Diffusion Kinetics of Samarium and Neodymium in Garnet, and a Method for Determining
Cooling Rates of Rocks
Author(s): J. Ganguly, M. Tirone, R. L. Hervig
Source: Science, New Series, Vol. 281, No. 5378 (Aug. 7, 1998), pp. 805-807
Published by: American Association for the Advancement of Science
Stable URL: http://www.jstor.org/stable/2896216
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REPORTS
es, the semi-infinite source model yielded a
better fit to the experimental data than the
depleting source model. Modeling of the data
from different depth profiles in the same
sample or in differentsamples annealedat the
same conditionyielded D values that differed
by a factor ?1.6. For constant D and diffusion in an isotropic medium, the unevenness
of a difftisant layer deposited on a crystal
surface does not affect the retrievedD value
(13). Three time series experiments (18.4,
J. Ganguly, M. Tirone, R. L. Hervig
41.8, and 76 hours) at 877?C did not show
Experimental determinations of the diffusion coefficients of samarium and
any systematic dependence of D(Nd) and
neodymium in almandine garnet and theoretical considerations show that one
D(Sm) on time, thus satisfying an important
cannot assign a sufficiently restricted range of closure temperature, Tc, to the
condition for the validity of the diffusion
samarium-neodymium decay system in garnet for the purpose of constraining
data. The results of modeling the diffusion
the cooling rate. However, it is shown that the samarium-neodymium cooling
profiles show that the D for the slightly
age of garnet can be used to calculate both cooling rate and Tc if the temsmaller cation (14) Sm (1.09 A) is 5 to 10%
larger than that of Nd (1.12 A). These diffuperature and age at the peak metamorphic conditions are known.
sion coefficients are similarto that of Mg, but
Garnets in metamorphicrocks are important the effect of fO2 on the diffusion. On com- about a factor of 10 larger than that of Fe at
candidatesfor radiometricage determinations pletion of an annealing experiment,the sam- f02 of graphite-oxygenequilibrium(Fig. 2).
throughuse of U-Pb, Rb-Sr, and Sm-Nd de- ple was cleaned by sonicationin 2 to 4 N HCl The effect of f02 on D determined in this
cay systems. Knowledge of the temperatures solution and rubbingon a soft polishing cloth work is compatible with the predicted 1/6
at which these systems closed in a garnet with ethanol to remove as much of the resid- power dependence of D onfO2 (15, 16).
crystal with respect to element diffusion ual solution from the sample surface as posThe Tc of the Sm-Nd decay system in
would provide importantconstraints on the sible, and analyzedby depthprofiling with an garnet has previously been estimated empircooling and exhumation history of the host ion probe (10). The polished surface of an ically (2-5) or calculated (1, 6, 17) from the
rock. The Tc of the Sm-Nd system in meta- annealed crystal appearedvery shiny in re- available diffusion data of Sm and Nd (18,
morphic garnethas been a subject of contin- flected light under an optical microscope, 19). At 1 bar and -700?C, our D(Sm) is at
ued debate, with the estimates varying from suggesting that there was no chemical reac- least three ordersof magnitudelower (Fig. 2)
-400? to 800?C (1-6). We present experi- tion between the crystal and the diffusant than that obtainedby the extrapolationof the
high P-T data of Harrison and Wood (18),
mental data on values of the tracer diffusion layer.
The samples were also analyzed simulta- which were derived as a by-product of the
coefficient (D) of Sm and Nd in garnet and
apply them to addressthe problemsof closure neously for 145Nd, 149Sm,30Si, 89Y,and 35C1 experimentalresults on Sm partitioningbetemperatureand cooling rates.
