40Ar39Ar thermochronology of isotopically zoned micas: Insights from the southwestern USA proterozoic orogen

Geochimica et Covnochimica Acta. Vol. 59. No. IS, pp. 3205-3220, 1995 Copyright 0 1995 Elsevier Science Ltd Printed in the USA. All rights reserved 00 16.7037195 $9.50 + .OO

Pergamon

0016-7037(95)00209-X

40Ar/39Arthermochronology of isotopically zoned micas: Insights from the southwestern USA Proterozoic orogen K. V.

HODGES AND S. A. BOWRING

Department of Earth, Atmospheric, and Planetary Science, Massachusetts (Received

Institute of Technology,

Cambridge,

MA 02139, USA

August 30, 1994; accepted in revised form April 25, 1995 )

Abstract-We have used three different 4”Ar/‘“Ar laser microprobe methods to explore the distribution of radiogenic 40Ar in 1.O- 1S-mm biotite crystals from the ca. 1680 Ma Horse Mountain monzogranite of central Arizona. Incremental heating of two single crystals with a defocused laser beam produced flat age spectra with near-plateau ages of - 1190 Ma, showing no indication of intracrystalline 4”Ar inhomogeneity. In contrast, total fusion of twenty-five biotite fragments ( - 100 pm) yielded apparent ages ranging from 1006.7 to 1212.0 Ma. Detailed age mapping in the ( 001) plane of two crystals, with the laser focused to a minimum spot size, confirms that the age dispersion in the fragment data reflects the existence of 200 m.y. age gradients in single crystals. The two mapped crystals display very different age distribution patterns that suggest radiogenic 4”Ar loss through two mechanisms: volume diffusion on a scale comparable to that of the grain radius, and more rapid diffusion along discrete zones of high crystal defect density. Simple inverse modeling of the overall age dispersion in the two mapped crystals and the fragment population is consistent with the development of the observed age gradients by slow cooling at an average rate of -0.5 K/m.y. The Horse Mountain results, as well as previously published studies, indicate that conventional, incremental heating of hydrous phases can homogenize intracrystalline gradients in 4”Ar, thereby masking important details of the thermal history of analyzed samples. In contrast, detailed isotopic mapping studies offer a wealth of information, and will become more powerful with continued improvement in the spatial resolution of 4”Ar/39Ar laser microprobes. Total-fusion studies of crystal fragment populations can be readily automated, making them less labor-intensive than mapping studies. Our preliminary experiment on a limited Horse Mountain fragment population suggests that this procedure has great potential as a reconnaissance tool for thermal history research. 1. INTRODUCTION

minerals during incremental heating experiments. In particular, studies by Gaber et al. (1988), Lee et al. (1991), and Wartho et al. ( 1991) demonstrated that the loss of Ar from these minerals in the high-vacuum environment of an Ar extraction system occurs by a variety of mechanisms in addition to simple volume diffusion. It is becoming increasingly clear that, at least for hydrous phases, the morphologies of many (perhaps most) release spectra do not provide accurate information about the distribution of argon isotopes within mineral grains and therefore cannot be used in any simple way to model thermal histories (Lee et al., 1990; Scaillet et al., 1992). Laser microprobes eliminate the need to use release spectra as proxies for Ar diffusion gradients, and they revive the hope that apparent age zoning patterns in minerals can be used to reconstruct the time-temperature evolution of geologic samples (Dodson, 1986). The important challenges now before us are ( 1) to devise the best analytical protocols for elucidating isotopic gradients within crystals and (2) to obtain a better understanding of the mechanisms of Ar loss in the geologic environment, so as to establish the appropriate theoretical context for the inverse modeling of observed zoning patterns. We present here the results of a ““Ar/“Ar laser microprobe study of biotites from the Proterozoic Horse Mountain monzogranite of central Arizona. Large 4”Ar/‘yAr age gradients (up to 300 Ma) have been documented previously in micas of the Crazy Basin monzogranite, a different pluton from the same geologic setting (Hodges et al., 1994; Hames and Bow-

As “‘Ar/“Ar laser microprobes with high spatial resolution have become more common in geochronology facilities around the world, an increasing number of studies have shown that single mineral grains sometimes contain large gradients in radiogenic 40Ar concentration and, thus, apparent age (Phillips and Onstott, 1988; Lee et al., 1990; Scaillet et al., 1990, 1992; Kelley and Turner, 1991) . In some cases, such zoning can be attributed to compositional variations or selective uptake of “excess” 4oAr at grain boundaries and along crystal defects; in others, the gradients appear to be related to diffusive loss (Kelley and Turner, 1991) . The documentation of ‘“Ar diffusive loss gradients in crystals using the laser microprobe supports the idea, first presented by Merrihue and Turner ( 1966), that the distribution of radiogenic 4”Ar within a geologic sample can be used to reconstruct its thermal history. Prior to the development of high-resolution laser microprobes, “‘Ar/“Ar geochronologists deduced the nature of argon isotopic gradients in minerals from the morphology of incremental-release spectra. They assumed that a stepwise heating experiment extracted Ar from a sample through volume diffusion, thereby providing an indication of its intracrystalline spatial distribution. This venerable methodology has formed the basis of many classic thermochronologic and empirical Ar diffusion studies (e.g., Harrison and McDougall, 1980; Berger and York, 1981), but its reliability is being seriously challenged by the results of recent investigations into the behavior of hydrous 3205

K. V. Hodges

3206

Nevada,

/

ii?’

I

/I

Middle

Proterozoi

Horse Mountain

Yi, California

1.

FIG. 1. Generalized map of the distribution of Middle and Early Proterozoic rocks in Arizona and adjacent parts of Nevada, California, and Mexico. Thin dashed lines correspond to boundaries between

the Basin and Range province (southwest), the Colorado Plateau (northeast), and the intervening transition zone. Heavy lines correspond to important structural boundaries. Filled circles indicate the locations of the Horse Mountain and Crazy After Bowring and Karlstrom (1990).

Basin

monzogranites.

and S. A. Bowring Bowring, 1988; Bowring and Karlstrom, 1990). The Crazy Basin and Horse Mountain monzogranites intruded > 1.72 Ga volcanic arc rocks of the Big Bug block during the -1.7 Ga “Yavapai orogeny”, an event during which the Yavapai province of central Arizona was assembled from four disparate crustal fragments including the Big Bug block (Karlstrom and Bowring, 1993). Preliminary U-PI, zircon data indicate a crystallization age of 1680 ? 5 Ma for the Horse Mountain monzogranite and 1700 2 IO Ma for the Crazy Basin pluton (S. A. Bowring, unpubl. data). The dominant rock type in the Horse Mountain intrusion is a foliated, porphyritic monzogranite. Large (-I cm) twinned phenotrysts of K-feldspar occur in a matrix of quartz + plagioclase + biotite + fine-grained K-feldspar. We analyzed biotites from a crushed sample of this lithology collected in the interior of the pluton (well-removed from its contact zone with the country rock) by Dr. Kevin Chamberlain (University of Wyoming) at 34”14’6”N; 112”23 ‘45’W. Small cleavage fragments were separated for totalfusion experiments (described below), but our study focused on handpicked, relatively pristine crystals. Although the edges of all crystals were broken to some extent during separation, each displayed two or more intact crystal faces. When viewed perpendicular to the ( 001) cleavage plane, individual crystals typically exhibited internal fractures. Some of these are planar, trend parallel to (010 ] and [ 1101, and are interpreted as primary growth features; others are curved and may represent postcrystallization deformation or fracturing during sample preparation. Preliminary examination of the separates using a petrographic microscope revealed no inclusions. Two of the crystals were studied in greater detail using a Jeol733 electron microprobe at the Massachusetts Institute of Technology (beam current = 10 nA; accelerating voltage = 15 kV). Scanning and backscattered electron images provide no evidence of microinclusions that had escaped detection with the petrographic microscope, of fine-scale intergrowths with another mineral (such as chlorite), or of alteration

TableL HMC~tainB&titeCompo&ion

1994). We designed

the Horse Mountain study to determine whether or not the remarkable age gradients observed in the Crazy Basin micas could be found in other samples

ring,

from the region. The new dataset, which includes information obtained with a variety of laser-based 4oAr/‘9Ar techniques, confirms the presence of large age gradients in single biotite crystals from this part of the southwestern United States Proterozoic orogen. Detailed age contour maps reveal complex radiogenic 4oAr distributions related to discrete, fast-diffusion pathways, the significance of which varies considerably from crystal to crystal. Despite these complications, our findings suggest that inverse modeling of overall age gradients preserved in relatively pristine crystals provides a powerful tool for reconstructing the thermal evolution of geologic samples. Moreover, they suggest that total fusion studies of large populations of crystal fragments from geologic samples may provide useful information regarding the extent and significance of argon isotopic zoning in intact crystals, and may evolve into an important tool for reconnaissance thermochronologic studies. 2. GEOLOGIC

SETTING

AND SAMPLE

DESCRIPTION

The Horse Mountain monzogranite (Anderson, 1989b) occupies an area of - 100 km* in the southern Bradshaw Mountains of central Arizona, and lies about 5 km west of the previously studied Crazy Basin monzogranite (Fig. 1). Both bodies belong to a suite of broadly synorogenic plutons found along the length of the southwestern United States Proterozoic erogenic belt from New Mexico to California. The orogen as a whole consists of numerous tectonostratigraphic blocks that were accreted to the southern margin of the Archean Wyoming craton in Early Proterozoic time (Karlstrom and

SiO2 TiO2

36.3lXO.32) 2.68(0x@)

A1203

16.60(0.2424)

Fe0

22.51tO.27)

Mno

0.64(0.04)

MS0 cao

0.02(0.03)

Na20

0.05(0.02)

K20

9.37CO.10)

Total

7.62cO.13)

95.78 Formuh Basis II Orygens

Si

2.797(0.010)

Ti

0.155(0.005)

Al

1.508(0.014)

Fe

1.451(0.019)

Mn

0.042(0.003)

Mg Ca

0.001(0.002)

Na

O.c07(0.003)

K

0.921(0.@4@)

Total

0.876(0.016)

7.758

0.383(0.004) &mn Nun&es in parentheses refer to 2a analytical uncertainties. &nn = mole fraction of annite component (Fe/R + Mg + Ti + &).

