10.5 Thermochronometry

The thermal history of meteorites was interpreted in section 10.2.4 in terms of short-lived thermal events, including their initial cooling and any subsequent collisions, separated by long periods under cold conditions. However, Turner (1969) recognised that in different circumstances, slow cooling from a single event could yield an age spectrum rather similar to that produced by episodic thermal events.

10.5.1 Arrhenius modelling

A special feature of the Ar–Ar step heating method is that argon release in the laboratory should be controlled by the same diffusional properties of minerals that cause argon loss in nature. The long time-scales of geological events obviously preclude laboratory analysis under natural conditions. However, if diffusion obeys the Arrhenius law, a rapid argon-release experiment at high temperature in the laboratory can mimic much slower argon release at lower temperatures in the crust. Hence, step heating data may be used to reconstruct thermal histories such as post-orogenic cooling.

The result of slow cooling in a young intrusive body is illustrated by the age spectrum of a biotite from the La Encrucijada pluton in Venezuela (Fig. 10.35). Unfortunately, this approach can rarely be used on terrestrial rocks because the low-temperature part of the profile, which is critical in the determination of a precise cooling rate, becomes ‘corrupted’ by minor diffusional loss of argon at ambient temperatures over geological time.

Fig. 10.35. ⁴⁰Ar/³⁹Ar age spectrum of La Encrucijada biotite, Venezuela, compared to predicted cooling curves based on modelling of Ar diffusion in biotite. After York (1984).

A more useful approach to quantifying the cooling history of crustal rocks is the blocking temperature concept (section 3.3.2), whose theoretical basis was examined by Dodson (1973). Argon loss from a mineral can be described by the thermal diffusion coefficient:

D = D₀ e^!E/RT [10.14]

where D₀ is the thermal diffusivity of the mineral, E is the activation energy of argon diffusion, R is the gas constant and T is absolute temperature. The exponent makes D a very strong function of temperature. Therefore a small drop in temperature can cause a transition from a state where Ar loss by diffusion is rapid to a state where Ar loss by diffusion is very slow. This relatively sharp transition constitutes the process of blocking. The blocking temperature T_B is defined by Dodson (1973) as follows:

E

T_B = ))))))))))) [10.15]

R ln (A J D₀/a²)

where A is a geometrical parameter which takes account of the crystal form of the argon-bearing mineral (55, 27 or 9 for a sphere, cylinder or sheet respectively), a is the length of the average diffusion pathway from the interior to the surface of the grain, and J is the cooling time constant. The latter is in turn defined as follows:

J = R T_B² / (!C_B E) [10.16]

where !C_B is the cooling rate at the blocking temperature T_B. Hence, substituting equation [10.15] into [10.14] yields:

| R T_B² D₀ |

T_B R = E / ln | A @ )))) @ ) | [10.17]

| !C_B E a² |

A method to calculate blocking temperatures from Ar)Ar spectrum plots was proposed by Buchan et al. (1977) and developed by Berger and York (1981a). A plateau age must be available on a mineral from a slowly cooled terrane. For each heating step in the plateau, the volume of radiogenic ⁴⁰Ar released in a given time is used to calculate D/a². For planar minerals such as biotite the diffusion equation has the following general form (e.g. Harrison and McDougall, 1981):

D (q f)²

) = ))) [10.18]

a² t

where f is the fractional loss of argon, t is the heating time, and q is a geometric factor.

The results are plotted on a log scale against the reciprocal temperature of each step, forming an Arrhenius plot (e.g. Fig. 10.36). If diffusional Ar loss obeys the Arrhenius law as expected then the steps in the plateau should define a straight line whose slope is the activation energy E and whose y intercept is the frequency factor D₀/a². These values allow equation [10.17] to be solved, provided the cooling rate !C_B at the blocking temperature (T_B) can be estimated. Fortunately, the temperature solution has a weak dependence on the cooling rate, such that an order of magnitude change in this value causes only a 10% change in the calculated blocking temperature. Because T_B appears on both sides of equation [10.17], it must be solved iteratively, but it converges quickly. The power of this technique is that the mineral blocking temperature is calculated directly on the dated material, rather than having to depend on generalised blocking temperatures for various types of minerals from the literature, which might not be applicable to the specific cooling conditions under study.

Fig. 10.36. Arrhenius plot for hornblende from a Grenville diorite, Haliburton Highlands, Ontario. The blocking temperature was determined from the array of 7 solid data points. Error bars are 1F. After Berger and York (1981a).

Berger and York (1981a) applied this ‘thermochronometry’ method to a study of post-orogenic cooling in the Grenville Province of southern Ontario, Canada. Plutonic ages in the Grenville belt vary from 1.0 to 2.7 Byr, but most K)Ar dates fall below 1 Byr, and are attributed to uplift and cooling after collisional orogeny (Harper, 1967). Berger and York studied dioritic and gabbroic plutons from the Haliburton Highlands, both to determine a detailed cooling curve for the area and to interpret paleomagnetic data on these rocks.

Fig. 10.37. 40)39 age spectra for the hornblende, biotite and K-feldspar analyses used to determine blocking temperatures in Figs. 10.36 and 10.38. Modified after Berger and York (1981a).

Typical 40)39 profiles from Haliburton diorites which gave reasonable plateaus are shown in Fig. 10.37. These samples are plotted on Arrhenius plots in Figs. 10.36 and 10.38. The hornblende displays a relatively simple array in Fig. 10.36, although low-temperature and high-temperature points must be excluded from the regression. K-feldspar displays coherent low-temperature behaviour, but high-temperature data are irregular, possibly due to disruption of the lattice above 900 ^oC. The most unusual behaviour was demonstrated by biotite, which in many cases gave rise to two heating pulses which defined sub-parallel arrays (such as in Fig. 10.38). Nevertheless, the blocking temperatures calculated from the two segments were usually within error. Berger and York speculated that the break in regular behaviour was due to structural breakdown.

Fig. 10.38. Arrhenius plot for Grenville K-feldspar ( > , Î ) and biotite ( # , Q ) dated in Fig. 10.37. Blocking temperature calculations were based on solid data points only. Errors are 1F. After Berger and York (1981a).

Results from all of the analysed minerals are shown on a diagram of blocking temperature against age (Fig. 10.39). Points without error bars failed a reliability criterion which required both the age plateau and Arrhenius correlation line to have four or five statistically well-fitting data points. The data show a clear picture of fairly rapid cooling (ca. 5 ^oC/Myr) from the hornblende blocking temperature of ca. 700 ^oC at 980 Myr to the biotite blocking temperature of ca. 380 ^oC at 900 Myr. Thereafter, the data are mainly from plagioclase, which displays considerable scatter. Berger and York’s original interpretation (solid line in Fig. 10.39) called for very slow cooling (under 1 ^oC/Myr) for a further 300 Myr. However, in a study of gabbro from the Hastings Basin of the Grenville (ca. 80 km east of the Haliburton Highlands), Berger and York (1981b) recognised that the apparently slow cooling curve after 900 Myr might really represent a more recent thermal event.

