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Alpha-recoil track densities in mica and radiometric age determination
Radiation Measurements 40 (2005) 503 – 508 www.elsevier.com/locate/radmeas
Alpha-recoil track densities in mica and radiometric age determination K. Stübner∗ , R.C. Jonckheere, L. Ratschbacher Institut für Geowissenschaften, Technische Universität Bergakademie Freiberg, Bernhard-von-Cottastraße 2, D-09599 Freiberg, Sachsen, Germany Received 27 August 2004; received in revised form 26 April 2005; accepted 11 May 2005
Abstract Recoiling daughters of -decaying U and Th impurities in mica and other minerals produce localised lattice damage: alpharecoil tracks. The age of a sample can be calculated from the number of tracks per unit volume (NART ). To this end, the mica is etched and the etch pits at the sites of recoil-tracks are counted under the optical microscope. Because the measured track densities increase with etching time, NART is calculated from the fitted regression line. A number of problems inherent in this approach are overcome by the etch–anneal–etch and the mirror-image methods. The track densities determined with these methods are independent of etching time. Although both methods need improvement, they hold the potential of a precise determination of NART from a single measurement in future recoil-track dating. © 2005 Elsevier Ltd. All rights reserved. Keywords: Alpha-recoil-track; Track density; Phlogopite; Radiometric dating
1. Introduction Huang and Walker (1967) identified numerous shallow etch pits in muscovite mica as sites of localised lattice damage produced by the recoil nuclei resulting from alphadisintegration of uranium and thorium impurities. They proposed that these could constitute the basis of a recoil-track dating method, based on similar principles as the fissiontrack method (Fleischer et al., 1975; Wagner, 1998). In contrast to the fission-track method, the recoil-track method has not achieved the status of a geochronological dating method to this date. However, Huang and Walker (1967) pointed out that the accumulation rate of recoil tracks is ∼ 106 times that of fission tracks so that, despite their ∼ 103 times smaller range, the number of recoil tracks in an etched mineral ∗ Corresponding author. Tel.: +49 3731 39 3813; fax: +49 3731 39 3599. E-mail address: [email protected] (K. Stübner).
1350-4487/$ - see front matter © 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.radmeas.2005.05.009
surface is ∼ 103 times that of fission tracks. This allows dating very young objects like Quarternary volcanics (Gögen and Wagner, 2000; Glasmacher et al., 2003) and prehistoric and early ceramics (Garrison et al., 1978). The calculation of a recoil-track age requires measurements of the concentrations of uranium and thorium and the determination of the number of recoil tracks per unit volume of the sample. The first presents practical difficulties due to the ppb-concentrations of uranium and thorium in micas but no problems of principle because these elements can be measured with different techniques. The challenge lies in the determination of the density of recoil tracks. To make the tracks visible the mica is etched in HF (e.g. Hashemi-Nezhad, 1998) and the resulting etch pits are observed under an optical microscope. The number of track etch pits in mica is a function of etching time (Khan and Durrani, 1972; Gögen and Wagner, 2000) and the derivation of the volumetric track density of the sample is not a straightforward matter. The formation and accumulation of alpha-recoil tracks in dark mica is briefly reviewed in Section 2, visualization
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of the tracks by means of etching is shortly introduced in Section 3, and four different approaches to a determination of the volumetric track density of a mica sample are presented in Section 4. Two methods are based on etching-time dependent track counts. High statistical errors intrinsic to these methods and to this date incomplete understanding of the underlying etch process limit their application. Two more elaborate methods—the etch–anneal–etch method and mirror-image analysis—are based on etching-time independent track counts and allow the precise determination of the volumetric track density with a single measurement.
2. Recoil tracks The common -decaying nuclides in natural minerals are
238 U, 235 U, and 232 Th, and their daughters. Recoil energies
of the daughter nuclides are between 70 and 170 keV. The localised region of damaged lattice resulting from the atomic collision cascades initiated by the recoil nuclide is called the alpha-recoil-track (ART). The range of recoil nuclei in most minerals is of the order of 30–50 nm (SRIM, Ziegler et al., 1985). Each recoil event produces radiation damage but because the daughter nuclides lie within or at the margin of the recoil track created by their parent isotopes, its -decay does not give rise to a separate track but instead increases the size of the existing track. Because the directions in which the alpha particles are emitted and the daughter nuclides recoil are random, tracks resulting from a number of successive disintegrations will be more or less equidimensional in all directions. The size distribution of recoil tracks depends on the time of track accumulation and is in general bimodal with maxima at ∼ 30 and ∼ 125 nm (Jonckheere and Gögen, 2001; Stübner and Jonckheere, 2005).