Age-distribution

patterns

along internal fractures. Detailed analytical traverses indicate no major element zoning; the average composition of Horse Mountain biotite, based on thirty-three wavelength-dispersive analyses, may be found in Table I. 3. ANALYTICAL

METHODS

Single crystals and cleavage fragments of the Horse Mountain biotite were washed in acetone, ethanol, and distilled water prior to packaging in Al foil for neutron irradiation. Along with flux monitor MMhb-I hornblende (520.4 Ma; Samson and Alexander, 1987) and synthetic salts to allow corrections for interfering nuclear reactions, the samples were encapsulated in an Al disk, shielded with Cd foil, and irradiated in position 5C of the McMaster University reactor (irradiation parameter J = 0.0140 2 0.0001 (2~)). Gas extraction was accomplished through heating of an irradiated sample with a Coherent Innova 210 Ar-ion laser running in multiline configuration (457.9-514.5 nm wavelengths). Because one of the goals of this study was to establish appropriate experimental protocols for the analysis of crystals zoned in radiogenic @Ar, we tried three different extraction procedures: spot-fusion mapping of single crystals, incremental heating of single crystals, and total fusion of crystal fragments. Spot-fusion mapping was performed on two single crystals (referred to hereafter as Crystals 1 and 2). Their approximate grain sizes were 1.4and 1.1 mm, respectively. Previous studies had shown that Ar transport in trioctahedral micas occurs primarily parallel to ( 001) (Giletti, 1974; Phillips and Onstott, 1988), so we mounted the crystals on a flat Cu surface such that their c-axes were parallel to the beam path, and we concentrated our mapping efforts on clean ( 001) cleavage surfaces. After focusing the laser beam to a diameter of -30 pm on the sample, individual “spots” were melted by firing five, 100 ms bursts from the laser using a power level of 0.30 W. The use of multiple, low-power bursts rather than a single burst at higher power permitted much better control on the size and geometry of melt pits and minimized the extent of sample heating outside of the melt zone. The melt pits for this experiment were roughly hemispherical and ranged in size from 35 to 85 pm. Larger pit sizes resulted from analysis of spots along fractures within a crystal, presumably due to an increase of surface area under the beam and internal reflections of the laser energy. Incremental heating experiments were performed on two separate crystals (grain size - 1.4 mm) mounted on a flat Cu surface with their c-axes parallel to the laser beam path. The beam was defocused to a diameter roughly 50% larger than the biotite grains in order to minimize temperature gradients related to high light-intensity gradients near the edges of the beam. Each experiment involved heating a grain for two min at successively higher power levels (0.15- 1.58 W for Crystal 3; 0.08-I .59 W for Crystal 4), which were controlled by varying the plasma tube current for the laser. Twenty-five cleavage fragments, - 100 pm in their longest dimensions, were selected for total-fusion experiments. Inspection of the Horse Mountain monzogranite sample prior to crushing indicated that all biotites were of relatively uniform initial grain size, so we feel confident that the small fragments used for total fusion were pieces broken during crushing from grains that were approximately the same size as Crystals 1-4. Each fragment was placed in a 1 mm-diameter well in a Cu sample holder and degassed by heating for 15 s using a - 1.6 W laser beam focused to fill the well with light. This procedure converted the fragments to uniform, roughly spherical glass beads. Repeat analysis of one of these beads yielded no 4oAr above blank level, confirming that a 15 s heating period was sufficient to extract essentially all Ar from the biotite fragments. Gasses liberated by all three procedures were purified for five min using Al-Zr and Fe-Zr-V getters prior to isotopic analysis on a MAP 215-50 mass spectrometer. All measurements were made using an electron multiplier (sensitivity = 2.67 x 10” Vlmol). Total system blanks were measured before each step-heating experiment and before sets of ten spot- or total-fusion analyses. Typical blanks for M/e 40, 39, 38, 37, and 36 (in moles) were 3 x 10-‘h, 9 x IO-‘“, 3 x IO-‘“, 1 x IO-“, and 3 X lo-‘*, and the total variation in blank levels over the course of all Horse Mountain experiments was less than 20%. All measurements were corrected for system blanks, neu-

of individual

mica flakes

3207

tron-induced interferences, and mass fractionation prior to age calculations and statistical analysis. Apparent ages were calculated using an assumed initial “‘Ar/“Ar ratio of 295.5 and decay constants KCommended by Steiger and Jgger ( 1977). Age uncertainties are reported throughout the text of this paper at the 2u confidence level and result from the propagation of errors in isotopic measurements, corrections for interfering reactions, and J. The error in J makes the largest single contribution to the age uncertainty for most analyses, and the magnitude of uncertainties calculated both with and without the J-error contribution are shown in the data tables.

4. SPOT-FUSION

MAPPING

treLaser spot mapping of Crystals 1 and 2 demonstrated mendous inhomogeneity in the distribution of ““Ar in single crystals of Horse Mountain biotite. Crystal 1 displayed a straightforward zoning pattern, with apparent ages ranging from 1241.2 ? 6.5 Ma near the core to 1034.7 + 5.7 Ma at one point on the rim (Table 2; Fig. 2). The age contours shown in Fig. 2 were fitted by eye and are thus subjective, but the data density for this sample is sufficiently high that we can be confident of the overall concentric pattern of decreasing ages from core to rim, even if the detailed contour geometry is incorrect. Rim analyses along pristine crystal faces resulted in ages between 1117.2 and 1142.4 Ma. Spots 11- 13 lie along a broken edge of the crystal and yielded somewhat older ages. The youngest age was obtained from a broken edge of the crystal at the mouth of a “valley” in the contour map that extends almost to the core of the crystal. Such valleys or troughs are common in 4”Ar/‘9Ar age zoning maps (e.g., Onstott et al., 1991; Hames and Hodges, 1993) and are thought to reflect the presence of fast diffusion pathways such as subgrain boundaries and other zones of high dislocation density. In this case, we observe no obvious correlation between microscopically visible planar structures in Crystal 1 and the contour pattern in Fig. 2. In contrast, Crystal 2 exhibited complicated age zoning that appears to be related to enhanced depletion of radiogenic 40Ar near internal fracture systems (Table 3; Fig. 3). The oldest apparent age (1217.6 2 6.4 Ma) was measured at a spot roughly halfway from the geometric center of the grain to the rim, and there is no simple pattern of older ages in the core and younger ages at the rim, such as that observed for Crystal 1. The most obvious feature of the contour map for Crystal 2 is a valley of young ages that extends most of the way across the lower part of the crystal as shown in Fig. 3. Along much of its length, this valley is centered along an internal cleavage plane that extends from spots 10 to 22. Spot 22 yielded the youngest apparent age for this crystal ( 1046.7 + 5.9 Ma). Rim ages along pristine crystal faces were highly variable, ranging from 1069.9 to 1165.0 Ma. 4.1. Interpretation

of Age Variations

There are four possible interpretations for the spatial variation in ages observed in these crystals: ( 1) the biotites contain inclusions of other minerals with different Ar retentivities, and fusion analyses that sampled these inclusions yielded spurious ages; (2) the samples were isotopically heterogeneous at the time of crystallization, containing large intracrystalline gradients in initial ““Ar/‘“Ar; (3) the crystals were contaminated inhomogeneously after crystallization with

K. V. Hodges and S. A. Bowring

1 2 3 4 5 6 1 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

10.37C1.24) 4.19C2.01) 3.200.79) 8.74t3.84) 2.06C3.36) 2.98C1.45) 0.80(1.66) 0.78C1.65) 2.94C22.69) 9.22C11.32) 0.13C5.85) 0.2OC3.74) 1.34C1.92) 7.85C3.27) 3.5W.64) 0.38C7.20) 1.85C1.27) 5.830.79) 29.4500.42) 26.1809.36) 7.97C6.31) 3.34C3.49) 2.08CO.86) 3.07C1.80) 0.69C12.96) 11.5OC6.50) 7.25C4.18) 9.58C5.56) 0.34C9.21) l.Ol(5.68) 0.96C5.26) 8.18C4.35) 2.38C4.31) 5.22C4.18) 0.39(10.53) 25.23C27.82)

1.435CO.030) 1.435(0.035) 1.446CO.036) 1.452(0.035) 1.406CO.046) 1.472(0.038) 1.495(0.040) 1.466CO.039) 1.483(0.177) 1.566CO.093) 1.554CO.060) 1.533CO.048) 1.557(0.040) 1.573(0.047) 1.582(0.041) 1.521(0.071) 1.614(0.040) 1.576(0.036) 1.650(0.088) 1.555CO.152) 1.551CO.060) 1.569CO.047) 1.572CO.037) 1.53OCO.039) 1.554(0.113) 1.441CO.055) 1.477CO.048) 1.476CO.056) 1.527CO.034) 1.425CO.034) 1.451CO.038) 1.502CO.033) 1.491(0.037) 1.46OCO.034) 1.453(0.040) 1.606(0.046)

1.917 1.151 1.301 0.610 0.257 0.626 0.552 0.539 0.040 0.085 0.161 0.234 0.492 0.295 0.59 1 0.122 0.781 0.541 0.098 0.049 0.152 0.276 1.116 0.523 0.069 0.137 0.218 0.163 0.154 0.230 0.255 0.321 0.320 0.324 0.126 0.054

96.9 98.8 99.1 97.4 99.4 99.1 99.8 99.8 99.1 97.3 99.8 99.9 99.6 97.7 99.0 99.9 99.5 98.3 91.3 92.3 97.7 99.0 99.4 99.1 99.8 96.6 97.9 97.2 99.9 99.7 99.7 97.6 99.3 98.5 99.9 92.6

Average’

1200.6 1217.2 1213.2 1194.9 1241.2 1198.2 1190.3 1207.5 1191.8 1129.1 1157.2 1170.0 1153.6 1128.6 1134.7 1176.5 1122.3 1132.0 1034.7 1091.1 1140.2 1142.4 1144.0 1164.3 1157.3 1194.2 1184.0 1178.3 1172.8 1232.0 1212.3 1167.1 1188.2 1199.5 1216.3 1067.3 1179.1

f f f. + -k f f k + + + k f + + f f ?r * f + f k k * f + + f ik ?r f ?: f k f

7.3C3.7) 6.7C2.2) 6.8t2.5) 6.40.2) 6.5CO.7) 6.4C1.3) 6.3 (1.2) 6.4C1.4) 6.3CO.5) 6.OCO.5) 6.1 (0.6) 6.2CO.7) 6.2Cl.l) 6.0(0.8) 6.1 (1.3) 6.2CO.6) 6.2C1.6) 6.1Cl.O) 5.7CO.6) 5.9CO.5) 6.1CO.6) 6.1CO.7) 6.4C2.1) 6.2Cl.l) 6.1CO.5) 6.3CO.5) 6.2CO.6) 6.2CO.6) 6.2CO.3) 6.4CO.5) 6.3CO.5) 6.2CO.5) 6.6CO.6) 6.3CO.6) 6.3CO.3) 5.8CO.2) 1.1

