 10.2. The presence of any 36Ar signal shows that common or non-radiogenic argon is present. This is almost inevitable, because of the great difficulty of removing all atmospheric argon from the system. However, if the sample was completely outgassed at the time of its formation, it will not contain any inherited non-radiogenic Ar. In this case the measured 40Ar peak can be corrected for atmospheric contamination by subtracting 295.5 times the 36Ar peak:

 

                40Ar*  =  40Artotal  !  295.5  36Ar                                           [10.3]

 

A value of 0.063% of atmospheric argon is similarly subtracted from the 38Ar peak. The 40Ar and 36Ar peaks must also be corrected for small fractions of these isotopes in the spike. The amount of radiogenic 40Ar* in the sample is then found by comparison with the size of the net 38Ar peak, formed by a known quantity of spike. (In other words, this is an isotope dilution determination). Given the abundances of 40Ar and 40K in the sample, the age is calculated by re-arranging equation [10.2]:

 

                         1         | 40Ar*    8total                |

            t  =       ))  ln   | )))  @ ))))   +  1    |                                   [10.4]

                        8total     | 40K     8EC                  |

 

            K)Ar ages depend on closed-system behaviour of the sample for K and Ar throughout its history. In addition, it is necessary to assume that the sample contains no initial argon (usually called ‘excess’ argon), because this might have a 40Ar/36Ar ratio different from that of atmospheric argon. This would lead to a mixture with indeterminate 40Ar/36Ar ratio which could not be corrected for atmospheric contamination.

Fig. 10.2. Schematic argon isotope mass spectrum showing fractions of each peak due to radiogenic Ar (white), spike (stipple) and atmospheric contamination (hatched). Size fractions are not shown to scale. After Dalrymple and Lanphere (1969).

 

            The 36Ar/40Ar ratio must be analysed to very high precision because the atmospheric Ar correction magnifies any errors in this measurement by a factor of ca. 300. The importance of this effect is shown in Fig 10.3, where the effect of error in the measurement of 36Ar is shown in terms of the resulting error on the calculated age (Cox and Dalrymple, 1967). Once atmospheric contamination exceeds 70% of total argon, errors in 36Ar have serious consequences for the age measurement. This correction is not a problem for old and/or K-rich samples, but is the principal limitation to dating young material.

Fig. 10.3. Error magnification in K)Ar dating (y axis) resulting from atmospheric argon contamination. Curves are calculated for 0.5, 1, 2 and 5 % errors in the measurement of 36Ar. After Cox and Dalrymple (1967).

 

            Since 1967, great improvements in measurement precision have been made, allowing the dating of very young rocks. However, Mussett and Dalrymple (1968) showed that volcanic rocks contain ‘locked-in’ atmospheric (non-radiogenic) argon, some of which cannot be removed even by baking in a vacuum. Hence, even with a low-blank analytical system, a small residual atmospheric fraction is almost unavoidable in terrestrial lavas.

 

 

10.1.2  Inherited argon and the K)Ar isochron diagram

 

Since 36Ar is used as a monitor of atmospheric contamination, there is no facility in K)Ar dating to correct for initial argon incorporated into minerals or rocks at the time of crystallisation. Hence, it must be assumed to be absent. However, early work by Damon and Kulp (1958) showed the presence of initial or ‘excess’ argon in beryl, cordierite and tourmaline. Since these minerals all have a ring structure, it was initially assumed that the stacking of rings created channels in which excess argon inherited from fluids could reside. Hence, Damon and Kulp suggested that this problem might also occur in hornblende, where partial vacancy of the alkali-cation site might provide a location for excess argon.

 

            However, excess argon was subsequently also found in pyroxenes by Hart and Dodd (1962). Since the pyroxene structure does not have any suitable voids for accommodation of argon, Hart and Dodd argued that it must be located in crystal dislocations and defect structures. This implies that excess argon is a product of the environment of crystallisation rather than the host mineral. Hart and Dodd noted that their analysed pyroxenes were from originally deep-seated rocks, unlike the volcanic or shallow intrusive rocks normally used in K)Ar dating. Hence they warned that excess argon might be a common feature in samples from deep-seated (plutonic) environments.

Fig. 10.4. Contents of (excess) radiogenic 40Ar in submarine pillows from Hawaii, plotted against inward distance from the pillow rim. Apparent K)Ar ages for each sample are noted in Myr. After Dalrymple and Moore (1968).

 

            The known occurrence of excess argon was extended to submarine lavas by Dalrymple and Moore (1968). They dated glassy pillow rims and whole-rock pillow cores from flows at 500 ) 5000 m depth on the northeast ridge of Kilauea volcano, Hawaii. Various geological lines of evidence suggested a historical age for the samples, but K)Ar ages of up to 43 Myr were found. Furthermore, a series of samples from rim to interior of one pillow (from 2590 m depth) showed an inverse correlation of apparent K)Ar age with distance from the rim (Fig. 10.4). The results were attributed to entrapment of initial or excess argon which was inherited from the mantle source by the magmas. Dalrymple and Moore concluded that because these magmas were quenched under substantial hydrostatic pressure, inherited argon was not completely outgassed at the time of eruption, as usually occurs in terrestrial lavas. It was subsequently able to escape from the slowly crystallising core of the pillow, but was retained in the glassy rim.

