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The thermal significance of potassium feldspar K-Ar ages inferred from 40Ar39Ar age spectrum results
0016-7037/82/101811-iOSO3.00/0
Gewhlmica ct Camochimica Afro Vol. 46, PP. 181 l-1820 Q ~ergamon Press Ltd. 1982. Printedin U.S.A.
The thermal si~ifi~~ce of potpie feldspar K-Ar ages inferred from 40Ar/39Ar age spectrum results T. MARK HARRISON* and IAN MCDOUGALL ResearchSchool of Earth Sciences, The Australian National University, Canberra, A.C.T. 2600, Australia (Received
December
1, 1981; accepted in revisedform
June 8, 1982)
A~ct-~Ar/~Ar age spectrum analyses of three. microcline separates from the Separation Point Batholith, northwest Nelson, New Zealand, which cooled slowly (--S”C-Ma-‘) through the temperature zone of partial radiogenic “Ar accumulation are characterized by a linear age increase over the first 65 percent of gas release with the lowest ages (-80 Ma) corresponding to the time that the samples cooled below about 100°C. The last 35 percent of ‘9Ar released from the microelines yields plateau ages (103,99 and 93 Ma) which reflect the different bulk mineral ages, and correspond to cooling temperatures between about 130 to 16O*C. Theoretical calculations confirm the likelihood of diffusion gradients in feldspars cooling at rates sS”C-Ma-‘. Diffusion parameters calculated from the 39Ar release yield an activation energy, E = 28.8 + 1.9 kcal-mol-‘, and a frequency factor/grain size parameter, Do/l’ = 5.6+$ see-‘. This Arrhenius relationship corresponds to a closure temperature of I32 t 13°C which is very similar to the inde~ndently estimated temperature. From the observed diffusion compensation correlation, this Do/P implies an average diffusion half-width of about 3 am, similar to the half-width of the parthite lamellae in the feldspars. The range in microcline K-Ar ages from the Separation Point Batholith is the result of relatively small temperature differences within the pluton during cooling. Comparison of the diffusion laws determined for microcline with those for anorthoclases and other homogen~us K-feldspars (E = 40 to 52 kcal-mol-‘) reveals that Ar diffusion is more highly temperature dependent in the disordered structural state than in the ordered structural state. Previously published U-shaped age spectra are probably the result of the superimposition of excess “Ar upon diffusion profiles of the kind described here. I~DDU~ON FROM the time of the early application
of the K-Ar dating method to geological material, it was apparent that many K-feldspars did not quantitatively retain radiogenic ‘OAr(*Ar*) at moderately elevated temperatures. This effect was variously ascribed to the degree of perthitization (Sardarov, 1957), differing unmixing rates of K and Na (Brandt and Bartnitskiy, 1964), and deformation (Kuz’min, 196 1). In a review of Ar diffusion literature, Musset (1969) noted that a number of studies using K-feldspars provided diffusion coefficients that varied by as much as six orders of magnitude at any one temperature. On the basis of a diffusion study using a homogeneous orthoclase, Foland (1974) concluded that the low retentivity of Ar and variability in diffusion parameters in perthites is a result of the exsolution lamellae behaving as the effective diffusion radius of the mineral. Foland (1974) calculated that substantial 40Ar* loss could occur from these regions at relatively low temperatures (- 1SO’C) over geological time. In a study of the cooling history of a forcefully emplaced granitoid, Harrison et al. (1979) interpolated an effective retention or closure temperature (Dodson, 1973) for a perthitic K-feldspar of about 150°C. In a similar study, Harrison and McDougall (1980a) found a range of K-Ar microcline ages from samples taken
* Present Address: Dept. of Geological Sciences, State University of New York at Albany, Albany, New York 12222 U.S.A.
throughout the Separation Point 3atholith, northwest Nelson, New Zealand, corresponding to a closure temperature range of between about 130” to 160°C. This study reports 40Arf3vAr age spectrum measurements and X-ray diffraction results on several of these microclines which clarify the origin of the discordant ages and highlight the usefulness of such information in reconstructing temperature histories of mild thermal events. Comparison of these results with recently published “Arj3’Ar analyses of anorthoclases reveal that the behavior of Ar transport in these two structural states is very different. EXPERIMENTAL High purity microcline separates, sized to between 0.25 and 0.125 mm in diameter, were irradiated for 120 hours in a fast neutron flux in the X-33 position of the HIFAR reactor of the Australian Atomic Energy Commission at Lucas Heights, New South Wales, along with intralaboratory standard GA1550 biotite. This mica has a K-Ar age of 97.9 Ma calculated using the decay constants and isotopic abundances recommended by Steiger and Jtrger (1977). Sample and flux monitor geometry during irradiation was described by Tetley ef al. (1980). The irradiation cannister, which was cladded by 0.2 mm of Cd to absorb thermal neutrons, was inverted end-for-end midway through the irradiation to minimi~ the effect of the fast neutron flux gradient to about one percent across the cannister. Factors used to correct the effects of interfering neutron reactions were (“Ar/39Ar)x = 2.70 X lo-‘, 06Ar/ “Arlc. = 3.06 X 10m4and (39Ar/‘7Ar)cs = 7.27 X lop4 (Tetley et al.. 1980). Subsequent Ar extractions from the irradiated samples were carried out in a machined MO crucible within a high vacuum extraction system. Heating was by means of a radio 1811
--------_---
78-592
T~6t.t 1 ““Ar/JYAr resu/Ls tw rmcrociine samples from the Separation i’o~nt Batholith. -.._--..-_. -. . .._._..____--___ ..__.__.-._____..-. _ _. _ _ _._. _.
mlcroclzne 63.02
24.47 22.20 67.45 23.51 18.96 19.24 19.54 19.87 20.11 20.34 20.61 21.03 2i.G 21.93 22.3% 22.79 23.59 23.74 23.99
0.141: 3.097 5.467 2.344 2.371 2.674 3.2'74 4.175 4.992 6.111 6.46~3 5.845 3.829 1.884 1.553 1.908 i.766 1.020 3.320
FM-1; FM72
26.22 26.46
TF’
22.39
410 570 620 670 690 ?30 770 810 800
49.70 24.24 19.80 19.86 20.05 20.38 20.67 20.85 21.21 21.55 21.08 22.47 22.91 23.32 23.97 24.24 24.26 24.22 23.79 24.74
5,874 0.0 5.412 0.0 2.200 7.018 7.776 7.300 4.107 13.01 9.372 14.57 15.47 5.012 4.110 0.9512 5.900 7.742 3.654 2.574 10.87 54.69 27.03
127.5 137.6 15.21 322.2 48.57 13.40 4.710 1.152 0.0050 2.561 1.249 1.685 0.8903 3.337 7.720 9.826 11.03 11.95 15.63 19.86 21.09 13.34 32.93
0.903 2.48 1.89 0.0631 0.433 1.00 1.i9 1.16 1.05 1.30 1.20 0.889 0.776 0.730 1.31 1.32 1.64 2.97 4.69 3.43 2.15 0.100 0.0516
1.581 1.174 2.016 0.0 15.16 4.290 2.421 0.7582 1.733 8.087 1.046 0.4021 3.627 6.252 5.998 s.379 1.379 4.223 1.683 0.0 0.0 4.810
139.2 140.5 7.066 491.5 94.30 32.17 15.44 10.01 4.766 2.960 1.450 2.870 2.209 2.178 2.247 2.398 2.078 2.285 2.867 4.000 4.546 8.900 1.626 5.154 4,967
2.23 6.93 2.31 0.0297 0.177 0.455 0.644 1.23 1.72 3.71 1.36 2.53 2.85 2.87 2.35 2.54 2.60 3.50 3.37 6.23 a.03 5.17
g: 350 450 520 570 610 650 680 720 770 820 870 940 1000 1050 1100 1140 1300 rTFh
78-629
0. 7564
35.%3 1148.0 60.00 10.30 4.262 3.359 2.580 3.163 4.186 4.027 6.203 h.015 9.339 12.61 13.74 27.49 41.38 45.92
6.78 0.0670 1.13 3.43 2.73 5.63 4.21 2.89 3.41 2.41 2.60 2.46 4.45 3.58 4.99 8.16 10.5 0.859
“.
91:.
,
0.106 1.88 7.28 11.6 20.5 27.1 31.6 37.0 40.8 44.9 48.8 55-8 61.4 69.3 82.1 98.6 1OO.Q
95.1 48.1; 92.0 98.1 99.0 99.3 99.4 99.2 99.1 99.1 98.8 98.9 98.5 98.1 98.0 96.4 94.7 V3.R
0.230 1.84 5.49 9.82 i4.1 17.9 22.6 27.0 30.2 33.0 35.7 40.5 45.3 51.2 62.0 79.1 91.6 99.4 99.8 100.0
83.8 83.9 97.5 75.9 92.3 96.9 98.4 98.9 99.1 99.0 98.9 98.1 98.6 98.2 98.2 98.0 98.0 98.2 97.8 97.2 97.5 90.8 83.L
22.209 ‘?I.110 33.495 21.706 18.629 19.087 19.414 19.771 19.988 20.189 20.471 20.817 21.178 21.626 21.981 22.353 22.749 22.487 22.610
940 990 1030 1070 1110 1140 1165 1200 1250 1350
;:';;;l 22.515 40.155 22.779 19.385
19.707 19.998 20.335 20.577 20.798 21.153 21.511 21.760 22.220 22.593 22.970 23.602 23.753 23.651 23.583 23.431 23.769
ITF6
FM-l* FM-z*
ITS 350 450 515 560 610 640 680 720 760 800 850 900 950 1000 1060 1110 1160 1210 1260 1280 1310 1310 ITT'
to.4
93 7
‘0.5
microcline
900
78-638
3Z.J '0.5 146.!)? 1.7 95.7 to.5 82.5 to.4 84.4 85.9 to.4 87.4 tQ.5 88.3 to.5 89.1 to.5 90.4 trJ.5 91.9 LO.5 93.5 LO.5 95.4 '0.5 v6.9r0.5 98.5 io.5 100.2 ro.5 99.1 to.5 9v.c
22.410
1
98.3 to.5 171.8 il.6 99.520.5 85.0 2 0.4 86.4 kO.4 87.6 10.4 89.1 t0.s 90.1 ? 0.5 91.0 to.5 42.5 to.5 94.1 to.5 95.120.5 97.1 to.5 98.7 20.5 100.3 fO.5 103.0 f0.5 103.6ZO.5 103.2 to.5 102.9 to.5 102.2 to.9 103.7 r2.1 98.1
micxocline 26.68 26.69 20.59 54.42 21.49 18.65 18.31 18.62 18.84 19.08 19.37 19.44 19.57 19.75 19.94 20.20 20.45 20.73 20.95 21.3L 21.32 21.51 26.43 37.07 36.02
6.259 0.0 88.54
0.607 0.350 0.0821
0.057 0.395 1.26 2.53 4.88 8.17 15.2 17.8 22.7 28.1 33.6 38.1 42.9 47.9 54.5 61.0 72.8 88.2 98.0 99.2 99.8 100.0
’ Corrected for line blank of 2 X 1O-‘3 mol 40Ar. 2 Corrected for decay of “Ar, 3 Obtained by manometric measurement of gas calibrated using “Ar spike. ’ FM = flux monitor GA1550 biotite; K-Ar age = 97.9 Ma: K/Ca = 38.5. STF = total fusion split. 6 ITF = incremental total fusion age. ’ h”K = 5.543 X 10-‘Oa’“‘.
