Pergamon Geochimica et Cosmochimica Acta,Vol. 58, No. 7, pp. 1747-1757, 1994 Copyright 0 I994 Elsevier Science Ltd Printed in the USA. All rights reserved 0016-7037/94 $6.00 +.OO Helium isotope diffusion in natural diamonds R. C. WIENS,* D. LAL, W. RISON,+ and J. F. WACKER* Geological Research Division, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093-0220, USA (Received April 22, 1993; accepted in revisedform December 2, 1993) Abstract-Stepped heating experiments in the range of 1200- 1700°C were performed on terrestrial dia- monds, some containing substantial cosmic ray-produced 3He, in order to study the diffusion coefficients and release characteristics of ‘He and 4He. Cosmogenic 3He is shown to be much more retentive than 4He in the same sample, with as little as 0.3% of the total 3He, and up to 27.4% of the 4He released by 1700°C from diamonds in which cosmogenic ‘He predominates (bulk 3He/4He = 176 RA). A tentative determination, from the data, of the site activation energy for cosmogenic ‘He gives - 150 kJ/mol. The diffusion equation, with Do = 6.1 X lo-” cm’/s, yields an extrapolated diffusivity at 1200°C of 1.9 X 1 O-l6 cm*/s. Other helium components are difficult to distinguish from each other by their apparent diffusion coefficients. In diamonds expected to have relatively low proportions of cosmogenic 3He, apparent D(3He) N a4He), with measured and inferred diffusivities at 1200°C of 1 O-l3 to lo-” cm’/s. The higher apparent diffusivities of these components indicate a difference in distribution and siting relative to the homogeneous cosmogenic component. Diffusion coefficients from repeat isothermal extractions are successively lower, possibly indicating that near-surface or dislocation sites are depleted at lower temperatures. We predict that surface-correlated helium, such as that implanted from external radioactive decays, should be easily distinguishable by studies comparing grain size separates. Helium sited in isolated inclusions may be expected to have lower effective D than cosmogenic 3He, since removal from the inclusions is the rate- limiting step in low solubility systems (TRULL and KURZ, 1993). However, this was not observed in our study. Bulk retention of trapped mantle helium over the age of most diamonds (>I Ga) would require effective diffusion coefficients at least several orders of magnitude lower than that inferred for the cos- mogenic helium component at 12OO”C, typical of mantle temperatures. INTRODUCTION THE SUBJECT OF HELIUMdiffusion in diamonds has become important in recent years, because it is relevant to discussions of the sources of helium in diamond and the helium isotopic composition of the mantle. Because of the great age of dia- monds and the high temperatures to which they are subjected in the mantle, diffusivity would need to be very low for any gas trapped in situ during formation to remain unaffected by exchange with the environment. The diamond stability field corresponds to depths greater than 150 km (COHEN and Ro- SENFELD, 1979). Thermobarometry of several diamonds containing garnet inclusions suggest crystallization temper- atures of 900-1400°C (BOYD et al., 1985), consistent with temperatures expected at such depths and pressures (CLARK and RINGWOOD, 1964). Additionally, the presence of inclu- sions containing magnesiowustite (cf., HARRIS, 1992) stable at 224 GPa and 2r 16OO”C, gives evidence for production of some diamonds at depths greater than 670 km (RINGWOOD, 1989). The crystallization ages of most diamonds appear to be much older than the kimberlites in which they were erupted (RICHARDSON et al., 1984), suggesting very long upper man- * Present address: Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, USA. t Present address: Geophysical Research Center, New Mexico In- stitute of Mining and Technology, Socorro, NM 8780 I, USA. *Present address: Battelle Pacific Northwest Laboratories, P.O. Box 999, Richland, WA 99352, USA. tie/lower crust residence times on the order of one to several Ga. BURGESSet al. (1992) recently showed that 40Ar-39Ar dating of syngenetic inclusions can erroneously give the age of kimberlite eruption, or an intermediate date, rather than the diamond age. They attributed the phenomenon to loss of argon when the diamonds were cleaved to expose the in- cluded mineral prior to analysis. This would occur if the high temperatures of the mantle caused radiogenic argon to diffuse to the diamond-inclusion boundary, so that only the argon produced since the end of the heating (e.g., the kimberlite eruption) remained inside the included mineral grain. With this in mind, HARRIS (1992) summarized the reliable dia- mond ages as 0.99-l .67 Ga for diamonds with eclogitic in- clusions, and 3.2-3.3 Ga for peridotitic diamonds. So far, only the Premier kimberlite gives overlapping ages between the diamond and its host rock, and in this case, HARRIS (1992) argues from nitrogen aggregation characteristics that the dia- monds are xenocrysts even at Premier. Thus, all diamonds dated so far are extremely old, and they have spent a signif- icant amount of time in the upper mantle/lower crust prior to emplacement. Both ofthese factors place rigorous demands on the retentivity of gases in diamonds if the original mantle component is to be retained. Several diffusion experiments have been undertaken for helium in diamonds. However, the results span a wide range in diffusivity. LUTHER and MOORE (1964) found a diffusivity of - 3 X lo-’ cm2/s at 1250°C for helium in irradiated syn- thetic diamonds. This very high value is almost certainly due to radiation damage of the matrix during the irradiation of 1747
Transcript
Pergamon Geochimica et Cosmochimica Acta, Vol. 58, No. 7, pp. 1747-1757, 1994
Copyright 0 I994 Elsevier Science Ltd Printed in the USA. All rights reserved
0016-7037/94 $6.00 +.OO
Helium isotope diffusion in natural diamonds
R. C. WIENS,* D. LAL, W. RISON,+ and J. F. WACKER*
Geological Research Division, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093-0220, USA
(Received April 22, 1993; accepted in revisedform December 2, 1993)
Abstract-Stepped heating experiments in the range of 1200- 1700°C were performed on terrestrial dia- monds, some containing substantial cosmic ray-produced 3He, in order to study the diffusion coefficients and release characteristics of ‘He and 4He. Cosmogenic 3He is shown to be much more retentive than 4He in the same sample, with as little as 0.3% of the total 3He, and up to 27.4% of the 4He released by 1700°C from diamonds in which cosmogenic ‘He predominates (bulk 3He/4He = 176 RA). A tentative determination, from the data, of the site activation energy for cosmogenic ‘He gives - 150 kJ/mol. The diffusion equation, with Do = 6.1 X lo-” cm’/s, yields an extrapolated diffusivity at 1200°C of 1.9 X 1 O-l6 cm*/s.
Other helium components are difficult to distinguish from each other by their apparent diffusion coefficients. In diamonds expected to have relatively low proportions of cosmogenic 3He, apparent D(3He) N a4He), with measured and inferred diffusivities at 1200°C of 1 O-l3 to lo-” cm’/s. The higher apparent diffusivities of these components indicate a difference in distribution and siting relative to the homogeneous cosmogenic component. Diffusion coefficients from repeat isothermal extractions are successively lower, possibly indicating that near-surface or dislocation sites are depleted at lower temperatures. We predict that surface-correlated helium, such as that implanted from external radioactive decays, should be easily distinguishable by studies comparing grain size separates. Helium sited in isolated inclusions may be expected to have lower effective D than cosmogenic 3He, since removal from the inclusions is the rate- limiting step in low solubility systems (TRULL and KURZ, 1993). However, this was not observed in our study.