Fig. 10.39. Plot of calculated mineral blocking temperatures against plateau ages to show a model for crustal cooling after the Grenville orogeny. Solid and open symbols indicate minerals from different plutons. After Berger and York (1981a).

The latter interpretation of the plagioclase data was supported by Hanes et al. (1988), based on Ar)Ar dating of the Elzevir and Skootamata plutons of the Hastings basin. Hanes et al. presented Ar)Ar data for three plagioclase samples, which displayed a range of rather mediocre plateau ages between 400 and 600 Myr. Variations in ³⁷Ar/³⁹Ar ratio with the fraction of ³⁹Ar released were used as an index of the Ca/K ratios of different domains within the minerals. A pronounced hump in the middle of these profiles indicated that the analysed plagioclases were multi-phase systems. They display two different types of alteration, which may be of different ages. Hanes et al. suggested that scattered coarse epidote and muscovite alteration might have formed at high temperatures soon after plutonism, while fine-grained sericitic alteration probably represents an event younger than 400 Myr.

The evidence for structural breakdown in biotite points to a weakness in the thermochronometry method of Berger and York. Because biotite is a hydrous mineral, diffusional loss of Ar during vacuum heating may not accurately mimic Ar loss in nature under (probable) hydrothermal conditions, as suggested by Giletti (1974). This problem was confirmed by Gaber et al. (1988), who demonstrated large differences in argon diffusivity between hydrothermal and vacuum heating experiments on biotite and hornblende.

The susceptibility of these hydrous minerals to structural breakdown during vacuum heating has largely discredited the application of step-heating analysis to determine their blocking temperatures. Instead, attention has switched to K-feldspar, the most common anhydrous K-bearing mineral. As an anhydrous phase, the behaviour of this mineral during vacuum degassing can mimic argon loss in nature with some accuracy (section 10.5.3). However, studies of diffusional argon loss from hydrous minerals have been continued using laser spot analysis. For example, this method has been applied to the study of complex argon diffusion models in micas and amphiboles.

10.5.2 Complex diffusion models

The traditional approach to mineral blocking temperatures is based on ‘Fickian’ behaviour, which means that argon diffusion in minerals is assumed to occur by volume diffusion, obeying Fick’s first law (e.g. McDougall and Harrison, 1999). However, detailed analysis of Ar–Ar ages in minerals has revealed breakdowns in this simple model, requiring more complex models of Argon diffusion to be proposed. The advent of the laser probe has allowed the detailed spatial analysis of minerals in order to test these more complex models.

It has long been known that large biotite grains can lose radiogenic strontium or argon more rapidly than predicted by volume diffusion (e.g. section 3.3.2). This behaviour was also seen in argon diffusion experiments using hydrothermal bombs, and can be explained if biotite has an ‘effective diffusion radius’ of about 150 :m (e.g. Harrison et al., 1985). This implies that biotite grains consist of domains of ca. 150 :m radius, within which argon moves by volume diffusion, but between which there is a mechanism of enhanced transport along crystallographic defects.

The increased amount of spatial argon data available from the laser probe has allowed complex diffusion models to be tested using natural mineral systems. Phillips and Onstott (1988) made the first such study, based on mantle-derived phlogopites from the Premier kimberlite, South Africa. ‘Chrontour’ mapping of 75 laser spots revealed apparent ages of1.2 – 1.4 Byr in the rim of a large grain, rising to a maximum of 2.4 Byr in the core. This pattern was attributed to the loss of inherited mantle argon from the rim of the grain during kimberlite emplacement1.2 Byr ago. However, the shape of the argon loss profile (boxes in Fig. 10.40) did not fit a volume diffusion model (curves in Fig. 10.40). Phillips and Onstott attributed the observed patterns to enhanced diffusive loss of argon from a wide band (round the rim of the grain) due to structural defects. However, the nature of these defects was unknown.

Fig. 10.40. Plot of ⁴⁰Ar concentrations along two transects (solid and open boxes) from core to rim of a metamorphosed phlogopite grain. Predicted argon loss curves based on volume diffusion fail to explain the data. After Phillips and Onstott (1988).

Hodges et al. (1994) compared argon diffusion patterns in muscovite and biotite using the laser probe. Single mica grains were analysed from the 1700 Myr-old Crazy Basin monzogranite of central Arizona, which has been argued to display either very slow cooling or multiple metamorphic events. Laser step heating of both muscovite and biotite gave very similar plateau ages of 1412 and 1410 Myr. However, for muscovite, the gas release steps which form the plateau occurred after melting had begun. Therefore, this plateau undoubtedly results from argon homogenisation during melting, and the similarity to the biotite plateau age is probably a coincidence. These findings are consistent with the work described above, where argon homogenisation was shown to be a greater problem in laser step heating than conventional step heating (section 10.3.2).

Laser spot dating revealed very different age patterns in other muscovite and biotite grains from the same sample. Muscovite spot ages ranged from 1270 Myr at the rim to 1650 Myr (the ‘true’ age) in a small core area, with a roughly concentric pattern (Fig. 10.41a). This age distribution fits a simple volume diffusion model for cylindrical geometry with an effective diffusion radius similar to the grain size. On the other hand, laser spot ages in the biotite grain had a quite different distribution, with ages ranging from 1150 Myr at the rim to 1420 Myr in a large core area (Fig. 10.41b). The large area with (re-set) 1400 Myr ages, together with an asymmetrical zone of young ages approaching the core, was evidence of the operation of fast diffusion pathways. Hodges et al. interpreted the data in terms of small domains with an effective diffusion radius of 150 :m, as postulated in hydrothermal experiments.

Fig. 10.41. Comparison between ‘chrontour’ age maps for muscovite and biotite determined from laser spot dating. Numbers indicate ages in hundreds of Myr. After Hodges et al. (1994).

Lee and Aldama (1992) attempted to explain complex diffusion behaviour by combining mechanisms for diffusion within the crystal lattice with enhanced (‘short-circuit’) diffusion between lattice domains into a general model termed ‘multi-path’ diffusion. In this model, diffusion in both of the pathways (lattice and short-circuit) is Fickian, but is of very different magnitude in each pathway. In addition, the transfer of species from the crystal lattice to the high-diffusivity paths, and vice-versa, is attributed to two exchange coefficients, termed K2 and K1 respectively. The magnitude of these coefficients is critical in determining whether multi-path diffusion will occur in a given situation.

The operation of the multi-path diffusion model can be examined on an Arrhenius plot (Fig. 10.42). At high temperatures (> 800 ^oC), volume diffusion in the crystal lattice is the dominant mechanism for argon loss from a mineral. However, if the exchange coefficient (K2) is relatively large, this causes a sudden change from lattice-dominated to short-circuit argon transport as temperature falls, forming a sigmoidally shaped diffusion curve. On the other hand, smaller values of K2 inhibit the role of short-circuit diffusion, maintaining a lattice-dominated diffusion mechanism to lower temperatures (< 500 ^oC).