84.5 84.3 98.9 65.2 82.6 92.6 95.8 97.4 96.5 99.2 99.3 99.2 99.4 99.3 99.1 99.2 99.2 99.3 99.2 99.2 99.1 98.5 80.7 57.9 55.6
201353 39.673 18.696 17.678 17.824 18.295 18.676 18.977 19.301 19.334 19.479 19.661 19.856 20.109
88.7 iO.5 169.9 t1.6 81.6 to.5 77.3 to.4 77.9 to.4 79.9 to.4 81.6 to.4 82.8 $0.4 84.2 1.0.4 84.4 to.4 85.0 kO.4 85.8+0.4 86.6 to.4 87.7 to.4
20.364 20.641 20.838 21.165 21,163 21.225 21.594 21.810 21.411
88.8 20.4 89.9 10.5 90.8L0.5 92.2 co.5 92.1 tn.5 92.4 to.5 93.9 to.5 94.9t0.6 93.2 to.8 RR.4
1813
K-feldspar K-Ar ages mbh2.
unit-csu
#I*10
XlrbuOf r9flactiml
m-592
18
76-594
21
76-629
20
78-636
20
p.ruterr
of sepration
Point edholith
l
&I
5,
8.5883 *0.0069 8.5744 to.0023 8.5850 t0.0013 8.5651 f0.0093
12.9558 to.0033 12.9724 fo.0028 12.9627 *0.Oo65 12.992. tO.0338
(4, 7.2203 fO.0057 7.2166 fo.0020 7.2117 to.0057 7.21.2 fO.oO92
a 90.67% *o.o62o %.6o44 *o.o439 90.6247 *0.1205 eo.l9oo fO.3766
K-feldrpars.
B 115.8455 *o.o709 US.%% tO.0248 116.0701 to.0666 115.8730 t0.Oe22
Y 87.7173 to.0310 87.9415 tO.0358 87.7839 fO.066. 86.9943 fO.3639
aa*-i* I Of 0.97
96.6
0.88
94.9
0.95
92.5
0.40
97.9
frequency generator and temperatures were monitored by a thermocouple within the crucible and an optical pyrometer reading at the top of the crucible. Due to a thermal gradient within the crucible, the temperature measured using the optical pyrometer was in some cases higher than the temperature recorded by the thermaoouple by about 130°C. It is thought that the actual sample temperature is closer to the thermocouple reading and it is this temperature that is given for each step in Table 1. Uncertainty in these temperatures is about rt3O’C. The evolved gas at each temperature step was isotopically analyzed for At
history of the Separation Point Batholith foliowing its forceful emplacement into the Paleozoic country rocks, 114 Ma ago. The cooling history (Fig. 3, Harrison and McDougall, 1980a) is characterized by a logarithmic decay in temperature following crystallization, reaching about 180” by 100 Ma ago. The subsequent cooling rate was at about 5”C-Ma-’ until -80 Ma when the temperature dropped below about 100°C as evidenced by the apatite fission track ages.
using a rare gas mass spectrometer: samples 78-629 and 78-638 were measured using a Micromass 1200 instrument
Slow cooling versus episodic loss
and sample 78492 was analyzed using a much modified AEI MS10. Un~~ainty in the derived ‘aAr/BAr age includes the precision of the isotope ratio measurements in both the sample and flux monitor and the additional uncertainty in the J parameter of 0.5 percent. 40Ar/‘gAr results are given in Table 1. X-ray diffr~tion rne~ur~en~ were made on powdered samples by Dr. R. A. Eggleton, using a Gunnier camera arrangement. Measured angles of up to 21 reflections per sample were used in a least-squares program to determine the unit-cell parameters given in Table 2.
RESULTS AND DISCUSSI0N 40Ar/39Ar incremental release measurements have been made on microcline samples 78-59278-629 and 78-638 which have K-Ar ages of 92.7 + 0.7, 96.8 f 1.0 and 88.5 + 0.8 Ma, respectively (Harrison and McDougall, 1980a). These results are shown together on an age spectrum plot in Fig. 1. Results of *Ar/*Ar total fusion analyses and the incremental total fusion ages, obtained by summing the individual steps (Table l), agree very well with the K-Ar ages. The U’Ar/39Ar age spectra of the microclines (Fig. 1) imply ‘OAr* ~n~ntration gradients within the crystals with the initial low temperature gas fractions yielding ages on the order of 80 Ma. In all three cases, the subsequent gas release reveals a monotonic rise in age until about 65 percent of the 39Ar has been released, at which point the age remains essentially constant for the remainder of gas release at 103 Ma (78-629), 99 Ma (78-592), and 93 Ma (78638). These ages reflect the relative differences seen in the K-Ar ages and average about 6 Ma older than the conventional ages. The amounts of gas evolved at any step are relatively constant up to extraction temperatures of about 1050°C (Table 1) at which point larger quantities of gas are released, It is believed that the incongruent melting of microline to leucite and melt at about this temperature (Deer et al., 1966) is responsible for the enhanced outgassing. Using isotopic data and heat flow theory, Harrison and McDougall (1980a) reconstructed the cooling
The shape of the age spectra (Fig. 1) do not conform well to a model of episodic loss of =Ar* (Turner, 1969) as the observed gradients are linear rather than convex, although this may be explained by a nonuniform grain size distribution. At any rate, the thermal history determined by Harrison and McDougall (1980a) precludes having an episodic QAr* loss at around 80 Ma which would be required to explain the age spectra in these terms. However, Turner (1969) noted that it was likely that samples cooling very slowly through their partial @‘Ar* retention region of perhaps -2O”C, would likely develop some form of mAr* gradient.
:i~lI’ Separotian
0
20
Point Batholith
40
X ‘*Ar
Microctincr
60
80
loo
RELEASED
FIG. 1. “‘Ar/39Ar age spectra of slowly cooled microclines from the Separation Point Batholith. The cooling history for 78492 (see text) is shown on the right vertical axis. The linear form of the @Ar* gradients is related to the slow accumulation of ‘@Arduring cooling. The low-temperature ages of between 77 and 85 Ma correspond to the time the samples cooled to below - 110°C. The differences in bulk K-Ar age and plateau portion of the age spectra is a result of relatively smail temperature differences within the batholith during cooling.
i
-or----
-_.-,._ ,.,__ __ ~.~~ .__.r_-._...r_.~
FIG. 2. The concentration distributions across the halfwidth, I, of a plane sheet resulting from slow cooling (curve 1) and episodic loss (curve 2). The concentration, C, is given in terms of a deficit of what would have existed had cooling taken place infinitely fast at t K C = 1 or episodic heating not occurred at r cc C = 0. The slow cooling-curve was only evaluated to x/I = 0.95. The closure age (slow cooling) and ‘hybrid’ age (episodic loss) both correspond to t K C = 0.5.
In his mathematical development of the theory of closure temperatures in cooling geochronological systems, Dodson (1973) produced expressions for the limiting concentration distribution of the diffusing isotope within crystals of different geometries. The concentration distribution across a plane sheet after slow cooling as a function of distance, x, from the center of the slab is given by Dodson (1973):
x cos ((n - %)TX) In {y(n - Y2)7r27M) (1) (n - ‘/2)7r Where h is the 40Ar* production constant, 7 is the cooling time constant; B is dimensionless time; M = @0)/r’ is the value of the combined diffusion coefficient/grain size parameter at the commencement of cooling; y = e’ where c is Euler’s constant; and C,/ C, is the ratio of concentration of the daughter product over the concentration of the parent. We have chosen to use the solution for a plane sheet to describe the loss of 40Ar* from microperthitic microcline as the incoherent boundaries provided by the exsolution lamellae probably control the effective diffusion radius. Loss from an infinitely long slab would closely approximate this geometry. Equation (1) can be rewritten (M. H. Dodson, pers. comm.):
x cos ((82- M)7rx) In ((n - %)A) (n - ‘%)7r
(2)
where I, is the apparent closure temperat.ur-c at 3: E is the activation energy; &,/I2 is the frcyuenc) Factor/grain size parameter; and R is the gas constant. Since it is implicit in these calcuiatiorls that cooling proceeds linearly as l/7’, the app;irrnt 7, corresponds to an age, or daughter concentration, ;~t x. We have evaIuated (2) using E = 28.8 kc&m&‘. &/f2 = 5.6 sec.‘. 7 :-T7.65 x IO’” see and the cooiing rate dT/dt -7 S”C-Ma’ ’ for reasons discussed later. These results are shown as curve I in Fig. 7, which shows the model distribution of “Ar* within the microcline tamellae following slow cooling. The curve is characterized by a smooth increase in age or concentration to an x/l value of about 0.3 at which point the concentration distribution flattens out and remains essentially constant to the center of the plane sheet. Also shown in Fig. 2 for comparison is the concentration profile produced as a result of episodic 40Ar* loss from a plane sheet (curve 2). The daughter concentration, c, is given for any distance. A, from the center of the slab by the expression {Crank, 1975):
where co = 1 is the initial uniform concentration; c!, is the zero boundary concentration; D is the diffusion coefficient; and I is the slab half-width. This distribution for a Dt/1’ value of 0.08 is shown in Fig. 2. The curve generated for an episodic loss (Fig. 2) has a somewhat more linear concentration gradient than the slow cooling curve with virtually no plateau near the center of the slab. In both cases of slow cooling (curve 1, Fig. 2) and episodic loss (curve 2, Fig. 2) the resulting mineral age corresponds to a C: value of 0.5. Clearly the forms of these two curves are similar enough to preclude our using this information as a diagnostic tool for choosing between these two hypotheses. However, we can modify the form of the slow cooling curve (curve 1, Fig. 2) by slowing the cooling rate late in the cooling history to produce a nearly linear concentration gradient between 1.0 > x/r z 0.4 which would yield an age spectrum similar to what we have observed. This may have been the case as the calculated T, at x/l = 0.95 is only 88°C which is significantly lower than that indicated by the apatite fission track ages and thermal model (Harrison and McDougall, 1980a) at about 80 Ma.