Bulk retention of trapped mantle helium over the age of most diamonds (>I Ga) would require effective diffusion coefficients at least several orders of magnitude lower than that inferred for the cos- mogenic helium component at 12OO”C, typical of mantle temperatures.
INTRODUCTION
THE SUBJECT OF HELIUM diffusion in diamonds has become important in recent years, because it is relevant to discussions of the sources of helium in diamond and the helium isotopic composition of the mantle. Because of the great age of dia- monds and the high temperatures to which they are subjected in the mantle, diffusivity would need to be very low for any gas trapped in situ during formation to remain unaffected by exchange with the environment. The diamond stability field corresponds to depths greater than 150 km (COHEN and Ro- SENFELD, 1979). Thermobarometry of several diamonds containing garnet inclusions suggest crystallization temper- atures of 900-1400°C (BOYD et al., 1985), consistent with temperatures expected at such depths and pressures (CLARK and RINGWOOD, 1964). Additionally, the presence of inclu- sions containing magnesiowustite (cf., HARRIS, 1992) stable at 224 GPa and 2r 16OO”C, gives evidence for production of some diamonds at depths greater than 670 km (RINGWOOD, 1989).
The crystallization ages of most diamonds appear to be much older than the kimberlites in which they were erupted (RICHARDSON et al., 1984), suggesting very long upper man-
* Present address: Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125, USA.
t Present address: Geophysical Research Center, New Mexico In- stitute of Mining and Technology, Socorro, NM 8780 I, USA.
*Present address: Battelle Pacific Northwest Laboratories, P.O. Box 999, Richland, WA 99352, USA.
tie/lower crust residence times on the order of one to several Ga. BURGESS et al. (1992) recently showed that 40Ar-39Ar dating of syngenetic inclusions can erroneously give the age of kimberlite eruption, or an intermediate date, rather than the diamond age. They attributed the phenomenon to loss of argon when the diamonds were cleaved to expose the in- cluded mineral prior to analysis. This would occur if the high temperatures of the mantle caused radiogenic argon to diffuse to the diamond-inclusion boundary, so that only the argon produced since the end of the heating (e.g., the kimberlite eruption) remained inside the included mineral grain. With this in mind, HARRIS (1992) summarized the reliable dia- mond ages as 0.99-l .67 Ga for diamonds with eclogitic in- clusions, and 3.2-3.3 Ga for peridotitic diamonds. So far, only the Premier kimberlite gives overlapping ages between the diamond and its host rock, and in this case, HARRIS (1992) argues from nitrogen aggregation characteristics that the dia- monds are xenocrysts even at Premier. Thus, all diamonds dated so far are extremely old, and they have spent a signif- icant amount of time in the upper mantle/lower crust prior to emplacement. Both ofthese factors place rigorous demands on the retentivity of gases in diamonds if the original mantle component is to be retained.
Several diffusion experiments have been undertaken for helium in diamonds. However, the results span a wide range in diffusivity. LUTHER and MOORE (1964) found a diffusivity of - 3 X lo-’ cm2/s at 1250°C for helium in irradiated syn- thetic diamonds. This very high value is almost certainly due to radiation damage of the matrix during the irradiation of
1747
1748 R. C. Wiens et al.
Tabk 1. ‘He and %e cmcmtmtions, )He/+He ratios, and dimision coef!kh?ats for applicable steps, in
Temp. Time
(“C) (min.)
Aust. (295 mpt+ 1300 61
1300 36
13w 36
1700 36
1700 36
17&l 36
1900 Cornbusts
1900 Combust 45
19iW Combust 45
Total aas tvleased
CDM-5 cl26 a@ 1300 71
1500 41
1700 31
1900 Combust 30
1900 Combust 45
1900 Combust 45
1900 Combust 45
19M3 Combust 45
Total aas released
S. Afr. (219 mpf 1300 61
1300 40
1300 36
1700 36
1700 36
1700 36
1900 Combust 45
1900 Combust 45
1900 Combust 45
Totat aas reiea~+
48 __
__
_I
12
22
44
__
__
-_
__
85 43
87 51
69 56
73
__
__
66
-
__
86
73
“.
56
72
B
1300 61 27
17w 38 7
1700 36 55
1700 36 66
1900 Combust 45
1900 Combust 45
1900 Combust 45
TV
9
1
25
37
0.0121 ~0.0017
___
__. ___
3.4 x 10.” _- __
* 1.1 __ __ ._
-_ __ __ -. __
0.0829 ~0.0021
0.041 +0.003
0.0139 *0.0014
1.16 20.03
2.55 to.13
0.1364 -+O.W68
4.00 i.13
.__ 3.6 x 10‘” -- --
___ + 0.3
3.8 x 1O-‘3 _-
0.0093 +o.w/1
0.0443 +0.0075
0.2120 * 0.0042
0.0184 +0.0029
OLX?4 LO12
__ t 0.5
1.6 x lo-‘” 7.1 x l@ 0.48 f 0.3 (0.4-21r 20.37
0.028 + 0.005
0.0831 t O.w46
0.096 iO.016
o.oso7 z0027
0.0045 0.035 lro.O#2 to.017
0.0039 0.019 + 0.003 1 +0.016
0.0117 0.038 * 0.0020 * 0.053
0.0030 1.66
2 0.0030 i 0.23 0.0133 16.57
+o.KJ49 20.33 0.0075 7.80
t0.0045 20.16 0.0110 0.109
*OX@41 +0.019 0.0589 1.799
+0.0088 kO.018 0.114 28.03
LO13 f.41
5.1 x 10’s 4.7 x 10’6 5.5 (0.5-15) (1.3-11) 24.7 2.2 x lir= 1.2 x ruu 3.4
(0.15-6.4) 2.2 x 10”
(0.07-3.6) 23.9 5.4 x lo-” 2.3
+ 1.5 (<a.) k3.2 400
+4!xi 890
2330 740
*440 7.1
r1.3 21.8
23.3 176
fZ0
0.0057 +0.0018
___
0.0064 ~O.OC96
0.014 ~0.010
___ .__
8.3 x lO= 5.8 x lo-*’ 0.8 (4.0-14) (C36.) * 1.5
-_ 7.8 x 10” -- (0.7-31)
._ _I __
0.0076 +0.0018
___
0.0067 to.0094
0.015 +0.010
I. .__
6.2 x w 7.6 x I@ 0.6 (3.4-11) (<36.) 21.4
__ 2.4 x 10” -- (0.15-8.8)
-. -_ _.
0.5226 0.064 203 *0.OU23 to.012 f 0.43
0.0772 0.367 3.40 * 0.0093 *0.011 + 0.42
0.0097. 0.0527 4.1 f o.w27 f 0.0058 il.3
0.122 0.526 3.07 *AI10 i.026 Lt.29
0.0452 0.417 7.1 x lo’” 8.3 x lo’” 6.59 *0.0027 t0.025 + 0.7 + 1.1 + 0.56
0.221 2.91 4.4 x 10‘” 8.9 x I@‘* 9.41 *0.CX?4 to.17 % 0.8 If 1.1 + 0.58
0.0136 0.127 5.5 x IO-” 7.9 x 1P 6.1 ~O.wJ20 +0.022 (4.1-6.6) t 1.5
* Blank contribution as a percentage of the total gas released for each temperature ste P
up to combustion. For combustion steps blan!a did not constitute more than 30% for ‘He or 6% for He of the total gas released. Where the blank was too high lo give a meaningful result, the percent blank is not given.