Fig. 10.42. Predicted effect of an ‘exchange coefficient’ (K2) in changing the dominant diffusive mechanism from volume to short-circuit diffusion. Curves a, b, and c represent exchange coefficients of –10 ^-13, –10 ^-14 and –10 ^-15 s ^-1 for the transfer of species from the crystal lattice to high-diffusivity paths. After Lee (1995b).

Although the multi-path model is an attempt to create a realistic representation of the physical movement of argon in minerals, McDougall and Harrison (1999) argued that it is of limited use in analysing thermal histories from geological samples, because the postulated exchange coefficients cannot be determined by laboratory measurement. In addition, the model cannot explain the results of ‘cycling step heating’, a method developed by Lovera et al. (1991) for K-feldspar thermochronometry (see below). In this method, the heating schedule in an Ar–Ar degassing experiment is not increased monotonically as in a conventional analysis, but is increased in short ‘bursts’ with a period in between when the temperature is either reduced or maintained at a constant level for a relatively long time. An example of such a heating schedule is shown in Fig. 10.43.

Fig. 10.43. Demonstration of a cyclic heating schedule for Ar–Ar analysis. After Richter et al. (1991).

According to the multi-path diffusion model, the short-circuit diffusion path should be ‘replenished’ by volume diffusion out of the lattice during the backward-cycling stage of the step heating procedure, so that the subsequent increasing-temperature cycles reproduce the low-temperature behaviour from the beginning of the experiment. However, such behaviour was not seen (McDougall and Harrison, 1999). Therefore, if the short-circuit pathway exists, it may be more like an independent reservoir of stored argon, perhaps sampling argon from defect sites, than a pathway fed by lattice diffusion. In fact, McDougall and Harrison (1999) pointed out that if the exchange coefficients are ignored, the multi-path diffusion model is mathematically equivalent to argon diffusion from two different domain sizes in the multi domain model (section 10.5.3). In other words, argon extraction over relatively long distances along high-diffusivity pathways is equivalent to volume diffusion from very small lattice domains.

Complex diffusion models can be tested against the results of hydrothermal diffusion experiments on hornblende and biotite at different grain sizes (Fig. 10.44). Lee (1995b) argued that the enhanced diffusivities for large grain sizes favour the multi-path model over simple volume diffusion. However, the data can also be explained by a domain model, in which the lattice domains controlling volume diffusion are smaller in size than the complete crystal.

In the hydrothermal experiments, the behaviour of hornblende and biotite may result from similar styles of alteration, both in the laboratory and natural systems. For example, Onstott et al. (1991) suggested that fast diffusion pathways in hydrothermal biotite may be created during the experiment by the breakdown of chlorite layers, whereas Kelley and Turner (1991) attributed fast diffusion pathways in natural hornblende to biotite alteration.

Fig. 10.44. Plot of bulk argon diffusion coefficients against grain radius. Measurements from hydrothermal experiments on hornblende and biotite are compared with the predicted results of volume and short-circuit diffusion models. After Lee (1995b).

Experiments using the UV laser ablation microprobe (UVLAMP) suggest that in pristine, unaltered grains of biotite, most argon diffusion out of (or into) the grains occurs by volume diffusion. For example, Pickles et al. (1997) demonstrated such behaviour in biotite grains of various sizes (50 to 4500 :m diameter) in a pegmatite affected by Alpine metamorphism. During the metamorphic event, excess ⁴⁰Ar diffused into the grains from the grain boundary fluid and created diffusion profiles. In several grains, diffusion profiles up to 100 :m long were successfully modelled by volume diffusion. In the largest grain, the diffusion profile spanned a distance of nearly 300 :m, although the outermost 90 :m of the profile was disrupted by argon loss during a later alteration event.

Other experiments suggest that short-circuit diffusion is principally a feature of low temperatures of argon release. For example, Lo et al. (2000) found low temperature argon diffusivities two to four orders of magnitude faster than the values that would result from extrapolation of hydrothermal experiments to low temperature conditions. However, they suggested that this low temperature release might represent argon that had accumulated in radiation-induced lattice defects. Evidence for this interpretation comes from the fact that the outgassing of ³⁹Ar usually exceeds that of ⁴⁰Ar during very low temperature argon release (ca. 400 ^oC), which would be consistent with the preferential release of recoiled ³⁹Ar atoms residing in defect sites. In this case the occurrence of short-circuit diffusion might be to some extent an artifact of the irradiation procedure involved in the Ar–Ar method. Similar doubts have been expressed about the meaning of the lowest temperature emission step from K-feldspars (section 10.2.7 and below).

10.5.3 K-feldspar thermochronometry

K-feldspars have long been known to exhibit complex diffusion behaviour. Because of the unpredictable effects of perthitic exsolution, K-feldspars have very variable blocking temperatures, which must be determined for individual dated samples by the step-heating method. Heizler et al. (1988) demonstrated this technique in determining the cooling curve of the Chain of Ponds pluton, NW Maine. They obtained quite distinct blocking temperatures and ages on three feldspar separates, establishing a post-Appalachian cooling curve from 330 ^oC to 180 ^oC (solid symbols in Fig. 10.45).

Fig. 10.45. Plot of calculated K-feldspar blocking temperature against plateau age to model cooling of the Chain of Ponds pluton, NW Maine. Solid symbols show the single-plateau analysis of Heizler et al. (assuming uniform domain size). Open symbols show the sub-plateau analysis of Lovera et al. (assuming variable domain size). After Harrison (1990).

Other workers (e.g. Foland, 1974) suggested that diffusion in K-feldspars is controlled by microstructural domains of variable size, rather than on a whole-grain scale. The variable domain sizes invoked by this model can explain the traditional reputation of K-feldspars for having such poor argon retentivity as to be useless as a dating tool. The smallest of the domains do indeed suffer argon loss at near ambient temperatures. However, the larger domains, sampled in a step-heating analysis, can have blocking temperatures as high as biotite. Therefore, if this variation in blocking temperatures can be exploited using the step heating method, K-feldspar can be a powerful tool in thermochronometry. Because this method is based on the assumption of domains of various sizes, it is termed the multi-diffusion-domain (MDD) model.

Adopting the MDD model, Lovera et al. (1989) re-interpreted the data of Heizler et al. (1980) by breaking each Ar)Ar analysis into a series of sub-plateaus with distinct ages and blocking temperatures. They attributed these sub-plateaus to diffusional domains within each feldspar grain, varying in size by two orders of magnitude. This model was tested by comparing measured step-heating data with model spectra based on different domain-size distributions, as applied by Turner et al. (1966) to meteorite studies (section 10.2.4). The variable domain-size model was shown to fit the experimental data much better than the uniform model, thus confirming its usefulness. The result of this approach was that each analysis yielded a separate but overlapping cooling curve segment (open symbols in Fig. 10.45), rather than a single point on the cooling curve. Further experiments on single feldspar crystals by Lovera et al. (1991) showed that domains of varying size are an intrinsic property of alkali feldspars, which therefore cannot be separated by hand picking of material for analysis.