Superimposed on the right-hand side of the 40Ar/ “Ar age spectra of the Separation Point Batholith microclines (Fig. 1) is the temperature history of 7% 592 from Fig. 3 of Harrison and McDougalI ( 1980a). As was shown in equation (2), different portions of the mineral and therefore the age spectrum corre-
1815
K-feldspar K-Ar ages spend to different temperatures with the last *Ar* loss occurring at a temperature of about 110°C. Turner et al. (1978) have suggested that it may be possible to obtain some kinetic ~nfo~atio~ from the #Ar/3~Ar age spectrum experiment by using the observed gas loss at any given temperature to calculate a combined diffusion coefficient/grain size parameter (O/p). Regression of these data on an Arrhenius plot would produce both the activation energy, E, and the frequency factor/grain size parameter, &/r’. This information could in turn be used to calculate a geelogical closure temperature (7’J forthe sample. Harrison and McDo~~~il(l98Ob~ have argued that this practise is inappropriate for hydrous phases (e.g., Berger and York, 1979) as structural breakdown in the vacuum likely obscures the natural diffusion behavior. However, for anhydro~s phases, such as feldspars, this method could be useful in determining kinetic parameters (Turner et al,, 1978; Harrison and McDougall, 1981; Berger and York, 1981). Values for D/l2 were calculated from the measured “Ar release from 78-592.78-629 and 78-638 microclines (Table 1) using the equations given by Harrison and McDougall (1981). The data for 78-638 yields a linear array on an Arrhenius plot, corresponding to an E of -29 kcai-mol-‘, for extraction temperatures up to about 9009C, excluding the first step which contains less than 0.1 percent of the 39Ar released (Fig. 3). Above that temperature, the slope flattens indicating a change in the diffusion mechanism. Since it is our intention to extrapolate the diffusion data to temperatures on the order of iOO”C, it is reasonable that we exclude data from consideration beyond the temperature at which the diffusion mechanism changes. It is difficult to assign uncertainties to the diffusion coefficients calculated by this method, but the errors are large enough to preclude de~nition of more than one slope from the data shown in Fig. 3. A similar treatment of 78-629 data (Fig. 3) yields an E of -28 kcal-mol”’ up to extraction temperatures of about 800°C. However, the data for 78-592 (Pig. 3) plot above the curve defined by 78-638 and 79-629 and do not yield a linear array above extraction temperatures of about 600°C. The reason for the difference in behavior of this sample is unknown, although the offset of L)fP values at a given temperature from the data of 78438 and 7% 629 may be related to the large uncertainty in both absolute and relative temperature monitoring, partly the result of the different extraction lines used for 78-592. Regression of the well correlated 78-638 and 78-629 data (York, 1969) yield an E = 28.8 k 1.9 kcal-mol-’ and a L&J!’ = 5.6”_::‘9see-‘. Using these parameters, a closure temperature for these samples can be calculated from the expression of Dodson (1973):
4
78-636 + 78-629 a 76-592 l
E = 28.8 kc+mole’ Do.& = 5.6 set-’ 8
FSG. 3. Arrhenius plot of -log D/l’ values calculated from measured “AT loss versus the reciprocal absolute temperature of the extraction step, for samples 78-592, 78-629 and 78-638. The data shown is for the low temperature, linear portion of the diffusion curves (see text).
where A, a geometry factor = 8.7 for a plane sheet; R = 1.987 cal-mol-‘-deg-r; and dT/dt = 5 %-Ma-‘. The calculated T, is within uncertainty of that predicted for 78-592 by the cooling history (Fig. 1). These internally consistent observations suggest that microcline geothermometry using kinetic data obtained via the step-heat experiment may yield meaningful temperature information although we reiterate that temperature control for these extractions was poor. Having established these diffusion parameters, we can use the analysis of Hart ( 198 1) to determine the average perthite radius in these mierochnes assuming that this dimension is also the effective diffusion radius, I. Hart (1981) has observed a diffusion compensation effect in feldspars by which the activation energy and frequency factor are positively correlated through the expression:
For our E of 28.8 kcal-mol-*, this equation predicts a Do of 3.6 X lo-’ cm2-set-‘. If this is indeed the intrinsic frequency factor, then our De/f of 5.6Zif9 see-’ implies an average perthite lamelfae width between about 3 and 9 pm which is on the order of that observed in thin sections.
Previous 40Ar/39Ar age spectrum analyses of microclines (Albarede et al., 1978; Maluski, 1978; Berger et al., 1979; Berger, 1975) have indicated the ability of K-feldspars to record the effects of mild metamorphisms, but have generally been characterized by U-shaped age spectra in which the low temperature portion of gas release contains very old apparent ages which decrease to a minims before rising smoothly to geologically reasonable ages. Har-
IXlh
!
M.
Harrison and I. McDougaii
rison and McDougall (1980b) have shown that excess “‘Ar which diffuses into the near surface region of crystals can produce a similar effect to that observed in the K-feldspars. We believe that these age spectra are the result of the superimposition of excess 40Ar on diffusion loss profiles within the feldspar lamellae which produces the U-shaped appearance. Although the solubility of Ar in feldspars is not especially large (Harrison and McDougall, 1981). the relatively rapid diffusion of Ar in K-feldspars at low temperature allows these samples to become contaminated while the co-existing mica and amphibole would not be significantly affected. Age discrepancies in microclines The six samples of microcline from the Separation Point Batholith give K-Ar ages in the range of 99.0 to 88.5 Ma (Harrison and McDougall, 1980a). Three possible explanations for this range in ages are: 1) the samples have experienced different thermal histories, 2) the feldspars are of different structural states leading to different diffusion behavior, and 3) the average perthite lamellae widths are variable from sample to sample. To assess the possibility that different structural states might control the gas loss, unit-cell parameters were determined by X-ray diffraction methods on four samples and these results are given in Table 2. The unit-cell dimensions of all samples plot close to maximum microcline and all four samples contain about the same percent orthoclase component (%Or) and 6ol*y* parameters (Smith, 1974) within uncertainty (Table 21, ruling out crystallographic control on gas loss. The difference in the diffusion results could be the result of different perthite widths in the samples causing only the grain size parameter, I, to vary. Harrison and McDougall (1980a) report an unsuccessful attempt to determine the average perthite widths of these samples as the broad width distribution precluded finding any fine inter-sample distinctions, but an implication of this result is that large inter-sample variations are unlikely. The other possible explanation of the microcline K-Ar age differences is that the samples have experienced different cooling histories. The sample with the oldest age (78-629) is closest to the contact with the country rock while the sample with the youngest age (78-638) is furthest away. Since heat will be dissipated more rapidly from the margins of the pluton than the center, this correlation between age and position within the batholith may be evidence for this explanation. Indeed, the coexisting biotite K-Ar ages of samples 78-629, 78-592 and 78-638 of 110.8 + 1.1, 107.8 * 0.7, and 103.9 + 2.1 Ma, respectively, also show this effect indicating that different temperatures very likely existed at different positions in the batholith fairly soon after emplacement. Temperature differences on the order of only -3O*C could account for the very different microcline ages as the cooling rate was only about
S”C-Ma-’ at that time. We believe that this explanation accounts for the first order differences observed but cannot rule out the possibility that differing structural states and perthite lamellae widths have also contributed in a small way to the age discrepancy between these microclines. Comparison of division parameters between high and low temperature K-feidspars Anorthoclases separated from pumice clasts contained within the KBS Tuff at Koobi Fora, adjacent to the northeastern shores of Lake Turkana, northern Kenya, were measured by the “eAr/39Ar age spectrum technique and the results reported by McDougali ( I98 1f. They yielded excellent flat age spectra, interpreted as indicating that the feldspars have remained thermally undisturbed since their crystallization 1.88 f 0.02 Ma ago. These anorthoclases have a composition of about Or3? and X-ray diffraction measurements (referred to in McDougall et al. (1980)) show that the feldspars are highly disordered and structurally close to the sanidine-high albite series, with no evidence for significant unmixing or strain resulting from exsolution. However, optically some crystals show extremely closely spaced (-2 pm) polysynthetic twinning. As for the microclines discussed previously, the ~Ar~39Ar age spectrum data can be used to examine the question of Ar diffusion from the anorthoclases. Diffusion coefficients were calculated from these data using both spherical and infinite slab models. Results for the assumption of spherical geometry provided considerably better fitting straight line Arrhenius relations than the slab, and this was taken as evidence that the polysynthetic twinning is not a significant diffusion boundary. In addition, previous workers who have studied diffusion in homogeneous fetdspars almost invariably have used a spherical geometry model, so that our results can be more readily compared if we also employ such a model. ~a1culations of diffusion coefficients were made using the equations given by Fechtig and Kalbitzer (1966). It was recognized during the 40Ar/39Ar age spectrum experiments on the anorthoclases that the measurements of the actual temperature of the samples for each step were not well controlled. The temperatures reported by McDougall (1981) were those determined by optical pyrometer focussed on the inside wall at the top of the MO crucible. Temperatures were also monitored by means of a thermocouple inserted vertically into a sleeve built into the base of the crucible, and these temperatures were 110” to 220°C lower than those given by the optical pyrometer. The difference between the two temperature measurements in any one step heating experiment was nearly constant. These data indicate the presence of substantial temperature gradients in the crucible. 1n subsequent experiments we have measured the temperature with the optical pyrometer focussed di-
1817
78-1047 step heat
71-1031 stephe4tI 600 700 770 820 870 915 940 970 1000 lo40 1070 LllO ll.60 1225 1360 lb70
78-1038
760 830 890 930 970 loo0 1030 1065 1100 1150 1200 lb30
550 650
12.94
10.83
TY83
10.07 9.59
7.02 6.55
~~:: a:53 8.31 8.18 7.86 7.67 7.115 1110
ll75 1310 lb20
I:;: 6.32 5.91
6.21 6.02 5.77 5.69 5.43 5.22 5.10 1.95 L.91 4.44 4.Ob -
.wph.?&2 660 710 775 820 %: 915 950 990 lob0 1090 1320
600 720
520 650
790 850 GO
840
540
970 1WO 1045 1076 1130 1180 I.210 1250 I.320
::: 880 915 91r5 980 lb15 1070 1110 1150 1170 12110
12.61 10.83 10.12 9.45 8.99 8% 8.L2 8.21
7.45 7.23 7.03 6.93 6.61
7.29 6.63 6.18 5.88 5.68 5.50 5.26 5.09 4.83 4.53 L.52 4.21
79-14 step APat 10.72 10.17 9.Q b.i5 8.87 8.64 8.42 8.18 7.92 1.62 7.34 6.28
8.02 6.95 6.42
E )r:33 -
600 700 730 760 820 880 930 965 1wo 1045 1100 1150 1250 1400
--
rectly on the sample, and found that the value is intermediate between the two other readings. Thus for the KBS Tuff anorthoclases we have revised the published temperatures downward by 50’ to 1 10°C in each case accepting the average of the two temperatures measured in those experiments. It should be recognized that the revised temperatures are still relatively poorly known with an uncertainty in the order of 30°C but that the temperature interva1 between successive steps is probably correct to about 10°C. Data used in the construction of the Arrhenius plots are given in Table 3, results are shown in Fig. 4, and regression results are listed in Table 4 using the York (1969) two error regression method for calculating the best fit straight lines. Diffusion coe-fficients have not been calculated for the first two steps for 78-1047 and the first step of 78-1038(l) because the amount of gas extracted was extremely small, less than 0.5% of the total. On the Arrhenius diagram (Fig. 4) it is seen that data from each step heating experiment are well aligned, although the results for 79-14 show somewhat greater scatter than is found for the other samples. Regression data and derived values for the activation energy and Da/a2 values are given in Table 4. The two experiments on 78-1038 do not agree within experimental error, although both yield extremely well fitting straight lines. The explanation for the differences probably is associated with the problems of temperature measurement. If data from all four experiments are regressed together a mean
5:; 665 700
~..
E 870 900 930 980 1025 1075 X175 1325
12.15 11.01 10.66 10.28 9.78 9.15 8.75 8.53 8.31 7.98
8.66 8.29 7.90 7.26 6.11 5.76 5.20 ::z 4.88
:::,"
value for E = 40.9 + 1.4 kcal-mol-’ is found together with a De/a2 = 88?# set-‘. The good alignment of the data on the Arrhenius plot provides strong evidence that the Ar transport m~hanism conforms to a model of volume diffusion, with no significant change in structure of the anorthoclase during the “Ar/“Ar step heating experiments in vacua. Assuming that the measured grain size corresponds to the effective diffusion radius, a reasonable assumption in view of the good fit of the data to a spherical diffusion model, the Arrhenius relations given in Table 4 all lie close to or on the diffusion compensation line for feldspars defined by Hart (1981). Foland ( 1974) reported an Ar diffusion study on a homogeneous orthoclase and showed that using vacuum extraction techniques he obtained results that were indistin~ishable from those obtained on the same sample in which Ar loss was induced in isothermal heating experiments under hydrothermal conditions. Foland’s data therefore provide additional justification for using our *Ar ,J=Ar step heating data to derive diffusion parameters from the Kfeldspars samples. Roland (1974) found a value for E = 44 kcal-mol-’ for Ar diffusion from the orthoclase, and he also demonstrate that earlier diffusion experiments on homogeneous sanidines by Baadsgaard ef al. ( 196 1 ), Fechtig et al. ( 196 1) and Frechen and Lippolt (I 965) all yielded activation energies for Ar diffusion in the range 40 to 52 kcal-mol-‘. Our estimate for the activation energy for Ar diffusion in anorthoclase (E = 40.9 f 1.4 kcal-mol-‘) lies near
i
---
M. Harrison and I. McDougali
___- -‘I _..._~.~._...._ __ ~____ __.__
---- ~‘.T -. ---___)__
-7---
,l
= 79-14 E=44.5?2.7
I % v)
7 -
l
78-1047
E=42.6+-l-2
8-
N (3
4
Anorthoclase kcol-mol-’
Anorthoclase kcol-mol-’
D,/a2=137!