3. Etch pits Mica is a strongly anisotropic sheet silicate, which splits along the basal plane forming sheet-like crystals. To make the tracks visible, the mica plate is etched in HF. The vertical etching velocity vv acts perpendicular to the basal plane. Material is preferentially removed from the sites of radiation damage thus producing submicroscopic etch pits where recoil tracks intersect the surface. Dissolution proceeds by removal of material from the etch pits walls. The horizontal etching velocity vh parallel to the basal plane is about 7 times faster than vv (Gögen and Wagner, 2000). As etching proceeds, the etch pits grow laterally and become visible under the optical microscope (Fig. 1a). The image quality is improved if an incident light device combined with Nomarski-Differential Interference Contrast is applied. The reflectivity of the surface is enhanced by coating the sample with a thin layer of carbon, allowing track counts under magnification as low as 200× (Fig. 1b). Observa-
tions were also made with transmitted light (Gögen and Wagner, 2000) or with Scanning force microscopy (Lang et al., 2003). The latter is primarily applied on samples with artificial ion tracks; track densities in young geological samples are in general too low to be counted under such high magnification. The triangular shape of the etch pits is controlled by the mineral (Jonckheere et al., 2005): in phlogopite KMg3 AlSi3 O10 (OH, F)2 the etch pits have almost straight sides; with increasing Fe-content (biotite, K(MgFe)3 AlSi3 O10 (OH, F)2 ) etch pits are increasingly rounded (Hashemi-Nezhad, 1998). The depth of an individual recoil track etch pit increases with etching time (Lang et al., 2003) and reaches a plateau in the range of few 10 nm, which is controlled by the vertical extent of the actual radiation damage or the effective etchable size of the track. Once a track etch pit is formed, its diameter continues to increase, thus the etch pits of tracks situated in the layer removed by etching continue to be visible. Recoil tracks are produced by -decay of nuclides that are distributed randomly in three dimensions over the crystal. Because of surface etching, recoil-tracks from deeper mica layers are exposed in the course of etching. For statistical reasons the number of recoil-track etch pits therefore increases with etching time (Fig. 1b and c). At longer etching times, this increase is limited by overlap of the etch pits, leading to saturation. The relationship between the number of etch pits per unit surface (ART ) that can be counted with the aid of an optical microscope and the number of latent recoil tracks per unit volume of the mineral (NART ) is crucial for the calculation of a recoiltrack age. This relationship depends on the size of the latent tracks, the etching mechanism, and the limits of the observation method. An etch model which describes the relationship between ART (te ) and NART has been published only recently by Gögen and Wagner (2000). 4. Determination of the volumetric track density NART 4.1. Etching-time dependent track counts According to the etch model of Gögen and Wagner (2000) the number of etch pits per unit area (ART ) is described by (Fig. 2, curve a) ART = NART · [Re + vv te ],
(1)
where NART is the volumetric track density, vv is the vertical etching velocity specific to the mineral and the etching conditions, te is the etching time, and Re is the effective etchable range of the latent track. NART Re is the number of recoil tracks intersecting a unit area of the unetched surface and NART vv te is the number of tracks per unit surface added by etching. In principle NART can be calculated from either the slope or the intercept of the regression line fitted to a series of track counts at different etching times. Eq. (1)
K. Stübner et al. / Radiation Measurements 40 (2005) 503 – 508
505
Fig. 1. Etched (40% HF) phlogopite surfaces observed under an optical microscope with incident light and N-DIC. (a) microscopic magnification of 500×, etching time 210 s (b) and (c) microscopic magnification 200×. Etching times are (b) 60 s and (c) 300 s. Track etch pits become visible under such low magnification when the sample is coated with a thin layer of carbon.
curve b and c):
areal track density ρART
a) b) c)
a) ρART = NART (Re + vv te) b) ρART = NART (Re - R0+ vv te) c) ρART = NART (Rc(te) + vv te)
etching time te Fig. 2. The increase of the areal track density ART with etching time te .
is equivalent to the equations of Kahn and Durrani (1972) for a fission track detector with c = 0. Eq. (1) has to be modified to account for the limited resolution of the microscope. When a recoil track is exposed in the course of etching a certain time passes before it becomes visible under the microscope. Therefore a fraction of etch pits resulting from tracks < R0 escape observation. R0 is in principle a characteristic of the microscope depending on the settings, but also on the sample and even on the observer. Unpublished data show that R0 cannot be assumed to be constant a priori, but for high microscopic magnification is a function of etching time (Jonckheere and Stübner, 2005). Because the value of neither R0 nor the effective etchable range Re is known or can be determined easily we introduce the combined factor Rc (te ) = Re − R0 (te ) (Fig. 2,
ART = NART [Re − R0 (te ) + vv te ] = NART [Rc (te ) + vv te ].