Conventional thermochronometry is based on linear Arrhenius relationships observed when ³⁹Ar is released from diffusion domains of uniform size and K content which obey a simple diffusion law. In their development of the K-feldspar method, Lovera et al. (1989) showed that non-linear Arrhenius trends produced by conventional step heating could be resolved into separate linear segments by cycling the heating schedule up and down.

Subsequent work on a variety of samples showed that these line segments were effectively parallel, indicating relative constancy of diffusional activation energies. The vertical separation between different linear segments on the Arrhenius diagram can then be interpreted in terms of relative domain size. If the effective diffusion radius of the domain which generates the first, low-temperature array is set arbitrarily to be r₀ (‘r’ is the equivalent of ‘a’ in section 10.5.1), then the relative diffusion dimension of each subsequent gas-release point can be calculated using the following relation:

r | DT | | DT |

log – = | log ))) | – | log ))) | [10.19]

r₀ | r² | | r₀² |

))))))))))))))))))))))))))

2

Because we are only interested in the relative diffusion dimension, the exact geometry assumed (slab or sphere etc.) has little effect on the calculations. Richter et al. (1991) proposed that each value of log (r/r₀) should be plotted against cumulative ³⁹Ar release in a manner analogous to an age spectrum plot (Fig. 10.46b). This plot therefore bridges the gap between the age spectrum diagram and the Arrhenius diagram.

Fig. 10.46. Comparison between different data presentations for K-feldspar thermochronometry: a) traditional age spectrum plot; b) r/r₀ plot; c) resulting solution of volume fraction against relative domain size. After Richter et al. (1991).

The working of the ‘Richter plot’ was demonstrated on an analysis from the Quxu pluton of the Himalayas. The diagram gave evidence of four plateaus, of which the three highest temperature ones correspond to plateaus on the age spectrum plot (Fig. 10.46a). The lowest temperature plateau had no corresponding age because the first five steps were perturbed by excess ⁴⁰Ar, which probably diffused into the grains after cooling of the pluton. However, this did not affect the ³⁹Ar released during this part of the analysis, which can still be used to obtain diffusional data. On the other hand, the highest temperature step gave an age, but no diffusional information, because it occurred during sample melting. After the gas release has been broken into plateaus, the volume fraction of each is calculated, and an iterative program is used (Lovera, 1992) to determine the actual radius ratios of the domains which will model the observed profile of relative diffusion dimensions. The solution is shown in Fig. 10.46c. Finally, a cooling curve is determined (iteratively), which will yield the observed age spectrum.

In several experiments on K-feldspars from different orogens, the radius ratio of largest to smallest domains was determined to be between 100 and 500. Lovera et al. (1993) performed step heating experiments on the Chain of Ponds pluton, Maine (sample MH-10) in an attempt to find the absolute sizes of these domains. After crushing, K-feldspar grains were separated into four size fractions, averaging 425, 138, 54 and 42 :m in diameter. Following irradiation, a full step-heating analysis was performed on each size fraction, and the resulting Arrhenius plots were compared (Fig. 10.47). The results showed a dramatic decrease in argon retentivity between the 138 :m and 54 :m size fractions, attributed to the ‘breaking open’ of the largest diffusion domain in crushing to 54 :m. Hence, the diameter of this domain was inferred to be in the range 50 – 100 :m. Based on relative domain size ratios, the smallest domain was then estimated to be ca. 0.1 :m in size.

Fig. 10.47. Arrhenius plot for K-feldspar from the Chain of Ponds pluton, Maine. Parallel linear arrays were obtained from the low temperature gas releases, after crushing to four different grain sizes. After Lovera et al. (1993).

In an accompanying optical and TEM study, FitzGerald and Harrison (1993) attempted to determine the crystallographic identities of the different domain sizes. They tentatively correlated the largest domains with blocks of K-feldspar surrounded by fractured and turbid zones, and the smallest with the 0.1 :m (100 nm) distance between albite exsolution lamellae. However, they were unable to identify any intermediate sized domains.

More recent studies have attempted to achieve a better understanding of argon diffusion in K-feldspar by studying gem-quality crystals, which are expected to display simpler diffusional behaviour. Two of these studies were performed on the same gem-quality orthoclase from Madagascar. The first study (Arnaud and Kelley, 1997) primarily used cyclic step-heating experiments to investigate the argon release behaviour of the orthoclase. This experiment revealed that Ar release occurred in two stages with different activation energies. The main argon release was consistent with simple volume diffusion from a single domain size. However, the low-temperature release could be explained by either rapid diffusion pathways (e.g. short circuit diffusion) or multi diffusion domains. However, this release stage represented only 0.5% of the total ³⁹Ar inventory of the sample, so Arnaud and Kelley speculated that it actually represented argon release from the surface of the sample, which had possibly been damaged during sample preparation.

The second study of this material used the UV laser ablation microprobe to perform depth profiles of the sample surface (Wartho et al., 1999). This study revealed that argon release from the surfaces of the orthoclase crystal was controlled by volume diffusion, just like the crystal interior. In fact, calculations of the effective diffusion radius for the low temperature release and the main argon release gave values of 1.8 and 1.3 mm respectively, both of which were consistent with the 2 – 3 mm dimensions of the analysed fragments. Therefore, despite the different activation energies of the different release stages, they both reflected volume diffusion from a single domain, consistent with the unflawed nature of the analysed fragments. Possibly, the low temperature release represented argon from vacancy sites in the mineral. It was concluded from these experiments that cyclic step heating faithfully measured the diffusion parameters of the sample. However, they could not provide further help in understanding complex metamorphic K-feldspars.

Because the estimated size of the smallest diffusion domains in the MDD model is similar to the ³⁹Ar recoil distance, doubts have been expressed (section 10.2.7) about the meaning of the lowest-temperature argon emission data. In addition, Parsons et al. (1999) argued that many K-feldspars display micro-structural complexity that is metastable during step-heating experiments. Therefore, they suggested that alkali feldspar thermochronology using the MDD model is a ‘mathematical mirage’ rather than a method that can be used to recover real thermal histories. However, there have been several empirical demonstrations where cooling curves based on K-feldspar thermochronology are in good agreement with other geochronological evidence. For example, Lee (1995a) demonstrated good agreement of K-feldspar cooling curves with 40–39 muscovite ages and fission track apatite ages in a study of tectonic uplift in the Snake Range, Nevada (Fig. 10.48).

Fig. 10.48. Comparison of cooling data for the Snake Range, Nevada. Shaded fields derived from K-feldspar thermochronometry are consistent with control points from apatite fission track analysis and Ar–Ar muscovite analysis (boxes). After Lee (1995a).