’ Grain diameters were 50-lOO/rm (mean = 80pm) unless noted otherwise. All diamonds are industrial
( grade except Braz-1 and Russ-l, as noted (see text). Numbers given in parentheses represent the range of uncertainty. All uncertainties are given at the one- sigma level.
’ Oxygen was present for the 1900 ‘C steps to complete the He release. Samples were graphitized and . . partially cornbusted (see text). Combustion times are irrelevant to the diffusion results.
The Zaire-2 portion used for combustion was a fresh aliquot of the same sample. so that the combustion represents the total concentration for this sample.
1750 R. C. Wiens et al.
the boron-doped diamonds to produce in situ helium for the diffusion measurements. GOBEL et al. (1978) calculated a D/a2 of - 10M6 for cosmogenic 3He in ureilite diamonds of radius < 1 Nrn, giving a diffusivity of < lO-‘4 cm*/s at 1230°C. LAL et al. (1987b) measured diffusivities of lo-” cm2/s at 1200°C for naturally occurring helium in terrestrial dia- monds, and 1.4 X 10-‘” cm’/s for a diamond soaked in an ambient helium atmosphere at 1250°C.
On the other hand, HONDA et al. (1987) concluded that helium is practically immobile in diamonds on terrestrial time scales because only 3.4% of the helium from one sample was released in two 30 min steps below the graphitization temperature of - 1900°C. KURZ et al. (1987) concluded that significant diffusion was unlikely to occur within diamonds because substantial heterogeneity was observed between var- ious fragments of the same diamond. These would have pre- sumably equilibrated if diffusion was significant. OZIMA ( 1989) suggested that all helium degassing is related to graph- itization, with microscale graphitization occurring at lower temperatures, preceding bulk gmphitization. If this is true, then the release of gases is a process of decrepitation, not related to diffusion. However, simple extrapolations of the data from higher temperatures to 1300°C, giving apparent diffusivities of - lo-r9 cm’/s, have been used for some time now to argue that p~mordial helium has been quantitatively retained in diamonds (OZIMA and ZASHU, 1988; OZIMA, 1989).
In addition to gas trapped during diamond formation, re- cent studies have conclusively shown that helium in diamonds arises from several sources. Cosmic ray intemctions produce substantial amounts of 3He in alluvial diamonds (LAL et al., 1987a). Some 4He is also implanted in diamonds from decay of nearby radioactive elements after crustal emplacement (LAL, 1989; KURZ et al., 1987; MCCONVILLE et al., 1991). This is thought to be a small (though signifi~nt) addition to the original trapped helium component, and may occur mostly in alluvial diamonds (LAL et al., 1989; MCCONVILLE and REYNOLDS, 1989; WIENS et al., 1990).
The purpose of our work was to gather a larger database on tem~ratu~ releases of naturally occurring helium in dia- monds, in order to (1) study the lower temperature regimes (1200-l 3OO’C) which are similar to mantle conditions and maximum crustal metamorphism temperatures, (2) study the nature of helium release when a diamond sample was main- tained at a certain temperature for several extractions (to determine whether gas release actually followed classical dif- fusion laws), and finally (3) study the release characteristics of cosmogenic 3He in contradistinction to other helium com- ponents, mostly by way of 4He. For this we picked samples with diverse helium sources and contents: CDM-5 and S. Leone-C were known to contain large 3He concentrations (LAL et al., 19891, while the rest were expected to have pri- marily mantle 3He/4He ratios modified partly by additions of radiogenic 4He and/or cosmogenic 3He.
EXPERIMENTAL
The diamond samples in this study were industrial grade, with the exception of samples designated Braz-1 and Russ-l, which were jewel quality. The exact locations of the samples are unknown, due in part to the proprietary nature of the industry. Samples are identified by
their country of origin (Australia, South Africa, Sierra Leone, Zaire. Brazil, and Russia), with the following two exceptions: CDM-5 is from Consolidated Diamond Mines, which has operations on various beaches in Namibia between the Orange River and Luderitz; and this diamond is almost certainly from an alluvial deposit. EMB dia- monds are predominantly from Zaire (LAL et al., i 989).
Samples were crushed lightly to 300-400 pm and inspected under stereo microscope to remove all identifiable inclusions, The selected portions were then ground to different sizes given in Table 1, in most cases to 50-100 pm diameter. The crushed diamonds were loaded into tantalum tubes which had been previously outgassed at 1900°C for 10 min. Gases were extracted from the diamonds by resistance- heating in a Bieri-type furnace (CRAIG and LUPTON, 1976) at the temperatures and for the time intervals given in Table 1. Temperatures were calibrated using a thermocouple wire and are estimated to be accurate to ?lOO”C. All steps at 1900°C were done in the presence of oxygen from hot CuO in order to remove the remaining helium. The oxygen partial pressure was increased with each successive step at 1900°C up to - I50 Pa for the last step, although the partial pressure in contact with the samples may have been slightly lower, due to oxidation of the tantalum and diamond surfaces. Active gases were gettered with titanium sponge material, and the remaining gases were split into two equal fractions and removed in 1720 glass breakseals. The extraction system was made of stainless steel, except for an in- line diffusion pump and Toepler pump, which were of 1720 glass; for further details see LAL et al. (1989). Helium isotope analyses were made on the ‘He/“He mass spectrometer GAD (CRAIG and LUPTON, 1976). Concentrations were determined by calibrating mass spec- trometer sensitivity daily, matching the measured abundances using known amounts of helium. Blanks were extracted and calibrated using exactly the same procedure as the samples.
RESULTS
The results are given in Table 1, and include earlier data on some diamonds (LAL et al., 1987b). Estimated uncertain- ties on measured 3He/4He ratios are lower than +5%. Hot blanks were 0.0029-0.0038 FCC ‘He with a ‘He14He ratio of 1 .O R, (= air isotopic ratio). Blanks accounted for relatively large fractions of the total gas released in some cases due to the small sample releases at temperatures below 1900°C, il- lustrating the difficulty of this type of study. Relative blank cont~butions to the 3He and 4He releases are given in Table 1. One-sigma uncertainties given for the sample totals take into account signal and discrimination uncertainty, as well as uncertainty associated with the blank subtraction, but do not include systematic sensitivity uncertainty, which is ac- curate to -f 10% absolute, but should not vary from sample to sample. Effective diffusion coefficients are also given in Table 1 for both isotopes, determined by the equations given in the Appendix. Diffusivities were not determined for the 1900°C steps, as a phase transition (graphitization) took place, facili~ting nondiffusive gas release; the sole purpose of these 1900°C steps was to complete the gas release in order to determine the diffusion coefficients for the noncombustion steps. Observations made from the data follow.
Gas Release Patterns
Figure 1 shows the cumulative gas release patterns for 3He and 4He from the CDM-5 diamond, which has the highest bulk 3He/4He ratio, at 176 RA (e.g., times the air ratio of 1.399 + .013 X lo-$ MAMYRIN et al., 1970). At 1700°C only 0.3% of the total 3He had been released from the dia- mond, while 17.6% of the 4He had already been released. In the S. Leone-C diamond which, at 19.05 RA has the second
Diffusion of He isotopes in diamonds 1751
1300 1400 1500 1600 1700 1800 1900
Temperature ("C)
FIG. I. Cumulative helium release of each isotope as a function of temperature for the CDM-5 diamond, which had the highest bulk 3He/4He ratio, at 176 R,. A much lower proportion (only 0.3%) of the 3He is released below graphitization at 1900°C than 4He.
highest bulk 3He/4He in this study, the difference is not as
spectacular: 12.6% of the 3He and 27.4% of the 4He released by 1700°C. Thus, in the samples with the highest bulk 3He/4He ratios, 3He is much more retentive than 4He. Samples with lower ‘HerHe ratios have more similar release patterns be- tween the two isotopes. The gas fraction released at or below 1700°C has a mean of 2 1% for 4He and 32% for 3He for all samples in Table 1. Though this parameter is obviously only
qualitative due to the differences in temperatures, durations, and numbers of steps, it shows that a significant fraction of the helium is released at or below 1700°C.