‘: Numbers in parentheses indicate 20 errors in individual ratios. *: number of moles of K-derived s9Ar (“Ara) released during each fusion analysis. “: percentage of radiogenic “‘AT (‘OAr’) in the total “AT for each analysis. ‘: Uncertainties, quoted at 20, include propagated error in the irradiation parameter J. Uncertainties in parentheses indicate the contribution of analytical error to the overall uncertainty. 0: Mean age for all spots, weighted by the number of moles of 39ArK released during each fusion analysis. Assigned uncertainty corresponds to two standard errors of the weighted mean.

varying amounts of “excess ” 40Ar, such that some spot-fusion ages are anomalously old, or (4) the crystals retain 4oAr diffusive loss gradients that developed during their postcrystallization thermal history. As we stated earlier, examination of the Horse Mountain biotites with the petrographic microscope and the electron microprobe revealed no evidence of solid inclusions of other phases. Furthermore, the lack of strong correlations between “ArlWAr and “Ar140Ar for the two populations of spot-fusion analyses (Figs. 4, 5) implies that the age dispersion was not controlled by inclusions with K/Ca ratios different from those of the host biotite. An explanation involving nonuniform initial 40Ar/7bAr ratios seems highly unlikely. The measured ““Ar for each spot is sufficiently radiogenic (Tables 2,3 ) that the assumed initial 40Ar/‘6Ar ratios would have to vary by a factor of 30 to produce the observed age range. Adjusting the ages of many of the spots to 1140 or 1180 Ma (the average ages of the two crystals) would require the impossible assumption of a negative initial ratios! If 4”Ar gradients in a mineral were produced by an influx of excess 40Arfrom the local environment after crystallization,

we might expect to find older apparent ages near the rim (cf. Phillips and Onstott, 1988; Lee et al., 1990) and along internal fractures that might have served as 40Ar conduits. Just the opposite is true for Crystals 1 and 2, in which the youngest apparent ages occurred near internal fractures and along the crystal margins. It has been demonstrated that fluid inclusions are hosts for excess 40Ar in many minerals (vonBlanckenburg and Villa, 1988; Burgess et al., 1992; Cumbest et al., 1994), so we also examined the spot mapping data for possible correlations between Cl-derived 38Ar and apparent age (or ‘8Ar/ 40Ar and ‘9Ar/40Ar) that might indicate the presence of excess 4oAr in Cl-rich fluid inclusions. This exercise failed to reveal any evidence for statistically significant correlations (e.g., Figs. 4, 5). The simplest explanation of Figs. 2 and 3 is that the Horse Mountain biotite crystals are zoned with respect to age because of postcrystallization diffusive loss of radiogenic 4oAr. However, the complicated patterns evident in these maps indicate that 4oAr loss was not controlled by a single mechanism, such as volume diffusion on the grain scale, and it is clear that the relative importance of competing loss mechanisms varies from crystal to crystal.

Age-distribution patterns of individual mica flakes no additional “‘Ar ratio.

information

5.1. Interpretation

FIG. 2. Age distribution maps for Crystal 1. The top drawing shows the position of spot fusion analyses listed in Table 2; enclosing circles indicate the approximate maximum size of fusion pits. Thin lines within the crystal outline correspond to visible fractures. The edges outlined by double-headed arrows appear to be unbroken crystal faces. The shaded area in the upper right-hand comer of the crystal designates a fragment broken from the principle (001) cleavage plane mapped by spots l-35. Spot 36 was mapped on a separate cleavage plane (two sheets down from the l-35 plane, in map perspective) that remained attached to Crystal 1. The lower drawing is an interpretive contour map, based on the Table 2 data; contours are labeled in Ga with an interval of 0.04. Positions of oldest and youngest measured ages are indicated.

5. INCREMENTAL

HEATING EXPERIMENTS

One of our most important findings was that incremental heating experiments failed to resolve age gradients in the Horse Mountain biotites. Crystals 3 and 4 exhibited similar Ar release characteristics during incremental heating (Table 4; Fig. 6). Most K-derived 39Ar (“‘Ark) was released in the first few increments, at laser power levels of less than 0.3 W. These early steps also define very flat segments of the release spectra with weighted-mean ages of 1194.9 + 3.2 Ma for Crystal 3 (cumulative % ‘9ArK = 83.7) and 1188.2 2 4.0 Ma for Crystal 4 (88.9% “Ark). We refer to these segments as “near-plateaus” because they do not strictly conform to the definition of plateaus advocated by Fleck et al. (1977): the ages of all steps on the flat segments do not overlap at 20 when the J-error contribution is ignored. All release steps for Crystals 3 and 4 were characterized by very low 76Ar/40Ar ratios and a restricted range of ‘9Ar/40Ar ratios; as a consequence, examination of both samples using 39Ar/40Ar vs. ‘hAr/40Ar isotope correlation diagrams (Figs. 7, 8) provided

3209 regarding

their age or initial 4”Ar/

of Age Spectra

The flat age spectra in Fig. 6 suggest that the incremental heating procedure homogenized preexisting radiogenic 4oAr gradients in the analyzed crystals. Crystals 1, 3, and 4 were approximately the same size and shape; if the incrementally heated crystals were isotopically homogenized during analysis, we might expect the total gas ages for Crystals 3 and 4 ( 1189.8 and 1182.1 Ma) to compare favorably with the weighted mean age of the fusion spots in Crystal 1 ( 1179.1 Ma). The similarities are striking, especially since the spot mapping experiment was designed to resolve intracrystalline age gradients, not to provide a statistically meaningful “average” age for Crystal 1. Note that the weighted mean age of the fusion spots in Crystal 2 is substantially younger ( 1139.9 Ma), partly because it contains better developed fast diffusion pathways and partly because it is roughly 27% smaller than the other analyzed crystals. Crystals 3 and 4 underwent similar textural changes during laser heating, providing insight regarding the mechanism of Ar loss in vacua and causes for the homogenization of age gradients. Within a few seconds of the beginning of its first heating step, each crystal swelled noticeably and began to delaminate along { 001) cleavages. By the end of the first increment, the top surface of the crystal had developed a uniform drusy film. Previous experience (based on electron microprobe analysis of other mica samples after equivalent experiments) leads us to attribute the film to dehydroxylization. The next major textural change was surface melting, which began during the 13.8 A (0.30 W) step for Crystal 3 and the 13.0 A (0.25 W) step for Crystal 4. Roughly 90% of the total “ArK in these samples was released prior to melting. The first appearance of surface melt corresponded to a slight (but statistically significant) drop in apparent ages. There is no evidence that the lower ages reflect degassing of a second solid phase with a different K/Ca ratio; plots of ‘9Ar/40Ar vs. “‘Ar/ 40Ar (Figs. 7, 8) reveal no significant correlations. However, the onset of melting did correspond to a dramatic decrease in the amount of Cl-derived “Ar released in subsequent steps (Fig. 9). Assuming that chlorine in these biotites resides in hydroxyl sites and in fluid inclusions (if present), we suggest that most of the Ar release during the step-heating experiments was accomplished through dehydroxylization reactions and/or fluid inclusion decrepitation rather than volume diffusion through the biotite structure.

6. FRAGMENT TOTAL FUSION Total fusion analyses of crystal fragments yielded highly variable ages ranging from 1006.7 5 6.7 to 1212.0 ? 7.6 Ma, with a weighted mean of 1134.8 + 1.7 Ma (Table 5). Figure 10a illustrates the distribution of apparent ages in the form of a histogram. Figure lob is a smoothed version of the frequency plot that accounts for measurement uncertainties. Both representations of the data indicate that the distribution is skewed toward younger ages.

3210

K. V. TABLE 3. “AI?% spot Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

%rPAr k 109’ 17.65c6.45) 16.33(8.11) 17.99(10.16) 8.07c4.16) 9.08(9.00) 6.42c2.14) 9.70(6.41) 6.06(3.52) 2.2N2.19) 3.96U.73) 0.40(2.27) 8.9Oc8.66) 0.62c2.62) 1.91(3.05) 2.9U3.20) 1.75c3.89) O.ll(3.08) 3.47c2.35) 1.45c2.46) 2.48c3.18) 3.37C4.73) 0.91(1.92) 2.38(1.60) 2.46(2.90) 1.28(2.39) 2.34c7.37) 4.30(3.69) 1.38c3.33) 5.03(4.51) 2.87c1.73) 2.64c1.41)

Hodges

and S. A. Bowring

Spot Fusion Data for Horse Mountain

Biotite

Crystal 2

JSATPAI (x 10-V 1.596(0.042) 1.586cO.037) 1.605(0.040) 1.594(0.040) 1.609(0.038) 1.637(0.037) 1.519(0.033) 1.516(0.032) 1.578(0.033) 1.529(0.040) 1.506(0.036) 1.669(0.039) 1.576(0.039) 1.444(0.035) 1.449(0.033) 1.52UO.0331 1.490(0.031) 1.712(0.035) 1.455(0.036) 1.486(0.034) 1.528(0.039) 1.775(0.043) 1.595(0.034) 1.605(0.039) 1.520(0.034) 1.646(0.031) 1.514(0.037) 1.537(0.034) 1.584(0.039) 1.622cO.034) 1.539(0.037)

0.399 0.315 0.255 0.617 0.288 1.238 0.382 0.696 0.670 0.823 0.604 0.179 0.560 0.440 0.420 0.362 0.449 0.678 0.547 0.435 0.300 0.847 0.928 0.515 0.587 0.206 0.383 0.428 0.326 0.873 1.014

94.8

95.2 94.7 97.6 97.3 98.1 97.1 98.2 99.3 98.8 99.9 97.4 99.8 99.4 99.1 99.5 99.9 99.0 99.6 99.3 99.0 99.7 99.3 99.3 99.6 99.3 98.7 99.6 98.5 99.2 99.2 AVPEWP~

1091.8 1100.0 1086.2 1117.0 1106.8 1099.0 1153.7 1164.6 1140.1 1162.5 1184.7 1077.0 1145.1 1217.6 1211.8 1173.0 1194.6 1069.9 1212.3 1190.9 1165.0 1046.7 1130.6 1125.1 1174.5 1104.4 1170.1 1164.8 1130.0 1115.4 1160.5

k k + k + f k + + f f + f + ? + f ? + + f f i ? ? i f + + i f

5.9cO.9) 5.9(0.7) 5.9(0.6) 6.U1.3) 5.9(0.6) 6.2c2.1) 6.1(0.8) 6.2cl.O) 6.Ul.O) 6.3c1.7) 6.3c1.2) 5.8(0.4) 6.2cl.l) 6.4cO.9) 6.4tO.8) 6.2cO.7) 6.3cO.9) 5.9cl.l) 6.4cl.O) 6.3cO.7) 6.2cO.6) 5.9(1.7) 6.2c1.4) 6.1(1.0) 6.3(1.2) 5.9(0.4) 6.2cO.8) 6.2cO.8) 6.OcO.7) 6.2c1.7) 6.4c1.9)

11.19

+

1 I

I)

‘: Numbers in parentheses indicate 20 errors in individual ratios. *: number of moles of Kderived =Ar PAr,) released durine each fusion analvsis. *: Dercentaee of radiorrenic uAr PAr*) in the total *AT for’each analysis. ‘:-Uncertainties, qu&d at-au, in&de propagated error in the irradiation parameter J. Uncertainties in parentheses indicate the contribution of analytical error to tbe overall uncertainty. 0:Mean age for all spots, weighted by the number of moles of .wArK released during each fusion analysis. Assigned uncertainty corresponds to two standard errors of the weighted mean.