$‘z set-1 _-.
.____
n78-1038(2) E=41.0?1.7
Anorthoclase
kcol-mol-I
678-
E=37.0?0.8 D.,/a2=12~I~ 1200
7
I00
kcal-mol-I 4’4 3.2 see-I IO00
.. so0
800
8
9
700
IO
I
II
600-c t
h
I2
I 04/‘K FIG. 4. Arrhenius plots of -log D/a2 calculated from measured .“Ar loss versus the reciprocal absolute temperature of the extraction step, for anorthoclase samples analysed by McDougall (1981). The diffusion parameters are distinctly different from those calculated for microcline and indicate that Ar diffusion in mixed K-feldspars is more strongly temperature dependent than in exsolved, low-temperature K-feldspars.
the lower end of the range previously reported for homogeneous sanidine and orthoclase, which have relatively high K contents. The anorthoclases used in this study have K contents of about 5.1% (McDougall et al. 1980). It would appear that for homogeneous alkali feldspars there is little compositional effect in terms of Ar diffusion phenomena. However, these results are significantly different from the diffusion parameters we have reported for microclines. If the enhanced diffusion of Ar in microclines were only a consequence of the much lowered diffusion radius brought about by perthite exsolution, then we would expect a similar E between anorthoclase and microcline, but a significantly reduced Dofl2for microcline. The observation of much higher activation energies in homogeneous K-feldspars (40 to 52 kcal-mol-‘) than in microclines (-29 kcal-mol-‘) indicates that the mixed, high temperature feldspar structure requires a diffusing Ar atom to have considerably more thermal energy to make a lattice jump than does an unmixed, low-temperature structure. For both high and low structural states, it has been demonstrated that internally consistent kinetic information can be obtained, as a by-product of the age spectrum experiment, that may be used to calculate geological closure temperatures.
CONCLUSIONS The principal conclusions of this study are: 1) 40Ar/‘gAr age spectra of microclines which have cooled slowly (--S’C-Ma-‘) through the zone of partial 40Ar* retention are characterized by a linear age increase over the first 65 percent of 3gAr release, followed by an age plateau for the remainder of the gas release. The initial low-temperature ages in the spectra correspond to the time that the samples cooled below about 100°C. Theoretical calculations confirm the likelihood of diffusion gradients in feldspars cooling at rates of s;S”C-Ma-‘. 2) Calculation of Ar diffusion parameters from the measured )‘Ar loss observed during the age spectrum experiment yield an activation energy, E, of 28.8 + 1.9 kcal-mol-’ and a frequency factor grain size parameter, Do/I', of 5.6”:: set-‘, for a plane sheet geometry. Using these values and the cooling rate of S”C-Ma-‘, a closure temperature of - 13OO”C can be calculated which is within uncertainty of the value interpolated for the samples from an independent analysis of the thermal history of the region. 3) From the observation of a diffusion compensation effect in feldspars, an effective diffusion halfwidth for the microclines of - 3 pm can be calculated from the knowledge that Do/j2 = 5.6 set-‘. This dif-
K-feldspar K-Ar ages
T&-la38(1)
37.0* 0.8
12.11;';
1.33
Au data exceptsoo"cstep cvx J 1.0 CVY = a.5
78-103812)
41.0f 1.7
119+=4 -61
1.08
Ail aeta except660% step CVK 3 1.0, cw * z.0
18-1047
42.6+ 1.2
137+a3 -52
0.69
,m data except520,650% stepn cvx = 1.0, m-f t 0.5
79-14
44.5 f 2.7
&1593 -435
L.60
All data,LX = 3.0,CIY = 2.0
~a-1038t1) 7a-103aw
37.7* 1.3
2..l+14.7 -8.5
I.21
Ae Bbove.CYX = 2.0, CVX = 1.0
78-x038(1) Ta-1038(2) 78-LO47
39.1f_1*2
35-7-13.5 +21.6
0.95
Aa above.CVX = 2.0,CVY = 1.0
0a+68 -38
1.17
AP above,cvx = 3.0,CVY = 1.0
v3-1038~1t 40.9 * 1.4 7;r-:;4387(21 .-
1819
n-14
fusion dimension is on the order of the perthite lamellae widths observed in thin sections. 4) Microchne samples from the Separation Point Batholith yield a spread of K-Ar ages as a result of relatively small temperature differences within the Batholith. The effect of differing sample structural states and perthite widths may also contribute to the age discrepancy. 5) Activation energies for anorthoclases and other homogeneous feldspars calculated from Ar vacuum degassing kinetics are significantly higher (40 to 52 kcai-mol-r) than for micro&es (-29 kcaI-mol-‘1, probably a result of the random nature of the high temperature structure. ~ck~~ie~g~~n~~-We wish to thank Terry Davies for technical assistance with the age spectrum experiments and to Dr. R. A. Eggleton who carried out the XRD measurements. Irradiation of the samples was made possible by a grant from the Austrahan Institute of Nuclear Science and Engineering. Reviews from Martin Dodson, Grenviile Turner and EImar Jessberger improved the manuscript. REFERENT Albarede F., Feraud G., Kaneoka I. and Allt?gre C. J. (1978) *Ar/=Ar dating: the importance of K-feldspars on multi-mineral data of polyorogenic areas. J. Geof. 89, 581-598. Baadsgaard H., Lipson 3. and Folinsbee R. E. ( i961) The leakage of radiogenic argon from sanidine. Geochim. Ctwmochim. Actn 25, l47- 157. Berger G. W. (1975) 40Ar/‘9At step heating of thermally overprinted biotite, hornblende and potassium feldspar from Efdora, Colorado. Earth Planet. Sci. Lett. Z&387408. Berger G. W. and York D. (1979) *Ar/pAr dating of multi-component magnetizations in the Archean Shelby Lake Granite, northwestern Ontario. Can. J. Earth Sci. 16, 1922-1940. Berger G. W. and York D. fl381) Geothermomet~ from
*Ar/‘$Ar dating experiments. Geochim. Cosmochim. Acta 45, 795-8 11. Berger G. W., York D, and Dunlop D. J. (1979) CsIibration of Grenvillian pafaeopoIes by “Ar/‘9Ar dating. Natwe 277,46-48. Brandt S. B. and Bartnitskiy E. N. (1964) Losses of radiogenic argon in potassium-sodium feldspars on heat activation. fnr. Geoi. Rev. 6, 1483. Crank 3, (1975) The ~athern~t~c~ of ~~~~~i~n. Qxford Press, 2nd ed. 414 pp. Deer W. A., Howie R. A. and Zussman J. (1966) An Introduction to the Rack-Forming Minerals. Longman. 528 pp. Dodso~ M. H. (1973) Closure temperature in cooling geochronolo8i~l and petrological systems. Cuntrib. Mineraf. Petrol. 40, 259-274. Foland K. A. (1974) @Ar diffusion in homogeneous ortho&se and an interpretation of Ar diffusion in K-feldspar. Geochim. Cosmockim. Acta 38, 15 1- 146. Fechtig H., Gentner W. and Kalbitzer S. (1961) Argonbestimmungen an Kalium-minerralien-IX. Geochim. Cosmochim. Acta 25,297-311. Fechtig H. and Kalbitzer S. (1966) The diffusion of argon in ~t~~urn-~ar~g so&. fn PQt~ssi~m-Argue Dating teds. 0. A. Schaeffer and J. Zahringer). Springer-Verlag, 68-107. Frechen J. and Lippolt H. J. ( 1965) Kaiium-Argon-Daten zum alter des Laacher Vulkanismus, der Rheinterras~n und der Eisxeith. Eiszeitalter Gegen. 16, 5-30. Harrison T. M., A~stroug R. L., Naeser C. W. and Harakal 3. E. (1979) Ceochronology and thermal history of the Coast Plutonic Complex, near Prince Rupert, B.C. Can. .I, Earth Sci. 16, 400-410. Harrison T. M. and McDougall I. (198Oa) fnvestigations of an intrusive contact, northwest Nelson, New ZeaiandI. Thermal, chronological and isotopic constraints. Geochim. Gasmochim. Acta 44, 1985-2004. Harrison T. M. and McDougall 1. (198Ob) Inv~tigations of an intrusive contact, northwest Nelson, New ZealandIL Di~u~on of radiogenic and excess *Ar in hornblende revealed by @Ar13’Ar age spectrum analysis. Geachim. Cosmockim. Acta && 2005-2020. Harrison T. M. and McDougall I. (1981) Excess MAr in metamorphic rocks from Broken Hill, New South Wales: ~mp~i~tions for ~Ar/39Ar age spectra and the thermal
1820
f M. Harrison and I. McDougall
history of the region. Earrh Planer. Sri. l&f. 55, 1% 149. Hart S. R. (1981) DilIusion compensation in natural silicates. Geochim. Cosmochim. A& 45, 279-291. Kuz’min A. M. (1961) Retention of argon in microcline. Geochemistry 5, 485-488. Maluski H. (1978) Behaviour of biotites, amphiboles, plagioclases and K-feldspars in response to tectonic events with the 40Ar/39Ar radiometric method. Example of a Corsican granite. Geochim. Cusmochim. ,4na 42, 16 191633. McDougall I. ( 198 1) mAr/39Ar age spectra from the KBS Tuff, Koobi Fora Formation. Nature 294, 120-I 24. McDougall I., Maier R., Sutherland-Hawkes P. and Gleadow A. J. W. (1980) K-Ar age estimate for the KBS Tuff. Nature t84, 230-235. Musset A. E. (1969) Diffusion measurements and the potassium-argon method of dating. Geophys. J. Roy. Astr. Sot. IS, 257-303.
Sardarov S. S. (1957) Retention of radiogemc argon m microcline. Geochemistry 3, 233-231. Smith J. V. ( 1974) Feldspar Minerals. Springer-Verlag, _ Berlin. Steiger R. H. and Jtiger E. (1977) Subcommission on geochronology: convention on the use of decay constants in geo- and cosmochronology. Earth Planet. Sci. Letr. 36, 359-362. Tetley N., McDougall 1. and Heydegger R. (1980) Thermal neutron interferences in the 40Ar/39Ar dating technique. J. Geophys. Res. 85,7101-7205. Turner G. (1969) Thermal histories of meteorites by the wAr/‘9Ar method. In Meteorite Research (ed. P. M. Millman). D. Reidel. 407-417. Turner G., Enright M. C. and Cadogan P. J. (1978) The early history of chondrite parent bodies inferred from 40Ar/‘qAr ages. Proc. 9th Lunar Sci. Conf 1,989-1025. York D. (1969) Least squares fitting of a straight line with correlated errors. Earth Planet. Sci. Left. 5, 320-324.