Figure 2 shows 3He/4He ratios of the individual steps as a
function of cumulative 4He released for the CDM-5 and S. Leone-C diamonds. The 3He/4He ratio for an individual combustion step of CDM-5 goes as high as 1.25 X 10d3, or 890 RA. This is a factor of several above the solar helium
ratio of -280 Rn, an order of magnitude greater than the
CDM-5 Combustions
0.003 0.01 0.03 0.1 Cumulative 4He (186 ccSTPlg1
30 1 S. Leone-C m 1
0.03 0.1 0.3 1 Cumulative 4He (10-G ccSTP/p)
FIG. 2. 3He/4He ratios vs. cumulative 4He release for (a) the CDM- 5 diamond and (b) the S. Leone-C diamond. The combustion steps, shown as open circles, were at 1900°C.
so-called planetary ratio found in meteorites, and a factor of 30 higher than the highest 3He/4He ratio measured in other
mantle-derived rocks (cf., also, ZADNIK et al., 1987). LAL et al. (1987a) showed that using ‘*Be that cosmic ray production can account for a significant faction of the 3He in diamonds
having 3He/4He ratios of only several RA. This suggests that well over 90% of the 3He in CDM-5 is cosmogenic. This assumption allows some observations to be made on the dis- tribution and/or sites of the ‘He by comparison. Since cos-
mogenic 3He is produced on the surface of the earth to a depth of several meters, and is produced from the carbon the diamond is made of, it should be ubiquitous and completely random within the C matrix. If 4He were similarly sited and had a similar distribution, a plot of 3He/4He vs. 4He would
be nearly flat, with initial ratios very slightly above average because of the mass effect. Instead of being flat, the differences
between steps in Fig. 2 are so great that a linear scale will not suffice. Because the 3He/4He ratios start much lower than the bulk average values, a large proportion of the 4He must
be located near the surface or near defects, where diffusion pr~umably occurs more readily. After reaching a maximum single step 3He/4He ratio of 890 RA, the final combustion steps of CDM-5 show a drop in 3He/4He in Fig. 2a, indicating
higher retentivity for about half of the 4He. Combustion steps for S. Leone-C (Fig. 2b) are above the bulk ratio except for the last step, which has very little gas. KURZ et al. (1987)
noted that, for diamonds mined at -40 m depth from the Orapa kimberlite pipe, in nearly every case, the last com- bustion step had the highest 3He/4He, often dramatically
higher than the first combustion step. In their case the effect was not due to cosmogenic 3He.
Effective Diffusion Coefficients
Figure 3 shows effective D(3He) and D(4He) values from Table 1 plotted against each other for temperatures between
hii 3 -15
d
-16
-17
* CDM-5 0 S.L.-c a Aust. 0 S. Afr. 0 Zaire-2 + EMB = Russ. A Braz. c Others
4
-13 -1% -11 -10 -9 -8
Log [D(*H~) (cm2/s)]
FIG. 3. Diffusion coefficients o(3He) vs. o(4He) for 1200- 1700°C temperature steps ofthe diamonds given in Table I. The line ofequal diffusivity is also shown. Samples for which all extractions are at or above 1500°C are represented by filled symbols, while those with at least some extractions below 1500°C are represented by unfilled symbols. Samples represented by filled circles are S. Leone-A, S. Leone-B, and Zaire-l (S.L.-C stands for S. Leone-C). Where more than one extraction was done at the same temperature for a given sample, the mean If: std. dev. was plotted. Error bars in other cases represent one-sigma uncertainties in the diffusion coefficients from each extraction.
1752 R. C. Wiens et al.
1200 and 1700°C. The spread in D(‘He), plotted over eight orders of magnitude, is noticeabiy greater than D(4He). Cos- mogenic ‘He has very low diffusion coe%cients, as evidenced by the fact that CDM-5 is nearly three orders of magnitude below the solid line marking D(‘He) = @4He), while a num- ber of samples, presumably dominated by other components, lie above the line. Samples with diffusion coefficients deter- mined at several different temperatures plot along lines roughly parallel to the equal diffusivity line, indicating that each sample has a characteristic ratio of ~3He)/~4He).
= 1.0
iti ~--(--- m i
2 0.0 __i_&__-_ h
l
G --l.O a q
_ cd p_-2.0 c
0.1 0.3 1 3 10 30 100
3He (lo-l2 ccSTP/g)
D
$-I 1 * _ ---_____ . q
c
-4.0 ’ ’ ” I
0.1 0.3
4He (IO-:ccS’I’P/i) 10
FIG. 4. Ratio of diffusion coefficients ry3He)/ry4He) as a function of (a) ‘HePHe, (b) ‘He, and (c) 4He. Symbols and error bars are as in Fig. 3. Samples witb large cosmogenic 3He contributions and high 3He/4He ratios tend towards low m3He)/Q4He) because the ho- mogeneous distribution and lattice siting of the cosmogenic 3He is more retentive than other helium components. By contrast, samples with 3He/4He ratios significantly lower than MORB (-8 RA) tend towards higher D(‘He)/R4He) ratios due to the similar siting of 3He and ‘He, though the tendency towards q3He)/D(4He) < 1 is not we11 understood. Plots (b) and (c) show that the correlation may also hold when piotted against ‘He (c), but not for 3He (b).
=: -8 I-
5 -e ,-_===
E -IO ii 0
2 - -II
L -13 - ! Q--_
7 -12 ---z== --_= -- =R, -4 X
e -14 - ~:
M_p- ---- --__
3 -16 7 -f
-17 1 ’ I
-15 - ’ I I
0.50 0.55 0.60 0.65 0.70
looo/(T WI)
FIG. 5. Arrhenius plots for ‘He (a) and 4He (b). Symbols are as in the preceding figures. Lines are drawn more as visual aids than to define linear correlations, as more than two temperature steps would be needed to verify such correlations. The spread over several orders of magnitude in diffusivities at a given temperature indicates that different components with different distributions and sites are being compared. In spite of this, there is no evidence for different slopes between upper and lower temperature regimes. In (a) the data for S. Afr., S. Leone-C, and Aust. (1700°C) are nearly coincident. The three points available for CDM-5 (stars), at least for “He (a), are nearly collinear, and an activation energy of 150 kJ/mol is given as a tentative value for cosmogenic 3He in diamond. The extractions at 1200- 1300°C show, without the need for extra~lations, that at least some He components are mobile in diamonds at mantle temperatures.
Figure 4 shows these ratios of diffusion coefficients, Q3He)/ Q4He) vs. ‘He14He (a), 3He (b), and 4He (c). Bulk helium concentmtions and ratios are used in all cases. The most obvious feature is a possible trend, best seen in Fig. 4a, towards low D(3He)/D(4He) with high 3He/4He. This trend crosses the horizontal line ofequal diffisivity at roughly the MORB ‘HetHe value. The trend does not hold when plotted as a function ofbulk 3He (Fig. 4b), but it may hold for 4He (Fig. 4~). CDM- 5 is the lowest sample on all three plots. S. Leone-C again shows the same tendencies as CDM-5, though to a lesser degree.