(Fig. 1). The depthprofiles for the nondiffus- tween garnet and melt. For comparisonwith
The diffusion experiments were carried ing species 30Si and 89Y allowed monitoring our results, we adjusted Coghlan's data for
of the stability of analyses, whereas that of
out at a pressureof 1 bar and temperatureof
8
7770 to 827?C for -146 to 48 hours. Natural
35C1(absentin garnet)allowed location of the
35ICI
crystal surface. Plateau intensities for 89Y
almandine crystals (Alm75Py22) were polished on one side to a mirror finish by a and 30Si were not achieved for several meacombinationof mechanicaland chemical polsurement cycles, and the count rates for the
06
ishing (7) and then thermallyannealed for at diffusants were ignored for these cycles. A
least 8 hours at or close to the T-f02 (oxygen controlgarnetsample,which was not subject1500
30_
fugacity) condition of the experiment so that ed to diffusion anneal, showed the same sta500/
it had an equilibriumor nearly equilibrium bilization behavior of 89Y and 30Si. The difdefect concentration for the experimental fusion depths of 149Sm and 145Nd varied
condition. A drop of a solution (8) consisting between -1100 and 3000 A. The energeti,
of both 149Smand 145Nd (-100 to 200 parts cally most favorable diffusion mechanism of
a tracer isotope is by replacement of the
per million of each) was added to the polished surface of a ciystal. After drying, the isotopes of the same element that are already
x
z
4O
100
150
400
650
1150
1400
900
crystal was suspended inside a vertical gas- present in the crystal.
Distance(Angstrom)
mixing furnace, which was preheated to a
Modeling was calTiedout in two ways. In
Fig. 1. Illustrationof the depth profilesof the
desired temperature.ThefO2 was controlled the first, the crystal surface was assumed to
by a computer-regulatedCO-CO2 mixture have a fixed concentrationof each diffusing diffusingand nondiffusingisotopes.The crystal
surface(X = 0) was locatedby monitoring35Cl,
and was maintainedat the wiistite-iron (WI) species (semi-infinitereservoirmodel). In the whereas
simultaneousstabilizationof 30Siand
buffer (9), with the exception of one experi- second, the surface concentrationof a diffus- 89y were used to select data for the diffusant
ing species was allowed to deplete with time, (145Nd)for use in the determination
ment at 800?C, which was conducted at 2.1
of the diffulogarithmic units above this buffer (the ap- t. Assuming constantD, solutions of the dif- sion coefficient.All 145Nddata have been normalized accordingto 1145Nd(X)- 145Nd(oo)]/
proximatelimit of almandinestability)to test fusion equation (11) for the two cases yield
whereX is the distance.
expressionsof the concentrationas a function 1145Nd(t= 0) - Nd(oo)],
The solid line throughthe data points is the
Dt
conin
of
and
a
of distance, C(x), terms
calculateddiffusionprofilewithD = 1.3 X 10-17
J. Ganguly and M. Tirone, Department of Geosciences,
stant term, A. We solved for both D and A
cm2/s at the experimentalconditionof 1 bar,
University of Arizona, Tucson, AZ 85721, USA. R. L.
simultaneouslyby incorporatingthe solutions 8770C,f 2WI buffer.Datafor 149Smdataare
Hervig, Center for Solid State Science, Arizona State
indistinguishable
fromthose of 145Ndin the plot.
into an optimizationprogram(12). In all casUniversity, Tempe, AZ 85287, USA.
Diffusion Kinetics of Samarium
and Neodymium in Garnet, and
a Method for Determining
Cooting Rates of Rocks
www.sciencemag.org
SCIENCE VOL 281
7 AUGUST 1998
805
REPORTS
Nd diffusion (19) to thef02 condition of WI
buffer, assuming that D cc (f02) 6. These
data, which are much lower than ours, are
problematic for two reasons: the activation
energy for D(Nd) is 44 + 7 kcal/mol, which
is much lower thanthat (-60 to 70 kcal/mol)
of the smaller divalent cations Mg, Fe, and
Mn (7, 20); and the experiments were performed under hydrothermnal
condition (2 kb,
Ni-NiO buffer), resultingin extensive surface
dissolution of most garnets.It is possible that
the apparentlyclean analyzed areas also suffered from dissolution or hydrationreaction,
but at a scale at which they could not be
detected optically. In a reaction-diffusion
process, one would determine an apparent
diffusion coefficient that is smaller than the
true one (11, eqn. 14.3). Observationaldata
also suggest that D(Nd) data of Coghlan are
too low (4).