(2)
For an age determination from the intercept of (2) the combined factor Rc (te ) has to be determined for each sample to be dated. The precision the intercept can be determined with is limited by the steep slope of the regression line and the fact that it lies well outside the data range. Therefore the intercept of a regression line to a set of data points is not suitable for a calculation of NART , even if a constant R0 and linearity of ART can be assumed. The slope of the regression line can be determined much more precisely (∼ 2%, compared to ∼ 50% of the intercept, Jonckheere and Stübner, 2005). For the calculation of NART the vertical etch velocity vv of the sample is required. vv varies with the chemical composition; it can be measured with different methods (Lang et al., 2003), but these measurements are intricate (alternate etching and measuring of depth profiles with atomic force microscopy; etching times of ∼ 80 h in 4% HF), precision is limited (1-error between 6 and 60%), and it is suspected that the bulk etch velocity of the mica crystal vv is not constant, especially during the first stages of etching (Rufe and Hochella, 1999; Jonckheere and Stübner, 2005). Besides, the dependence of R0 on te casts doubt on the validity of the assumption that the slope is accurately defined by NART vv . In addition, age determinations of small samples or samples with inhomogeneous uranium and thorium distribution are problematic for etching time dependent track counts. More elaborate counting techniques allow the determination of a track density, which is independent of etching time. For statistical reasons the result of a single measurement of an etching-time independent track density is much more
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Fig. 3. In samples that were annealed prior to etching, the surface is rougher and etch pits have a less distinct triangular shape, compared to unannealed samples. (a) Pre-etching time 10 s, total etching time 300 s, magnification 500×; (b) pre-etching time 5 s, total etching time 240 s, magnification 200×. Etching solution: 40% HF. Both samples were annealed at 350 ◦ C for 18 h.
precise than the extrapolated intercept of a regression line, calculated from a series of track density measurements. Because of its independence of the etching behaviour no determination of vv is necessary for the calculation of NART . The rationale is to measure the number of tracks intersecting a unit area of surface. It is a constant fraction of NART represented by the effective track size Re . The number of tracks intersecting a unit area is then [ART ]s = NART Re . 4.2. Etching-time independent track counts Following two experiments aim at the determination of the surface track density [ART ]s . For the etch–anneal–etch experiment the mica sample is etched for a short initial etching time ti . Damaged material inside the surface-intersecting recoil tracks is quasi instantaneously removed and submicroscopic etch pits are produced. For an etching time ti → 0 virtually no material is removed from the intact lattice and no subsurface tracks are exposed. Subsurface tracks are removed by annealing the sample (phlogopite e.g. 350 ◦ C, 18 h, Gögen, 1999). Then in a post-annealing etch step the submicroscopic etch pits are enlarged, resulting in pits that are observable and countable under the optical microscope, without subsurface tracks being added in the course of etching. In theory the etch–anneal–etch method will yield the etch-time independent surface track density [ART ]s . In practice, because of the finite pre-etching time a number of
subsurface tracks NART vv ti will be exposed during the first etch step, so that the surface-track density is overestimated by that amount. The deviation can however be minimized by using low-concentration etchants. The main limitation of this method is to this date the rough surface of mica samples that are annealed prior to etching (Fig. 3a, b). This roughness is probably caused by migrating point defects, which are pinned at the mica surface and act as nucleation points for additional etch pits. For the same reason the distinct triangular shape of recoil-track etch pits is obliterated in annealed samples (Fig. 3a). An accurate and precise determination of NART by means of the etch–anneal–etch method will be facilitated by a modified etching method, which enhances etching parallel to the basal plane of the mica with respect to the perpendicular direction. A promising approach might be the application of NH4 F·HF or of an HF + HCl etchant (Rufe and Hochella, 1999). The mirror-image analysis is a different approach to obtain [ART ]s . Latent recoil tracks intersecting a cleavage plane of phlogopite extend some way above and below this plane and should therefore be etched in both halves of the sample split along it. If no deeper seated tracks were added during etching, the pattern of etched tracks in one half should be the mirror-image of that in the other half. Deeper seated tracks are however also revealed in both halves. Assuming that the distribution of latent tracks through the sample is random, the likelihood that the pattern of deeper seated
K. Stübner et al. / Radiation Measurements 40 (2005) 503 – 508
507
Fig. 4. Mirror-images: corresponding surfaces of a mica sample that was split prior to etching. Track etch pits that appear on both mica halves on mirror-image positions are marked with black arrows and interpreted as surface tracks. Etch pits resulting from sub-surface tracks have random positions. Etching time was 180 s in 40% HF, magnification 200×.