Figure 5 shows Arrhenius plots of Q3He) (a) and q4He) (b) vs. l/T. At a given temperature, there is a spread of over six orders of magnitude for 3He (a), and for 4He (b), over four orders of magnitude. Apparent diffusion coefficients in the 1200-l 300°C range are between lo-” to lOwi6 cm’,% for 3He, and lO-‘O to 10-15 cm”/s for 4He. General trends between low and high temperature steps are roughly parallel, as in- dicated by the lines, drawn as visual aids, connecting data from the same samples. With sufficient gas to carry out ex- tractions at intermediate steps, it would be possible to confirm whether linear correlations existed for the samples, yielding activation energies, as will be discussed later. However, from
Diffusion of He isotopes in diamonds 1753
the present data, with the exception of the 17OO’C step of temperatures. The opposite is true if D(4He) > D(3He) in the Braz., there is no evidence for a change in the general slope initial step. These observations are suggestive of heteroge- between the low- and high-temperature results. neous 4He and/or 3He distributions (cf., KURZ et al., 1987).
DISCUSSION Observations on Successive Extraction Steps
For some ofthe samples, the temperature was held constant over several successive extractions to determine whether the effective diffusivity would yield a constant value. Although data in Table 1 are limited because of insufficient gas releases in some of the repeat extractions, data from S. Leone-C, Zaire- 1, and 4He data from Australia give slightly decreasing diffusion coefficients with time at constant temperature. Zaire-2, which was held at 1200°C for 12 h, shows a one and one-half order-of-magnitude decrease in D(3He), the greatest observed. It appears from the evidence that this is an outlier, because the step at 1360°C gives a lower diffusivity. For the remaining samples, it is difficult to assess the significance of this effect, though we note that the only exception to the trend is with 3He in the South African sample between the two sets of steps which were above blank level.
Distribution of Helium Components
It is crucial to point out that the homogeneity of, and in cases ofinhomogeneous distributions the location of, helium within the diamond strongly affects the apparent diffusion coefficients as determined by stepped heating. The determi- nation assumes a homogeneous distribution of atoms within the sample, but heterogeneous distributions of helium in dia- monds have been discovered (KURZ et al., 1987) and can also be inferred from the gross changes in 3He/4He between extraction steps (Fig. 2). We must, therefore, discuss the dis- tribution and sites of helium attributed to various components before we can make any conclusions about their apparent diffusion coefficients.
Cosmogenic ‘He TRULL et al. (1991) and TRULL and KURZ (1993) discuss
the phenomenon of differing isothermal diffusion coefficients in detail. Downward-trending diffusion coefficients, occurring when nearly all of the gas is depleted from the sample can be attributed to grain-size variations, as the smaller grains exhaust their gases before the larger grains are completely depleted. Variations in shape from the assumed sphericity should produce only small variations in effective D. Samples with porous structures or fractured grains may also cause D to drop with successive isothermal extractions. In our case, the gas depletion fractions were not large-S. Leone-C: f4 = 27%, f3 = 13%; Zaire-2:f4 = 37%,f, = 61%; Zaire-l:_& = 5 I%-except 3He in Zaire-l cf3 = 9 l%), so none except the last one can be attributed to grain-size variations. Dia- monds are not porous, though diamond coats can be fibrous, and often contain submicron inclusions (GUTHRIE et al., 199 1). The coats may be less retentive than interior portions of the diamond, while the inclusions may be significant sources of helium. Another possibility is that the helium re- leased in these steps was implanted into the diamond by nu- clear recoils from neighboring radioactive minerals. However, as will be discussed later, this is unlikely to be the source of much 3He. On the other hand. 3He appears to be depleted more quickly than 4He in at least some cases, as it is observed that 3He/4He ratios decrease slightly in successive same-tem- perature steps, and also as temperature is increased below graphitization. This is most easily seen in the 1700°C steps of S. Leone-C (Fig. 2b). Lastly, since it is a high-pressure mineral, the temperature steps might possibly induce relax- ation along dislocations in the diamond, thereby expelling gases in the vicinity ofthe dislocation. Additional extractions at the same temperature would not, in this scenario, release nearly as much helium as the first extraction.
As mentioned earlier, cosmogenic 3He should be ubiqui- tous and completely random within the diamond matrix. Diffusivities determined from stepped heating should thus be reliable for cosmogenic 3He in samples in which it dom- inates.
Implanted 4He (and ‘He)
Helium implanted into the diamond from radioactive de- cays in the surrounding rock is located within the outer layer of the diamond, with a sharp gradient of decreasing concen- tration inward from the surface. Because it is located only near the surface, the effective diffusion coefficient for the im- planted component depends on the grain size used for dif- fusion calculations, as illustrated in Fig. 6. For a grain that is large (Fig. 6a), relative to the mean implantation depth of - 17 pm (LAL, 1989) the apparent diffusivity would be very high, since the helium would be depleted much sooner than if it were distributed homogeneously. But if an implantation- dominated sample is crushed to a size comparable to the mean ol-implantation depth, the 4He distribution would ap- pear homogeneous relative to the new grain boundaries (Fig. 6b), and diffusion coefficients determined using the new radii would approach the actual diffusion coefficient. Unless ra- diation damage became significant, one would intuitively ex- pect this rate to be the same as cosmogenic ‘He, since im- planted helium would approach a random distribution. Con- firmation of this effect would require a separate study using grain size separates.
In situ radiogenic 4He
In addition to the observations of D on repeat isothermal extractions, diffusion coefficients for the two helium isotopes become more disparate with subsequent steps, whether or not they are at the same temperature. If D(3He) > D(4He), Dt3He) has less tendency to decrease in successive same-tem- perature steps, and increases more rapidly in going to higher
4He produced from radioactive decays of uranium, thorium within the diamond itself is distributed around the inclusion(s) containing the parent elements. The same is true for any 3He produced by neutron capture by lithium or boron within the diamond, as discussed below. The mean distance from the inclusions will be on the order of tens of microns, similar to implanted ‘He. Whether this can be considered a homoge-
1754 R. C. Wiens et al
FIG. 6. An illustration showing how helium implanted from ra- dioactive decays in the surrounding matrix can give incorrectly high apparent diffusivity in diamond fragments that are large relative to the mean implantation depth of - 17 Frn. The diffusion calculation assumes helium is randomly located within the spherical grain. Since the actual path length in (a) is much shorter on average than for a grain with a homogeneous distribution. the result yields an incorrectly high diffusion coefficient. If the same grain is crushed to fragments at least as small as the mean implantation depth, as in (b), the diffusion calculation based on the new (crushed) grain diameter will yield a correct result for implanted radiogenic helium.
neous distribution depends on the number and distribution of the inclusions containing the parent elements and the size
of the diamond fragments used in stepped heating.