Dodson (21) derived an expression of Tc
of a diffusing species in a mineral, assuming
that it is surToundedby a semi-infinitehomogeneous reservoirof that species. In a mineral
with retrogradezoning, the species concentration"freezes"at progressively lower temperaturesfrom the core to rim, so that this Tc
is a weighted average of the values for Tc in
Fig. 2. Comparison of the tracer
diffusion coefficients of
and
the different palts. Dodson (21, 22) also assumed that the composition of the mineral is
sufficiently removed at all points from its
initial homogeneous composition attained at
the peak temperature,To. However, this assumption, which makes Tc independent of
T., is not usually satisfiedby slowly diffusing
species, such as Sm and Nd in garnet.Using
an extension (23) of Dodson's formulation
that excludes this restrictionand the diffusion
data from this study, we calculated (Fig. 3)
the mean Tc of Sm-Nd decay system in garnet as a function of grain size, cooling rate,
and To at 7 kb and f02 of graphite-oxygen
buffer. These conditions approximatethe average conditions of metamorphic rocks in
which garnet ages are often determined
throughuse of the Sm-Nd decay system. Due
to the lack of any data on the pressuredependence of their diffusion coefficients, we assumed that the rare-earthelements have the
same activationvolume, AV+, as Mn2" (largest cation for which data are available in
garnet), which is 6 cm3/Mol (20), and that D
cc (f2)16. We thus obtained an Arrhenian
graphitebuffer)
expression of D (7 kb,f02
= Do exp[-Q(P)]IRT with Do = 4.7 X 10-5
cm2/s and Q(P) = Q(lbar) + PAlV+ =
-11-
Harrison
&Wood
Sm
Nd (squares and triangles,
\
respectively)in almandinegarnet determined in this work at 1
bar (open symbols:f02
WIl
E
above WI buffer) with other dif-
:
fusiondata in garnet.D(Mg)and
D(Fe)are the self (-tracer) diffusionof Mgand Fe (7) atfO2 of
?
(g
\N\
' 15
D(Nd,Sm)
Timeseries(Nd):877?C
A
Gt1
Gtl6V
Gt6R
40
-17-20
60
8I
WI
6
Ti2e(hr)
graphite-02 buffer (normalized
Fig. 3 (left). Closure temperature(TJ) of Sm-Nd
~
(e
buffer;symbol with cross above
the Arrhenianfit: 2.1 log units
to 1 bar). (Inset) Results of a
time series study at 877?C;the
datum for the longest run is
plotted in the main figure.
3
D
-13-
Ti-(r
19-
10 0OC
1,50
5
6
7
3
750
0
1000
80.5
T.=700.
.... 5..
Tcm0
E
o.
*
C
50
o0
..
700/1
|
1
L0
_
/T0(c)/am)
\
650
------ Dodson
Thiswork
600
30
40
50
0
10
20,
valuesof To,with the single curve for the same
T(?C/Ma)
grainsizecalculatedfrom(21) at smallvaluesof the coolingrate.
Fig.4 (right).Cooling
rate of sphericalgarnet crystalas a functionof the difference(At) between the peak
metamorphicand Sm-Ndcoolingages of garnet,the initialtemperature(TO),and grain
radius(a). (Inset)Sensitivityof the coolingrateto lAt.