tracks in the two halves of the sample will also build mirrorimages is small; all tracks that occur as mirror-images in two halves of a sample can be counted as surface-intersecting tracks, the so-called “paired-tracks”, whereas all tracks in either half for which there is no corresponding track in the other half have been added as a result of surface etching (Fig. 4). The number of track pairs that a human observer or a computer program determines from the mirror images depends on the maximum distance r between two etch pits to be regarded as paired tracks. Besides others r depends on the precision the position of an etch pit can be determined with. The number of deeper seated tracks, which are erroneously regarded as surface tracks because their positions incidentally are closer than r depends on two factors: the overall track density and the value of r. Thus the surface track density is the density of paired tracks, corrected for coincidence [ART ]s = [ART ]P − 2ART r 2 ,
(3)
where [ART ]P is the measured density of track pairs, consisting of paired and coincident tracks, ART = [ART ]R = [ART ]L is the overall track density on either mirror-image and [ART ]s is the corrected value of paired tracks, i.e. the surface track density. Eq. (3) is valid only if the maximum number of possible combinations of track pairs is counted if a track coincides with more than one track in the mirror image. It is clear that only two of these tracks can be paired, but in this case (3) gives an exact correction. In the course of etching the surface of the mica becomes increasingly rough. Searching for track pairs therefore creates a bias leading to an overestimation of [ART ]s , this bias being stronger for long etching times. For short etching times on the other hand it cannot be guaranteed that all tracks are visible. To minimize overestimation we rec-
ommend computer-supported processing of the mirror image pairs: All track etch pits should be marked on both images first and the patterns of marked tracks should then be compared. With suitable image analysis software all track pairs closer than the minimum distance r can be detected and with a coincidence correction according to (3) the surface track density [ART ]s can be calculated. [ART ]s was determined with mirror-image analysis with a 1-error of ∼ 10%, which can be further reduced by the suggested improvements (Jonckheere and Stübner, 2005).
5. Discussion and conclusions The accumulation of alpha-recoil tracks in phlogopite and other minerals allows, in principle, to determine their radiometric age. The calculation of the recoil-track age requires a precise determination of the uranium- and thorium-content and of the number of alpha-recoil tracks per unit volume. Earlier research has shown that the number of track etch pits per unit area ART increases as a function of etching time. In principle, NART can be calculated from the intercept or the slope of a regression line fitted to ART (te ), provided that it is a linear function of te . But because ART (te ) is not strictly linear, slope and intercept are influenced, among other factors, by the data range used for their calculation. Both values are thus to some extent inaccurate but the magnitude of their systematic errors is unknown. Because ART (te ) increases rapidly with te , the slope of the regression line is steep, and particularly the intercept and to a lesser extent the slope can be determined with limited precision. For the calculation of NART by means of the slope a determination of the vertical etch velocity is necessary. This constitutes an additional problem, because to this date
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K. Stübner et al. / Radiation Measurements 40 (2005) 503 – 508
no method is established, with which vv can be determined fast and reliably. The etch–anneal–etch and mirror-image methods are designed to investigate if the number of recoil tracks that intersect a unit surface [ART ]s can be determined directly. [ART ]s is independent of the etching time, therefore a single track count suffices to determine NART . Even a single measurement of an etching-time independent track density is more precise than the intercept or slope of a regression line fitted to a set of data points. And because [ART ]s is independent of the etching behaviour of the sample the calculation of NART does not rely on a determination of vv . Thus the mirror-image and etch–anneal–etch methods offer better prospects for accurate and precise measurements of NART . Although these methods must be improved, they yielded consistent results with 1-errors in the range of ∼ 10%. These errors can be further reduced by application of a modified etching method and, in the case of the mirrorimage analysis, by computer-supported processing of the microscopic images. Acknowledgements The research was supported by the German Science Foundation (DFG), grant Ra 442/20. We thank Prof P. De Paepe (Geological Institute, University Gent) for making the sample available. This research has benefited from discussions with K. Gögen and E. Enkelmann. We are indebted to two anonymous referees for their constructive comments that helped to improve the manuscript. References Fleischer, R.L., Price, B.P., Walker, R.M., 1975. Nuclear Tracks in Solids. University of California Press, Berkeley. Garrison, E.G., McGimsey, C.R., Zinke, O.H., 1978. Alpharecoil tracks in archeological ceramic dating. Archaeometry 20, 39–46.