Trapped helium
Helium trapped during diamond formation in the mantle will partition between dissolution into lattice sites and en- trapment in inclusions, vesicles, and other lattice imperfec- tions. The solubility of helium in diamond is very low, at 20 f 2 pee/g atm. at 1250°C (LAL et al., 1987b), very close to the 22 t&g estimated for olivine (TRULL and KURZ, 1993). This is probably an upper limit for diamond, because diffusion into inclusions during such a soak experiment is possible. From the solubility data, if a 2 mm diamond formed with a
35 pm gas inclusion, at least half of the original mantle helium would be trapped in the inclusion, with the rest dissolved in
the lattice. This size inclusion might go unnoticed by normal inspection, so that it is easily possible that a significant fraction of the trapped mantle component is sited in inclusions. KURZ et al. (1987) concluded that most of the 4He in diamonds was sited interstitially rather than in vesicles or inclusions, since crushing a diamond liberated only 10% of the 4He. However, the KLJRZ et al. (1987) experiment only crushed the diamond to ~200 pm, so that a number of inclusions of,
e.g., -35 pm or smaller, could have remained unbreached. If a significant fraction of the trapped mantle component
is sited in vesicles or inclusions, the distribution of this com-
ponent will be determined by the distribution of vesicles and inclusions. In some octahedral diamonds, numerous small inclusions are found near the surface, in coats (GUTHRIE et al., 1991). Coats have also been found to contain higher noble gas concentrations than interior diamond sections (OZIMA and ZASHU, 199 l), suggesting that near-surface inclusions carry the bulk of the gas. If this is true, then apparent diffu- sivities determined for this component by stepped heating of
grains which are large in comparison to the distribution of
near-surface inclusions will yield a high effective diffusivity,
similar to the case illustrated in Fig. 6 for implanted 4He. If the effective diffusivity is used to estimate the retention time, the short diffusion path length is automatically taken into consideration.
Helium d@iusin~ into the diamond subsequent to formation
The helium soak experiment which established the helium
solubilily (LAL et al., 1987b) showed unequivocally that he- lium can diffuse into diamonds, whatever the eventual sites are. However, it is unclear whether diamonds experienced
high enough ambient helium concentrations, and at suffi- ciently elevated temperatures, for this to occur at some time subsequent to their removal from the original formation en- vironment in the mantle.
Proportions of the Components
LAL (1989) has shown that 4He implantation from the surrounding kimberlite matrix is, on average, a larger effect than in situ radiogenic production ifthe diamond has resided in the crust for a significant fraction of its lifetime. This as- sumption may not be true, given the ages of most diamonds
(BURGESS et al., 1992; HARRIS, 1992). However, it was also shown that implantation can account for the bulk of the 4He when crustal emplacement ages exceed - 10’ years (LAL, 1989). Unfortunately, kimberlite ages for the diamonds in this study are not known, and in general, these ages are often indeterminable for alluvial diamonds, unless the kimberlite
source can be identified. Further, the distribution of uranium and thorium in kimberlite is typically very heterogeneous, as pointed out by MCCONVILLE et al. (1991). As a result, it is difficult to know what proportion of the 4He is due to implantation, even given the age of a particular kimberlite.
For ‘He, the nuclear reactions 6Li(n, cu)T + 3He and “B(n, T + 3He)9Be can be invoked as sources within the crust (the
nuclear reactions “C(n, 3He)‘oBe and “C(n, T + ‘He)“B responsible for cosmogenic 3He have too high thresholds, at
19.5 and 18.9 MeV, respectively, for reaction with uranium and thorium fission-produced neutrons). Neutron fluxes are
thought to be much lower in the mantle, so that only crustal residence times are significant to first order. For the 6Li re- action, crustal production estimates range from 0.8 X lo-l5 cc/g/Ma (HONDA et al., 1987) to 3.3 X IO-l5 cc/g/Ma (KURZ et al., 1987; cf., also LAL, 1989). For the boron reaction, HONDA et al. (1987) estimated a production rate of 1.4 X lo-” cc/g Ma, which they decided was insignificant. During 100 Ma or more of crustal residence time, which is typical for kimberlite ages, the lithium reaction could account for a significant fraction of the 3He in diamonds with low concen-
trations, such as Aust, S. Afr., and Russ- 1. The same reaction could generate 3He either in situ or as implanted 3H near the surface of the diamond. However, the above estimates of Li- produced 3He assumed concentrations of up to 1 ppm lith- ium. While this is typical for kimberlites, the only measure- ments of lithium in diamonds are much lower. LAL (1989) reported 170 ppb lithium in inclusion-rich Zaire diamonds. The PHINNEY (1988) ion probe analyses of some of the same diamonds studied in HONDA et al. (1987) gave between 0.14
Diffusion of He isotopes in diamonds 1755
and 2.75 ppb, several orders of magnitude too low for sig- nificant in situ production. In addition, LAL (1989) points out that for implantation, given average lithium, uranium, and thorium concentrations, the 3HepHe production ratio should be -3 X 10m9 (e.g., -0.002 RA), much lower than any diamond analyzed to date.
Figure 4 shows that there are a number of samples with 3He/4He c MORB which have higher effective D(3He) than D(“He). If 3He and ‘He atoms diffused from the same sites, the expected difference in the relative diffusion coefficients due to the mass difference is insignificant on a logarithmic scale. and accounts for only 0.06 log units in Fig. 4 (CRAIG and LUPTON, 1976). Thus, the scatter above the R3He)/ D(4He) = 1 line must be due to some effect other than the mass difference between the isotopes. What is needed to ex- plain this is either a reservoir of ‘He nearer the surface than the bulk of the 4He, or a reservoir with higher 3He/4He in sites with lower activation energy. It is very likely that cos- mogenic helium is not such a source, since samples with high 3He concentrations and high bulk 3He/4He do not show this behavior. LAL (1989) pointed out that the m~imum im- plantation depth for 3He (via ‘H) is -25% greater than for 4He, so that implantation of both isotopes should give the opposite effect on D(3He)/I?(4He). A trend to high o(3He) could be explained for small grain sizes if these samples con- tained significant implanted 4He, which diffused more slowly than 3He sited in near-surface inclusions. However, Braz-1 and Russ- 1, which have extraction grain sizes orders of mag- nitude larger that the mean implantation depth, and larger than the other samples, are among the samples with log [D(3He)/D(4He)] > 0. Another possibility is that these samples experienced a high-3He environment immediately before re- moval from high temperature regimes, allowing higher ‘He/ 4He to be frozen in near the surface. However, why such a mantle regime would have higher 3He/4He than the region of diamond formation is unclear.
Retention of Helium in Diamonds
In mineral samples containing a large amount of gas, mul- tiple components can be distinguished when the slope on the Arrhenius plot changes, as successive com~nents with char- acteristic sites and corresponding activation energies become dominant for a few temperature steps and then are depleted, leaving another component to dominate the gas release. With very low gas amounts ne~e~i~ting a very limited number of temperature steps, such a study is difficult, to say the least. With only two or three temperature steps, gas components are unlikely to deplete completely prior to the final steps. For all but 3He in CDM-5, the samples are likely to contain a mixture of gas components from different sites, so that the activation energy would not represent any one component. The very high 3He/4He ratio in this sample indicates a good likelihood that effectively all of the 3He is cosmogenic. The three data points for 3He in CDM-5 (Fig. 5b) are very nearly collinear, suggesting that diffusion was from one component. The parameters of the classical diffusion equation D = DoemE’Rr are calcu!ated to be & = 6.1 X lo-” cm”,& and E = 150 kJ/mol for this component. Higher activation ener- gies would be possible if any of the 3He in the 1300- 1700°C
temperature steps was noncosmogenic. A greater number of temperature steps would bear this out. The above value is above the helium activation energies for most minerals. For example, for quartz, E, = 100 kJ/mol (TRULL et al., 1991). A number of *Ar-retentive minerals yield E, values ranging from 70- 135 kJ/mol (LIPPOLT and WEIGEL, 1988). Our ac- tivation energy is above the 46 kJ/mol in ilmenite and 130 kJ/mol in oiivine done by relatively low-fluence ( lOI cm-’ @ 20 keV) ion implantation (~TAG~M~ et al., 1993). But, it is below the 420 kJ/mol also reported for olivine (TRULL et al., 199 1; TRULL and KURZ, 1993; cf., HART, 1984) and 290 kJ/mol for diopside (TRULL and KURZ, 1993). Our value is also far lower than the loo-20~ kJ/mol activation ener- gies in diamond suggested for high-temperature extractions close to 1900°C by OZIMA and ZASHU (1988). However, at these temperatures, the onset of graphitization may affect helium release, as the authors suggest. If this is truly the case, then the release of gases is due to a phase change, rather than simple diffusion.