6.1. Interpretation of Fragment Fusion Data Like the spot-mapping results, the observed distribution of fragment fusion data can be interpreted several different ways. There is no indication in thin section that the Horse Mountain monzogranite contains xenocrysts of biotite that might have been inadvertently sampled in the population of crushed fragments and might contribute to some of the dispersion in Fig. 10. Moreover, all of the measured fragment ages are substantially younger than the 1680 Ma crystallization age of the pluton. The isotope correlation matrix for the fragments (Fig. 11) again offers little support for the hypothesis that the observed age variations are due to the presence of solid or fluid inclusions, and explanations based on variable initial ““Ar/ ‘6Ar ratios are just as implausible as those we evaluated for the spot-fusion mapping data. In light of the Crystal 1 and 2 mapping results, the most reasonable explanation of the fragment data is that the original crystals of Horse Mountain biotite that were broken into fragments contained inhomogeneities in 40Ar on a scale larger than about 100 pm. One important effect of picking small fragments from a crushed separate of micas with physical grain sizes at least ten times larger is that the fragments will be more representative of crystal edges than crystal centers. Consequently, the younger ages obtained for the fragments (relative to the incrementally heated crystals) and the markedly

negative skewedness of the fragment age distribution imply that the original crystals contained more radiogenic 4oAr at their centers than at their edges. This possibility can be explored using a synthetic fragment datasets based on Crystals 1 and 2. We began with the contour map of Crystal 1, lining the inside of the outline with a series of 100 pm-diameter circles. Together these circles defined a “rim zone” with a thickness of 100 ,um. We evaluated the distribution of ages within the rim zone by noting the average age in each circle (using the contour map), counting the number of average ages falling within each of the 40 m.y. bins defined by the contour intervals, and plotting a smoothed frequency distribution curve. The rim zone distribution for Crystal 1 is shown as a solid line in Fig. 12a. We then defined a “core zone” for the crystal by scaling down an outline of the crystal such that it had an area equal to that of the rim zone and was geometrically centered within the original outline map. We also packed this zone with 100 pm circles and again created a smoothed frequency distribution curve (the dashed line in Fig. 12a). Comparison of the two distributions for Crystal 1 demonstrates that, despite some overlap, the core ages are generally older than the rim ages and a random sampling of 100 pm fragments from the rim is likely to be younger than a random sampling from the core.

Age-distribution

patterns

of individual

1.50

FIG. 3. Age distribution

maps for Crystal

2. See Fig. 2 caption for

mica flakes

1.60

0.50

1.50

FIG. 4. Argon isotope correlation matrix for Crystal 1 spot-fusion data. See Appendix for a guide to reading and interpreting this kind of diagram. Dashed lines in several of the cells are least-squares linear regression fits to the data and describe statistically nonzero correlations. For all cases, the coefficients of determination (R’) indicate that only a small proportion (~50%) of the variance in Y can be explained by variations in X.

explanation of symbols.

This might seem like a great deal of work to prove a point that is obvious from the more or less concentric nature of the age contours for Crystal 1, but the overall geometric distribution of ages in Crystal 2 is not so straightforward. Rim and core frequency distribution curves for this crystal are shown in Fig. 12b). Although we see greater dispersion, most core ages are still older than most rim ages. Given the probability of obtaining more rim fragments than core fragments in the crushing process, a population of fragments broken from Crystals 1 and 2 would likely yield a range of apparent ages spanning roughly 200 m.y., with a frequency distribution skewed toward younger ages. As it turns out, the negative skewedness we see in the fragment data probably is more than just a sampling artifact. An alternative way to establish the distribution of ages in Crystals 1 and 2 requires calculation of the areas between contours on the maps in Figs. 2 and 3. For each crystal, we determined the fraction of the total area corresponding to each 40 m.y. bin and created an array of 50 synthetic ages with the same distribution. The results for both crystals were combined to produce the smoothed frequency distribution curve shown in Fig. 12~. This diagram suggests that Horse Mountain biotites yield frequency distributions skewed toward younger ages even when the distributions are not corrupted by sample preparation effects. We attribute this additional factor to the presence of fast diffusion pathways, such as those apparent in the contour diagrams, that result in artificially young age zones in the interior

of crystals.

When the curve in Fig. 12~ and the smoothed distribution curve for the fragments (Fig. lob) are normalized to an arbitrary vertical scale and superimposed, their similarity is

%WOAr (x10-9

37Ad4OA.r (x10-3)

FIG. 5. Argon isotope correlation matrix for Crystal 2 spot-fusion data. Dashed lines indicate statistically nonzero, but very weak, correlations.

3212

K. V. Hodges and S. A. Bowring TABLE

4. pArl’Xr

Incremental

Heating

Tube CluTent

outputPower

=Arr@Ar

WI-AI

(A) CIyetol.9

WI

(x WY

(x lo-*)’

Date

for Horse

3)k (x l@” moles)’

Mountain

Cum.SgArK

Biotites *oAr

(%Y

(40)”

Age (Ma)’

11.60

0.15

0.7210.39)

1.493(0.015)

3.718

19.2

99.8

1191.8

!c

12.50

0.21

O.Ol(O.29)

1.485(0.017)

4.147

40.7

99.9

1197.9

i

7.2c3.6)

5.314

68.2

99.9

1193.1

i

11.9(10.2)

0.23(0.27)

6.7c2.5)

13.00

0.24

13.25

0.26

0.02(0.62)

1.492(0.029)

2.046

78.8

99.9

1193.7

i

6.9c3.0)

13.60

0.27

0.29(1.49)

1.485(0.038)

0.959

83.7

99.9

1197.1

k

6.5c1.9)

13.75

0.30

l.lO(2.01)

1.538(0.030)

0.742

87.6

99.7

1165.1

i

6.20.0)

14.00

0.31

l.ll(3.50)

1.631(0.038)

0.422

89.8

99.7

li69.0

i

6.ZO.9)

14.25

0.34

0.13(3.32)

1.512(0.034)

0.378

91.7

99.9

1182.2

t

6.2(0.8)

14.60

0.36

0.14 (3.76)

1.528(0.032)

0.311

93.3

99.9

1172.8

?

6.2cO.7)

14.75

0.41

1.65 (4.85)

1.566(0.040)

0.310

94.9

99.5

1147.4

k

6.1(0.7)

16.00

0.44

0.14c3.66)

1.568(0.034)

0.276

96.4

99.9

1150.5

*

6.1CO.6)

16.00

0.69

0.76c4.25)

1.567(0.041)

0.314

98.0

99.8

1149.8

i

6.1(0.7)

18.00

1.02

7.06c7.49)

1.524(0.042)

0.190

99.0

97.9

1157.5

i

6.1(0.4)

20.00

1.56

1.33(4.43)

1.510(0.040)

0.199

100.0

99.6

1180.0

t

6.2cO.4)

Total Gas”

1189.8

f

6.2

1.492(0.029)

clystor4 11.00

0.08

6.66cO.71)

1.473(0.032)

2.098

17.2

98.9

1195.7

i

7.Oc3.2)

12.00

0.16

l.lO(O.18)

1.513(0.012)

8.049

83.0

99.7

1178.7

f

8.0(5.0)

12.50

0.21

l.SO(2.01)

1.496(0.036)

0.723

88.9

99.6

1188.1

f

6.4c1.4)

13.00

0.25

3.02(2.29)

1.530(0.034)

0.652

94.3

99.1

1164.4

k

6.3c1.3)

13.50

0.28

3.62c4.34)

1.587(0.041)

0.356

97.2

98.9

1132.1

i

6.1(0.7)

14.00

0.32

0.46c12.42)

1.654(0.046)

0.100

98.0

99.9

1157.6

k

6.1cO.3)

14.50

0.37

0.47c12.32)

1.546(0.061)

0.081

98.7

99.9

1162.1

i

6.1cO.3)

15.00

0.44

0.24c6.17)

1.500(0.063,

0.060

99.2

99.9

1189.0

f

6.2cO.3)

15.60

0.52

10.26(27.95)

1.322(0.069)

0.043

99.5

97.0

1274.7

f

6.5(0.2)

16.00

0.61

1.59(41.28)

1.340(0.229)

0.011

99.6

99.5

1286.1

AZ 6.6cO.2)

18.00

1.04

0.49u7.901

1.456(0.047)

0.035

99.9

99.9

1214.1

k

6.3cO.2)

20.00

1.69

27.56(171.10)

1.823(0.106)

0.014

100.0

91.9

962.9

f

6.3cO.2)

1182.1

f

6.2

Total Gas”

‘: Numben in parenthales indicate20

errors in individual ratios. *: number of moles of K-derived =Ar (‘Qr,&eleeeed durin each : cumulative percentage of =ArK after each heating increment. ‘: percentage of radiogenie ‘PAr (“‘A?) in the total %AI for heating etep. ?? each analyeie. *: Uncertainties, quoted at 20, include propagated error in the irradiation parameter J. Uncertainties in parentheses indicata the wntribution analytical error to the overall uncertainty. * Total gas ages are calculated by summing “AT’ and =‘AQ for each increment. Aedgned uncertainties (20) include the propagatad errors in J and isotopic measurements.

of

striking (Fig. 12d). It is not difficult to imagine that total fusion analysis of 100 fragments rather than 25 might produce a distribution curve virtually identical to that obtained for the mapped crystals. Similarly, detailed mapping of several more crystals probably would result in some spot ages as young as the 1006.7 Ma fusion age obtained from one of the fragments. Considering the complexity of age zoning patterns in these micas, we find the overall consistency between the fragment fusion and mapping data to be remarkable. 7. DISCUSSION 7.1. Mechanisms

of Argon Loss

We interpret the age gradients shown in Figs. 2 and 3 as the result of two complimentary Ar loss processes. The most generally important is simple volume diffusion at the scale of the physical grain size. Several lines of evidence suggest this mechanism: ( 1) the zoning in Crystal 1 is broadly concentric with respect to the grain shape; (2) the core zones of grains yield statistically older apparent ages than the rim zones; (3) the smaller of the two mapped crystals (Crystal 2) has younger maximum and mean ages; and (4) the core and rim frequency distributions for the smaller crystal are shifted toward younger ages relative to those for Crystal 1. The existence of discrete valleys in the age contour maps, sometimes corresponding to visible subgrain boundaries, suggests a second mode of Ar loss: diffusion along zones of high dislocation density (Harrison, 1961). Following Lee ( 1993)) we refer to this as short-circuit (SC) diffusion. The strong dissimilarity between the zoning patterns in Crystals 1 and 2 suggests that the importance of SC diffusion varies greatly between grains

and is impossible to evaluate in a general way for Horse Mountain biotites without more data. For this reason, we will concentrate on the significance of grain-scale radiogenic 4oAr gradients for the remainder of our discussion.