To provide a more objective test of the reliability of K-feldspar thermochronology for recovering real thermal histories, Lovera et al. (1997, 2002) analysed the argon release patterns of a suite of nearly 200 basement samples. They found that the most common obstacle to the derivation of thermal histories from step heating results was inherited argon. This has long been recognised as a problem in K–Ar and Ar–Ar dating, and in the study of Lovera et al. it was manifested by saddle-shaped profiles (intermediate age minimum) on the age spectrum diagram. On the other hand, a second type of anomalous behaviour was manifested as an intermediate age maximum, attributed to low temperature alteration. Together, these problems affected about half of the total sample suite of 194 K-felspars studied. The remaining half of the sample suite was considered to be ‘well behaved’, and therefore suitable for analysis by the MDD model. In addition, the activation energies in these samples had a normal distribution (average = 46 " 6 kcal/mol), so that a standard protocol could be used to analyse all samples, thereby minimising subjectivity in the interpretation of the data.

Lovera et al. (2002) argued that the effectiveness of the MDD model in explaining the real thermal history of a sample could be assessed by the goodness of fit between the step-heating age spectrum and the pattern of changing effective diffusion radius ratio (r/r₀). If these two profiles matched in a K-feldspar analysis, this was held to be evidence that the laboratory argon release experiment successfully mimicked the diffusional loss of argon over the cooling history of the sample. However, in order to demonstrate the quality of fit between the two profiles, it was necessary to develop quantitative indices for comparing their shapes. Two indices were calculated for the middle part of the argon release curve, after low temperature inherited argon had essentially disappeared, and before the sample started to melt. These indices are compared in Fig. 10.49, which shows the analysis spectra from two K-feldspars, one with an ideal argon release pattern and one of poor quality.

Fig. 10.49. Age spectra and profiles of changing effective diffusion radius ratio (r/r₀) in two step-heating experiments on basement samples of K-feldspar, showing: a) excellent agreement between the two profile shapes; b) poor agreement between profile shapes. After Lovera et al. (2002).

The first index is a correlation coefficient, derived by fitting a polynomial function to each of the two patterns, extracting a series of discrete points at evenly spaced intervals, then calculating the correlation coefficient between the two series. This is shown in the lower right of each spectrum plot in Fig. 10.49. The second index is obtained simply by determining the average value of each series, and then determining where this point is achieved in the cumulative argon-release pattern. For the ideal experiment (Fig. 10.49a) the correlation coefficient was 0.98 and the mean points coincided. For the poor experiment the correlation coefficient was very poor (0.5) and the mean points did not coincide. On several other occasions, one or other of the criteria was satisfied, but not both.

The result of applying this analysis to the complete sample suite was that 40% of the samples had correlation coefficients above 0.9, leading Lovera et al. (2002) to suggest that most of the alteration-free samples without large inventories of inherited argon were suitable for thermal history analysis by the MDD model. In response to the criticism that the postulated Multi Diffusion Domains cannot be identified structurally, Lovera et al. argued that the empirical results are adequate in themselves to demonstrate the effectiveness of the method for recovering thermal histories, and that understanding the structural basis of the model was of secondary importance. Doubtless, this debate will continue.

References

Anders, E. (1964). Meteorite ages. Rev. Mod. Phys. 34, 287)325.

Arnaud, N. O. and Kelley, S. P. (1997). Argon behaviour in gem-quality orthoclase from Madagascar: experiments and some consequences for ⁴⁰Ar/³⁹Ar geochronology. Geochim. Cosmochim. Acta 61, 3227–55.

Baksi, A. K., Archibald, D. A. and Farrar, E. (1996). Intercalibration of ⁴⁰Ar/³⁹Ar dating standards. Chem. Geol. 129, 307–24.

Baksi, A. K., Hsu, V., McWilliams, M. O. and Farrar, E. (1992). ⁴⁰Ar/³⁹Ar dating of the Brunhes–Matuyama geomagnetic field reversal. Science 256, 356–7.

Beckinsale, R. D. and Gale, N. H. (1969). A reappraisal of the decay constants and branching ratio of ⁴⁰K. Earth Planet. Sci. Lett. 6, 289)94.

Berger, G. W. (1975). ⁴⁰Ar/³⁹Ar step heating of thermally overprinted biotite, hornblende and potassium feldspar from Eldora, Colorado. Earth Planet. Sci. Lett. 26, 387)408.

Berger, G. W. and York. D. (1981a). Geothermometry from ⁴⁰Ar/³⁹Ar dating experiments. Geochim. Cosmochim. Acta 45, 795)811.

Berger, G. W. and York. D. (1981b). ⁴⁰Ar/³⁹Ar dating of the Thanet gabbro, Ontario: looking through the metamorphic veil and implications for paleomagnetism. Can. J. Earth Sci. 18, 266)73.

Berggren, W. A. (1972). A Cenozoic time-scale ) some implications for regional geology and paleobiogeography. Lethaia 5, 195)215.

Brereton, N. R. (1970). Corrections for interfering isotopes in the ⁴⁰Ar/³⁹Ar dating method. Earth Planet. Sci. Lett. 8, 427)33.

Buchan, K. L., Berger, G. W., McWilliams, M. O., York, D. and Dunlop, D. J. (1977). Thermal overprinting of natural remanent magnetization and K/Ar ages in metamorphic rocks. J. Geomag. Geoelectr. 29, 401)10.

Cox, A. and Dalrymple, G. B. (1967). Statistical analysis of geomagnetic reversal data and the precision of potassium ) argon dating. J. Geophys. Res. 72, 2603)14.

Cox, A., Doell, R. R. and Dalrymple, G. B. (1963). Geomagnetic polarity epochs and Pleistocene geochronology. Nature 198, 1049)51.

Dalrymple, G. B. and Lanphere, M. A. (1969). Potassium ) Argon Dating. Freeman, 258 p.

Dalrymple, G. B. and Lanphere, M. A. (1971). ⁴⁰Ar/³⁹Ar technique of K)Ar dating: a comparison with the conventional technique. Earth Planet. Sci. Lett. 12, 300)8.

Dalrymple, G. B. and Lanphere, M. A. (1974). ⁴⁰Ar/³⁹Ar age spectra of some undisturbed terrestrial samples. Geochim. Cosmochim. Acta 38, 715)38.

Dalrymple, G. B. and Moore, J. G. (1968). Argon 40: excess in submarine pillow basalts from Kilauea Volcano, Hawaii. Science 161, 1132)5.

Damon, P. E. and Kulp, J. L. (1958). Excess helium and argon in beryl and other minerals. Amer. Miner. 43, 433)59.

Dodson, M. H. (1973). Closure temperature in cooling geochronological and petrological systems. Contrib. Mineral. Petrol. 40, 259)74.

Doell, R. R., Dalrymple, G. B. and Cox, A. (1966). Geomagnetic polarity epochs: Sierra Nevada data, 3. J. Geophys. Res. 71, 531)41.