As mentioned in LAL et al. (1989), diamonds of 1 mm and t cm radius would require diffusion coefficients of < 10v2’ and <lo-” cm2/s, respectively, to retain helium over the - 1 Ga age of diamonds. Extrapolation of the CDM-5 3He data from 1300- 1700°C to an assumed mean upper mantle tem- perature of - 1200°C gives D(3He) = 1.9 X IO-l6 cm*,& which would give retention times on the order of a million to several million years, depending on the diffusion path length. Crustal- and surface-derived components (implanted helium and cosmogenic ‘He) would of course not have seen mantle temperatures. However, if this diffusion coefficient also applies to mantle components, it is clearly not low enough for bulk retention of helium.
In contrast to the findings reported here, TRULL et al. (199 1) reported that cosmogenic 3He diffuses much faster (by more than 10’) than other helium components in quartz and olivine samples. They suggested two possibilities; either (1) radiation damage caused higher cosmogenic 3He di&sivities, or (2) other (radiogenic and primary) helium components are somehow retarded and do not follow volume diffusion laws (TRULL et al., 199 1). Neither explanation is very satis- fying, as radiation dosages from cosmic rays are neutron- dominated, and very low in comparison to many other systems, and invoking nonclassical diffusion from a homo- geneous distribution seems ad hoc for an inert gas such as helium. TRULL and KURZ f 1993) appear to have solved their own puzzle by showing that the mobility of gas originally held in inclusions is rate-limited in its removal from the in- clusion. This is effectively controlled by the solubility of the gas in the lattice. A dimensionless gas distribution coefficient & is defined as the equilib~um ratio of concentration (by volume) in the lattice to that in the inclusion. In the case where nearly all of the gas is partitioned into inclusions due to low lattice solubility, the effective diffusion rate D’ = DZ&, where L) is the true diffusion coelhcient. For diamond F& - 10v4 (cf., LAL et al., 1987b), so that the effective diffusion coefficient from inclusions could then be as low as -2 X 1 O-*’ cm’/s at 12OO”C, according to the model. Such a system would be effectively closed under mantle temperatures and diamond ages. However, invoking inclusion-held gas as a way of retaining the trapped mantle component has further
1756 R. C. Wiens et al.
difficulties, since a greater volume of inclusions generally im- plies higher uranium and thorium concentrations, which would dilute the original gas.
The above phenomenon of lower effective D values was not observed in this study. Extrapolation of our 4He data to 1200°C yields effective diffusivities of lo-l3 to lo-” cm’/s, with one exception, Aust., which has a low D(4He) and a low 3He/4He ratio, Actual data points at 1200°C are in the 5 X 10-l’ to lo-l3 cm2/s range (Fig. 5b). These could be higher than the cosmogenic diffusion coefficient due to distribution near the surface of the sample. Or, inclusions containing he- lium could be connected to the surface through crystal defects, or dislocations, which lead to rapid release. This was suggested by KURZ et al. (1987) to explain why diamonds containing inclusions released more 4He at low temperatures, and in fact, they suggested that the bulk of the total helium is as- sociated with defect-rich zones. Defect-assisted rapid diffusion has been demonstrated in some systems (YURIMOTO et al., 1992). If helium is predominantly sited either near the surface or in defect-rich zones, it would exchange with the outside environment relatively quickly at high tem~mtures.
CONCLUSIONS
Mantle helium is only one of several helium components in terrestrial diamonds. Each of the components may have different characteristic sites and distribution patterns, and hence, different release characteristics, as indicated by our observations and discussion:
1)
3)
4)
5)
6)
Release of cosmogenic ‘He in CDM-5, an alluvial dia- mond, gives a low diffusivity of 1.9 X lo-l6 cm*/s at 12OO”C, comparable to helium in ureilite diamonds (GOBEL et al., 1978). 3He in this sample had the lowest diffusion coefficient we observed. Diffusivities of 3He span a very broad range (5-7 orders of magnitude at any given temperature between 1200 and 1700°C). The maximum observed D(3He) values are in samples that do not have a signi~cant cosmogenic com- ponent. In these samples D(3He) x D(4He). Repeat isothermal extractions tend to give lower 3He/4He ratios, slightly lower effective diffusion coefficients, and slightly more disparate apparent ~3He)/~4He) ratios. Lower D(4He) could possibly be due to significant im- planted 4He near the surface. In theory, it should be possible to identify surface-im- planted 4He by its behavior as a function of analyzed grain size, with grain sizes on the order ofthe mean implantation depth giving effective diffusivities comparable to cosmo- genie 3He. In spite of the above observations, and within the very limited number of different-temperature steps (a maxi- mum of three on one sample), Arrhenius plot slopes were nearly parallel for the samples in the temperature range studied (1 ZOO- 17OO’C). The activation energy is approx- imately 150 kJ/mol for cosmogenic 3He. This is a prelim- inary conclusion. Measured and extrapolated effective 4He diffusivities at 1200°C are in the range IO-” to 1 O-l3 cm*/s. These are much higher than the actual D for cosmogenic 3He, which is known to be homogeneously sited. They are also much
higher than the lo-” to lo-*’ cm2/s required for quan- titative helium retention over diamond ages. Helium in isolated inclusions could have effective diffusion coeffi- cients up to lo4 iower than cosmogenic, according to the model, due to its low solubility and the rate-limiting func- tion that solubility plays in slowing the removal of gas from inclusions. Such low diffusion coefficients were not seen in our samples. It seems, therefore, that either non- cosmogenic helium in diamonds is dominated by near- surface components, or that most inclusions are physically connected to the surface by microcracks or dislocations. Trapped mantle helium may be a relatively small fraction of the total helium (LAL, 1989), so that the original quest for deep mantle He signatures, if possible in diamonds, is difficult indeed.
AcknuwiedgmenIs-We are very grateful to Ii. Craig for many con- tributions to the discussion of He diffusion in diamonds, as well as providing the use of his laboratory for He measurements. The con- tinuing discussions with J. Reynolds and M. Kurz on this subject are much appreciated. We are grateful to F. Begemann and two anon- ymous reviewers, for their reviews, and also to M. Ozima and F. Begemann for constructive comments on various eartier versions of this manuscript. D. S. Burnett is also thanked for his patience, and K. A. Farley for helpful suggestions. This research was supported by NSF grant EAR 89-04484 to D. La1 and NSF grant EAR 88- 16954 to H. Craig.