7.2. Origin

of Age Gradients:

Reheating

or Slow Cooling?

Argon diffusive loss gradients can develop through episodic reheating or protracted cooling, and the 4oAr/‘9Ar literature is filled with papers describing attempts to tell one kind of loss profile from another (see York ( 1984) and McDougall and’Harrison (1988) for useful reviews). Such an exercise seems impractical for the Horse Mountain data, because any robust solution would require much better definition of the near-rim gradients than was possible given the spatial resolution of our laser. Fortunately, the geologic record in central Arizona provides an independent constraint. The recovery of no 40Ar/“9Ar ages younger than - 1.0 Ga from the Horse Mountain biotites suggests that any reheating event responsible for the observed loss profiles would have occurred in Middle to Late Proterozoic time. Only two thermal events appear to have affected the Yavapai province in this interval: intrusion of “anorogenic” granites at - 1.42 Ga, and intrusion of an extensive swarm of diabase dikes at - 1.1 Ga (Anderson, 1989a; Howard, 1991; Karlstrom and Bowring, 1993). Despite the fact that rocks of both suites are widespread in the southwestern United States, none of them have been found in the vicinity of the Horse Mountain monzogranite; Fig. 13 shows the known limits of - 1.42 Ga granite and - 1.1 Ga diabase distributions (Howard, 1991; Karlstrom and Bowring, 1993; Anderson et al., 1993). Although further

Age-distribution

_ (a) Crystal

patterns

of individual

mica flakes

3213

3

$

B 1300 e llOO& 4 ’

9001

’

20

’

’ ’ ’ ’ 40 60 seAr Released (%)

’ 80

’

*“““I

1

I

(b) Crystal

3~ArPAr (x 10-l)

4

:

0

%a

36Ar/40Ar (x 10-Y

gooll---J

8

20

40 60 WAr Released (%)

1 4.

80

1.40

FIG. 6. Incremental heating spectra for Horse Mountain biotite Crystals 3 (a) and 4 (b). Uncertainties for individual increments (shown at the 2u confidence level) include measurement errors and uncertainties in the flux parameter J. Shaded steps &fine near-plateau ages of 1194.9 2 3.2 Ma and 1188.2 +- 4.0 Ma for Crystals respectively.

3 QO

3~ArPOAr (x 10”)

1.60

1.60

0.50

1.50

0.50

I

1.00

*”

FIG. 8. Argon isotope correlation matrix for Crystal 4. Dashed line in the “ArpAr vs. ‘hAr/40Ar cell indicates a weak, non-robust correlation.

3 and 4,

work might reveal evidence of Middle Proterozoic thermal events in this area, all available data lead us to infer that the age gradients recorded in the Horse Mountain biotites are the result of protracted cooling.

crystal

0

1o.004

7.3. Estimation of Integrated Cooling Rate If the gradients related to volume diffusion of 4oAr were produced by slow cooling, we should be able to invert them to recover a portion of the postcrystallization thermal history of the Horse Mountain pluton. The limited resolution of our laser mapping study, as well as the complexities in the zoning profiles that are related to SC diffusion, restrict our ability to reconstruct this history in great detail. However, we can say something about the average or “integrated” cooling rate over the Ar retention interval for these biotites: an important

’ 0

??

.

.

0.0

0.4

0.8

1.2

1.6

Laser Power(w)

1.50

1.52

0.50

1.50

1.00

3.00

FIG. 7. Argon isotope correlation matrix for Crystal 3. Dashed lines indicate weak, non-robust correlations.

FIG. 9. Relationships between laser power output (W) and evolved Cl-derived ‘“Ar (moles) for individual heating steps during the Crystal 3 and Crystal 4 experiments. Errors in ‘*Arc, indicate 2a analytical precision limits. Superimposed lines indicate the power levels at which surface melting began for Crystals 3 (short dashes) and 4 (long dashes).

K. V. Hodges and S. A. Bowring

3214

TABLE &OAr/“Ar

Data for Eons

=%Ph

Number

%rPAx (x 10-v

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

2.610.54) 1.43CO.67) 5.10(1.21) 3.93t1.72) 4.670.03) 2.24CO.96) 2.05t1.54) 3.16C2.93) 2.520.51) 2.19(0.93) 2.41t3.78) ‘I.lO(2.05) 2.78tO.81) 9.40(1.87) 2.4OCO.28) 3.85CO.85) 2.39CO.42) 4.81CO.46) 2.39(0.44) 2.03(0.42) 1.16CO.56) 1.72CO.31) 2.78CO.47) 1.27CO.45) 2.33CO.42)

1.525tO.037) 1.528(0.016) 1.642(0.041) 1.614(0.038) 1.628(0.028) 1.634(0.039) 1.513(0.037) 1.513(0.037) 1.461CO.035) 1.522(0.036) 1.549(0.039) 1.677CO.035) 1.579(0.030) 1.822CO.042) 1.684(0.040) 1.534CO.027) 1.552(0.033) 1.617CO.032) 1.715(0.038) 1.538(0.037) 1.457(0.035) 1.551CO.036) 1.584(0.038) 1.543CO.036) 1.569(0.037)

Fragment

(x llw

Mountain

=A%

(x lo’” moles)’ 1.94s 4.473 2.692 1.848 3.147 3.258 1.919 1.018 1.915 3.247 0.803 1.627 3.834 1.948 5.868 1.695 3.425 3.399 3.664 3.408 2.368 4.605 3.179 3.095 3.497

Biotite

Fragments

aAr*

Age

(%Y

(Ma)

99.2 99.6 98.5 98.8 98.6 99.3 99.4 99.1 99.3 99.4 99.3 97.9 99.2 97.2 99.3 98.9 99.3 98.6 99.3 99.4 99.7 99.5 99.2 99.6 99.3

1168.1 1169.6 1099.9 1117.1 1107.8 1110.8 1176.7 1173.9 1206.1 1170.9 1155.3 1077.7 1138.3 1006.7 1085.7 1160.0 1153.7 1113.4 1071.0 1162.4 1212.0 1156.0 1135.5 1161.4 1144.7

f ‘7.2C3.7) k 7.3C4.0) * 8.OC5.4) + 6.8(3.4) + 6.3C2.3) + 8.5t6.0) -t 7.2C3.6) f 6.5Cl.S) C 7.2C3.6) f 8.6C5.9) + 6.3C1.6) + 6.3C2.4) Lk 7.3C4.1) f 6.7C3.8) f 15.5C14.3) + 6.3C1.3) f 7.9C5.0) f 8.1C5.6) If 8.8C6.6) + 8.8C6.3) + 7.6C4.3) f 10.4C8.4) + 8.5C6.0) + 8.3C5.6) f 8.8C6.4)

Average0

1134.8

Lt 1.7

+: Numbers in parentheses indicate 20 errors in individual ratios. *: number of moles of Kderived =Ar PAra) released during each heating step. ‘: percentage of radiogenie “Ar PAr.1 in the total ‘OAT for each analysis. *: Uncertainties, quoted at 20, include propagated en-or in the irradiation parameter J. Uncertainties in parentheses indicate the contribution of analytical error to the overall uncertainty. “Mean age for all fragments, weighted by the number of moles of “ArK released during each fusion analysis. Assigned uncertainty corresponds to two standard err& of the weight4 mean.

first-order constraint that can be augmented by more detailed work. Thermochronology is predicated on our ability to assign closure temperatures to the ages we measure. Conventional K-Ar or 4oAr/‘9Ar geochronology involves the determination of integrated ages for whole mineral grains or multigrain aggregates, and Dodson ( 1973) developed a mathematical protocol to estimate the appropriate integrated closure temperature for such samples assuming a volume diffusion mechanism of Ar loss. In a later paper (Dodson, 1986), he noted that volume diffusion theory predicts the existence of age gradients in slowly cooled geologic materials and derived equations to describe closure temperature as a function of position within a crystal. Because local variations in age gradients within the Horse Mountain biotites are complex and controlled by an Ar loss mechanism other than simple volume diffusion, we used the Dodson ( 1973,1986) method to examine the overall gradient from the core to the rim of each crystal. The closure temperatures for these positions should be functions of the volume diffusivity of Ar in biotite (Harrison et al., 1985), the distance between the rim and the core, and the instantaneous cooling rates at the times of rim and core closure. The dependence of closure temperature at a given position on instantaneous cooling rate is not very strong, and we introduced relatively little error into our calculations by making the assumption of the same instantaneous cooling rate for both core and rim. We began with an arbitrary choice of instantaneous cooling rate and solved the appropriate equations from Dodson ( 1986) for core and rim closure temperatures. Using these temperatures

and the measured ages, we calculated an “integrated” cooling rate over the closure interval. This result was substituted for the original arbitrary cooling rate, and the equations were again solved for new estimates of core and rim closure temperatures. After about five iterations, this procedure converges on a robust estimate of the integrated cooling rate. Table 6 displays the results of such calculations for Crystals 1 and 2. In each case, we defined the “core” of the crystal as the spot yielding the oldest apparent age. When we assumed that the youngest measured age along a crystal margin was representative of the “rim”, Crystals 1 and 2 yielded similar estimates of the integrated cooling rate (0.50 and 0.59 K/m.y.). We also were able to use the Dodson ( 1986) method to predict the integrated closure temperatures (and therefore, the integrated or mean ages) of the crystals if simple volume diffusion was the only mechanism of Ar loss. The predicted mean age of Crystal 1 ( 1193 Ma) compares reasonably well with the weighted mean of the spot fusion ages for this crystal ( 1179 Ma), reflecting the apparently limited significance of SC diffusion in producing the observed age distribution in this sample. SC effects are much more obvious in the age contour map for Crystal 4, and it comes as no surprise that the predicted mean age of this crystal ( 1178 Ma) is somewhat older than the mean of its spot fusion ages ( 1139.9 Ma). However, the similarity between the predicted mean ages of both crystals and the weighted mean and plateau ages of the incrementally heated samples is remarkable, and it strongly supports the assumption that a volume diffusion model can account for the first-order characteristics of the overall age gradients observed in the Horse Mountain biotites.