806
100m
100
To(?0)
of the familyof Tcversus
cooling rate curvesfor a
given grainsize, as calculated here for different
1
_a=mm
rate, initial temperature
(T0), and grainradius(a).
which are independent of
To. Note the coincidence
10
(K)
104/T
800
decay system in spherical
garnet(almandine)
crystal
as a function of cooling
Alsoshown (dashedlines)
arethe valuesof Tc calculated from Dodson (21),
7JO
9
8
61,674 cal/mol. It is evident from Fig. 3 that
one cannot define a unique or even a restricted range of Tc of the Sm-Nd decay system in
gamet, and that Dodson's formulation (21)
progressively overestimates Tc with increasing cooling rate and grain size and decreasing
To.
In additionto grain size, Tc is also sensitive to To, except at very slow cooling rate,
but at this condition Tc is itself too sensitive
to cooling rate to be useful in the reconstruction of the temperature-timepath of a rock
duringcooling. However, the cooling rate of
a rock can be retrieved by noting that any
point on a curve in Fig. 3 defines T., Tc, and
an average cooling rate within this temperature range, which is given by (T. - Tc)lAt,
where At represents the difference between
the peak metamolphic age and Sm-Nd cooling age of garnet (that is, the elapsed time
until the Sm-Nd decay system closed within
gamet crystalsduringcooling). Thus, if T., a,
and At are known, one can find the point on
the appropriatecurve that satisfies the known
value of At [given by the ratio of (T. - Tc)
to the cooling rate defined by the point]. The
coordinatesof this point specify both Tc and
the averagecooling ratebetween T. and Tc of
the garnet.
As an example of applicationof the relation of the average cooling rate between To
and Tc versus At, as derivedaccordingto the
above analysis for different combinations of
To and grain size (Fig. 4), we consider the
data of Mezger et al. (3) for the Archean
Pikwitonei GranuliteDomain of the Superior
Province, Canada. Using two-feldspar thermometry,they estimated To 750?C for the
peak metamorphismat -2640 million years
ago (Ma), as determined by U-Pb ages of
zircon and garnet, which is -30 Ma older
than the Sm-Nd cooling age of garnet.In thin
sections, the size (or apparentdiameter) of
the garnet crystals varied between -1 and 5
7 AUGUST 1998
VOL 281
0.5
o
0
SCIENCE www.sciencemag.org
0.5
1
Iog(AtJa2) (MaImm2)
1.5
2
REPORTS
mm. Using these data, we obtain from Fig. 4
cooling rate -2 to 4 K/Ma, which is in
excellent agreement with that of -2 K/Ma
deduced independently(3). For very slowly
cooled rocks, the retrieved cooling rate is
quite insensitive to errorsin At. However, for
relatively rapidly cooled rocks (for example,
dT/dt > 50 K/Ma for T. = 800?C), small
errorin At leads to very large errorin dT/dt.
Thus, for these rocks, it would be more appropriateto define a minimum cooling rate,
taking into account the errorin At.
22. _
_,
Mat. Sci. Forum7, 145 (1986).
23. J. GanguLy,in preparation.The geometric parameter
A in the expression of mean Tc in Dodson's (21) eqn.
23 equals exp(G), where G is the spatiatty averaged
value of the closure function G(x) of his (22) eqn. 20.
In deriving the expression for G(x), Dodson (22) assumed that the dimensionlessquantityM >> 1, which
impties removat of the composition of the crystal
from its initiat composition in aLLparts. The cLosure
function has been modified so that it is valid for any
arbitrary vatue of M, numericatty evatuated as a
function of the normalized radial distance from the
center of a grain,and then spatially averagedto yield
average closure function versus M; for example, G(M
= 0.001)
= 0.9018,
G(0.01)
= 2.7603,
G(0.10) =
3.8693, G(0.4) = 4.0041, as compared to Dodson's
(22) G = 4.0066.
24. S. W. J. CLement,W. Compston, G. Newstead, in
Proceedings InternationalSecondary Ion Mass Spectrometry Conference, A. Bennighoven, Ed. (Witey,
Munster,Germany, 1991), pp. 289-293.