Gewhlmica ct Camochimica Afro Vol. 46, PP. 181 l-1820 Q ~ergamon Press Ltd. 1982. Printedin U.S.A.
The thermal si~ifi~~ce of potpie feldspar K-Ar ages inferred from 40Ar/39Ar age spectrum results T. MARK HARRISON* and IAN MCDOUGALL ResearchSchool of Earth Sciences, The Australian National University, Canberra, A.C.T. 2600, Australia (Received
December
1, 1981; accepted in revisedform
June 8, 1982)
A~ct-~Ar/~Ar age spectrum analyses of three. microcline separates from the Separation Point Batholith, northwest Nelson, New Zealand, which cooled slowly (--S”C-Ma-‘) through the temperature zone of partial radiogenic “Ar accumulation are characterized by a linear age increase over the first 65 percent of gas release with the lowest ages (-80 Ma) corresponding to the time that the samples cooled below about 100°C. The last 35 percent of ‘9Ar released from the microelines yields plateau ages (103,99 and 93 Ma) which reflect the different bulk mineral ages, and correspond to cooling temperatures between about 130 to 16O*C. Theoretical calculations confirm the likelihood of diffusion gradients in feldspars cooling at rates sS”C-Ma-‘. Diffusion parameters calculated from the 39Ar release yield an activation energy, E = 28.8 + 1.9 kcal-mol-‘, and a frequency factor/grain size parameter, Do/l’ = 5.6+$ see-‘. This Arrhenius relationship corresponds to a closure temperature of I32 t 13°C which is very similar to the inde~ndently estimated temperature. From the observed diffusion compensation correlation, this Do/P implies an average diffusion half-width of about 3 am, similar to the half-width of the parthite lamellae in the feldspars. The range in microcline K-Ar ages from the Separation Point Batholith is the result of relatively small temperature differences within the pluton during cooling. Comparison of the diffusion laws determined for microcline with those for anorthoclases and other homogen~us K-feldspars (E = 40 to 52 kcal-mol-‘) reveals that Ar diffusion is more highly temperature dependent in the disordered structural state than in the ordered structural state. Previously published U-shaped age spectra are probably the result of the superimposition of excess “Ar upon diffusion profiles of the kind described here. I~DDU~ON FROM the time of the early application
of the K-Ar dating method to geological material, it was apparent that many K-feldspars did not quantitatively retain radiogenic ‘OAr(*Ar*) at moderately elevated temperatures. This effect was variously ascribed to the degree of perthitization (Sardarov, 1957), differing unmixing rates of K and Na (Brandt and Bartnitskiy, 1964), and deformation (Kuz’min, 196 1). In a review of Ar diffusion literature, Musset (1969) noted that a number of studies using K-feldspars provided diffusion coefficients that varied by as much as six orders of magnitude at any one temperature. On the basis of a diffusion study using a homogeneous orthoclase, Foland (1974) concluded that the low retentivity of Ar and variability in diffusion parameters in perthites is a result of the exsolution lamellae behaving as the effective diffusion radius of the mineral. Foland (1974) calculated that substantial 40Ar* loss could occur from these regions at relatively low temperatures (- 1SO’C) over geological time. In a study of the cooling history of a forcefully emplaced granitoid, Harrison et al. (1979) interpolated an effective retention or closure temperature (Dodson, 1973) for a perthitic K-feldspar of about 150°C. In a similar study, Harrison and McDougall (1980a) found a range of K-Ar microcline ages from samples taken
* Present Address: Dept. of Geological Sciences, State University of New York at Albany, Albany, New York 12222 U.S.A.
throughout the Separation Point 3atholith, northwest Nelson, New Zealand, corresponding to a closure temperature range of between about 130” to 160°C. This study reports 40Arf3vAr age spectrum measurements and X-ray diffraction results on several of these microclines which clarify the origin of the discordant ages and highlight the usefulness of such information in reconstructing temperature histories of mild thermal events. Comparison of these results with recently published “Arj3’Ar analyses of anorthoclases reveal that the behavior of Ar transport in these two structural states is very different. EXPERIMENTAL High purity microcline separates, sized to between 0.25 and 0.125 mm in diameter, were irradiated for 120 hours in a fast neutron flux in the X-33 position of the HIFAR reactor of the Australian Atomic Energy Commission at Lucas Heights, New South Wales, along with intralaboratory standard GA1550 biotite. This mica has a K-Ar age of 97.9 Ma calculated using the decay constants and isotopic abundances recommended by Steiger and Jtrger (1977). Sample and flux monitor geometry during irradiation was described by Tetley ef al. (1980). The irradiation cannister, which was cladded by 0.2 mm of Cd to absorb thermal neutrons, was inverted end-for-end midway through the irradiation to minimi~ the effect of the fast neutron flux gradient to about one percent across the cannister. Factors used to correct the effects of interfering neutron reactions were (“Ar/39Ar)x = 2.70 X lo-‘, 06Ar/ “Arlc. = 3.06 X 10m4and (39Ar/‘7Ar)cs = 7.27 X lop4 (Tetley et al.. 1980). Subsequent Ar extractions from the irradiated samples were carried out in a machined MO crucible within a high vacuum extraction system. Heating was by means of a radio 1811
--------_---
78-592
T~6t.t 1 ““Ar/JYAr resu/Ls tw rmcrociine samples from the Separation i’o~nt Batholith. -.._--..-_. -. . .._._..____--___ ..__.__.-._____..-. _ _. _ _ _._. _.
mlcroclzne 63.02
24.47 22.20 67.45 23.51 18.96 19.24 19.54 19.87 20.11 20.34 20.61 21.03 2i.G 21.93 22.3% 22.79 23.59 23.74 23.99
0.141: 3.097 5.467 2.344 2.371 2.674 3.2'74 4.175 4.992 6.111 6.46~3 5.845 3.829 1.884 1.553 1.908 i.766 1.020 3.320
FM-1; FM72
26.22 26.46
TF’
22.39
410 570 620 670 690 ?30 770 810 800
49.70 24.24 19.80 19.86 20.05 20.38 20.67 20.85 21.21 21.55 21.08 22.47 22.91 23.32 23.97 24.24 24.26 24.22 23.79 24.74
5,874 0.0 5.412 0.0 2.200 7.018 7.776 7.300 4.107 13.01 9.372 14.57 15.47 5.012 4.110 0.9512 5.900 7.742 3.654 2.574 10.87 54.69 27.03
127.5 137.6 15.21 322.2 48.57 13.40 4.710 1.152 0.0050 2.561 1.249 1.685 0.8903 3.337 7.720 9.826 11.03 11.95 15.63 19.86 21.09 13.34 32.93
0.903 2.48 1.89 0.0631 0.433 1.00 1.i9 1.16 1.05 1.30 1.20 0.889 0.776 0.730 1.31 1.32 1.64 2.97 4.69 3.43 2.15 0.100 0.0516
1.581 1.174 2.016 0.0 15.16 4.290 2.421 0.7582 1.733 8.087 1.046 0.4021 3.627 6.252 5.998 s.379 1.379 4.223 1.683 0.0 0.0 4.810
139.2 140.5 7.066 491.5 94.30 32.17 15.44 10.01 4.766 2.960 1.450 2.870 2.209 2.178 2.247 2.398 2.078 2.285 2.867 4.000 4.546 8.900 1.626 5.154 4,967
2.23 6.93 2.31 0.0297 0.177 0.455 0.644 1.23 1.72 3.71 1.36 2.53 2.85 2.87 2.35 2.54 2.60 3.50 3.37 6.23 a.03 5.17
g: 350 450 520 570 610 650 680 720 770 820 870 940 1000 1050 1100 1140 1300 rTFh
78-629
0. 7564
35.%3 1148.0 60.00 10.30 4.262 3.359 2.580 3.163 4.186 4.027 6.203 h.015 9.339 12.61 13.74 27.49 41.38 45.92
6.78 0.0670 1.13 3.43 2.73 5.63 4.21 2.89 3.41 2.41 2.60 2.46 4.45 3.58 4.99 8.16 10.5 0.859
“.
91:.
,
0.106 1.88 7.28 11.6 20.5 27.1 31.6 37.0 40.8 44.9 48.8 55-8 61.4 69.3 82.1 98.6 1OO.Q
95.1 48.1; 92.0 98.1 99.0 99.3 99.4 99.2 99.1 99.1 98.8 98.9 98.5 98.1 98.0 96.4 94.7 V3.R
0.230 1.84 5.49 9.82 i4.1 17.9 22.6 27.0 30.2 33.0 35.7 40.5 45.3 51.2 62.0 79.1 91.6 99.4 99.8 100.0
83.8 83.9 97.5 75.9 92.3 96.9 98.4 98.9 99.1 99.0 98.9 98.1 98.6 98.2 98.2 98.0 98.0 98.2 97.8 97.2 97.5 90.8 83.L
22.209 ‘?I.110 33.495 21.706 18.629 19.087 19.414 19.771 19.988 20.189 20.471 20.817 21.178 21.626 21.981 22.353 22.749 22.487 22.610
940 990 1030 1070 1110 1140 1165 1200 1250 1350
;:';;;l 22.515 40.155 22.779 19.385
19.707 19.998 20.335 20.577 20.798 21.153 21.511 21.760 22.220 22.593 22.970 23.602 23.753 23.651 23.583 23.431 23.769
ITF6
FM-l* FM-z*
ITS 350 450 515 560 610 640 680 720 760 800 850 900 950 1000 1060 1110 1160 1210 1260 1280 1310 1310 ITT'
to.4
93 7
‘0.5
microcline
900
78-638
3Z.J '0.5 146.!)? 1.7 95.7 to.5 82.5 to.4 84.4 85.9 to.4 87.4 tQ.5 88.3 to.5 89.1 to.5 90.4 trJ.5 91.9 LO.5 93.5 LO.5 95.4 '0.5 v6.9r0.5 98.5 io.5 100.2 ro.5 99.1 to.5 9v.c
22.410
1
98.3 to.5 171.8 il.6 99.520.5 85.0 2 0.4 86.4 kO.4 87.6 10.4 89.1 t0.s 90.1 ? 0.5 91.0 to.5 42.5 to.5 94.1 to.5 95.120.5 97.1 to.5 98.7 20.5 100.3 fO.5 103.0 f0.5 103.6ZO.5 103.2 to.5 102.9 to.5 102.2 to.9 103.7 r2.1 98.1
micxocline 26.68 26.69 20.59 54.42 21.49 18.65 18.31 18.62 18.84 19.08 19.37 19.44 19.57 19.75 19.94 20.20 20.45 20.73 20.95 21.3L 21.32 21.51 26.43 37.07 36.02
6.259 0.0 88.54
0.607 0.350 0.0821
0.057 0.395 1.26 2.53 4.88 8.17 15.2 17.8 22.7 28.1 33.6 38.1 42.9 47.9 54.5 61.0 72.8 88.2 98.0 99.2 99.8 100.0
’ Corrected for line blank of 2 X 1O-‘3 mol 40Ar. 2 Corrected for decay of “Ar, 3 Obtained by manometric measurement of gas calibrated using “Ar spike. ’ FM = flux monitor GA1550 biotite; K-Ar age = 97.9 Ma: K/Ca = 38.5. STF = total fusion split. 6 ITF = incremental total fusion age. ’ h”K = 5.543 X 10-‘Oa’“‘.