Glasmacher, U.A., Lang, M., Klemme, S., Moine, B., Barbero, L., Neumann, R., Wagner, G.A., 2003. Alpha-recoil tracks in natural dark mica: dating geological samples by optical and scanning force microscopy. Nucl. Instr. Meth. B 209, 351–356. Gögen, K., 1999. The alpha-recoil-track dating method: theoretical and experimental development and dating of mica. Dissertation Thesis, Rupertus Carola University of Heidelberg. Gögen, K., Wagner, G.A., 2000. Alpha-recoil track dating of quarternary volcanics. Chem. Geol. 166, 127–137. Hashemi-Nezhad, S.R., 1998. The triangular track contours in phlogopite mica detectors and discontinuity of the etchable damage. Nucl. Instr. Meth. B 142, 98–110. Huang, W.H., Walker, R.M., 1967. Fossil alpha-recoil tracks: a new method of age determination. Science 155, 1103–1106. Jonckheere, R., Gögen, K., 2001. A Monte-Carlo calculation of the size distribution of latent alpha-recoil tracks. Nucl. Instr. Meth. B 183, 347–357. Jonckheere, R., Stübner, K., 2005. Alpha-recoil track dating: determination of the track density in dark-mica Chem. Geol., in review. Jonckheere, R., Enkelmann, E., Stübner, K., 2005. Observations on the geometries of etched fission and alpha-recoil tracks with reference to models of track revelation in minerals. Radiat. Meas. 39, 577–583. Khan, H.A., Durrani, S.A., 1972. Prolonged etching factor in solid state track detection and its applications. Radiat. Eff. 13, 257–266. Lang, M., Glasmacher, U.A., Neumann, R., Wagner, G.A., 2003. Etching behaviour of alpha-recoil tracks in natural dark mica studied via artificial ion tracks. Nucl. Instr. Meth. B 209, 357–361. Rufe, E., Hochella Jr., M.F., 1999. Quantitative assessment of reactive surface area of phlogopite during acid dissolution. Science 285, 874–876. Stübner, K., Jonckheere, R., 2005. A Monte-Carlo calculation of the size distribution of latent alpha-recoil tracks in phlogopite: implications for the recoil-track dating method. Radiat. Meas., in press. Wagner, G.A., 1998. Age Determination of Young Rocks and Artifacts. Springer, Berlin. Ziegler, J.F., Biersack, J.P., Littmark, U., 1985. The Stopping and Range of Ions in Solids. Pergamon Press, New York.
Alpha-recoil track densities in mica and radiometric age determination K. Stübner∗ , R.C. Jonckheere, L. Ratschbacher Institut für Geowissenschaften, Technische Universität Bergakademie Freiberg, Bernhard-von-Cottastraße 2, D-09599 Freiberg, Sachsen, Germany Received 27 August 2004; received in revised form 26 April 2005; accepted 11 May 2005
Abstract Recoiling daughters of -decaying U and Th impurities in mica and other minerals produce localised lattice damage: alpharecoil tracks. The age of a sample can be calculated from the number of tracks per unit volume (NART ). To this end, the mica is etched and the etch pits at the sites of recoil-tracks are counted under the optical microscope. Because the measured track densities increase with etching time, NART is calculated from the fitted regression line. A number of problems inherent in this approach are overcome by the etch–anneal–etch and the mirror-image methods. The track densities determined with these methods are independent of etching time. Although both methods need improvement, they hold the potential of a precise determination of NART from a single measurement in future recoil-track dating. © 2005 Elsevier Ltd. All rights reserved. Keywords: Alpha-recoil-track; Track density; Phlogopite; Radiometric dating
1. Introduction Huang and Walker (1967) identified numerous shallow etch pits in muscovite mica as sites of localised lattice damage produced by the recoil nuclei resulting from alphadisintegration of uranium and thorium impurities. They proposed that these could constitute the basis of a recoil-track dating method, based on similar principles as the fissiontrack method (Fleischer et al., 1975; Wagner, 1998). In contrast to the fission-track method, the recoil-track method has not achieved the status of a geochronological dating method to this date. However, Huang and Walker (1967) pointed out that the accumulation rate of recoil tracks is ∼ 106 times that of fission tracks so that, despite their ∼ 103 times smaller range, the number of recoil tracks in an etched mineral ∗ Corresponding author. Tel.: +49 3731 39 3813; fax: +49 3731 39 3599. E-mail address: [email protected] (K. Stübner).
1350-4487/$ - see front matter © 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.radmeas.2005.05.009
surface is ∼ 103 times that of fission tracks. This allows dating very young objects like Quarternary volcanics (Gögen and Wagner, 2000; Glasmacher et al., 2003) and prehistoric and early ceramics (Garrison et al., 1978). The calculation of a recoil-track age requires measurements of the concentrations of uranium and thorium and the determination of the number of recoil tracks per unit volume of the sample. The first presents practical difficulties due to the ppb-concentrations of uranium and thorium in micas but no problems of principle because these elements can be measured with different techniques. The challenge lies in the determination of the density of recoil tracks. To make the tracks visible the mica is etched in HF (e.g. Hashemi-Nezhad, 1998) and the resulting etch pits are observed under an optical microscope. The number of track etch pits in mica is a function of etching time (Khan and Durrani, 1972; Gögen and Wagner, 2000) and the derivation of the volumetric track density of the sample is not a straightforward matter. The formation and accumulation of alpha-recoil tracks in dark mica is briefly reviewed in Section 2, visualization
504
K. Stübner et al. / Radiation Measurements 40 (2005) 503 – 508
of the tracks by means of etching is shortly introduced in Section 3, and four different approaches to a determination of the volumetric track density of a mica sample are presented in Section 4. Two methods are based on etching-time dependent track counts. High statistical errors intrinsic to these methods and to this date incomplete understanding of the underlying etch process limit their application. Two more elaborate methods—the etch–anneal–etch method and mirror-image analysis—are based on etching-time independent track counts and allow the precise determination of the volumetric track density with a single measurement.