Age-distribution patterns of individual mica flakes

3215

spot fusion ages for this sample. This discrepancy may be an experimental artifact: volume diffusion theory predicts the existence of large radiogenic 40Ar gradients near the rims of slowly cooled crystals, and there are practical difficulties associated with making reproducible measurements within this zone given a spatial resolution of only 35-85 pm. It seems reasonable that calculations made using the oldest measured rim age provide reliable estimates of the maximum integrated cooling rate. The better consistency of cooling rate and mean age estimates made for the mapped crystals and the fragments using the youngest measured ages suggests to us that the integrated cooling rate of the Horse Mountain pluton was -0.5 K/m.y. over the - 1240- 1010 Ma interval. 7.4. Comparisons with Biotites from the Crazy Basin Monzogranite 980

1030

1080 Apparent

1130

1180

1230

Age (Ma)

FIG. 10. Age-frequency distribution plots for fragment total-fusion data. (a) Histogram of measured values. Thin vertical line indicates the mean age of all fragments weighted by the amount of “‘)ArKin each fusion analysis. (b) Smoothed representation of the frequency distribution that accounts for analytical uncertainties. The smoothed plot was produced by creating a lOO-element array of “synthetic ages” for each fragment, such that the mean of the array corresponded to the measured age of the fragment and the standard deviation of the mean was equal to the 1s analytical uncertainty for the fragment’s age. The smoothed plot represents the frequency distribution of all 2500 values thus produced. Vertical lines indicate important ages for other analyzed samples of Horse Mountain biotiteshort dashes: “ArK-weighted mean of Crystal 1 spot-fusion analyses; solid line: “Ar,-weighted mean of Crystal 2 spot-fusion analyses; long dashes: total gas age of Crystal 3; intermediate-length dashes: total gas age of Crystal 4.

The range of biotite grain sizes for the Horse Mountain monzogranite was rather limited ( - l.O- 1.5 mm). Having some idea of the dimension represented by the observed age

dispersion, we also experimented with the application of the Dodson ( 1986) method to the fragment fusion data. Assuming that the age difference between the youngest and oldest fragment developed over a 750-500 pm distance, we calculated an integrated cooling rate of OS l-0.50 K/m.y. The similarity between this result and the estimates based on Crystals 1 and 2 suggests that fragment fusion analysis alone can provide useful insights regarding the cooling history of slowly cooled geologic samples. Measured ages along the rims of Crystals 1 and 2 were variable, and it is important to ask what effect this variability has on estimates of the integrated cooling rate. Table 6 also shows the results of calculations made assuming that different measured ages along intact crystal faces were representative of the “rim” age. The complex zoning pattern of Crystal 2 results in highly variable estimates that can be dismissed as corrupted by SC diffusion effects. The estimated rates for Crystal 1 show more limited dispersion (0.90- 1.10 K/m.y.), but are a factor of two larger than the rate calculated using the youngest spot age. The mean ages for the crystal predicted using the spot ages measured along intact crystal faces are substantially older than the estimate made using the youngest spot age, and less consistent with the weighted mean of all

Although the samples used for this study and our previously published work on the Crazy Basin monzogranite (Hodges et al., 1994) were collected only a few kilometers from one another, they contain biotite phenocrysts with dramatically different closure ages. Laser incremental heating of a -700 pm biotite crystal from the Crazy Basin sample yielded a flat release spectrum, with fifteen increments (corresponding to 94% of the “‘ArK released during the experiment) defining an isotope correlation age of 1410 Ifr 10 Ma. Laser mapping of a biotite grain of similar size displayed age gradients ranging from 1420 2 10 Ma near the core to 1150 ? 10 Ma along one segment of the rim. While this range is similar in magnitude to that observed in mapped Horse Mountain crystals, it is mostly older, and the mean ages of the Crazy Basin and Horse Mountain biotites are discrepant by nearly 200 million years.

Fragments

36ArY40Ar

6.00

(x10-5)

3.00

6.00

1.00

3.00

FIG. Il. Argon isotope correlation matrix for biotite crystal fragments. Dashed lines describe statistically nonzero correlations. Only the “Arp”Ar vs. ‘6Ar/40Arcorrelation is robust, and its low R' value indicates that it is weak.

3216

K. V. Hodges and S. A. Bowring

b. Cystal 2

25 0

I

t

the argon isotopic systematics of biotites analyzed for this study, we tentatively attribute the discrepancy between the Horse Mountain and Crazy Basin datasets to long-lived, lateral heterogeneities in the thermal structure of the region. If such heterogeneities occurred, their significance in controlling the isotopic systematics of minerals in the two plutons would have been magnified by very slow cooling. Despite the absolute age discrepancies, the integrated cooling rate calculated from the age-zoning pattern in the Crazy Basin biotite (-0.3 K/m.y.; Hodges et al., 1994) is not much different than our estimate for the Horse Mountain biotites ( -0.5 K/m.y.) . At such cooling rates, local perturbations in the thermal structure of a region can have profound effects on the isotopic closure behavior of minerals, producing large variations in apparent ages (Onstott et al., 1989). A better understanding of the regional significance and tectonic implications of slow cooling in the southwestern United States Proterozoic orogen must await a more comprehensive database. 7.5. Analytical Tactics for Thermochronology in Slowly Cooled Terrains

1000

1080

1160

1240

Apparent Age (Ma) FIG. 12. Comparisons of synthetic age frequency distribution plots for mapped crystals with fragment fusion and incremental heating results. (a) Age distribution curves for a 100 pm rim zone and a core zone of equal area from Crystal 1. (b) Equivalent curves for Crystal 2. (c) Total age frequency distribution for both mapped crystals. Vertical lines indicate important ages for Crystals 1-4; see Fig. lob caption for explanation. (d) Synthetic age distributions for both mapped crystals (from c, unpatterned) and biotite fragments (from Figure lob, shaded), normalized to the same arbitrary scale.

This inconsistency cannot be explained by appealing to differences between the effective diffusion dimensions of biotites from the two samples. The mapped Crazy Basin biotite, although much smaller, yielded older apparent closure ages. Experimental data for biotites and phlogopites indicates a strong influence of FelMg on the diffusivity of Ar in these minerals, with higher Fe contents corresponding to lower closure temperatures (Harrison et al., 1985). Unfortunately, this characteristic cannot be used to reconcile the Crazy Basin and Horse Mountain data: biotites from the Crazy Basin biotites are actually more Fe-rich than the Horse Mountain biotites (X,,, = 0.485 vs. 0.383). Unless we are willing to entertain the possibility that the Crazy Basin biotites are uniformly and heavily contaminated with excess 4oAr (an interpretation for which we see no evidence in the Ar isotopic data), we must conclude that the Crazy Basin and Horse Mountain plutons had much different thermal histories despite coming from the same tectonic block. Because geologic mapping of the area has not revealed the presence of late (post-l 150 Ma) intrusive rocks in the vicinity of the Horse Mountain pluton that may have disturbed

Many conventional 4oAr/79Ar, Sm-Nd, and U-Pb thermochronologic studies in Precambrian orogens have yielded evidence for very slow cooling (Dallmeyer and Sutter, 1980; Berger and York, 1981; Humpbries and Cliff, 1981; Harley and Black, 1987; Onstott and Peacock, 1987; Costa, 1989; Onstott et al., 1989; Mezger et al., 1989, 1990, 1991; Wright et al., 1991, among others). Diffusion theory, as well as our empirical data from central Arizona, suggest that grain-scale gradients in radiogenic isotopes should be common in crystals from such terrains. In some cases, failure to recognize the

Granite

0

Zone of no - 1.42 Ga Granitoids

FIG. 13. Map showing the locations of the Horse Mountain and Crazy Basin monzogranites with respect to the known distribution of - 1.1 Ga diabases (after Howard, 1991). Based on available mapping md geochronologic data, the shaded region between heavy dashed lines contains no -1.42 Ga granitoids. Other lines correspond to those in Fig. 1.

Age-distribution patterns of individual mica flakes TABLE 6. Integrated Pomt MX&*

Cooling

Rate CaIcuIatione FrediFgean Ap: Y

Distance (urn)’

3217

In~;M~wling Y.Y

Crystal 1 - Coreto Intact Ctystd Faces 5-10

355

597

496

1215

0.90

5-17

751

620

512

1214

0.91

5-21

699

620

512

1218

1.08

5-22

716

621

512

1218

1.10

603

500

1193

0.50

0.91

Crystal 1 - core to Youngest spot 5-19

580

Crystal 2 - Core to Intact Crystal Faces 14-6

713

618

510

1190

14-7

403

610

505

1203

1.64

14-18

662

612

506

1183

0.72

14-21

326

606

502

1205

1.98

14-29

514

612

507

1197

1.21

1431

663

627

517

1204

1.94

598

496

1178

0.59

Crystal2

* core

to Youngest

14-22 Fmgments

spot

446

_Oldest

to Youngest

21-14

750

611

505

1164

0.51

21-14

500

598

497

1165

0.50

‘:values correspond to analysis numbers in Tables 2.3, and 5. +: straight-line distance between the point pairs. ‘:closure temperatures for the first (core) and second (rim) points of the pair, derived with the algorithm of Dodson (1986). ‘: mean age of the sample (calculated with Dodson’s algorithm) given the specified diffusion dimension and the assumption that all zoning is a consequence of volume diffusion. O:linear cooling rate between the times of rim and core closure, assuming calculated core and rim closure tempera&es

existence of these gradients and can lead to misconceptions about the cooling history of a sample. For example, 4oAr/‘9Ar incremental heating analysis of micas from the Crazy Basin pluton suggested a cooling rate nearly two orders of magnitude higher than that indicated by age mapping results (Hodges et al., 1994). Although diffusive loss gradients can thus compromise the results of conventional studies, they offer a promising way to obtain detailed information about the thermal evolution of the crust if used to our advantage. The Horse Mountain biotite results suggest that fragment fusion analysis can be an extremely useful reconnaissance tool in slowly cooled regions. As automated laser microprobes become more commonplace, measuring a large number of fragment ages is a relatively rapid procedure: the fragment data reported in this paper were acquired in the MIT lab over a six-hour period without an operator in attendance. Fifty to one hundred fragments should be sufficient for an adequate characterization of the frequency distribution of ages in a population, provided that the fragments are much smaller than the crystals from which they were broken. Our preliminary calculations for the Horse Mountain biotites show that the total dispersion of ages obtained from fragments provides a good working approximation of the range of ages likely to be encountered in a single-crystal mapping experiment. When the grain size of mica in a sample is relatively uniform, the range of fragment ages can be inverted for a useful estimate of the integrated cooling rate for the sample over that age range. In theory, it should be possible to develop more sophisticated mathematical methods to invert the geometric characteristics of a well-characterized frequency distribution curve for relatively detailed time-temperature path information.