Dong, H., Hall, C. M., Peacor, D. R. and Halliday, A. N. (1995). Mechanisms of argon retention in clays revealed by laser ⁴⁰Ar–³⁹Ar dating. Science 267, 355–9.

Esser, R. P., McIntosh, W. C., Heizler, M. T. and Kyle, P. R. (1997). Excess argon in melt inclusions in zero-age anorthoclase feldspar from Mt Erebus, Antarctica, as revealed by the ⁴⁰Ar/³⁹Ar method. Geochim. Cosmochim. Acta 61, 3789–3801.

FitzGerald, J. D. and Harrison, T. M. (1993). Argon diffusion domains in K-feldspar I: microstructures in MH-10. Contrib. Mineral. Petrol. 113, 367–80.

Foland, K. A. (1974). Ar⁴⁰ diffusion in homogeneous orthoclase and an interpretation of Ar diffusion in K-feldspars. Geochim. Cosmochim. Acta 38, 151)66.

Foland, K. A., Linder, J. S., Laskowski, T. E. and Grant, K. (1984). ⁴⁰Ar)³⁹Ar dating of glauconies: measured ³⁹Ar recoil loss from well-crystallized specimens. Chem. Geol. (Isot. Geosci. Section) 46, 241)64.

Gaber, L. J., Foland, K. A. and Corbato, C. E. (1988). On the significance of argon release from biotite and amphibole during ⁴⁰Ar/³⁹Ar vacuum heating. Geochim. Cosmochim. Acta 52, 2457)65.

Garner, E. L., Machlan, L. A. and Barnes, I. L. (1976). The isotopic composition of lithium, potassium, and rubidium in some Apollo 11, 12, 14, 15, and 16 samples. Proc. 6th Lunar Sci. Conf. Pergamon, pp. 1845)1855.

Giletti, B. J. (1974). Diffusion related to geochronology. In: Hofmann, A. W., Giletti, B. J., Yoder, H. S. and Yund, R. A. (Eds), Geochemical Transport and Kinetics. Carnegie Inst. Wash., pp. 61)76.

Hale, C. J. (1987). The intensity of the geomagnetic field at 3. 5 Ga: paleointensity results from the Komati Formation, Barberton Mountain Land, South Africa. Earth Planet. Sci. Lett. 86, 354)64.

Hanes, J. A., Clark, S. J. and Archibald, D. A. (1988). An ⁴⁰Ar/³⁹Ar geochronological study of the Elzevir batholith and its bearing on the tectonothermal history of the southwestern Grenville Province, Canada. Can. J. Earth Sci. 25, 1834)45.

Harland, W. B., Cox, A. V., Llewellyn, P. G., Pickton, C. A. G., Smith, A. G. and Walters, R. (1982). A Geologic Time Scale 1982. Cambridge Univ. Press., 131 p.

Harper, C. T. (1967). On the interpretation of potassium)argon ages from Precambrian shields and Phanerozoic orogens. Earth Planet. Sci. Lett. 3, 128)32.

Harrison, T. M. (1990). Some observations on the interpretation of feldspar ⁴⁰Ar/³⁹Ar results. Chem. Geol. (Isot. Geosci. Section) 80, 219)29.

Harrison, T. M., Duncan, I. and McDougall, I. (1985). Diffusion of ⁴⁰Ar in biotite: temperature, pressure and compositional effects. Geochim. Cosmochim. Acta 49, 2461)8.

Harrison, T. M. and McDougall, I. (1981). Excess ⁴⁰Ar in metamorphic rocks from Broken Hill, New South Wales: implications for ⁴⁰Ar/³⁹Ar age spectra and the thermal history of the region. Earth Planet. Sci. Lett. 55, 123)49.

Hart, S. R. (1964). The petrology and isotopic)mineral age relations of a contact zone in the Front Range, Colorado. J. Geol. 72, 493)525.

Hart, S. R. and Dodd, R. T. (1962). Excess radiogenic argon in pyroxenes. J. Geophys. Res. 67, 2998)9.

Heirtzler, J. R., Dickson, G. O., Herron, E. M., Pitman, W. C. and LePichon, X. (1968) Marine magnetic anomalies, geomagnetic field reversals, and motions of the ocean floor and continents. J. Geophys. Res. 73, 2119)36.

Heizler, M. T., Lux, D. R. and Decker, E. R. (1988). The age and cooling history of the Chain of Ponds and Big Island Pond plutons and the Spider Lake granite, west-central Maine and Quebec. Amer. J. Sci. 288, 925)52.

Hodges, K. V., Hames, W. E. and Bowring, S. A. (1994). ⁴⁰Ar/³⁹Ar age gradients in micas from a high-temperature – low-pressure metamorphic terrane: evidence for very slow cooling and implications for the interpretation of age spectra. Geology 22, 55–8.

Johnson, R. G. (1982). Brunhes–Matuyama magnetic reversal dated at 790,000 yr B.P. by marine–astronomical correlations. Quaternary Res. 17, 135–47.

Kaneoka, I. (1974). Investigation of excess argon in ultramafic rocks from the Kola peninsula by the ⁴⁰Ar/³⁹Ar method. Earth Planet. Sci. Lett. 22, 145–56.

Kapusta, Y., Steinitz, G., Akkerman, A., Sandler, A., Kotlarsky, P. and Nagler, A. (1997). Monitoring the deficit of ³⁹Ar in irradiated clay fractions and glauconites: modelling and analytical procedure. Geochim. Cosmochim. Acta 61, 4671–8.

Kelley, S. P. (2002). Excess argon in K–Ar and Ar–Ar geochronology. Chem. Geol. 188, 1–22.

Kelley, S. P. and Turner, G. (1991). Laser probe ⁴⁰Ar–³⁹Ar measurements of loss profiles within individual hornblende grains from the Giants Range granite, northern Minnesota, USA. Earth Planet. Sci. Lett. 107, 634–48.

Kelley, S. P., Arnaud, N. O. and Turner, S. P. (1994). High spatial resolution ⁴⁰Ar/³⁹Ar investigations using an ultra-violet laser probe extraction technique. Geochim. Cosmochim. Acta 58, 3519–25.

LaBrecque, J. L., Kent, D. V. and Cande, S. C. (1977). Revised magnetic polarity time scale for Late Cretaceous and Cenozoic time. Geology 5, 330)5.

Lanphere, M. A. and Dalrymple, G. B. (1966). Simplified bulb tracer system for argon analysis. Nature 209, 902)3.

Lanphere, M. A. and Dalrymple, G. B. (1971). A test of the ⁴⁰Ar/³⁹Ar age spectrum technique on some terrestrial materials. Earth Planet. Sci. Lett. 12, 359)72.

Lanphere, M. A. and Dalrymple, G. B. (1976). Identification of excess ⁴⁰Ar by the ⁴⁰Ar/³⁹Ar age spectrum technique. Earth Planet. Sci. Lett. 32, 141)8.

Layer, P. W., Hall, C. M. and York, D. (1987). The derivation of ⁴⁰Ar/³⁹Ar age spectra of single grains of hornblende and biotite by laser step-heating. Geophys. Res. Lett. 14, 757)60.