84.5 84.3 98.9 65.2 82.6 92.6 95.8 97.4 96.5 99.2 99.3 99.2 99.4 99.3 99.1 99.2 99.2 99.3 99.2 99.2 99.1 98.5 80.7 57.9 55.6
201353 39.673 18.696 17.678 17.824 18.295 18.676 18.977 19.301 19.334 19.479 19.661 19.856 20.109
88.7 iO.5 169.9 t1.6 81.6 to.5 77.3 to.4 77.9 to.4 79.9 to.4 81.6 to.4 82.8 $0.4 84.2 1.0.4 84.4 to.4 85.0 kO.4 85.8+0.4 86.6 to.4 87.7 to.4
20.364 20.641 20.838 21.165 21,163 21.225 21.594 21.810 21.411
88.8 20.4 89.9 10.5 90.8L0.5 92.2 co.5 92.1 tn.5 92.4 to.5 93.9 to.5 94.9t0.6 93.2 to.8 RR.4
1813
K-feldspar K-Ar ages mbh2.
unit-csu
#I*10
XlrbuOf r9flactiml
m-592
18
76-594
21
76-629
20
78-636
20
p.ruterr
of sepration
Point edholith
l
&I
5,
8.5883 *0.0069 8.5744 to.0023 8.5850 t0.0013 8.5651 f0.0093
12.9558 to.0033 12.9724 fo.0028 12.9627 *0.Oo65 12.992. tO.0338
(4, 7.2203 fO.0057 7.2166 fo.0020 7.2117 to.0057 7.21.2 fO.oO92
a 90.67% *o.o62o %.6o44 *o.o439 90.6247 *0.1205 eo.l9oo fO.3766
K-feldrpars.
B 115.8455 *o.o709 US.%% tO.0248 116.0701 to.0666 115.8730 t0.Oe22
Y 87.7173 to.0310 87.9415 tO.0358 87.7839 fO.066. 86.9943 fO.3639
aa*-i* I Of 0.97
96.6
0.88
94.9
0.95
92.5
0.40
97.9
frequency generator and temperatures were monitored by a thermocouple within the crucible and an optical pyrometer reading at the top of the crucible. Due to a thermal gradient within the crucible, the temperature measured using the optical pyrometer was in some cases higher than the temperature recorded by the thermaoouple by about 130°C. It is thought that the actual sample temperature is closer to the thermocouple reading and it is this temperature that is given for each step in Table 1. Uncertainty in these temperatures is about rt3O’C. The evolved gas at each temperature step was isotopically analyzed for At
history of the Separation Point Batholith foliowing its forceful emplacement into the Paleozoic country rocks, 114 Ma ago. The cooling history (Fig. 3, Harrison and McDougall, 1980a) is characterized by a logarithmic decay in temperature following crystallization, reaching about 180” by 100 Ma ago. The subsequent cooling rate was at about 5”C-Ma-’ until -80 Ma when the temperature dropped below about 100°C as evidenced by the apatite fission track ages.
using a rare gas mass spectrometer: samples 78-629 and 78-638 were measured using a Micromass 1200 instrument
Slow cooling versus episodic loss
and sample 78492 was analyzed using a much modified AEI MS10. Un~~ainty in the derived ‘aAr/BAr age includes the precision of the isotope ratio measurements in both the sample and flux monitor and the additional uncertainty in the J parameter of 0.5 percent. 40Ar/‘gAr results are given in Table 1. X-ray diffr~tion rne~ur~en~ were made on powdered samples by Dr. R. A. Eggleton, using a Gunnier camera arrangement. Measured angles of up to 21 reflections per sample were used in a least-squares program to determine the unit-cell parameters given in Table 2.
RESULTS AND DISCUSSI0N 40Ar/39Ar incremental release measurements have been made on microcline samples 78-59278-629 and 78-638 which have K-Ar ages of 92.7 + 0.7, 96.8 f 1.0 and 88.5 + 0.8 Ma, respectively (Harrison and McDougall, 1980a). These results are shown together on an age spectrum plot in Fig. 1. Results of *Ar/*Ar total fusion analyses and the incremental total fusion ages, obtained by summing the individual steps (Table l), agree very well with the K-Ar ages. The U’Ar/39Ar age spectra of the microclines (Fig. 1) imply ‘OAr* ~n~ntration gradients within the crystals with the initial low temperature gas fractions yielding ages on the order of 80 Ma. In all three cases, the subsequent gas release reveals a monotonic rise in age until about 65 percent of the 39Ar has been released, at which point the age remains essentially constant for the remainder of gas release at 103 Ma (78-629), 99 Ma (78-592), and 93 Ma (78638). These ages reflect the relative differences seen in the K-Ar ages and average about 6 Ma older than the conventional ages. The amounts of gas evolved at any step are relatively constant up to extraction temperatures of about 1050°C (Table 1) at which point larger quantities of gas are released, It is believed that the incongruent melting of microline to leucite and melt at about this temperature (Deer et al., 1966) is responsible for the enhanced outgassing. Using isotopic data and heat flow theory, Harrison and McDougall (1980a) reconstructed the cooling
The shape of the age spectra (Fig. 1) do not conform well to a model of episodic loss of =Ar* (Turner, 1969) as the observed gradients are linear rather than convex, although this may be explained by a nonuniform grain size distribution. At any rate, the thermal history determined by Harrison and McDougall (1980a) precludes having an episodic QAr* loss at around 80 Ma which would be required to explain the age spectra in these terms. However, Turner (1969) noted that it was likely that samples cooling very slowly through their partial @‘Ar* retention region of perhaps -2O”C, would likely develop some form of mAr* gradient.
:i~lI’ Separotian
0
20
Point Batholith
40
X ‘*Ar
Microctincr
60
80
loo
RELEASED
FIG. 1. “‘Ar/39Ar age spectra of slowly cooled microclines from the Separation Point Batholith. The cooling history for 78492 (see text) is shown on the right vertical axis. The linear form of the @Ar* gradients is related to the slow accumulation of ‘@Arduring cooling. The low-temperature ages of between 77 and 85 Ma correspond to the time the samples cooled to below - 110°C. The differences in bulk K-Ar age and plateau portion of the age spectra is a result of relatively smail temperature differences within the batholith during cooling.
i
-or----
-_.-,._ ,.,__ __ ~.~~ .__.r_-._...r_.~
FIG. 2. The concentration distributions across the halfwidth, I, of a plane sheet resulting from slow cooling (curve 1) and episodic loss (curve 2). The concentration, C, is given in terms of a deficit of what would have existed had cooling taken place infinitely fast at t K C = 1 or episodic heating not occurred at r cc C = 0. The slow cooling-curve was only evaluated to x/I = 0.95. The closure age (slow cooling) and ‘hybrid’ age (episodic loss) both correspond to t K C = 0.5.
In his mathematical development of the theory of closure temperatures in cooling geochronological systems, Dodson (1973) produced expressions for the limiting concentration distribution of the diffusing isotope within crystals of different geometries. The concentration distribution across a plane sheet after slow cooling as a function of distance, x, from the center of the slab is given by Dodson (1973):
x cos ((n - %)TX) In {y(n - Y2)7r27M) (1) (n - ‘/2)7r Where h is the 40Ar* production constant, 7 is the cooling time constant; B is dimensionless time; M = @0)/r’ is the value of the combined diffusion coefficient/grain size parameter at the commencement of cooling; y = e’ where c is Euler’s constant; and C,/ C, is the ratio of concentration of the daughter product over the concentration of the parent. We have chosen to use the solution for a plane sheet to describe the loss of 40Ar* from microperthitic microcline as the incoherent boundaries provided by the exsolution lamellae probably control the effective diffusion radius. Loss from an infinitely long slab would closely approximate this geometry. Equation (1) can be rewritten (M. H. Dodson, pers. comm.):
x cos ((82- M)7rx) In ((n - %)A) (n - ‘%)7r
(2)
where I, is the apparent closure temperat.ur-c at 3: E is the activation energy; &,/I2 is the frcyuenc) Factor/grain size parameter; and R is the gas constant. Since it is implicit in these calcuiatiorls that cooling proceeds linearly as l/7’, the app;irrnt 7, corresponds to an age, or daughter concentration, ;~t x. We have evaIuated (2) using E = 28.8 kc&m&‘. &/f2 = 5.6 sec.‘. 7 :-T7.65 x IO’” see and the cooiing rate dT/dt -7 S”C-Ma’ ’ for reasons discussed later. These results are shown as curve I in Fig. 7, which shows the model distribution of “Ar* within the microcline tamellae following slow cooling. The curve is characterized by a smooth increase in age or concentration to an x/l value of about 0.3 at which point the concentration distribution flattens out and remains essentially constant to the center of the plane sheet. Also shown in Fig. 2 for comparison is the concentration profile produced as a result of episodic 40Ar* loss from a plane sheet (curve 2). The daughter concentration, c, is given for any distance. A, from the center of the slab by the expression {Crank, 1975):
where co = 1 is the initial uniform concentration; c!, is the zero boundary concentration; D is the diffusion coefficient; and I is the slab half-width. This distribution for a Dt/1’ value of 0.08 is shown in Fig. 2. The curve generated for an episodic loss (Fig. 2) has a somewhat more linear concentration gradient than the slow cooling curve with virtually no plateau near the center of the slab. In both cases of slow cooling (curve 1, Fig. 2) and episodic loss (curve 2, Fig. 2) the resulting mineral age corresponds to a C: value of 0.5. Clearly the forms of these two curves are similar enough to preclude our using this information as a diagnostic tool for choosing between these two hypotheses. However, we can modify the form of the slow cooling curve (curve 1, Fig. 2) by slowing the cooling rate late in the cooling history to produce a nearly linear concentration gradient between 1.0 > x/r z 0.4 which would yield an age spectrum similar to what we have observed. This may have been the case as the calculated T, at x/l = 0.95 is only 88°C which is significantly lower than that indicated by the apatite fission track ages and thermal model (Harrison and McDougall, 1980a) at about 80 Ma.