2. Recoil tracks The common -decaying nuclides in natural minerals are
238 U, 235 U, and 232 Th, and their daughters. Recoil energies
of the daughter nuclides are between 70 and 170 keV. The localised region of damaged lattice resulting from the atomic collision cascades initiated by the recoil nuclide is called the alpha-recoil-track (ART). The range of recoil nuclei in most minerals is of the order of 30–50 nm (SRIM, Ziegler et al., 1985). Each recoil event produces radiation damage but because the daughter nuclides lie within or at the margin of the recoil track created by their parent isotopes, its -decay does not give rise to a separate track but instead increases the size of the existing track. Because the directions in which the alpha particles are emitted and the daughter nuclides recoil are random, tracks resulting from a number of successive disintegrations will be more or less equidimensional in all directions. The size distribution of recoil tracks depends on the time of track accumulation and is in general bimodal with maxima at ∼ 30 and ∼ 125 nm (Jonckheere and Gögen, 2001; Stübner and Jonckheere, 2005).
3. Etch pits Mica is a strongly anisotropic sheet silicate, which splits along the basal plane forming sheet-like crystals. To make the tracks visible, the mica plate is etched in HF. The vertical etching velocity vv acts perpendicular to the basal plane. Material is preferentially removed from the sites of radiation damage thus producing submicroscopic etch pits where recoil tracks intersect the surface. Dissolution proceeds by removal of material from the etch pits walls. The horizontal etching velocity vh parallel to the basal plane is about 7 times faster than vv (Gögen and Wagner, 2000). As etching proceeds, the etch pits grow laterally and become visible under the optical microscope (Fig. 1a). The image quality is improved if an incident light device combined with Nomarski-Differential Interference Contrast is applied. The reflectivity of the surface is enhanced by coating the sample with a thin layer of carbon, allowing track counts under magnification as low as 200× (Fig. 1b). Observa-
tions were also made with transmitted light (Gögen and Wagner, 2000) or with Scanning force microscopy (Lang et al., 2003). The latter is primarily applied on samples with artificial ion tracks; track densities in young geological samples are in general too low to be counted under such high magnification. The triangular shape of the etch pits is controlled by the mineral (Jonckheere et al., 2005): in phlogopite KMg3 AlSi3 O10 (OH, F)2 the etch pits have almost straight sides; with increasing Fe-content (biotite, K(MgFe)3 AlSi3 O10 (OH, F)2 ) etch pits are increasingly rounded (Hashemi-Nezhad, 1998). The depth of an individual recoil track etch pit increases with etching time (Lang et al., 2003) and reaches a plateau in the range of few 10 nm, which is controlled by the vertical extent of the actual radiation damage or the effective etchable size of the track. Once a track etch pit is formed, its diameter continues to increase, thus the etch pits of tracks situated in the layer removed by etching continue to be visible. Recoil tracks are produced by -decay of nuclides that are distributed randomly in three dimensions over the crystal. Because of surface etching, recoil-tracks from deeper mica layers are exposed in the course of etching. For statistical reasons the number of recoil-track etch pits therefore increases with etching time (Fig. 1b and c). At longer etching times, this increase is limited by overlap of the etch pits, leading to saturation. The relationship between the number of etch pits per unit surface (ART ) that can be counted with the aid of an optical microscope and the number of latent recoil tracks per unit volume of the mineral (NART ) is crucial for the calculation of a recoiltrack age. This relationship depends on the size of the latent tracks, the etching mechanism, and the limits of the observation method. An etch model which describes the relationship between ART (te ) and NART has been published only recently by Gögen and Wagner (2000). 4. Determination of the volumetric track density NART 4.1. Etching-time dependent track counts According to the etch model of Gögen and Wagner (2000) the number of etch pits per unit area (ART ) is described by (Fig. 2, curve a) ART = NART · [Re + vv te ],
(1)
where NART is the volumetric track density, vv is the vertical etching velocity specific to the mineral and the etching conditions, te is the etching time, and Re is the effective etchable range of the latent track. NART Re is the number of recoil tracks intersecting a unit area of the unetched surface and NART vv te is the number of tracks per unit surface added by etching. In principle NART can be calculated from either the slope or the intercept of the regression line fitted to a series of track counts at different etching times. Eq. (1)
K. Stübner et al. / Radiation Measurements 40 (2005) 503 – 508
505
Fig. 1. Etched (40% HF) phlogopite surfaces observed under an optical microscope with incident light and N-DIC. (a) microscopic magnification of 500×, etching time 210 s (b) and (c) microscopic magnification 200×. Etching times are (b) 60 s and (c) 300 s. Track etch pits become visible under such low magnification when the sample is coated with a thin layer of carbon.
curve b and c):
areal track density ρART
a) b) c)
a) ρART = NART (Re + vv te) b) ρART = NART (Re - R0+ vv te) c) ρART = NART (Rc(te) + vv te)
etching time te Fig. 2. The increase of the areal track density ART with etching time te .