Lee, J. (1995a). Rapid uplift and rotation of mylonitic rocks from beneath a detachment fault: insights from potassium feldspar ⁴⁰Ar/³⁹Ar thermochronology, northern Snake Range, Nevada. Tectonics 14, 54–77.

Lee, J. K. W. (1995b). Multipath diffusion in geochronology. Contrib. Mineral. Petrol. 120, 60–82.

Lee, J. K. W. and Aldama, A. A. (1992). Multipath diffusion: a general numerical model. Comput. Geosci. 18, 531–55.

Lee, J. K. W., Onstott, T. C., Cashman, K. V., Cumbest, R. J. and Johnson, D. (1991). Incremental heating of hornblende in vacuo: implications for ⁴⁰Ar/³⁹Ar geochronology and the interpretation of thermal histories. Geology 19, 872)6.

Lee, J. K. W., Onstott, T. C. and Hanes, J. A. (1990). An ⁴⁰Ar/³⁹Ar investigation of the contact effects of a dyke intrusion, Kapuskasing Structural Zone, Ontario. Contrib. Mineral. Petrol. 105, 87)105.

Lo, C.-H., Lee, J. K. W. and Onstott, T. C. (2000). Argon release mechanisms of biotite in vacuo and the role of short-circuit diffusion and recoil. Chem. Geol. 165, 135–166.

Lopez Martinez, M., York, D., Hall, C. M. and Hanes, J. A. (1984). Oldest reliable ⁴⁰Ar/³⁹Ar ages for terrestrial rocks: Barberton Mountain komatiites. Nature 307, 352)4.

Lovera, O. M. (1992). Computer programs to model ⁴⁰Ar/³⁹Ar diffusion data from multidomain samples. Comput. Geosci. 18, 789–813.

Lovera, O. M., Grove, M. and Harrison, T. M. (2002). Systematic analysis of K-feldspar ⁴⁰Ar/³⁹Ar step heating results II: relevance of laboratory argon diffusion properties to nature. Geochim. Cosmochim. Acta 66, 1237–55.

Lovera, O. M., Grove, M., Harrison, T. M. and Mahon, K. I. (1997). Systematic analysis of K-feldspar ⁴⁰Ar/³⁹Ar step heating results: I. Significance of activation energy determinations. Geochim. Cosmochim. Acta 61, 3171–92.

Lovera, O. M., Heizler, M. T. and Harrison, T. M. (1993). Argon diffusion domains in K-feldspar II: kinetic properties of MH-10. Contrib. Mineral. Petrol. 113, 381–93.

Lovera, O. M., Richter, F. M. and Harrison, T. M. (1989). The ⁴⁰Ar/³⁹Ar thermochronometry for slowly-cooled samples having a distribution of domain sizes. J. Geophys. Res. 94, 17917)35.

Lovera, O. M., Richter, F. M. and Harrison, T. M. (1991). Diffusion domains determined by ³⁹Ar released during step heating. J. Geophys. Res. 96, 2057)69.

Lowrie, W. and Alvarez, W. (1981). One hundred million years of geomagnetic polarity history. Geology 9, 392)7.

Mankinen, E. A. and Dalrymple, G. B. (1979). Revised geomagnetic polarity time scale for the interval 0 to 5 m.y. B.P. J. Geophys. Res. 84, 615)26.

McDougall, I. and Harrison, T. M. (1988). Geochronology and Thermochronology by the ⁴⁰Ar/³⁹Ar Method. Oxford Univ. Press, 212 p.

McDougall, I. and Harrison, T. M. (1999). Geochronology and Thermochronology by the ⁴⁰Ar/³⁹Ar Method, 2nd Edn. Oxford Univ. Press, 269 p.

McDougall, I., Polach, H. A. and Stipp, J. J. (1969). Excess radiogenic argon in young subaerial basalts from the Auckland volcanic field, New Zealand. Geochim. Cosmochim. Acta 33, 1485)1520.

McDougall, I. and Tarling, D. H. (1964). Dating geomagnetic polarity zones. Nature 202, 171)2.

Megrue, G. H. (1967). Isotopic analysis of rare gases with a laser microprobe. Science 157, 1555)6.

Megrue, G. H. (1973). Spatial distribution of ⁴⁰Ar/³⁹Ar ages in lunar breccia 14301. J. Geophys. Res. 78, 3216)21.

Merrihue, C. and Turner, G. (1966). Potassium)argon dating by activation with fast neutrons. J. Geophys. Res. 71, 2852)7.

Min, K., Mundil, R., Renne, P. R. and Ludwig, K. R. (2000). A test for systematic errors in ⁴⁰Ar/³⁹Ar geochronology through comparison with U/Pb analysis of a 1.1-Ga rhyolite. Geochim. Cosmochim. Acta 64, 73–98.

Mitchell, J. G. (1968). The argon-40/argon-39 method for potassium)argon age determination. Geochim. Cosmochim. Acta 32, 781)90.

Mussett, A. E. and Dalrymple, G. B. (1968). An investigation of the source of air Ar contamination in K)Ar dating. Earth Planet. Sci. Lett. 4, 422)6.

Onstott, T. C., Hall, C. M. and York, D. (1989). ⁴⁰Ar/³⁹Ar thermo-chronometry of the Imataca complex, Venezuela. Precamb. Res. 42, 255)91.

Onstott, T. C., Miller, M. L., Ewing, R. C., Arnold, G. W. and Walsh, D. S. (1995). Recoil refinements: implications for the ⁴⁰Ar/³⁹Ar dating technique. Geochim. Cosmochim. Acta 59, 1821–34.

Onstott, T. C., Phillips, D. and Pringle-Goodell, L. (1991). Laser microprobe measurement of chlorine and argon zonation in biotite. Chem. Geol. 90, 145–68.

Parsons, I., Brown, W. L. and Smith, J. V. (1999). ⁴⁰Ar/³⁹Ar thermochronology using alkali feldspars: real thermal history or mathematical mirage of microtexture? Contrib. Mineral. Petrol. 136, 92–110.

Phillips, D. and Onstott, T. C. (1988). Argon isotopic zoning in mantle phlogopite. Geology 16, 542–6.

Pickles, C. S., Kelley, S. P., Reddy, S. M. and Wheeler, J. (1997). Determination of high spatial resolution argon isotope variations in metamorphic biotites. Geochim. Cosmochim. Acta 61, 3809–33.

Renne, P. R. (2000). ⁴⁰Ar/³⁹Ar age of plagioclase from Acapulco meteorite and the problem of systematic errors in cosmochronology. Earth Planet. Sci. Lett. 175, 13–26.

Renne, P. R. (2001). Reply to Comment on “⁴⁰Ar/³⁹Ar age of plagioclase from Acapulco meteorite and the problem of systematic errors in cosmochronology” by Paul. R. Renne. Earth Planet. Sci. Lett. 190, 271–3.