 

            Even some sub-aerially erupted lavas were subsequently found to contain inherited argon. For example, McDougall et al. (1969) encountered measurable radiogenic 40Ar contents in historical age subaerial basalts from New Zealand. Lavas shown by 14C dating of wood inclusions to be less than 1 kyr old nevertheless gave K)Ar ages of up to 465 kyr. This led McDougall et al. to consider whether such cases of inherited argon could be detected and/or corrected.

Fig. 10.5. K)Ar isochron plot for a lava of historical age from Mount Wellington, New Zealand, showing a best-fit slope age of 75 kyr. After McDougall et al. (1969).

 

            They proposed that the raw 40Ar signal (uncorrected for atmospheric contamination) be divided by 36Ar and plotted against the K/Ar ratio to form an isochron diagram analogous to that for Rb)Sr (Fig. 10.5). This is achieved by expanding the initial Ar term in equation [10.1] to include both atmospheric and excess components, and by dividing throughout by 36Ar:

 

 (40Ar)              (40Ar)                 40K          8EC

 ())))   =        ())))     +         ))) @ ))))))  (e8total t !1)             [10.5]

 (36Ar)total          (36Ar)atm+excess      36Ar    8EC + 8$

 

This equation has the form:

 

             y   =    c    +   x  m                                                                  [10.6]

 

When a suite of samples is analysed from a single completely-outgassed system such as a lava flow, the c term is entirely atmospheric. Therefore, the analysed points, when plotted on an isochron diagram, should define a straight line with an intercept of 295.5, whose slope yields the age of eruption. In fact, this array is merely a mixing line between the samples and atmospheric argon. When the atmospheric correction is performed on a single analysis, we effectively make 295.5 the origin and determine the slope.

 

            In the case studied by McDougall et al. (1969), the lavas are of approximately zero age. Hence, the analyses which make up their ‘isochrons’ (e.g. Fig. 10.5) represent argon trapped in the magma and later variably mixed with atmospheric argon. McDougall et al. speculated that the trapped argon might originate from partially digested crustal xenocrysts.

 

            Roddick and Farrar (1971) considered the case of a geologically old sample suite displaying both inherited argon and atmospheric contamination (Fig. 10.6). With inherited and radiogenic argon only, the array ABC is defined, but if variable atmospheric contamination occurs, a scatter (DEF) may result. In principle, a good linear array on the K)Ar isochron diagram should indicate that both the age and initial Ar isotope ratio are meaningful. However, it may be possible for the slope of the line to swing round in a systematic way due to complex mixing processes, so that it yields a good array of meaningless slope. Nevertheless, the isochron diagram is a useful test of K)Ar data where the presence of inherited Ar is suspected.

Fig. 10.6. Schematic K)Ar isochron diagram to show the effect of mixing inherited and radiogenic argon (A, B, C), coupled with variable atmospheric contamination (D, E, F). After Roddick and Farrar (1971).

 

            Lanphere and Dalrymple (1976) drew a distinction between inherited argon and excess argon. They defined the former as argon which ‘originates within mineral grains by decay of 40K prior to the rock-forming event’. Hence, this definition includes the examples given above. However, excess argon has a wider definition that also applies to sources of extraneous argon that diffuse into a system from outside. Lanphere and Dalrymple (1971, 1976) pioneered the use of the 40Ar/39Ar method to identify excess argon in rocks (section 10.2.5).

 

 

10.1.3  Argon loss

 

The K)Ar method is unique amongst the major radiometric dating methods in having a gaseous daughter product. This means that the K)Ar system reacts differently from lithophile isotope systems such as Rb)Sr in response to thermal and hydrothermal events. Because argon is a non-reactive gas, its partition into the fluid phase is limited. Therefore, the K)Ar system may be more resistant than Rb)Sr to hydrothermal metamorphism. On the other hand, no mineral phase preferentially takes up argon when it is lost from the mineral where it was originally produced. This means that in K)Ar dating, whole-rock analysis confers no additional resistance to metamorphic re-setting (as it does for the Rb)Sr method). On the contrary, in K)Ar analysis a whole-rock sample is only as resistant to re-setting as its least retentive phase. Consequently whole-rock K)Ar analysis is a last resort, when all mineral phases in the rock are too fine-grained for mineral separation.

 

            A good comparison of argon loss from various minerals during a thermal event is provided by contact metamorphism associated with the Eldora stock in the Colorado Front Ranges (Hart, 1964). The 54 Myr-old quartz monzonite stock is intruded into ca. 1350 Myr-old amphibolites and schists. Hart analysed biotite, hornblende and K-feldspar at increasing distances from the intrusive contact (Fig. 10.7), and found that despite the limited extent of petrographic alteration, K)Ar mineral ages were re-set at large distances from the stock. Hornblende displayed good Ar retention properties, with loss of argon confined primarily to within ten feet (ca. 3m) of the contact. However, coarse biotites were largely re-set at distances up to 1000 ft (300 m) from the contact, while K-feldspars had lost a substantial fraction of argon even 20 000 feet (6 km) from the contact. The latter can hardly be said to be within the thermal aureole of the stock, and reflects the now widely accepted view that K-feldspars may lose argon by diffusion even at ambient temperatures. It is now recognised that systems such as these, that have suffered open system behaviour of argon, must be studied by the 40Ar–39Ar technique (see below).

Fig. 10.7. Plot of apparent K)Ar mineral ages against outward distance from the contact of the 60 Myr-old Eldora stock, Colorado. After Hart (1964).

 

 

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