is equivalent to the equations of Kahn and Durrani (1972) for a fission track detector with c = 0. Eq. (1) has to be modified to account for the limited resolution of the microscope. When a recoil track is exposed in the course of etching a certain time passes before it becomes visible under the microscope. Therefore a fraction of etch pits resulting from tracks < R0 escape observation. R0 is in principle a characteristic of the microscope depending on the settings, but also on the sample and even on the observer. Unpublished data show that R0 cannot be assumed to be constant a priori, but for high microscopic magnification is a function of etching time (Jonckheere and Stübner, 2005). Because the value of neither R0 nor the effective etchable range Re is known or can be determined easily we introduce the combined factor Rc (te ) = Re − R0 (te ) (Fig. 2,
ART = NART [Re − R0 (te ) + vv te ] = NART [Rc (te ) + vv te ].
(2)
For an age determination from the intercept of (2) the combined factor Rc (te ) has to be determined for each sample to be dated. The precision the intercept can be determined with is limited by the steep slope of the regression line and the fact that it lies well outside the data range. Therefore the intercept of a regression line to a set of data points is not suitable for a calculation of NART , even if a constant R0 and linearity of ART can be assumed. The slope of the regression line can be determined much more precisely (∼ 2%, compared to ∼ 50% of the intercept, Jonckheere and Stübner, 2005). For the calculation of NART the vertical etch velocity vv of the sample is required. vv varies with the chemical composition; it can be measured with different methods (Lang et al., 2003), but these measurements are intricate (alternate etching and measuring of depth profiles with atomic force microscopy; etching times of ∼ 80 h in 4% HF), precision is limited (1-error between 6 and 60%), and it is suspected that the bulk etch velocity of the mica crystal vv is not constant, especially during the first stages of etching (Rufe and Hochella, 1999; Jonckheere and Stübner, 2005). Besides, the dependence of R0 on te casts doubt on the validity of the assumption that the slope is accurately defined by NART vv . In addition, age determinations of small samples or samples with inhomogeneous uranium and thorium distribution are problematic for etching time dependent track counts. More elaborate counting techniques allow the determination of a track density, which is independent of etching time. For statistical reasons the result of a single measurement of an etching-time independent track density is much more
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Fig. 3. In samples that were annealed prior to etching, the surface is rougher and etch pits have a less distinct triangular shape, compared to unannealed samples. (a) Pre-etching time 10 s, total etching time 300 s, magnification 500×; (b) pre-etching time 5 s, total etching time 240 s, magnification 200×. Etching solution: 40% HF. Both samples were annealed at 350 ◦ C for 18 h.
precise than the extrapolated intercept of a regression line, calculated from a series of track density measurements. Because of its independence of the etching behaviour no determination of vv is necessary for the calculation of NART . The rationale is to measure the number of tracks intersecting a unit area of surface. It is a constant fraction of NART represented by the effective track size Re . The number of tracks intersecting a unit area is then [ART ]s = NART Re . 4.2. Etching-time independent track counts Following two experiments aim at the determination of the surface track density [ART ]s . For the etch–anneal–etch experiment the mica sample is etched for a short initial etching time ti . Damaged material inside the surface-intersecting recoil tracks is quasi instantaneously removed and submicroscopic etch pits are produced. For an etching time ti → 0 virtually no material is removed from the intact lattice and no subsurface tracks are exposed. Subsurface tracks are removed by annealing the sample (phlogopite e.g. 350 ◦ C, 18 h, Gögen, 1999). Then in a post-annealing etch step the submicroscopic etch pits are enlarged, resulting in pits that are observable and countable under the optical microscope, without subsurface tracks being added in the course of etching. In theory the etch–anneal–etch method will yield the etch-time independent surface track density [ART ]s . In practice, because of the finite pre-etching time a number of
subsurface tracks NART vv ti will be exposed during the first etch step, so that the surface-track density is overestimated by that amount. The deviation can however be minimized by using low-concentration etchants. The main limitation of this method is to this date the rough surface of mica samples that are annealed prior to etching (Fig. 3a, b). This roughness is probably caused by migrating point defects, which are pinned at the mica surface and act as nucleation points for additional etch pits. For the same reason the distinct triangular shape of recoil-track etch pits is obliterated in annealed samples (Fig. 3a). An accurate and precise determination of NART by means of the etch–anneal–etch method will be facilitated by a modified etching method, which enhances etching parallel to the basal plane of the mica with respect to the perpendicular direction. A promising approach might be the application of NH4 F·HF or of an HF + HCl etchant (Rufe and Hochella, 1999). The mirror-image analysis is a different approach to obtain [ART ]s . Latent recoil tracks intersecting a cleavage plane of phlogopite extend some way above and below this plane and should therefore be etched in both halves of the sample split along it. If no deeper seated tracks were added during etching, the pattern of etched tracks in one half should be the mirror-image of that in the other half. Deeper seated tracks are however also revealed in both halves. Assuming that the distribution of latent tracks through the sample is random, the likelihood that the pattern of deeper seated
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Fig. 4. Mirror-images: corresponding surfaces of a mica sample that was split prior to etching. Track etch pits that appear on both mica halves on mirror-image positions are marked with black arrows and interpreted as surface tracks. Etch pits resulting from sub-surface tracks have random positions. Etching time was 180 s in 40% HF, magnification 200×.