Renne, P. R., Deino, A. L., Walter, R. C., Turrin, B. D., Swisher, C. C., Becker, T. A., Curtis, G. H., Sharp, W. D. And Jaouni, A.-R. (1994). Intercalibration of astronomical and radioisotopic time. Geology 22, 783–6.

Renne, P. R., Karner, D. B. and Ludwig, K. R. (1998a). Absolute ages aren’t exactly. Science 282 1840–41.

Renne, P. R., Swisher, C. C., Deino, A. L., Karner, D. B., Owens, T. L. and DePaolo, D. J. (1998b). Intercalibration of standards, absolute ages and uncertainties in ⁴⁰Ar/³⁹Ar dating. Chem. Geol. 145, 117)52.

Rex, D. C., Guise, P. G. and Wartho, J.-A. (1993). Disturbed ⁴⁰Ar/³⁹Ar spectra from hornblendes: thermal loss or contamination? Chem. Geol. (Isot. Geosci. Section) 103, 271)81.

Richter, F. M., Lovera, O. M., Harrison, T. M. and Copeland, P. (1991). Tibetan tectonics from ⁴⁰Ar/³⁹Ar analysis of a single K-feldspar sample. Earth Planet. Sci. Lett. 105, 266–78.

Roberts, H. J., Kelley, S. P. and Dahl, P. S. (2001). Obtaining geologically meaningful ⁴⁰Ar–³⁹Ar ages from altered biotite. Chem. Geol. 172, 277–90.

Roddick, J. C. and Farrar, E. (1971). High initial argon ratios in hornblendes. Earth Planet. Sci. Lett. 12, 208)14.

Schmitz, M. D. and Bowring, S. A. (2001). U–Pb zircon and titanite systematics of the Fish Canyon Tuff: an assessment of high-precision U–Pb geochronology and its application to young volcanic rocks. Geochim. Cosmochim. Acta 65, 2571–87.

Shackleton, N. J., Berger, A. and Peltier, W. R. (1990). An alternative astronomical calibration of the lower Pleistocene timescale based on ODP Site 677. Trans. Roy. Soc. Edinburgh: Earth Sci. 81, 251–61.

Smith, P. E., Evensen, N. M. and York, D. (1993). First successful ⁴⁰Ar/³⁹Ar dating of glauconies: argon recoil in single grains of cryptocrystalline material. Geology 21, 41)4.

Smith, P. E., Evensen, N. M., York, D. and Odin, G. S. (1998). Single-grain ⁴⁰Ar–³⁹Ar ages of glauconies: implications for the geologic time scale and global sea level variations. Science 279, 1517–9.

Spell, T. L. and McDougall, I. (1992). Revisions to the age of the Brunhes–Matuyama boundary and the Pleistocene geomagnetic polarity timescale. Geophys. Res. Lett. 19, 1181–4.

Steiger, R. H. and Jager, E. (1977). IUGS Subcommission on Geochronology: convention on the use of decay constants in geo- and cosmochronology. Earth Planet. Sci. Lett. 36, 359)62.

Tauxe, L., Deino, A. D., Behrensmeyer, A. K. and Potts, R. (1992). Pinning down the Brunhes/Matuyama and upper Jaramillo boundaries: a reconciliation of orbital and isotopic time scales. Earth Planet. Sci. Lett. 109, 561)72.

Trieloff, M., Jessberger, E. K. and Fieni, C. (2001). Comment on “⁴⁰Ar/³⁹Ar age of plagioclase from Acapulco meteorite and the problem of systematic errors in cosmochronology” by Paul. R. Renne. Earth Planet. Sci. Lett. 190, 267–9.

Turner, G. (1968). The distribution of potassium and argon in chondrites. In: Ahrens, L. H. (Ed.) Origin and Distribution of the Elements. Pergamon, pp. 387)97.

Turner, G. (1969). Thermal histories of meteorites by the ³⁹Ar)⁴⁰Ar method. In: Millman, P. M. (Ed.) Meteorite Research. Reidel, pp. 407)17.

Turner, G. (1971a). Argon 40)argon 39 dating: the optimisation of irradiation parameters. Earth Planet. Sci. Lett. 10, 227)34.

Turner, G. (1971b). ⁴⁰Ar/³⁹Ar ages from the lunar maria. Earth Planet. Sci. Lett. 11, 169)91.

Turner, G. (1972). ⁴⁰Ar)³⁹Ar age and cosmic ray irradiation history of the Apollo 15 anorthosite, 15415. Earth Planet. Sci. Lett. 14, 169)75.

Turner, G. and Cadogan, P. H. (1974). Possible effects of ³⁹Ar recoil in ⁴⁰Ar/³⁹Ar dating. Proc. 5th Lunar Sci. Conf. Pergamon, pp. 1601)15.

Turner, G., Miller, J. A. and Grasty, R. L. (1966). Thermal history of the Bruderheim meteorite. Earth Planet. Sci. Lett. 1, 155)7.

van Eysinga, F. W. B. (1975). Geological Time Table, 3rd. Edn. Elsevier.

van Hinte, J. E. (1976). A Cretaceous time scale. Amer. Assoc. Petroleum Geol. Bull. 60, 498)516.

Villa, I. M. (1997). Direct determination of ³⁹Ar recoil distance. Geochim. Cosmochim. Acta 61, 689–91.

Villa, I. M. (1998). Reply to the comment by T. M. Harrison, M. Grove, and O. M. Lovera on “Direct determination of ³⁹Ar recoil distance”. Geochim. Cosmochim. Acta 62, 349.

Vincent, E. A. (1960). Analysis by gravimetric and volumetric methods, flame photometry, colorimetry and related techniques. In: Smales, A. A. and Wager, L. R. (Eds), Methods in Geochemistry. Interscience. pp. 33)80.

York, D. (1978). A formula describing both magnetic and isotopic blocking temperatures. Earth Planet. Sci. Lett. 39, 89)93.

York, D. (1984). Cooling histories from ⁴⁰Ar/³⁹Ar age spectra: implications for Precambrian plate tectonics. Ann. Rev. Earth Planet. Sci. 12, 383)409.

York, D., Hall, C. M., Yanase, Y., Hanes, J. A. and Kenyon, W. J. (1981). ⁴⁰Ar/³⁹Ar dating of terrestrial minerals with a continuous laser. Geophys. Res. Lett. 8, 1136)8.

Wartho, J.-A., Kelley, S. P., Brooker, R. A., Carroll, M. R., Villa, I. M. and Lee, M. R. (1999). Direct measurement of Ar diffusion profiles in a gem-quality Madagascar K-feldspar using the ultra-violet laser ablation microprobe (UVLAMP). Earth Planet. Sci. Lett. 170, 141–53.

Wright, N., Layer, P. W. and York, D. (1991). New insights into thermal history from single grain ⁴⁰Ar/³⁹Ar analysis of biotite. Earth Planet. Sci. Lett. 104, 70)9.