Samples displaying a range of fragment ages that does not appear to be the result of compositional inhomogeneities (based on electron microprobe data and multicomponent, isotope correlation analysis) are good candidates for laser mapping studies. Although more tedious to acquire, detailed age contour maps are the only means of accurately establishing the scale of diffusion gradients in a sample and evaluating the relative importance of volume and SC diffusion mechanisms. In principle, age profiles from such maps can serve as the basis for highly refined inverse models of time-temperature paths; in practice, we have found that the spatial resolution of the Ar-ion laser is not adequate to constrain profile geometry in the necessary detail. Recently developed UV laser systems offer greatly enhanced spatial resolution (Kelley et al., 1994)) suggesting that we may soon be able to define and model diffusive loss gradients in more rapidly cooled samples using the 40Ar/“Ar laser microprobe. Despite our enthusiasm about 4oAr/‘9Ar laser microanalysis, we must sound a final note of caution. Spot and total fusion analyses produce model ages; they require an assumption regarding the initial 40Ar/‘“Ar ratio of a sample, commonly taken as that of modern atmosphere. In this regard, fusion analyses are equivalent to conventional K/Ar analyses and inherently inferior to incremental heating experiments, which can sometimes provide independent constraints on apparent age and initial “‘Ar/“Ar ratio through the 39Ar/4”Ar‘hAr/40Ar correlation diagram. The 40Ar/“Ar literature is filled with examples of nonatmospheric initial 40Ar/3hArratios in geologic samples, and the reliability of an assumed atmospheric ratio must be evaluated objectively as part of any @Ar/ “Ar laser microprobe study. For the Proterozoic Horse

K. V. Hodges

3218

Mountain biotites, 40Ar yields were highly radiogenic and a wide range of assumed initial ratios would have produced virtually indistinguishable results. Younger samples contain less radiogenic 40Ar per unit volume, and the dependence of apparent age on assumed initial ratio increases accordingly. As a consequence, the reliability of 40Ar/3yAr laser microprobe fusion ages becomes more suspect for samples of Mesozoic age and younger. Regardless, the magnitude of age gradients in a crystal should be independent of assumed initial ratio, unless that ratio was spatially variable. Since integrated cooling rates depend only on age dispersion and not on absolute age, most geologic samples containing age gradients should be amenable to the thermal history calculations described in this paper. 8. CONCLUSIONS Biotite crystals separated from the Horse Mountain monzogranite of central Arizona contain -200 Ma gradients in apparent 40Ar/‘yAr age developed over scales of several hundred microns. These crystals are not zoned with respect to their major element chemistry and contain no inclusions that can be discerned with an optical or scanning electron microscope. Explanations of the age dispersion based on spatially variable initial 40Ar/“hAr ratio seem improbable, and we relate the age range to diffusive loss gradients in radiogenic 4oAr. The pattern of ages illustrated by mapping with the laser microprobe imply that Ar loss through volume diffusion was augmented by SC diffusion to an extent that varied from crystal to crystal. Geologic considerations imply that the gradients resulted from slow cooling over a protracted period rather than episodic reheating. Simple inversions of the overall age pattern based on a volume diffusion model yield internally consistent estimates of -0.5 K/m.y. for the integrated cooling rate over the biotite closure interval. Even though the age gradients encountered in this study are complex, the apparent success of simple volume diffusion models in reconciling seemingly disparate results of incremental heating, fragment fusion, and laser mapping experiments suggests that our current understanding of Ar loss in natural samples, while incomplete, provides a useful framework for reconstructing the thermal history of erogenic belts. Detailed spot mapping provides the most complete view of argon isotopic gradients in individual mineral crystals and permits straightforward inversion for time-temperature information when the gradients can be attributed to diffusive loss of 40Ar. Our results suggest that automated total-fusion measurements of large populations of crystal fragments is an efficient reconnaissance tool that can establish useful first-order constraints on the thermal history of geologic samples. The inability of conventional incremental heating experiments to reveal the extent of age zoning in hydrous phases limits the usefulness of this approach and emphasizes the importance of laser microprobe methods in the study of samples with inhomogeneous distributions of 4oAr. Acknowledgments-We thank Kevin Chamberlain for collecting the sample used in this study, Bill Hames and Bill Olszewski for assistance in sample preparation and analysis, and John Brady, Bill Hames, Jim Lee, and Larry McKenna for fruitful discussions regarding the documentation of “‘Ar gradients in natural samples and sta-

and S. A.

Bowring

tistical analysis of argon isotopic data. Earlier versions of the manuscript benefitted from insightful comments by Yang Yu and an anonymous reviewer. This research was supported by National Science Foundation award EAR-9405696.

Editorial handling: D. E. Fisher

REFERENCES Anderson J. L. ( 1989a) Proterozoic

anorogenic granites of the southwestern United States. In Geologic Evolution of Arizona (ed. J. P. Jenney and S. J. Reynolds); Arizona Geol. Sot. Diges? 17, pp. 21 l-238. Anderson J. L., Wooden J. L., and Bender E. E. (1993) Mojave province of southern California and vicinity. In The Geology of North America: Precambrian: Coterminous U.S. (ed. J. C. Reed et al.), Vol. C-2, pp. 176-188. GSA. Anderson P. ( 1989b) Stratigraphic framework, volcanic-plutonic evolution, and vertical deformation of the Proterozoic volcanic belts of central Arizona. In Geologic Evolution of Arizona (ed. J. P. Jenny and S. J. Reynolds); Arizona Geol. Sot. Digest 17, pp. 57-147. Berger G. W. and York D. (1981) Geothermometry from 40Arl”Ar dating experiments. Geochim. Cosmochim. Actu 45,795811. Bowring S. A. and Karlstrom K. E. ( 1990) Growth, stabilization, and reactivation of Proterozoic lithosphere in the southwestern United States. Geology 18, 1203-1206. Burgess R., Kelley S. P., Parsons I., Walker F. D. L., and Worden R. H. (1992) 40Ar-99Ar analysis of perthite microtextures and fluid inclusions in alkali feldspars from the Klokken syenite, South Greenland. Earth Planet. Sci. I&t. 109, 147- 167. Chambers J. M., Cleveland W. S., KleinerB., andTukey P. A. (1983) Graphical Methods for Data Analysis. Duxbuty Press. Costa M. A. (1989) Cooling and inverted uplift/erosion history of the Grenville orogen, Ontario: constraints from 4oAr/‘9Ar thermochronology. Ph.D. dissertation, Univ. Michigan. Cumbest R. J., Johnson E. L., and Onstott T. C. ( 1994) Argon composition of metamorphic fluids: Implications for 4oAr/39Ar geochronology. GSA Bull. 106,942-95 1. Dallmeyer R. D. and Sutter J. F. (1980) Acquisitional chronology of remanent magnetization along the “Grenville Polar Path”: Evidence from 40Ar/‘9Ar ages of hornblende and biotite from the Whitestone diorite, Ontario. J. Geophys. Res. 85,3177-3186. Dodson M. H. ( 1973) Closure temperature in cooling geochronological and petrological systems. Contrib. Mineral. Petrol. 40, 259274. Dodson M. H. (1986) Closure profiles in cooling systems. Mat. Sci. Forum 7, 145-154. Fleck R. J., Sutter J. F., and Elliot D. H. (1977) Interpretation of discordant 4oAr/99Ar age spectra of Mesozoic tholeiites from Antarctica. Geochim. Cosmochim. Actu 41, 15-32. Gaber L. J., Foland K. A., and Corbad C. E. (1988) On the significance of argon release from biotite and amphibole during ““Arl ‘9Ar vacuum heating. Geochim. Cosmochim. Acta 52,2457-2465. Giletti B. J. ( 1974) Studies in diffusion I: Argon in phlogopite mica. In Geochemical Transport and Kinetics (ed. A. W. Hofmann et al.), Vol. 634, pp. 107-115. Carnegie Inst. Hames W. E. and Bowring S. A. ( 1994) An empirical evaluation of the argon diffusion geometry in muscovite. Earth Planet. Sci. Letf. 124,161-167. Hames W. E. and Hodges K. V. ( 1993) Laser ““Ar/‘9Ar evaluation of slow cooling and episodic loss of 4oAr from a sample of polymetamorphic muscovite. Science 261, 1721- 1723. Hamilton L. C. ( 1992) Regression with Graphics: A Second Course in Applied Statistics. Brooks/Cole. Harlev S. L. and Black L. P. ( 1987) The Archean geological evolutcon of Enderby Land, Antarctica. In Evolution if the-Lewisian and Comparable High-Grade Terrains (ed. R. G. Park and J. Tarney); Geol. Sot. London Spec. Publ. 27, pp. 285-296. Harrison L. G. (1961) Influence of dislocations on diffusion kinetics in solids with particular reference to the alkali halides. Trans. Faraday Sot. 57, 1191-1199.