tracks in the two halves of the sample will also build mirrorimages is small; all tracks that occur as mirror-images in two halves of a sample can be counted as surface-intersecting tracks, the so-called “paired-tracks”, whereas all tracks in either half for which there is no corresponding track in the other half have been added as a result of surface etching (Fig. 4). The number of track pairs that a human observer or a computer program determines from the mirror images depends on the maximum distance r between two etch pits to be regarded as paired tracks. Besides others r depends on the precision the position of an etch pit can be determined with. The number of deeper seated tracks, which are erroneously regarded as surface tracks because their positions incidentally are closer than r depends on two factors: the overall track density and the value of r. Thus the surface track density is the density of paired tracks, corrected for coincidence [ART ]s = [ART ]P − 2ART r 2 ,
(3)
where [ART ]P is the measured density of track pairs, consisting of paired and coincident tracks, ART = [ART ]R = [ART ]L is the overall track density on either mirror-image and [ART ]s is the corrected value of paired tracks, i.e. the surface track density. Eq. (3) is valid only if the maximum number of possible combinations of track pairs is counted if a track coincides with more than one track in the mirror image. It is clear that only two of these tracks can be paired, but in this case (3) gives an exact correction. In the course of etching the surface of the mica becomes increasingly rough. Searching for track pairs therefore creates a bias leading to an overestimation of [ART ]s , this bias being stronger for long etching times. For short etching times on the other hand it cannot be guaranteed that all tracks are visible. To minimize overestimation we rec-
ommend computer-supported processing of the mirror image pairs: All track etch pits should be marked on both images first and the patterns of marked tracks should then be compared. With suitable image analysis software all track pairs closer than the minimum distance r can be detected and with a coincidence correction according to (3) the surface track density [ART ]s can be calculated. [ART ]s was determined with mirror-image analysis with a 1-error of ∼ 10%, which can be further reduced by the suggested improvements (Jonckheere and Stübner, 2005).
5. Discussion and conclusions The accumulation of alpha-recoil tracks in phlogopite and other minerals allows, in principle, to determine their radiometric age. The calculation of the recoil-track age requires a precise determination of the uranium- and thorium-content and of the number of alpha-recoil tracks per unit volume. Earlier research has shown that the number of track etch pits per unit area ART increases as a function of etching time. In principle, NART can be calculated from the intercept or the slope of a regression line fitted to ART (te ), provided that it is a linear function of te . But because ART (te ) is not strictly linear, slope and intercept are influenced, among other factors, by the data range used for their calculation. Both values are thus to some extent inaccurate but the magnitude of their systematic errors is unknown. Because ART (te ) increases rapidly with te , the slope of the regression line is steep, and particularly the intercept and to a lesser extent the slope can be determined with limited precision. For the calculation of NART by means of the slope a determination of the vertical etch velocity is necessary. This constitutes an additional problem, because to this date
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no method is established, with which vv can be determined fast and reliably. The etch–anneal–etch and mirror-image methods are designed to investigate if the number of recoil tracks that intersect a unit surface [ART ]s can be determined directly. [ART ]s is independent of the etching time, therefore a single track count suffices to determine NART . Even a single measurement of an etching-time independent track density is more precise than the intercept or slope of a regression line fitted to a set of data points. And because [ART ]s is independent of the etching behaviour of the sample the calculation of NART does not rely on a determination of vv . Thus the mirror-image and etch–anneal–etch methods offer better prospects for accurate and precise measurements of NART . Although these methods must be improved, they yielded consistent results with 1-errors in the range of ∼ 10%. These errors can be further reduced by application of a modified etching method and, in the case of the mirrorimage analysis, by computer-supported processing of the microscopic images. Acknowledgements The research was supported by the German Science Foundation (DFG), grant Ra 442/20. We thank Prof P. De Paepe (Geological Institute, University Gent) for making the sample available. This research has benefited from discussions with K. Gögen and E. Enkelmann. We are indebted to two anonymous referees for their constructive comments that helped to improve the manuscript. References Fleischer, R.L., Price, B.P., Walker, R.M., 1975. Nuclear Tracks in Solids. University of California Press, Berkeley. Garrison, E.G., McGimsey, C.R., Zinke, O.H., 1978. Alpharecoil tracks in archeological ceramic dating. Archaeometry 20, 39–46.
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