25. E. K. Zinner and G Crozaz,Int. J. Mass Spectrom Ion
69, 17 (1986).
26. We thank M. H. Dodson and J. Ruiz for heLpfutdiscussions and for providing some of the isotopeenriched sotutions, respectivety. This research was
supported by U.S. Nationat Science Foundationgrant
EAR9418941 and EAR9805232.
30 Aprit1998; accepted 30 June 1998
References and Notes
1. F. J. Humphries and R. A. Ctiff, Nature 295, 515
(1982).
2. A. S. Cohen, R. K. O'Nions, R. Siegenthater, W. I.
Griffin,Contrib.Mineral.Petrol. 98, 303 (1988).
3. K. Mezger, E. J. Essene, A. N. Haltiday,EarthPlanet.
Sci. Lett. 113, 387 (1992).
4. K.Burton,M.J. Kohn,A. S. Cohen, R. K.O'Nions, ibid.
133, 199 (1992).
5. B. J. Hensen and B. Zhou, Geology 23, 225 (1995).
6. H. Becker,Contrib.Mineral.Petrol. 127, 224 (1997).
7. J. GanguLy,W. Cheng, S. Chakraborty,ibid. 131, 171
(1998).
8. The isotope-enriched sotution was prepared by first
dissoLvingmetaLs of Sm and Nd, enriched in the
isotopes 149Smand 145Nd,respectively, in 2 N HCl,
evaporating it to almost dryness, and then adding
triply distitted water. The nearly aqueous sotutions
were anatyzed by inductively coupted pLasma-mass
spectrometry (ICP-MS)and found to have 145Ndand
149Sm concentrations varying between -100 and
200 ppm in two different stock sotutions used in this
work.
9. H. St. C. O'Neill, Am. Mineral.73, 470 (1988)
10. The anatyses were obtained in a Cameca ims 3f SIMS
using a primarybeam of mass-fittered 160- acceterated to 10 keV.The samples were held at -+4.5 kV,
resuLtingin an impact energy of -14.5 keV. Two
approaches were used to avoid contribution of secondary ions from the crater waLts.For some of the
samples, a 50-nA primarybeam was focused onto a
spot and rasteredover a 200 p.m by 200 p.m area. An
aperture inserted into the path of the ions atLowed
only those originatingfrom a 60-p.m-diameter circuLararea in the center of the crater into the mass
spectrometer. For other sampLes,a 15- to 20-nA
primarybeam was focused by Kohleriltuminationto
generate a circutar,flat-bottomed crater --120 p.min
diameter (24). Secondaryions from the central 10 or
20 p.m of the crater were aLlowed into the mass
spectrometer by setecting either a 100- or 200-p.m
fieLdaperture.Inboth cases a 75-V offset was appLied
to the sample voltage to minimize the contribution
of motecutarions to the mass spectrum (25). Crater
depths were determined with a Dektak surface profiLometerand varied as a function of primarybeam
current and anatysis time (1 to 2 hours) between
-3000 and 7000 A.
11. J. Crank,The Mathematics of Diffusion (Clarendon,
Oxford, 1975).
12. F.James and M. Ross,Comput. Phys. 10, 343 (1975).
13. D. S. Tannhauser,Appl. Phys. 27, 662 (1956).
14. R.D. Shannonand C. T. Prewitt,Acta Crystallogr.B25,
925 (1969).
15. S. Chakrabortyand J. GanguLy,in Diffusion,Atomic
Orderingand MassTransport,J. GanguLy,Ed.(AdvancNew
es in PhysicatGeochemistry 8, Springer-VerLag,
York,1991), pp. 120-175.
16. M. Moriokaand H. Nagasawa, in (15), pp. 176-197.
17. D. J. Cherniak,J. M. Manchar,E. B. Watson, Chem.
Geol. 134, 289 (1997).