Superimposed on the right-hand side of the 40Ar/ “Ar age spectra of the Separation Point Batholith microclines (Fig. 1) is the temperature history of 7% 592 from Fig. 3 of Harrison and McDougalI ( 1980a). As was shown in equation (2), different portions of the mineral and therefore the age spectrum corre-
1815
K-feldspar K-Ar ages spend to different temperatures with the last *Ar* loss occurring at a temperature of about 110°C. Turner et al. (1978) have suggested that it may be possible to obtain some kinetic ~nfo~atio~ from the #Ar/3~Ar age spectrum experiment by using the observed gas loss at any given temperature to calculate a combined diffusion coefficient/grain size parameter (O/p). Regression of these data on an Arrhenius plot would produce both the activation energy, E, and the frequency factor/grain size parameter, &/r’. This information could in turn be used to calculate a geelogical closure temperature (7’J forthe sample. Harrison and McDo~~~il(l98Ob~ have argued that this practise is inappropriate for hydrous phases (e.g., Berger and York, 1979) as structural breakdown in the vacuum likely obscures the natural diffusion behavior. However, for anhydro~s phases, such as feldspars, this method could be useful in determining kinetic parameters (Turner et al,, 1978; Harrison and McDougall, 1981; Berger and York, 1981). Values for D/l2 were calculated from the measured “Ar release from 78-592.78-629 and 78-638 microclines (Table 1) using the equations given by Harrison and McDougall (1981). The data for 78-638 yields a linear array on an Arrhenius plot, corresponding to an E of -29 kcai-mol-‘, for extraction temperatures up to about 9009C, excluding the first step which contains less than 0.1 percent of the 39Ar released (Fig. 3). Above that temperature, the slope flattens indicating a change in the diffusion mechanism. Since it is our intention to extrapolate the diffusion data to temperatures on the order of iOO”C, it is reasonable that we exclude data from consideration beyond the temperature at which the diffusion mechanism changes. It is difficult to assign uncertainties to the diffusion coefficients calculated by this method, but the errors are large enough to preclude de~nition of more than one slope from the data shown in Fig. 3. A similar treatment of 78-629 data (Fig. 3) yields an E of -28 kcal-mol”’ up to extraction temperatures of about 800°C. However, the data for 78-592 (Pig. 3) plot above the curve defined by 78-638 and 79-629 and do not yield a linear array above extraction temperatures of about 600°C. The reason for the difference in behavior of this sample is unknown, although the offset of L)fP values at a given temperature from the data of 78438 and 7% 629 may be related to the large uncertainty in both absolute and relative temperature monitoring, partly the result of the different extraction lines used for 78-592. Regression of the well correlated 78-638 and 78-629 data (York, 1969) yield an E = 28.8 k 1.9 kcal-mol-’ and a L&J!’ = 5.6”_::‘9see-‘. Using these parameters, a closure temperature for these samples can be calculated from the expression of Dodson (1973):
4
78-636 + 78-629 a 76-592 l
E = 28.8 kc+mole’ Do.& = 5.6 set-’ 8
FSG. 3. Arrhenius plot of -log D/l’ values calculated from measured “AT loss versus the reciprocal absolute temperature of the extraction step, for samples 78-592, 78-629 and 78-638. The data shown is for the low temperature, linear portion of the diffusion curves (see text).
where A, a geometry factor = 8.7 for a plane sheet; R = 1.987 cal-mol-‘-deg-r; and dT/dt = 5 %-Ma-‘. The calculated T, is within uncertainty of that predicted for 78-592 by the cooling history (Fig. 1). These internally consistent observations suggest that microcline geothermometry using kinetic data obtained via the step-heat experiment may yield meaningful temperature information although we reiterate that temperature control for these extractions was poor. Having established these diffusion parameters, we can use the analysis of Hart ( 198 1) to determine the average perthite radius in these mierochnes assuming that this dimension is also the effective diffusion radius, I. Hart (1981) has observed a diffusion compensation effect in feldspars by which the activation energy and frequency factor are positively correlated through the expression:
For our E of 28.8 kcal-mol-*, this equation predicts a Do of 3.6 X lo-’ cm2-set-‘. If this is indeed the intrinsic frequency factor, then our De/f of 5.6Zif9 see-’ implies an average perthite lamelfae width between about 3 and 9 pm which is on the order of that observed in thin sections.
Previous 40Ar/39Ar age spectrum analyses of microclines (Albarede et al., 1978; Maluski, 1978; Berger et al., 1979; Berger, 1975) have indicated the ability of K-feldspars to record the effects of mild metamorphisms, but have generally been characterized by U-shaped age spectra in which the low temperature portion of gas release contains very old apparent ages which decrease to a minims before rising smoothly to geologically reasonable ages. Har-
IXlh
!
M.
Harrison and I. McDougaii
rison and McDougall (1980b) have shown that excess “‘Ar which diffuses into the near surface region of crystals can produce a similar effect to that observed in the K-feldspars. We believe that these age spectra are the result of the superimposition of excess 40Ar on diffusion loss profiles within the feldspar lamellae which produces the U-shaped appearance. Although the solubility of Ar in feldspars is not especially large (Harrison and McDougall, 1981). the relatively rapid diffusion of Ar in K-feldspars at low temperature allows these samples to become contaminated while the co-existing mica and amphibole would not be significantly affected. Age discrepancies in microclines The six samples of microcline from the Separation Point Batholith give K-Ar ages in the range of 99.0 to 88.5 Ma (Harrison and McDougall, 1980a). Three possible explanations for this range in ages are: 1) the samples have experienced different thermal histories, 2) the feldspars are of different structural states leading to different diffusion behavior, and 3) the average perthite lamellae widths are variable from sample to sample. To assess the possibility that different structural states might control the gas loss, unit-cell parameters were determined by X-ray diffraction methods on four samples and these results are given in Table 2. The unit-cell dimensions of all samples plot close to maximum microcline and all four samples contain about the same percent orthoclase component (%Or) and 6ol*y* parameters (Smith, 1974) within uncertainty (Table 21, ruling out crystallographic control on gas loss. The difference in the diffusion results could be the result of different perthite widths in the samples causing only the grain size parameter, I, to vary. Harrison and McDougall (1980a) report an unsuccessful attempt to determine the average perthite widths of these samples as the broad width distribution precluded finding any fine inter-sample distinctions, but an implication of this result is that large inter-sample variations are unlikely. The other possible explanation of the microcline K-Ar age differences is that the samples have experienced different cooling histories. The sample with the oldest age (78-629) is closest to the contact with the country rock while the sample with the youngest age (78-638) is furthest away. Since heat will be dissipated more rapidly from the margins of the pluton than the center, this correlation between age and position within the batholith may be evidence for this explanation. Indeed, the coexisting biotite K-Ar ages of samples 78-629, 78-592 and 78-638 of 110.8 + 1.1, 107.8 * 0.7, and 103.9 + 2.1 Ma, respectively, also show this effect indicating that different temperatures very likely existed at different positions in the batholith fairly soon after emplacement. Temperature differences on the order of only -3O*C could account for the very different microcline ages as the cooling rate was only about
S”C-Ma-’ at that time. We believe that this explanation accounts for the first order differences observed but cannot rule out the possibility that differing structural states and perthite lamellae widths have also contributed in a small way to the age discrepancy between these microclines. Comparison of division parameters between high and low temperature K-feidspars Anorthoclases separated from pumice clasts contained within the KBS Tuff at Koobi Fora, adjacent to the northeastern shores of Lake Turkana, northern Kenya, were measured by the “eAr/39Ar age spectrum technique and the results reported by McDougali ( I98 1f. They yielded excellent flat age spectra, interpreted as indicating that the feldspars have remained thermally undisturbed since their crystallization 1.88 f 0.02 Ma ago. These anorthoclases have a composition of about Or3? and X-ray diffraction measurements (referred to in McDougall et al. (1980)) show that the feldspars are highly disordered and structurally close to the sanidine-high albite series, with no evidence for significant unmixing or strain resulting from exsolution. However, optically some crystals show extremely closely spaced (-2 pm) polysynthetic twinning. As for the microclines discussed previously, the ~Ar~39Ar age spectrum data can be used to examine the question of Ar diffusion from the anorthoclases. Diffusion coefficients were calculated from these data using both spherical and infinite slab models. Results for the assumption of spherical geometry provided considerably better fitting straight line Arrhenius relations than the slab, and this was taken as evidence that the polysynthetic twinning is not a significant diffusion boundary. In addition, previous workers who have studied diffusion in homogeneous fetdspars almost invariably have used a spherical geometry model, so that our results can be more readily compared if we also employ such a model. ~a1culations of diffusion coefficients were made using the equations given by Fechtig and Kalbitzer (1966). It was recognized during the 40Ar/39Ar age spectrum experiments on the anorthoclases that the measurements of the actual temperature of the samples for each step were not well controlled. The temperatures reported by McDougall (1981) were those determined by optical pyrometer focussed on the inside wall at the top of the MO crucible. Temperatures were also monitored by means of a thermocouple inserted vertically into a sleeve built into the base of the crucible, and these temperatures were 110” to 220°C lower than those given by the optical pyrometer. The difference between the two temperature measurements in any one step heating experiment was nearly constant. These data indicate the presence of substantial temperature gradients in the crucible. 1n subsequent experiments we have measured the temperature with the optical pyrometer focussed di-
1817
78-1047 step heat
71-1031 stephe4tI 600 700 770 820 870 915 940 970 1000 lo40 1070 LllO ll.60 1225 1360 lb70
78-1038
760 830 890 930 970 loo0 1030 1065 1100 1150 1200 lb30
550 650
12.94
10.83
TY83
10.07 9.59
7.02 6.55
~~:: a:53 8.31 8.18 7.86 7.67 7.115 1110
ll75 1310 lb20
I:;: 6.32 5.91
6.21 6.02 5.77 5.69 5.43 5.22 5.10 1.95 L.91 4.44 4.Ob -
.wph.?&2 660 710 775 820 %: 915 950 990 lob0 1090 1320
600 720
520 650
790 850 GO
840
540
970 1WO 1045 1076 1130 1180 I.210 1250 I.320
::: 880 915 91r5 980 lb15 1070 1110 1150 1170 12110
12.61 10.83 10.12 9.45 8.99 8% 8.L2 8.21
7.45 7.23 7.03 6.93 6.61
7.29 6.63 6.18 5.88 5.68 5.50 5.26 5.09 4.83 4.53 L.52 4.21
79-14 step APat 10.72 10.17 9.Q b.i5 8.87 8.64 8.42 8.18 7.92 1.62 7.34 6.28
8.02 6.95 6.42
E )r:33 -
600 700 730 760 820 880 930 965 1wo 1045 1100 1150 1250 1400
--
rectly on the sample, and found that the value is intermediate between the two other readings. Thus for the KBS Tuff anorthoclases we have revised the published temperatures downward by 50’ to 1 10°C in each case accepting the average of the two temperatures measured in those experiments. It should be recognized that the revised temperatures are still relatively poorly known with an uncertainty in the order of 30°C but that the temperature interva1 between successive steps is probably correct to about 10°C. Data used in the construction of the Arrhenius plots are given in Table 3, results are shown in Fig. 4, and regression results are listed in Table 4 using the York (1969) two error regression method for calculating the best fit straight lines. Diffusion coe-fficients have not been calculated for the first two steps for 78-1047 and the first step of 78-1038(l) because the amount of gas extracted was extremely small, less than 0.5% of the total. On the Arrhenius diagram (Fig. 4) it is seen that data from each step heating experiment are well aligned, although the results for 79-14 show somewhat greater scatter than is found for the other samples. Regression data and derived values for the activation energy and Da/a2 values are given in Table 4. The two experiments on 78-1038 do not agree within experimental error, although both yield extremely well fitting straight lines. The explanation for the differences probably is associated with the problems of temperature measurement. If data from all four experiments are regressed together a mean
5:; 665 700
~..
E 870 900 930 980 1025 1075 X175 1325
12.15 11.01 10.66 10.28 9.78 9.15 8.75 8.53 8.31 7.98
8.66 8.29 7.90 7.26 6.11 5.76 5.20 ::z 4.88
:::,"
value for E = 40.9 + 1.4 kcal-mol-’ is found together with a De/a2 = 88?# set-‘. The good alignment of the data on the Arrhenius plot provides strong evidence that the Ar transport m~hanism conforms to a model of volume diffusion, with no significant change in structure of the anorthoclase during the “Ar/“Ar step heating experiments in vacua. Assuming that the measured grain size corresponds to the effective diffusion radius, a reasonable assumption in view of the good fit of the data to a spherical diffusion model, the Arrhenius relations given in Table 4 all lie close to or on the diffusion compensation line for feldspars defined by Hart (1981). Foland ( 1974) reported an Ar diffusion study on a homogeneous orthoclase and showed that using vacuum extraction techniques he obtained results that were indistin~ishable from those obtained on the same sample in which Ar loss was induced in isothermal heating experiments under hydrothermal conditions. Foland’s data therefore provide additional justification for using our *Ar ,J=Ar step heating data to derive diffusion parameters from the Kfeldspars samples. Roland (1974) found a value for E = 44 kcal-mol-’ for Ar diffusion from the orthoclase, and he also demonstrate that earlier diffusion experiments on homogeneous sanidines by Baadsgaard ef al. ( 196 1 ), Fechtig et al. ( 196 1) and Frechen and Lippolt (I 965) all yielded activation energies for Ar diffusion in the range 40 to 52 kcal-mol-‘. Our estimate for the activation energy for Ar diffusion in anorthoclase (E = 40.9 f 1.4 kcal-mol-‘) lies near
i
---
M. Harrison and I. McDougali
___- -‘I _..._~.~._...._ __ ~____ __.__
---- ~‘.T -. ---___)__
-7---
,l
= 79-14 E=44.5?2.7
I % v)
7 -
l
78-1047
E=42.6+-l-2
8-
N (3
4
Anorthoclase kcol-mol-’
Anorthoclase kcol-mol-’
D,/a2=137!