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patterns

Harrison T. M. and McDougall I. ( 1980) Investigations of an intrusive contact, northwest Nelson, New Zealand-II. Diffusion of radiogenic and excess “‘Ar in hornblende revealed by 4”Ar/‘9Ar age spectrum analysis. Geochim. Cosmochim. Acta 44, 200% 2020. Harrison T. M., Duncan I., and McDougall I. (1985) Diffusion of ““Ar in biotite: Temperature, pressure, and compositional effects. Geochim. Cosmochim. Acta 49,2461-2468. Hodges K. V., Hames W. E., and Bowring S. A. ( 1994) 4”Ar/‘9Ar age gradients in micas from a high temperature-low pressure metamorphic terrain: Evidence for very slow cooling and implications for the interpretation of age spectra. Geology 22,55-58. Howard K. A. ( 1991) Intrusion of horizontal dikes: Tectonic significance of Middle Proterozoic diabase sheets widespread in the upper crust of the southwestern United States. J. Geophys. Res. 96, 12461-12478. Humphries F. J. and Cliff R. A. ( 1981) Sm-Nd dating and cooling history of Scourian granulites, Sutherland. Nature 295, 515-517. Karlstrom K. E. and Bowring S. A. ( 1988) Early Proterozoic assembly of tectonostratigraphic terranes in southwestern North America. J. Geol. %, 561-576. Karlstrom K. E. and Bowring S. A. (1993) Proterozoic erogenic history of Arizona. In The Geology of North America: Precambrian: Coterminous U.S. (ed. J. C. Reed et al.), Vol. C-2, pp. 188211. GSA. Kelley S. P. and Turner Cl. ( 1991) Laser probe 40Ar-1yAr measurements of loss profiles within individual hornblende grains from the Giants Range granite, northern Minnesota, USA. Earth Planet. Sci. Lett. 107, 634-648. Kelley S., Turner G., Butterfield A. W., and Shepherd T. J. ( 1986) The source and significance of argon isotopes in fluid inclusions from areas of mineralization. Earth Planet. Sci. Lett. 79,303-318. Kelley S. P., Amaud N. O., and Turner S. I’. (1994) High spatial resolution ‘“Ar/“Ar investigations using an ultra-violet laser probe extraction technique. Geochim. Cosmochim. Acta 58,3519-3525. Lee J. K. W. ( 1993) The argon release mechanisms of hornblende in vacua. Chem. Geol. (Isotope Geoscience Section) 106, 133170. Lee J. K. W., Onstott T. C., and Hanes J. A. ( 1990) An 40Ar/“Ar investigation of the contact effects of a dyke intrusion, Kapuskasing structural zone, Ontario. Contrib. Mineral. Petrol. 105, 87105. Lee J. K. W., Onstott T. C., Cashman K. V., Cumbest R. J., and Johnson D. ( 199 1) Incremental heating of hornblende in vacua: Implications for “OAr/“Ar geochronology and the interpretation of thermal histories. Geology 19, 872-876. McDougall I. and Harrison T. M. ( 1988) Geochronology and Thermochronology by the 4”Ar/-‘vAr Method. Oxford Univ. Press. Merrihue C. M. and Turner Cl. ( 1966) Potassium-argon dating by activation with fast neutrons. J. Geophys. Res. 71, 2852-2857. Mezger K., Hanson G. N., and Bohlen S. R. ( 1989) High-precision U-Pb ages of metamorphic rutile: application to the cooling history of high-grade terranes. Earth Planet. Sci. Lett. 96, 106-l 18. Mezger K., Bohlen S. R., and Hanson G. N. ( 1990) Metamorphic history of the Archean Pikwitonei granulite domain and the Cross Lake subprovince, Superior Province, Manitoba, Canada. J. Petrol. 31,483-517. Mezger K., Rawnsley C. M., Bohlen S. R., and Hanson G. N. ( 1991) U-Pb garnet, sphene, monazite, and mtile ages: Implications for the duration of high-grade metamorphism and cooling histories, Adirondack Mtns., New York. J. Geol. 99,415-428. Onstott T. C. and Peacock M. W. ( 1987) Argon retentivity of homblende: A field experiment in a slowly cooled metamorphic terrane. Geochim. Cosmochim. Acta 51,2891-2903. Onstott T. C., Hall C. M., and York D. (1989) 4oAr/‘oAr thermochronometry of the Imataca complex, Venezuela. Precamb. Res. 42,255-291. Onstott T. C.. Phillips D., and Pringle-Goode11 L. (1991) Laser microprobe measurement of chlorine and argon zonation in biotite. Chem. Geol. 90, 145- 168. Phillips D. and Onstott T. C. ( 1988) Argon isotopic zoning in mantle phlogopite. Geology 16, 542-546.

of individual

mica flakes

3219

Press W. H., Teukolsky S. A., Vetterling W. T., and Flannery B. P. ( 1992) Numerical Recipes in C: The Art of Scientific Computing. Cambridge Univ. Press. Roddick J. C., Cliff R. A., and Rex D. C. (1980) The evolution of excess argon in Alpine biotites-A 4”Ar-‘YAr analysis. Earth Planet. Sci. L.ett. 48, 185-208. Samson S. D. and Alexander E. C. ( 1987) Calibration of the interlaboratory 4”Ar/‘9Ar dating standard, MMhb-1. Chem. Geol. 66, 27-34. Scaillet S., Feraud G., Lagabrielle Y., Balltvre M., and Ruffet Cl. ( 1990) “Ar/“‘Ar laser-probe dating by step heating and spot fusion of phengites from the Dora Maira nappe of the western Alps, Italy. Geology l&741-744. Scaillet S., Feraud Cl., Ballevre M., and Amouric M. ( 1992) MglFe and [( Mg,Fe)Si-Al21 compositional control on argon behaviour in high-pressure white micas: A 4oAr/z’Ar continuous laser-probe study from the Dora-Maira nappe of the internal western Alps, Italy. Geochim. Cosmochim. Acta 56,2851-2872. Steiger R. H. and Jager E. ( 1977) Subcommission on geochronology: convention on the use of decay constants in geo- and cosmochronology. Earth Planet. Sci. L.ett. 36, 359-362. vonBlanckenburg F. V. and Villa I. M. ( 1988) Argon retentivity and argon excess in amphiboles from the garbenschists of the western Tauem Window, Eastern Alps. Contributions Mineral. Petrol. 100, l-11. Wartho J., Dodson M. H., Rex D. C., and Guise P. Cl. ( 1991) Mechanisms of Ar release from Himalayan metamorphic hornblende. Amer. Mines-al. 76, 1446-1448. Wilkenson L. ( 1989) SYGRAPH: The System for Graphics. SYSTAT, Inc. Wright N., Layer P. W., and York D. ( 1991) New insights into thermal history from single grain “‘Ar/79Ar analysis of biotite. Earth Planet. Sci. L&t. 104, 70-79. York D. ( 1984) Cooling histories from “Ar/“Ar age spectra: Implications for Precambrian plate tectonics. Annual Reviews of Earth Planet. Sci. 12,383-409.

APPENDIX Graphical Matrices and MultiComponent

Isotope Correlation

As pointed out by Kelley et al. ( 1986). multicomponent isotope correlation diagrams reveal possible relationships between apparent ages and chlorine or Ca contents (using Cl-derived ‘sAr and Ca-derived “Ar), and they provide a straightforward (if not foolproof) way to test for the presence of “excess” ““Ar. In addition to using the traditional inverse isochron plots of ‘9Ar/40Ar vs. ‘6Ar140Ar (Roddick et al., 1980), we have searched for isotopic correlations in the Horse Mountain data using graphical matrices (Chambers et al., 1983; Wilkenson, 1989), which illustrate all possible bivariate correlations between S“Ar/40Ar, ‘8Ar/40Ar, ‘7Ar/4”Ar, and “‘Ar/“OAr (Figs. 4, 5, 7, 8, 1 I ). Axis variables in such diagrams correspond to row and column labels; for example, 3”Ar/4”Ar is the horizontal axis for all scatterplots in the “‘9Ar/ ““Ar” column, and ‘bAr/4”Ar is the vertical axis for all scatterplots in the ““Ar14”Ar” row. Graphs to the left and below the diagonal containing labels are conventional scatterplots of the data, showing measured ratio values and their 2a uncertainties. Scales for these plots are shown at the beginning of each row and column; numeric values in the scale labels are truncated for display purposes and should be multiplied by the power of ten indicated in the axis-label diagonal. Note that the scales of plots for the Horse Mountain data are greatly expanded; most plots show relatively little scatter compared to the measured uncertainties in ratios. Plots above and to the right of the axis-label diagonal are commonly referred to as influence plots (Wilkenson, 1989). In each of these, the size and fill pattern of each data point represents its influence on the coefficient of determination (R’) for the two plotted ratios; unfilled circles have a positive influence, filled circles have a negative influence, and larger circles have proportionately more influence than smaller circles. The value of R* for each plot (shown in an inset box) indicates the proportion of variation in one ratio that

3220

K. V. Hodges and S. A. Bowring

can be explained by linear variation in the other; a value of one indicates perfect correlation, zero indicates no correlation (Hamilton, 1992). The scales for these plots are similar to those for the conventional scatterplots but are not traditionally shown in statistical presentations; these diagrams are designed to emphasize overall patterns of variation, not the range of absolute values. The overall significance of an apparent correlation was evaluated with a nonparametric statistic: Spearman’s rank-order correlation coefficient (R,). When the value of R, implies a greater than 95% probability of nonzero correlation (Press et al., 1992), a least-squares, best-fit line has been drawn on the scatterplot. We use the combined information provided by R,, R’, and the influence plots to classify bivariate isotope ratio relationships as uncorrelated, weakly correlated, non-robustly correlated, and strongly correlated. Uncorrelated data yield an R, value insufficiently high to suggest a nonzero correlation. Weakly correlated

data have a probable nonzero correlation, but have R’ values of less than 0.7 (an arbitrary but reasonable value). The 77Ar/4”Ar vs. ‘6Ar/40Ar relationship in Fig. 4 is an example. In some cases, an apparently significant correlation between two isotopic ratios is strongly influenced by outliers in the data. Figure 7 provides a good illustration of this phenomenon. Based on the calculated value of R,, there is a statistically significant positive correlation between the ‘*Ar/40Ar and “Ar/“‘Ar ratios for the Crystal 3 incremental heating data. However, one datum is characterized by unusually high values of both ‘*Ar/““Ar and ‘6Ar/40Ar. It plots as a large, unfilled circle on the scatterplot and thus exerts a large, positive influence on the apparent correlation. If this point is ignored in statistical tests, the ‘*Ar/+“Ar and “‘Ar/“‘Ar ratios for the Crystal 3 data show no significant correlation. We thus refer to the apparent 38Ar/40Ar-‘bAr/40Ar correlation for these data as non-robustly correlated.