18. W. J. Harrison and B. J. Wood, Contrib. Mineral.
Petrol. 72, 145 (1980).
19. R. A. N. CoghLan,thesis, Brown University, Providence, RI(1990).
20. S. Chakraborty and J. Ganguly, Contrib. Mineral.
Petrol. 111, 74 (1992).
21. M. H. Dodson, ibid. 40, 259 (1973).
Decoupled Temporal Patterns
of Evolution and Ecology in Two
Post-Paleozoic Clades
Frank K. McKinney,* Scott Lidgard,J. John Sepkoski Jr.,
Paul D. Taylor
Counts of taxonomic diversity are the prevailing standards for documenting
large-scale patterns of evolution in the fossil record. However, the secular
pattern of relative ecological importance between the bryozoan clades Cyclostomata and Cheilostomata is not reflected fully in compilations of generic
diversity or within-fauna species richness, and the delayed ecological recovery
of the Cheilostomata after the mass extinction at the Cretaceous-Tertiary
boundaryis missed entirely. These observations demonstrate that evolutionary
success and ecological dominance can be decoupled and profoundly different,
even over tens of millions of years.
Taxonomicdiversity,or richness(1, 2), is the
currentparadigmused to describehow Earth's
biota has changed over time. An alternative
approachexaminespatternsin biologicalactivity or habitatstructure(3, 4), but this has rarely
been associatedwith taxonomicdiversity.Here,
we describea differentapproach.We compiled
dataon skeletalmass of two coexistingmarine
bryozoanclades (Cyclostomataand Cheilostomata) to measureone aspect of relative local
ecologicaldominanceover geologicaltime (5).
Dominanceis usually measuredby the abundance of a group of organismsrelativeto cooccurringgroups, or less often by the relative
effect of a group on energy flow within a
community(6). Species are not equally abundantor importantenergetically,so lists of species alone may not reflect dominance.Moreover, despite calls for recognizingthe importance of abundancein large-scaleevolutionary
F. K. McKinney, Department of Geology, Appalachian
State University, Boone, NC 28608-2067, USA. S.
Lidgard,Department of Geology, Field Museum, Roosevelt Road at Lake Shore Drive, Chicago, IL 60605,
USA. J. J. Sepkoski Jr., Department of the Geophysical
Sciences, University of Chicago, Chicago, IL 60637,
USA. P. D. Taylor, Department of Palaeontology, The
Natural History Museum, Cromwell Road, London
SW7 5BD, UK.
*To whom correspondence should be addressed. Email: mckinneyfk@appstate.edu
www.sciencemag.org
SCIENCE VOL 281
pattems(7), there have been few applications
(4, 8).
We compared biyozoan abundance data
spanningthe past 150 million years with two
measuresof taxonomic diversityto assess the
degree of correspondencebetween the evolutionaiy success and ecological importance,or
dominance, of the two clades on continental
shelves, where they have similar ecological
distributions(9). During the past 150 million
years, cheilostome bryozoans radiatedto an
extent comparablewith the euteleost fishes,
neogastropods, and echinoids (2), whereas
diversificationof cyclostome bryozoans was
arrested.
Cyclostomebiyozoans survivedthe severe
crises at the end-Permianand Triassic mass
extinctions that removed the other stenolaemate biyozoan clades that had much higher
Paleozoic diversities (10). Cyclostome genera increased from four in the Early Jurassic
[Hettangian;206 to 202 million years ago
(Ma)] to a maximum of 176 in the latest
Cretaceous (Maastrichtian;71 to 65 Ma).
Cheilostomes did not appear until the Late
Jurassicand increasedfrom four generain the
mid-Cretaceous(Aptian; 121 to 112 Ma) to a
maximum of 178 in the Maastrichtian.The
Cretaceous-Tertiaiy(K-T) extinctionresulted
in a decrease to 111 genera of cheilostomes
and to 83 of cyclostomes by the late Paleo-
7 AUGUST 1998
807