$‘z set-1 _-.
.____
n78-1038(2) E=41.0?1.7
Anorthoclase
kcol-mol-I
678-
E=37.0?0.8 D.,/a2=12~I~ 1200
7
I00
kcal-mol-I 4’4 3.2 see-I IO00
.. so0
800
8
9
700
IO
I
II
600-c t
h
I2
I 04/‘K FIG. 4. Arrhenius plots of -log D/a2 calculated from measured .“Ar loss versus the reciprocal absolute temperature of the extraction step, for anorthoclase samples analysed by McDougall (1981). The diffusion parameters are distinctly different from those calculated for microcline and indicate that Ar diffusion in mixed K-feldspars is more strongly temperature dependent than in exsolved, low-temperature K-feldspars.
the lower end of the range previously reported for homogeneous sanidine and orthoclase, which have relatively high K contents. The anorthoclases used in this study have K contents of about 5.1% (McDougall et al. 1980). It would appear that for homogeneous alkali feldspars there is little compositional effect in terms of Ar diffusion phenomena. However, these results are significantly different from the diffusion parameters we have reported for microclines. If the enhanced diffusion of Ar in microclines were only a consequence of the much lowered diffusion radius brought about by perthite exsolution, then we would expect a similar E between anorthoclase and microcline, but a significantly reduced Dofl2for microcline. The observation of much higher activation energies in homogeneous K-feldspars (40 to 52 kcal-mol-‘) than in microclines (-29 kcal-mol-‘) indicates that the mixed, high temperature feldspar structure requires a diffusing Ar atom to have considerably more thermal energy to make a lattice jump than does an unmixed, low-temperature structure. For both high and low structural states, it has been demonstrated that internally consistent kinetic information can be obtained, as a by-product of the age spectrum experiment, that may be used to calculate geological closure temperatures.
CONCLUSIONS The principal conclusions of this study are: 1) 40Ar/‘gAr age spectra of microclines which have cooled slowly (--S’C-Ma-‘) through the zone of partial 40Ar* retention are characterized by a linear age increase over the first 65 percent of 3gAr release, followed by an age plateau for the remainder of the gas release. The initial low-temperature ages in the spectra correspond to the time that the samples cooled below about 100°C. Theoretical calculations confirm the likelihood of diffusion gradients in feldspars cooling at rates of s;S”C-Ma-‘. 2) Calculation of Ar diffusion parameters from the measured )‘Ar loss observed during the age spectrum experiment yield an activation energy, E, of 28.8 + 1.9 kcal-mol-’ and a frequency factor grain size parameter, Do/I', of 5.6”:: set-‘, for a plane sheet geometry. Using these values and the cooling rate of S”C-Ma-‘, a closure temperature of - 13OO”C can be calculated which is within uncertainty of the value interpolated for the samples from an independent analysis of the thermal history of the region. 3) From the observation of a diffusion compensation effect in feldspars, an effective diffusion halfwidth for the microclines of - 3 pm can be calculated from the knowledge that Do/j2 = 5.6 set-‘. This dif-
K-feldspar K-Ar ages
T&-la38(1)
37.0* 0.8
12.11;';
1.33
Au data exceptsoo"cstep cvx J 1.0 CVY = a.5
78-103812)
41.0f 1.7
119+=4 -61
1.08
Ail aeta except660% step CVK 3 1.0, cw * z.0
18-1047
42.6+ 1.2
137+a3 -52
0.69
,m data except520,650% stepn cvx = 1.0, m-f t 0.5
79-14
44.5 f 2.7
&1593 -435
L.60
All data,LX = 3.0,CIY = 2.0
~a-1038t1) 7a-103aw
37.7* 1.3
2..l+14.7 -8.5
I.21
Ae Bbove.CYX = 2.0, CVX = 1.0
78-x038(1) Ta-1038(2) 78-LO47
39.1f_1*2
35-7-13.5 +21.6
0.95
Aa above.CVX = 2.0,CVY = 1.0
0a+68 -38
1.17
AP above,cvx = 3.0,CVY = 1.0
v3-1038~1t 40.9 * 1.4 7;r-:;4387(21 .-
1819
n-14
fusion dimension is on the order of the perthite lamellae widths observed in thin sections. 4) Microchne samples from the Separation Point Batholith yield a spread of K-Ar ages as a result of relatively small temperature differences within the Batholith. The effect of differing sample structural states and perthite widths may also contribute to the age discrepancy. 5) Activation energies for anorthoclases and other homogeneous feldspars calculated from Ar vacuum degassing kinetics are significantly higher (40 to 52 kcai-mol-r) than for micro&es (-29 kcaI-mol-‘1, probably a result of the random nature of the high temperature structure. ~ck~~ie~g~~n~~-We wish to thank Terry Davies for technical assistance with the age spectrum experiments and to Dr. R. A. Eggleton who carried out the XRD measurements. Irradiation of the samples was made possible by a grant from the Austrahan Institute of Nuclear Science and Engineering. Reviews from Martin Dodson, Grenviile Turner and EImar Jessberger improved the manuscript. REFERENT Albarede F., Feraud G., Kaneoka I. and Allt?gre C. J. (1978) *Ar/=Ar dating: the importance of K-feldspars on multi-mineral data of polyorogenic areas. J. Geof. 89, 581-598. Baadsgaard H., Lipson 3. and Folinsbee R. E. ( i961) The leakage of radiogenic argon from sanidine. Geochim. Ctwmochim. Actn 25, l47- 157. Berger G. W. (1975) 40Ar/‘9At step heating of thermally overprinted biotite, hornblende and potassium feldspar from Efdora, Colorado. Earth Planet. Sci. Lett. Z&387408. Berger G. W. and York D. (1979) *Ar/pAr dating of multi-component magnetizations in the Archean Shelby Lake Granite, northwestern Ontario. Can. J. Earth Sci. 16, 1922-1940. Berger G. W. and York D. fl381) Geothermomet~ from
*Ar/‘$Ar dating experiments. Geochim. Cosmochim. Acta 45, 795-8 11. Berger G. W., York D, and Dunlop D. J. (1979) CsIibration of Grenvillian pafaeopoIes by “Ar/‘9Ar dating. Natwe 277,46-48. Brandt S. B. and Bartnitskiy E. N. (1964) Losses of radiogenic argon in potassium-sodium feldspars on heat activation. fnr. Geoi. Rev. 6, 1483. Crank 3, (1975) The ~athern~t~c~ of ~~~~~i~n. Qxford Press, 2nd ed. 414 pp. Deer W. A., Howie R. A. and Zussman J. (1966) An Introduction to the Rack-Forming Minerals. Longman. 528 pp. Dodso~ M. H. (1973) Closure temperature in cooling geochronolo8i~l and petrological systems. Cuntrib. Mineraf. Petrol. 40, 259-274. Foland K. A. (1974) @Ar diffusion in homogeneous ortho&se and an interpretation of Ar diffusion in K-feldspar. Geochim. Cosmockim. Acta 38, 15 1- 146. Fechtig H., Gentner W. and Kalbitzer S. (1961) Argonbestimmungen an Kalium-minerralien-IX. Geochim. Cosmochim. Acta 25,297-311. Fechtig H. and Kalbitzer S. (1966) The diffusion of argon in ~t~~urn-~ar~g so&. fn PQt~ssi~m-Argue Dating teds. 0. A. Schaeffer and J. Zahringer). Springer-Verlag, 68-107. Frechen J. and Lippolt H. J. ( 1965) Kaiium-Argon-Daten zum alter des Laacher Vulkanismus, der Rheinterras~n und der Eisxeith. Eiszeitalter Gegen. 16, 5-30. Harrison T. M., A~stroug R. L., Naeser C. W. and Harakal 3. E. (1979) Ceochronology and thermal history of the Coast Plutonic Complex, near Prince Rupert, B.C. Can. .I, Earth Sci. 16, 400-410. Harrison T. M. and McDougall I. (198Oa) fnvestigations of an intrusive contact, northwest Nelson, New ZeaiandI. Thermal, chronological and isotopic constraints. Geochim. Gasmochim. Acta 44, 1985-2004. Harrison T. M. and McDougall 1. (198Ob) Inv~tigations of an intrusive contact, northwest Nelson, New ZealandIL Di~u~on of radiogenic and excess *Ar in hornblende revealed by @Ar13’Ar age spectrum analysis. Geachim. Cosmockim. Acta && 2005-2020. Harrison T. M. and McDougall I. (1981) Excess MAr in metamorphic rocks from Broken Hill, New South Wales: ~mp~i~tions for ~Ar/39Ar age spectra and the thermal
1820
f M. Harrison and I. McDougall
history of the region. Earrh Planer. Sri. l&f. 55, 1% 149. Hart S. R. (1981) DilIusion compensation in natural silicates. Geochim. Cosmochim. A& 45, 279-291. Kuz’min A. M. (1961) Retention of argon in microcline. Geochemistry 5, 485-488. Maluski H. (1978) Behaviour of biotites, amphiboles, plagioclases and K-feldspars in response to tectonic events with the 40Ar/39Ar radiometric method. Example of a Corsican granite. Geochim. Cusmochim. ,4na 42, 16 191633. McDougall I. ( 198 1) mAr/39Ar age spectra from the KBS Tuff, Koobi Fora Formation. Nature 294, 120-I 24. McDougall I., Maier R., Sutherland-Hawkes P. and Gleadow A. J. W. (1980) K-Ar age estimate for the KBS Tuff. Nature t84, 230-235. Musset A. E. (1969) Diffusion measurements and the potassium-argon method of dating. Geophys. J. Roy. Astr. Sot. IS, 257-303.
Sardarov S. S. (1957) Retention of radiogemc argon m microcline. Geochemistry 3, 233-231. Smith J. V. ( 1974) Feldspar Minerals. Springer-Verlag, _ Berlin. Steiger R. H. and Jtiger E. (1977) Subcommission on geochronology: convention on the use of decay constants in geo- and cosmochronology. Earth Planet. Sci. Letr. 36, 359-362. Tetley N., McDougall 1. and Heydegger R. (1980) Thermal neutron interferences in the 40Ar/39Ar dating technique. J. Geophys. Res. 85,7101-7205. Turner G. (1969) Thermal histories of meteorites by the wAr/‘9Ar method. In Meteorite Research (ed. P. M. Millman). D. Reidel. 407-417. Turner G., Enright M. C. and Cadogan P. J. (1978) The early history of chondrite parent bodies inferred from 40Ar/‘qAr ages. Proc. 9th Lunar Sci. Conf 1,989-1025. York D. (1969) Least squares fitting of a straight line with correlated errors. Earth Planet. Sci. Left. 5, 320-324.