Editorial handling: G. Faure
REFERENCES
BOYD F. R., GURNEY J. J., and RICHARDSON S. H. (1985) Evidence for a 150-200-km thick Archaean lithosphere from diamond in- clusion thermobarometry. Nature 315, 387-389.
BURGESS R., TURNER G., and HARRIS J. W. (I 992) 40Ar-39Ar laser probe studies of clinopyroxene inclusions in eclogitic diamonds. Geochim. Cosm~him. Acta 56,389-402.
CARSLAW H. S. and JAEGER J. C. (1959) Conduction of Heat in Solids. Oxford Press.
CLARK S. P.. JR. and RINGWOOD A. E. (1964) Density distribution and constitution of the mantle. Rev. Geophys. 2, 35-88.
COHEN L. H. and ROSENFELD J. L. ( 1979) Diamond: depth of crys- tallization inferred from compressed included garnet. J. GeoE. 87, 333-340.
CRAIG H. and LUPTON J. E. (1976) Primordial neon, helium, and hydrogen in oceanic basalts. Earth Pt’anet. Sci. Lett. 31, 369-385.
CRANK J. (1956) ~a~~erna~jes afD~~sjan. Oxford Press. FECHTIC H. and KALBITZER S. (1966) The diffusion of argon in
potassium-bearing solids. In Potassium Argon Dating (ed. 0. A. SCHAEFFER and J. ZAHRINGER), pp. 68-107. Springer Verlag.
FUTAGAMI T., OZIMA M., NAGAI S., and AOKI Y. (1993) Experiments on thermal release of implanted noble gases from minerals and their implications for noble gases in lunar soil grains. Geochim. Cosmochim. Acta 57, 3177-3194.
G~BEL R., OTT U., and BEGEMANN F. (1978) On trapped nobIe gases in ureiiites. J. Geophys. Res. 83, 855-867.
GUTHRIE G. D. JR., VEBLEN D. R., NAVON O., and ROSSMAN G. R. (1991) Submicrometer fluid inclusions in turbiddiamond coats. Earth Planet. Sci. Lett. 105, I-12.
HARRIS J. W. (1992) Diamond geology. In The Properties ofNatural and Synthetic Diamond (ed. J. E. FIELD). pp. 345-393. Academic.
HART S. R. (1984) lie diffusion in olivine. Earth Planet. Sci. Left 70,297-302.
HONDA M., REYNOLDS J. H., ROEDDER E., and EPSTEIN S. (1987) Noble gases in diamonds: Occurrences of solar-like helium and neon. .J. Geophys. Res. 92, 12507- 1252 I.
KURZ M. I)., GURNEY J. J., JENKINS W. J., and Lorr D. E. (1987) Helium isotopic variability within single diamonds from the Orapa kimberlite pipe. Earth Pianet. Sci. Lett. 86, 57-68.
Diffusion of He isotopes in diamonds I757
LAL D. (1989) An important source of 4He (and ‘He) in diamonds. Earth Planet. Sci. Lett. 96, l-7.
LAL D., NISHIIZUMI K., KLEIN J., MIDDLETON R., and CRAIG H. (I 987a) Cosmogenic “Be in Zaire alluvial diamonds: Implications for ‘He contents of diamonds. Nature 328, 139-14 1.
LAL D., WACKER J. F., POREDA R., and CRAIG H. (1987b) Diffusion of helium in diamonds and implications for primordial helium in the earth (abstr.). Meteoritics 22, 437-438.
LAL D., CRAIG H., WACKER J. F., and POREDA R. (1989) ‘He in diamonds: The cosmogenic component. Geochim. Cosmochim. Acta 53, 569-574.
LIPFQLT H. J. and WEIGEL E. (1988) “He diffusion in 40Ar-retentive minerals. Geochim. Cosmochim. Acta 52, 1449- 1458.
LUTHER L. C. and MOORE W. J. (1964) Diffusion of helium in silicon, germanium, and diamond. J. Chem. Phys. 41, 1018-1026.
MAMYRIN B. A., ANUFRIYEV G. S., KAMENSKII I. L., and TOLSTI- KHIN I. N. (1970) Determination of the isotopic composition of atmospheric helium. Geochem. Intl. 7,498-505.
MCCONVILLE P. and REYNOLDS J. H. (1989) Cosmogenic helium and volatile-rich fluid in Sierra Leone alluvial diamonds. Geochim. Cosmochim. Acta 53,2365-2375.
MCCONVILLE P., RI~YNOLDS J. H., EPSTEIN S., and ROEDDER E. (199 I) Implanted ‘He, 4He, and Xe in further studies of diamonds from Western Australia. Geochim. Cosmochim. Acta 55, 1977- 1989.
OZIMA M. (1989) Gases in diamonds. Ann. Rev. Earth Planet. Sci. 17, 361-384.
OZIMA M. and ZAS~~U S. (1988) Noble gas diffusion in diamonds (abstr.). Eos 69, 5 1 1.
OZIMA M. and ZASHU S. (1991) Noble gas state of the ancient mantle as deduced from noble gases in coated diamonds. Earth Planet. Sri. Lett. 105, 13-27.
PHINNEY D. (1988) Lithium abundances in natural diamonds: An exploratory, ion-microprobe study (abstr.). Lunar Planet. Sci. XIX, 927-928.
RICHARDSON S. H., GURNEY J. J., ERLANK A. J., and HARRIS J. W. (1984) Origin of diamonds in old enriched mantle. Nature 310, 198-202.
RINGWOOD A. E. (1989) Constitution and evolution of the mantle. In Kimberlites and Related Rocks, Vol. I (ed. J. ROSS), pp. 457- 485. Blackwell Sci.
TRULL T. W., KURZ M. D., and JENKINS W. J. (1991) Diffusion of cosmogenic ‘He in olivine and quartz: implications for surface exposure dating. Earth Planet. Sci. Lett. 103, 241-256.
TRULL T. W. and KURZ M. D. (1993) Experimental measurements of ‘He and 4He mobility in olivine and clinopyroxene at magmatic temperatures. Geochim. Cosmochim. Acta 57, 13 13- 1324.
WIENS R., LAL D., and CRAIG H. (1990) Helium and carbon isotopes in Indian diamonds. Geochim. Cosmochim. Acta 54.2587-259 1.
YURIMOTO H., MORIOKA M., and NAGASAWA H. (1992) Oxygen self-diffusion along high diffusivity paths in forsterite. Geochem. J. 26, 181-188.
ZADNJK M. G., SMITH C. B., OTT U., and BEGEMANN F. (1987) Crushing of a terrestrial diamond: 3He/4He higher than solar (abstr.). Meteoritics 22, 541-542.
APPENDIX
Calculation of Diffusion Coefficients
Diffusion coefficients from initial temperature releases were cal- culated by iterating the exact solution for spheres
where F is the fraction of gas extracted, D is the diffusivity, t, the time, and R the sample radius, the diameters for which are given in Table 1 (Eqn. 6.20, CRANK, 1956); a similar derivation is given in $9.3 of CARSLAw and JAEGER (1959) and earlier editions. It has been shown that for subsequent temperature releases, correction must be made for the initial gas loss and redistribution (FECHTIG and KAL- BITZER, 1966). The following formulae apply:
D = (F2 - Fy_,)XR2 36t
F< 10% (2)
D=z[$F-.,+,T(+ -5F- ,jl -+)]
Fr90%
in which F is the total fraction of gas lost, F,_, is the fraction of gas lost prior to the step being calculated, and t is the time interval of the present step (FECHTIG and KALBITZER, 1966).
